%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU011+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:47 AM UTC 2025
% Result : Theorem 7.81s 7.98s
% Output : Proof 7.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU011+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:58:27 EDT 2025
% 0.12/0.33 % CPUTime :
% 7.81/7.98 % SZS status Theorem
% 7.81/7.98 % SZS output start Proof
% 7.81/7.98 tff(tptp_fun_C_10_type, type, (
% 7.81/7.98 tptp_fun_C_10: ( $i * $i ) > $i)).
% 7.81/7.98 tff(set_intersection2_type, type, (
% 7.81/7.98 set_intersection2: ( $i * $i ) > $i)).
% 7.81/7.98 tff(tptp_fun_A_12_type, type, (
% 7.81/7.98 tptp_fun_A_12: $i)).
% 7.81/7.98 tff(tptp_fun_B_11_type, type, (
% 7.81/7.98 tptp_fun_B_11: $i)).
% 7.81/7.98 tff(relation_composition_type, type, (
% 7.81/7.98 relation_composition: ( $i * $i ) > $i)).
% 7.81/7.98 tff(identity_relation_type, type, (
% 7.81/7.98 identity_relation: $i > $i)).
% 7.81/7.98 tff(apply_type, type, (
% 7.81/7.98 apply: ( $i * $i ) > $i)).
% 7.81/7.98 tff(in_type, type, (
% 7.81/7.98 in: ( $i * $i ) > $o)).
% 7.81/7.98 tff(relation_dom_type, type, (
% 7.81/7.98 relation_dom: $i > $i)).
% 7.81/7.98 tff(tptp_fun_D_0_type, type, (
% 7.81/7.98 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 7.81/7.98 tff(function_type, type, (
% 7.81/7.98 function: $i > $o)).
% 7.81/7.98 tff(relation_type, type, (
% 7.81/7.98 relation: $i > $o)).
% 7.81/7.98 tff(1,assumption,((~((~(set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(B!11, A!12))) | (~(((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11))) <=> in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)))))) | (~((set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(B!11, A!12)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(identity_relation(A!12)), B!11), A!12, B!11), B!11)) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(identity_relation(A!12)), B!11), A!12, B!11), A!12))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(identity_relation(A!12)), B!11), A!12, B!11), set_intersection2(relation_dom(identity_relation(A!12)), B!11)))))), introduced(assumption)).
% 7.81/7.98 tff(2,plain,
% 7.81/7.98 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))))),
% 7.81/7.98 inference(bind,[status(th)],[])).
% 7.81/7.98 tff(3,plain,
% 7.81/7.98 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 7.81/7.98 inference(quant_intro,[status(thm)],[2])).
% 7.81/7.98 tff(4,plain,
% 7.81/7.98 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 7.81/7.98 inference(pull_quant,[status(thm)],[])).
% 7.81/7.98 tff(5,plain,
% 7.81/7.98 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C)))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))))),
% 7.81/7.98 inference(bind,[status(th)],[])).
% 7.81/7.98 tff(6,plain,
% 7.81/7.98 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 7.81/7.98 inference(quant_intro,[status(thm)],[5])).
% 7.81/7.98 tff(7,plain,
% 7.81/7.98 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 7.81/7.98 inference(transitivity,[status(thm)],[6, 4])).
% 7.81/7.98 tff(8,plain,
% 7.81/7.98 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 7.81/7.98 inference(transitivity,[status(thm)],[7, 3])).
% 7.81/7.98 tff(9,plain,
% 7.81/7.98 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))))),
% 7.81/7.98 inference(bind,[status(th)],[])).
% 7.81/7.98 tff(10,plain,
% 7.81/7.98 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 7.81/7.98 inference(quant_intro,[status(thm)],[9])).
% 7.81/7.98 tff(11,plain,
% 7.81/7.98 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 7.81/7.98 inference(transitivity,[status(thm)],[10, 8])).
% 7.81/7.98 tff(12,plain,
% 7.81/7.98 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))), rewrite(((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B))))) <=> ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))) <=> (((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))), rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))))),
% 7.81/7.98 inference(bind,[status(th)],[])).
% 7.81/7.98 tff(13,plain,
% 7.81/7.98 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 7.81/7.98 inference(quant_intro,[status(thm)],[12])).
% 7.81/7.98 tff(14,plain,
% 7.81/7.98 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 7.81/7.98 inference(rewrite,[status(thm)],[])).
% 7.81/7.98 tff(15,axiom,(![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_xboole_0')).
% 7.81/7.98 tff(16,plain,
% 7.81/7.98 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 7.81/7.98 inference(modus_ponens,[status(thm)],[15, 14])).
% 7.81/7.98 tff(17,plain,(
% 7.81/7.98 ![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B))))))),
% 7.81/7.98 inference(skolemize,[status(sab)],[16])).
% 7.81/7.98 tff(18,plain,
% 7.81/7.98 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 7.81/7.98 inference(modus_ponens,[status(thm)],[17, 13])).
% 7.81/7.98 tff(19,plain,
% 7.81/7.98 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 7.81/7.98 inference(modus_ponens,[status(thm)],[18, 11])).
% 7.81/7.98 tff(20,plain,
% 7.81/7.98 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~((~((~(set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(B!11, A!12))) | (~(((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11))) <=> in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)))))) | (~((set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(B!11, A!12)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(identity_relation(A!12)), B!11), A!12, B!11), B!11)) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(identity_relation(A!12)), B!11), A!12, B!11), A!12))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(identity_relation(A!12)), B!11), A!12, B!11), set_intersection2(relation_dom(identity_relation(A!12)), B!11)))))))),
% 7.81/7.98 inference(quant_inst,[status(thm)],[])).
% 7.81/7.98 tff(21,plain,
% 7.81/7.98 ($false),
% 7.81/7.98 inference(unit_resolution,[status(thm)],[20, 19, 1])).
% 7.81/7.98 tff(22,plain,(~((~((~(set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(B!11, A!12))) | (~(((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11))) <=> in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)))))) | (~((set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(B!11, A!12)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(identity_relation(A!12)), B!11), A!12, B!11), B!11)) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(identity_relation(A!12)), B!11), A!12, B!11), A!12))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(identity_relation(A!12)), B!11), A!12, B!11), set_intersection2(relation_dom(identity_relation(A!12)), B!11))))))), inference(lemma,lemma(discharge,[]))).
% 7.81/7.98 tff(23,plain,
% 7.81/7.98 (((~((~(set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(B!11, A!12))) | (~(((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11))) <=> in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)))))) | (~((set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(B!11, A!12)) | (((~in(tptp_fun_D_0(set_intersection2(relation_dom(identity_relation(A!12)), B!11), A!12, B!11), B!11)) | (~in(tptp_fun_D_0(set_intersection2(relation_dom(identity_relation(A!12)), B!11), A!12, B!11), A!12))) <=> in(tptp_fun_D_0(set_intersection2(relation_dom(identity_relation(A!12)), B!11), A!12, B!11), set_intersection2(relation_dom(identity_relation(A!12)), B!11)))))) | ((~(set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(B!11, A!12))) | (~(((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11))) <=> in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)))))),
% 7.81/7.98 inference(tautology,[status(thm)],[])).
% 7.81/7.98 tff(24,plain,
% 7.81/7.98 ((~(set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(B!11, A!12))) | (~(((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11))) <=> in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11))))),
% 7.81/7.98 inference(unit_resolution,[status(thm)],[23, 22])).
% 7.81/7.98 tff(25,plain,
% 7.81/7.98 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 7.81/7.98 inference(bind,[status(th)],[])).
% 7.81/7.98 tff(26,plain,
% 7.81/7.98 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 7.81/7.98 inference(quant_intro,[status(thm)],[25])).
% 7.81/7.98 tff(27,plain,
% 7.81/7.98 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 7.81/7.98 inference(rewrite,[status(thm)],[])).
% 7.81/7.98 tff(28,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 7.81/7.98 tff(29,plain,
% 7.81/7.98 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 7.81/7.98 inference(modus_ponens,[status(thm)],[28, 27])).
% 7.81/7.98 tff(30,plain,(
% 7.81/7.98 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 7.81/7.98 inference(skolemize,[status(sab)],[29])).
% 7.81/7.98 tff(31,plain,
% 7.81/7.98 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 7.81/7.98 inference(modus_ponens,[status(thm)],[30, 26])).
% 7.81/7.98 tff(32,plain,
% 7.81/7.98 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(A!12, B!11) = set_intersection2(B!11, A!12))),
% 7.81/7.98 inference(quant_inst,[status(thm)],[])).
% 7.81/7.98 tff(33,plain,
% 7.81/7.98 (set_intersection2(A!12, B!11) = set_intersection2(B!11, A!12)),
% 7.81/7.98 inference(unit_resolution,[status(thm)],[32, 31])).
% 7.81/7.98 tff(34,plain,
% 7.81/7.98 (^[A: $i] : refl((~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 7.81/7.98 inference(bind,[status(th)],[])).
% 7.81/7.98 tff(35,plain,
% 7.81/7.98 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 7.81/7.98 inference(quant_intro,[status(thm)],[34])).
% 7.81/7.98 tff(36,plain,
% 7.81/7.98 (^[A: $i] : rewrite((relation(identity_relation(A)) & function(identity_relation(A))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 7.81/7.98 inference(bind,[status(th)],[])).
% 7.81/7.98 tff(37,plain,
% 7.81/7.98 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 7.81/7.98 inference(quant_intro,[status(thm)],[36])).
% 7.81/7.98 tff(38,plain,
% 7.81/7.98 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 7.81/7.98 inference(rewrite,[status(thm)],[])).
% 7.81/7.98 tff(39,axiom,(![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc2_funct_1')).
% 7.81/7.98 tff(40,plain,
% 7.81/7.98 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 7.81/7.98 inference(modus_ponens,[status(thm)],[39, 38])).
% 7.81/7.98 tff(41,plain,(
% 7.81/7.98 ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 7.81/7.98 inference(skolemize,[status(sab)],[40])).
% 7.81/7.98 tff(42,plain,
% 7.81/7.98 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 7.81/7.98 inference(modus_ponens,[status(thm)],[41, 37])).
% 7.81/7.98 tff(43,plain,
% 7.81/7.98 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 7.81/7.98 inference(modus_ponens,[status(thm)],[42, 35])).
% 7.81/7.98 tff(44,plain,
% 7.81/7.98 ((~![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))) | (~((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12)))))),
% 7.81/7.98 inference(quant_inst,[status(thm)],[])).
% 7.81/7.98 tff(45,plain,
% 7.81/7.98 (~((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))))),
% 7.81/7.98 inference(unit_resolution,[status(thm)],[44, 43])).
% 7.81/7.98 tff(46,plain,
% 7.81/7.98 (((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12)))) | function(identity_relation(A!12))),
% 7.81/7.98 inference(tautology,[status(thm)],[])).
% 7.81/7.98 tff(47,plain,
% 7.81/7.98 (function(identity_relation(A!12))),
% 7.81/7.98 inference(unit_resolution,[status(thm)],[46, 45])).
% 7.81/7.98 tff(48,plain,
% 7.81/7.98 (^[A: $i] : refl(relation(identity_relation(A)) <=> relation(identity_relation(A)))),
% 7.81/7.98 inference(bind,[status(th)],[])).
% 7.81/7.98 tff(49,plain,
% 7.81/7.98 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 7.81/7.98 inference(quant_intro,[status(thm)],[48])).
% 7.81/7.98 tff(50,plain,
% 7.81/7.98 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 7.81/7.98 inference(rewrite,[status(thm)],[])).
% 7.81/7.98 tff(51,axiom,(![A: $i] : relation(identity_relation(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k6_relat_1')).
% 7.81/7.98 tff(52,plain,
% 7.81/7.98 (![A: $i] : relation(identity_relation(A))),
% 7.81/7.98 inference(modus_ponens,[status(thm)],[51, 50])).
% 7.81/7.98 tff(53,plain,(
% 7.81/7.98 ![A: $i] : relation(identity_relation(A))),
% 7.81/7.98 inference(skolemize,[status(sab)],[52])).
% 7.81/7.98 tff(54,plain,
% 7.81/7.98 (![A: $i] : relation(identity_relation(A))),
% 7.81/7.98 inference(modus_ponens,[status(thm)],[53, 49])).
% 7.81/7.98 tff(55,plain,
% 7.81/7.98 ((~![A: $i] : relation(identity_relation(A))) | relation(identity_relation(A!12))),
% 7.81/7.98 inference(quant_inst,[status(thm)],[])).
% 7.81/7.98 tff(56,plain,
% 7.81/7.98 (relation(identity_relation(A!12))),
% 7.81/7.98 inference(unit_resolution,[status(thm)],[55, 54])).
% 7.81/7.98 tff(57,plain,
% 7.81/7.98 (^[A: $i, B: $i] : trans(monotonicity(rewrite((~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))) <=> (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))))), (((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))))))), rewrite(((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))), (((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))))),
% 7.81/7.98 inference(bind,[status(th)],[])).
% 7.81/7.98 tff(58,plain,
% 7.81/7.98 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))),
% 7.81/7.99 inference(quant_intro,[status(thm)],[57])).
% 7.81/7.99 tff(59,plain,
% 7.81/7.99 (^[A: $i, B: $i] : refl(((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))))),
% 7.81/7.99 inference(bind,[status(th)],[])).
% 7.81/7.99 tff(60,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 7.81/7.99 inference(quant_intro,[status(thm)],[59])).
% 7.81/7.99 tff(61,plain,
% 7.81/7.99 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))))),
% 7.81/7.99 inference(bind,[status(th)],[])).
% 7.81/7.99 tff(62,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 7.81/7.99 inference(quant_intro,[status(thm)],[61])).
% 7.81/7.99 tff(63,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 7.81/7.99 inference(transitivity,[status(thm)],[62, 60])).
% 7.81/7.99 tff(64,plain,
% 7.81/7.99 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), trans(monotonicity(rewrite(((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) <=> ((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))), rewrite(((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))) <=> ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))), ((((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) <=> (((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))), rewrite((((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) <=> (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))), ((((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) <=> (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))), (((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))) <=> (((~relation(B)) | (~function(B))) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))))), rewrite((((~relation(B)) | (~function(B))) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))), (((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))))),
% 7.81/7.99 inference(bind,[status(th)],[])).
% 7.81/7.99 tff(65,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 7.81/7.99 inference(quant_intro,[status(thm)],[64])).
% 7.81/7.99 tff(66,plain,
% 7.81/7.99 (^[A: $i, B: $i] : rewrite(((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | ((~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))) <=> ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))),
% 7.81/7.99 inference(bind,[status(th)],[])).
% 7.81/7.99 tff(67,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | ((~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))),
% 7.81/7.99 inference(quant_intro,[status(thm)],[66])).
% 7.81/7.99 tff(68,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 7.81/7.99 inference(rewrite,[status(thm)],[])).
% 7.81/7.99 tff(69,plain,
% 7.81/7.99 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C)))) <=> ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))), (((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C))))) <=> ((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))), rewrite(((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))) <=> ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))), (((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C))))) <=> ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))),
% 7.81/7.99 inference(bind,[status(th)],[])).
% 7.81/7.99 tff(70,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 7.81/7.99 inference(quant_intro,[status(thm)],[69])).
% 7.81/7.99 tff(71,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t34_funct_1')).
% 7.81/7.99 tff(72,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 7.81/7.99 inference(modus_ponens,[status(thm)],[71, 70])).
% 7.81/7.99 tff(73,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 7.81/7.99 inference(modus_ponens,[status(thm)],[72, 68])).
% 7.81/7.99 tff(74,plain,(
% 7.81/7.99 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | ((~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))),
% 7.81/7.99 inference(skolemize,[status(sab)],[73])).
% 7.81/7.99 tff(75,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))),
% 7.81/7.99 inference(modus_ponens,[status(thm)],[74, 67])).
% 7.81/7.99 tff(76,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 7.81/7.99 inference(modus_ponens,[status(thm)],[75, 65])).
% 7.81/7.99 tff(77,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 7.81/7.99 inference(modus_ponens,[status(thm)],[76, 63])).
% 7.81/7.99 tff(78,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))),
% 7.81/7.99 inference(modus_ponens,[status(thm)],[77, 58])).
% 7.81/7.99 tff(79,plain,
% 7.81/7.99 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12)))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12)))))),
% 7.81/7.99 inference(rewrite,[status(thm)],[])).
% 7.81/7.99 tff(80,plain,
% 7.81/7.99 (((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12))))) <=> ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12)))))),
% 7.81/7.99 inference(rewrite,[status(thm)],[])).
% 7.81/7.99 tff(81,plain,
% 7.81/7.99 ((~((~((identity_relation(A!12) = identity_relation(A!12)) | (~(relation_dom(identity_relation(A!12)) = A!12)) | (~((~in(tptp_fun_C_10(identity_relation(A!12), A!12), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_10(identity_relation(A!12), A!12)) = tptp_fun_C_10(identity_relation(A!12), A!12)))))) | (~((~(identity_relation(A!12) = identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))))))))) <=> (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12))))),
% 7.81/7.99 inference(rewrite,[status(thm)],[])).
% 7.81/7.99 tff(82,plain,
% 7.81/7.99 (((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((identity_relation(A!12) = identity_relation(A!12)) | (~(relation_dom(identity_relation(A!12)) = A!12)) | (~((~in(tptp_fun_C_10(identity_relation(A!12), A!12), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_10(identity_relation(A!12), A!12)) = tptp_fun_C_10(identity_relation(A!12), A!12)))))) | (~((~(identity_relation(A!12) = identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C)))))))))) <=> ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12)))))),
% 7.81/7.99 inference(monotonicity,[status(thm)],[81])).
% 7.81/7.99 tff(83,plain,
% 7.81/7.99 (((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((identity_relation(A!12) = identity_relation(A!12)) | (~(relation_dom(identity_relation(A!12)) = A!12)) | (~((~in(tptp_fun_C_10(identity_relation(A!12), A!12), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_10(identity_relation(A!12), A!12)) = tptp_fun_C_10(identity_relation(A!12), A!12)))))) | (~((~(identity_relation(A!12) = identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C)))))))))) <=> ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12)))))),
% 7.81/7.99 inference(transitivity,[status(thm)],[82, 80])).
% 7.81/7.99 tff(84,plain,
% 7.81/7.99 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((identity_relation(A!12) = identity_relation(A!12)) | (~(relation_dom(identity_relation(A!12)) = A!12)) | (~((~in(tptp_fun_C_10(identity_relation(A!12), A!12), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_10(identity_relation(A!12), A!12)) = tptp_fun_C_10(identity_relation(A!12), A!12)))))) | (~((~(identity_relation(A!12) = identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12))))))),
% 7.81/7.99 inference(monotonicity,[status(thm)],[83])).
% 7.81/7.99 tff(85,plain,
% 7.81/7.99 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((identity_relation(A!12) = identity_relation(A!12)) | (~(relation_dom(identity_relation(A!12)) = A!12)) | (~((~in(tptp_fun_C_10(identity_relation(A!12), A!12), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_10(identity_relation(A!12), A!12)) = tptp_fun_C_10(identity_relation(A!12), A!12)))))) | (~((~(identity_relation(A!12) = identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12)))))),
% 7.81/7.99 inference(transitivity,[status(thm)],[84, 79])).
% 7.81/7.99 tff(86,plain,
% 7.81/7.99 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((identity_relation(A!12) = identity_relation(A!12)) | (~(relation_dom(identity_relation(A!12)) = A!12)) | (~((~in(tptp_fun_C_10(identity_relation(A!12), A!12), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_10(identity_relation(A!12), A!12)) = tptp_fun_C_10(identity_relation(A!12), A!12)))))) | (~((~(identity_relation(A!12) = identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))))))))))),
% 7.81/7.99 inference(quant_inst,[status(thm)],[])).
% 7.81/7.99 tff(87,plain,
% 7.81/7.99 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12))))),
% 7.81/7.99 inference(modus_ponens,[status(thm)],[86, 85])).
% 7.81/7.99 tff(88,plain,
% 7.81/7.99 (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12)))),
% 7.81/7.99 inference(unit_resolution,[status(thm)],[87, 78, 56, 47])).
% 7.81/7.99 tff(89,plain,
% 7.81/7.99 (((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12))) | (relation_dom(identity_relation(A!12)) = A!12)),
% 7.81/7.99 inference(tautology,[status(thm)],[])).
% 7.81/7.99 tff(90,plain,
% 7.81/7.99 (relation_dom(identity_relation(A!12)) = A!12),
% 7.81/7.99 inference(unit_resolution,[status(thm)],[89, 88])).
% 7.81/7.99 tff(91,plain,
% 7.81/7.99 (A!12 = relation_dom(identity_relation(A!12))),
% 7.81/7.99 inference(symmetry,[status(thm)],[90])).
% 7.81/7.99 tff(92,plain,
% 7.81/7.99 (set_intersection2(A!12, B!11) = set_intersection2(relation_dom(identity_relation(A!12)), B!11)),
% 7.81/7.99 inference(monotonicity,[status(thm)],[91])).
% 7.81/7.99 tff(93,plain,
% 7.81/7.99 (set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(A!12, B!11)),
% 7.81/7.99 inference(symmetry,[status(thm)],[92])).
% 7.81/7.99 tff(94,plain,
% 7.81/7.99 (set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(B!11, A!12)),
% 7.81/7.99 inference(transitivity,[status(thm)],[93, 33])).
% 7.81/7.99 tff(95,plain,
% 7.81/7.99 ((~((~(set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(B!11, A!12))) | (~(((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11))) <=> in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)))))) | (~(set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(B!11, A!12))) | (~(((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11))) <=> in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11))))),
% 7.81/7.99 inference(tautology,[status(thm)],[])).
% 7.81/7.99 tff(96,plain,
% 7.81/7.99 ((~((~(set_intersection2(relation_dom(identity_relation(A!12)), B!11) = set_intersection2(B!11, A!12))) | (~(((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11))) <=> in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)))))) | (~(((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11))) <=> in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11))))),
% 7.81/7.99 inference(unit_resolution,[status(thm)],[95, 94])).
% 7.81/7.99 tff(97,plain,
% 7.81/7.99 (~(((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11))) <=> in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)))),
% 7.81/7.99 inference(unit_resolution,[status(thm)],[96, 24])).
% 7.81/7.99 tff(98,plain,
% 7.81/7.99 (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)) <=> in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))),
% 7.81/7.99 inference(monotonicity,[status(thm)],[94])).
% 7.81/7.99 tff(99,plain,
% 7.81/7.99 (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12)) <=> in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11))),
% 7.81/7.99 inference(symmetry,[status(thm)],[98])).
% 7.81/7.99 tff(100,plain,
% 7.81/7.99 ((~![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))) | (~((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11)))))),
% 7.81/7.99 inference(quant_inst,[status(thm)],[])).
% 7.81/7.99 tff(101,plain,
% 7.81/7.99 (~((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))))),
% 7.81/7.99 inference(unit_resolution,[status(thm)],[100, 43])).
% 7.81/7.99 tff(102,plain,
% 7.81/7.99 (((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11)))) | function(identity_relation(B!11))),
% 7.81/7.99 inference(tautology,[status(thm)],[])).
% 7.81/7.99 tff(103,plain,
% 7.81/7.99 (function(identity_relation(B!11))),
% 7.81/7.99 inference(unit_resolution,[status(thm)],[102, 101])).
% 7.81/7.99 tff(104,plain,
% 7.81/7.99 ((~![A: $i] : relation(identity_relation(A))) | relation(identity_relation(B!11))),
% 7.81/7.99 inference(quant_inst,[status(thm)],[])).
% 7.81/7.99 tff(105,plain,
% 7.81/7.99 (relation(identity_relation(B!11))),
% 7.81/7.99 inference(unit_resolution,[status(thm)],[104, 54])).
% 7.81/7.99 tff(106,plain,
% 7.81/7.99 (^[A: $i, B: $i] : refl(((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))) <=> ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))))),
% 7.81/7.99 inference(bind,[status(th)],[])).
% 7.81/7.99 tff(107,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))) <=> ![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 7.81/7.99 inference(quant_intro,[status(thm)],[106])).
% 7.81/7.99 tff(108,plain,
% 7.81/7.99 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A) & relation(B) & function(B)) <=> (~((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B))))), ((~(relation(A) & function(A) & relation(B) & function(B))) <=> (~(~((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B))))))), rewrite((~(~((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B))))) <=> ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)))), ((~(relation(A) & function(A) & relation(B) & function(B))) <=> ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B))))), rewrite((relation(relation_composition(A, B)) & function(relation_composition(A, B))) <=> (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))), (((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> (((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B))) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))))), rewrite((((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B))) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))) <=> ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))), (((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))))),
% 7.81/7.99 inference(bind,[status(th)],[])).
% 7.81/7.99 tff(109,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 7.81/7.99 inference(quant_intro,[status(thm)],[108])).
% 7.81/7.99 tff(110,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 7.81/7.99 inference(rewrite,[status(thm)],[])).
% 7.81/7.99 tff(111,plain,
% 7.81/7.99 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((relation(A) & function(A)) & relation(B)) <=> (relation(A) & function(A) & relation(B))), ((((relation(A) & function(A)) & relation(B)) & function(B)) <=> ((relation(A) & function(A) & relation(B)) & function(B)))), rewrite(((relation(A) & function(A) & relation(B)) & function(B)) <=> (relation(A) & function(A) & relation(B) & function(B))), ((((relation(A) & function(A)) & relation(B)) & function(B)) <=> (relation(A) & function(A) & relation(B) & function(B)))), (((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((relation(A) & function(A) & relation(B) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))))), rewrite(((relation(A) & function(A) & relation(B) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))), (((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))))),
% 7.81/7.99 inference(bind,[status(th)],[])).
% 7.81/7.99 tff(112,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 7.81/7.99 inference(quant_intro,[status(thm)],[111])).
% 7.81/7.99 tff(113,axiom,(![A: $i, B: $i] : ((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_funct_1')).
% 7.81/7.99 tff(114,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 7.81/7.99 inference(modus_ponens,[status(thm)],[113, 112])).
% 7.81/7.99 tff(115,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 7.81/7.99 inference(modus_ponens,[status(thm)],[114, 110])).
% 7.81/7.99 tff(116,plain,(
% 7.81/7.99 ![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 7.81/7.99 inference(skolemize,[status(sab)],[115])).
% 7.81/7.99 tff(117,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 7.81/7.99 inference(modus_ponens,[status(thm)],[116, 109])).
% 7.81/7.99 tff(118,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 7.81/7.99 inference(modus_ponens,[status(thm)],[117, 107])).
% 7.81/7.99 tff(119,plain,
% 7.81/7.99 (((~![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))))),
% 7.81/7.99 inference(rewrite,[status(thm)],[])).
% 7.81/7.99 tff(120,plain,
% 7.81/7.99 (((~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12))))))) <=> ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))))),
% 7.81/7.99 inference(rewrite,[status(thm)],[])).
% 7.81/7.99 tff(121,plain,
% 7.81/7.99 ((~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))) <=> (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12))))))),
% 7.81/7.99 inference(rewrite,[status(thm)],[])).
% 7.81/7.99 tff(122,plain,
% 7.81/7.99 (((~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12))))))) <=> ((~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))))),
% 7.81/7.99 inference(monotonicity,[status(thm)],[121])).
% 7.81/7.99 tff(123,plain,
% 7.81/7.99 (((~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12))))))) <=> ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))))),
% 7.81/7.99 inference(transitivity,[status(thm)],[122, 120])).
% 7.81/7.99 tff(124,plain,
% 7.81/7.99 (((~![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12))))))))),
% 7.81/7.99 inference(monotonicity,[status(thm)],[123])).
% 7.81/7.99 tff(125,plain,
% 7.81/7.99 (((~![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))))),
% 7.81/7.99 inference(transitivity,[status(thm)],[124, 119])).
% 7.81/7.99 tff(126,plain,
% 7.81/7.99 ((~![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))))),
% 7.81/7.99 inference(quant_inst,[status(thm)],[])).
% 7.81/7.99 tff(127,plain,
% 7.81/7.99 ((~![A: $i, B: $i] : ((~relation(A)) | (~relation(B)) | (~function(A)) | (~function(B)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12))))))),
% 7.81/7.99 inference(modus_ponens,[status(thm)],[126, 125])).
% 7.81/7.99 tff(128,plain,
% 7.81/7.99 ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12))))))),
% 7.81/7.99 inference(unit_resolution,[status(thm)],[127, 118])).
% 7.81/7.99 tff(129,plain,
% 7.81/7.99 (~((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))))),
% 7.81/7.99 inference(unit_resolution,[status(thm)],[128, 47, 105, 103, 56])).
% 7.81/7.99 tff(130,plain,
% 7.81/7.99 (((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12))))) | function(relation_composition(identity_relation(B!11), identity_relation(A!12)))),
% 7.81/7.99 inference(tautology,[status(thm)],[])).
% 7.81/7.99 tff(131,plain,
% 7.81/7.99 (function(relation_composition(identity_relation(B!11), identity_relation(A!12)))),
% 7.81/7.99 inference(unit_resolution,[status(thm)],[130, 129])).
% 7.81/7.99 tff(132,plain,
% 7.81/7.99 (^[A: $i, B: $i] : refl((relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B))) <=> (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B))))),
% 7.81/7.99 inference(bind,[status(th)],[])).
% 7.81/7.99 tff(133,plain,
% 7.81/7.99 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))),
% 7.81/7.99 inference(quant_intro,[status(thm)],[132])).
% 7.81/7.99 tff(134,plain,
% 7.81/7.99 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & relation(B)) <=> (~((~relation(A)) | (~relation(B))))), ((~(relation(A) & relation(B))) <=> (~(~((~relation(A)) | (~relation(B))))))), rewrite((~(~((~relation(A)) | (~relation(B))))) <=> ((~relation(A)) | (~relation(B)))), ((~(relation(A) & relation(B))) <=> ((~relation(A)) | (~relation(B))))), ((relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> (relation(relation_composition(A, B)) | ((~relation(A)) | (~relation(B)))))), rewrite((relation(relation_composition(A, B)) | ((~relation(A)) | (~relation(B)))) <=> (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))), ((relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))))),
% 7.81/7.99 inference(bind,[status(th)],[])).
% 7.81/7.99 tff(135,plain,
% 7.81/7.99 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))),
% 7.81/7.99 inference(quant_intro,[status(thm)],[134])).
% 7.81/7.99 tff(136,plain,
% 7.81/7.99 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 7.81/7.99 inference(rewrite,[status(thm)],[])).
% 7.81/7.99 tff(137,plain,
% 7.81/7.99 (^[A: $i, B: $i] : rewrite(((relation(A) & relation(B)) => relation(relation_composition(A, B))) <=> (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))))),
% 7.81/7.99 inference(bind,[status(th)],[])).
% 7.81/7.99 tff(138,plain,
% 7.81/7.99 (![A: $i, B: $i] : ((relation(A) & relation(B)) => relation(relation_composition(A, B))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 7.81/7.99 inference(quant_intro,[status(thm)],[137])).
% 7.81/7.99 tff(139,axiom,(![A: $i, B: $i] : ((relation(A) & relation(B)) => relation(relation_composition(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_relat_1')).
% 7.81/7.99 tff(140,plain,
% 7.81/7.99 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 7.81/7.99 inference(modus_ponens,[status(thm)],[139, 138])).
% 7.81/7.99 tff(141,plain,
% 7.81/7.99 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 7.81/7.99 inference(modus_ponens,[status(thm)],[140, 136])).
% 7.81/7.99 tff(142,plain,(
% 7.81/7.99 ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 7.81/7.99 inference(skolemize,[status(sab)],[141])).
% 7.81/7.99 tff(143,plain,
% 7.81/7.99 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))),
% 7.81/7.99 inference(modus_ponens,[status(thm)],[142, 135])).
% 7.81/7.99 tff(144,plain,
% 7.81/7.99 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))),
% 7.81/7.99 inference(modus_ponens,[status(thm)],[143, 133])).
% 7.81/7.99 tff(145,plain,
% 7.81/7.99 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))) | ((~relation(identity_relation(A!12))) | relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11))))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))) | (~relation(identity_relation(A!12))) | relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11))))),
% 7.81/7.99 inference(rewrite,[status(thm)],[])).
% 7.81/7.99 tff(146,plain,
% 7.81/7.99 ((relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12)))) <=> ((~relation(identity_relation(A!12))) | relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11))))),
% 7.81/7.99 inference(rewrite,[status(thm)],[])).
% 7.81/7.99 tff(147,plain,
% 7.81/7.99 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))) | (relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12))))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))) | ((~relation(identity_relation(A!12))) | relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11)))))),
% 7.81/8.00 inference(monotonicity,[status(thm)],[146])).
% 7.81/8.00 tff(148,plain,
% 7.81/8.00 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))) | (relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12))))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))) | (~relation(identity_relation(A!12))) | relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11))))),
% 7.81/8.00 inference(transitivity,[status(thm)],[147, 145])).
% 7.81/8.00 tff(149,plain,
% 7.81/8.00 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))) | (relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~relation(identity_relation(A!12))))),
% 7.81/8.00 inference(quant_inst,[status(thm)],[])).
% 7.81/8.00 tff(150,plain,
% 7.81/8.00 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(A)) | (~relation(B)))) | (~relation(identity_relation(A!12))) | relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11)))),
% 7.81/8.00 inference(modus_ponens,[status(thm)],[149, 148])).
% 7.81/8.00 tff(151,plain,
% 7.81/8.00 ((~relation(identity_relation(A!12))) | relation(relation_composition(identity_relation(B!11), identity_relation(A!12))) | (~relation(identity_relation(B!11)))),
% 7.81/8.00 inference(unit_resolution,[status(thm)],[150, 144])).
% 7.81/8.00 tff(152,plain,
% 7.81/8.00 (relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))),
% 7.81/8.00 inference(unit_resolution,[status(thm)],[151, 56, 105])).
% 7.81/8.00 tff(153,plain,
% 7.81/8.00 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~((~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~((~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C))))))))))),
% 7.81/8.00 inference(rewrite,[status(thm)],[])).
% 7.81/8.00 tff(154,plain,
% 7.81/8.00 (((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~((~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C)))))))))) <=> ((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~((~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C))))))))))),
% 7.81/8.00 inference(rewrite,[status(thm)],[])).
% 7.81/8.00 tff(155,plain,
% 7.81/8.00 ((~((~((relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C))))))))) <=> (~((~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C)))))))))),
% 7.81/8.00 inference(rewrite,[status(thm)],[])).
% 7.81/8.00 tff(156,plain,
% 7.81/8.00 (((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~((~((relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C)))))))))) <=> ((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~((~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C))))))))))),
% 7.81/8.00 inference(monotonicity,[status(thm)],[155])).
% 7.81/8.00 tff(157,plain,
% 7.81/8.00 (((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~((~((relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C)))))))))) <=> ((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~((~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C))))))))))),
% 7.81/8.00 inference(transitivity,[status(thm)],[156, 154])).
% 7.81/8.00 tff(158,plain,
% 7.81/8.00 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~((~((relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~((~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C)))))))))))),
% 7.81/8.00 inference(monotonicity,[status(thm)],[157])).
% 7.81/8.00 tff(159,plain,
% 7.81/8.00 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~((~((relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~((~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C))))))))))),
% 7.81/8.00 inference(transitivity,[status(thm)],[158, 153])).
% 7.81/8.00 tff(160,plain,
% 7.81/8.00 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~((~((relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C))))))))))),
% 7.81/8.00 inference(quant_inst,[status(thm)],[])).
% 7.81/8.00 tff(161,plain,
% 7.81/8.00 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~function(relation_composition(identity_relation(B!11), identity_relation(A!12)))) | (~((~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C)))))))))),
% 7.81/8.00 inference(modus_ponens,[status(thm)],[160, 159])).
% 7.81/8.00 tff(162,plain,
% 7.81/8.00 (~((~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C))))))))),
% 7.81/8.00 inference(unit_resolution,[status(thm)],[161, 78, 152, 131])).
% 7.81/8.00 tff(163,plain,
% 7.81/8.00 (((~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))) | (~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (~![C: $i] : ((~in(C, set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), C) = C)))))))) | ((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))),
% 7.81/8.00 inference(tautology,[status(thm)],[])).
% 7.81/8.00 tff(164,plain,
% 7.81/8.00 ((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)))))),
% 7.81/8.00 inference(unit_resolution,[status(thm)],[163, 162])).
% 7.81/8.00 tff(165,plain,
% 7.81/8.00 (^[A: $i, B: $i] : refl(((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B))) <=> ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B))))),
% 7.81/8.00 inference(bind,[status(th)],[])).
% 7.81/8.00 tff(166,plain,
% 7.81/8.00 (![A: $i, B: $i] : ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B))) <=> ![A: $i, B: $i] : ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B)))),
% 7.81/8.00 inference(quant_intro,[status(thm)],[165])).
% 7.81/8.00 tff(167,plain,
% 7.81/8.00 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), (((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A))) <=> (((~relation(B)) | (~function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A))))), rewrite((((~relation(B)) | (~function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A))) <=> ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B)))), (((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A))) <=> ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B)))))),
% 7.81/8.00 inference(bind,[status(th)],[])).
% 7.81/8.00 tff(168,plain,
% 7.81/8.00 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A))) <=> ![A: $i, B: $i] : ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B)))),
% 7.81/8.00 inference(quant_intro,[status(thm)],[167])).
% 7.81/8.00 tff(169,plain,
% 7.81/8.00 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)))),
% 7.81/8.00 inference(rewrite,[status(thm)],[])).
% 7.81/8.00 tff(170,plain,
% 7.81/8.00 (^[A: $i, B: $i] : rewrite(((relation(B) & function(B)) => (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A))) <=> ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A))))),
% 7.81/8.00 inference(bind,[status(th)],[])).
% 7.81/8.00 tff(171,plain,
% 7.81/8.00 (![A: $i, B: $i] : ((relation(B) & function(B)) => (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)))),
% 7.81/8.00 inference(quant_intro,[status(thm)],[170])).
% 7.81/8.00 tff(172,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t37_funct_1')).
% 7.81/8.00 tff(173,plain,
% 7.81/8.00 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)))),
% 7.81/8.00 inference(modus_ponens,[status(thm)],[172, 171])).
% 7.81/8.00 tff(174,plain,
% 7.81/8.00 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)))),
% 7.81/8.00 inference(modus_ponens,[status(thm)],[173, 169])).
% 7.81/8.00 tff(175,plain,(
% 7.81/8.00 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)))),
% 7.81/8.00 inference(skolemize,[status(sab)],[174])).
% 7.81/8.00 tff(176,plain,
% 7.81/8.00 (![A: $i, B: $i] : ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B)))),
% 7.81/8.00 inference(modus_ponens,[status(thm)],[175, 168])).
% 7.81/8.00 tff(177,plain,
% 7.81/8.00 (![A: $i, B: $i] : ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B)))),
% 7.81/8.00 inference(modus_ponens,[status(thm)],[176, 166])).
% 7.81/8.00 tff(178,plain,
% 7.81/8.00 (((~![A: $i, B: $i] : ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B)))) | ((relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(relation_dom(identity_relation(A!12)), B!11)) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))))) <=> ((~![A: $i, B: $i] : ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B)))) | (relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(relation_dom(identity_relation(A!12)), B!11)) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))))),
% 7.81/8.00 inference(rewrite,[status(thm)],[])).
% 7.81/8.00 tff(179,plain,
% 7.81/8.00 ((~![A: $i, B: $i] : ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B)))) | ((relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(relation_dom(identity_relation(A!12)), B!11)) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))))),
% 7.81/8.00 inference(quant_inst,[status(thm)],[])).
% 7.81/8.00 tff(180,plain,
% 7.81/8.00 ((~![A: $i, B: $i] : ((relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)) | (~relation(B)) | (~function(B)))) | (relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(relation_dom(identity_relation(A!12)), B!11)) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12)))),
% 7.81/8.00 inference(modus_ponens,[status(thm)],[179, 178])).
% 7.81/8.00 tff(181,plain,
% 7.81/8.00 ((relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(relation_dom(identity_relation(A!12)), B!11)) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12)))),
% 7.81/8.00 inference(unit_resolution,[status(thm)],[180, 177])).
% 7.81/8.00 tff(182,plain,
% 7.81/8.00 (relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(relation_dom(identity_relation(A!12)), B!11)),
% 7.81/8.00 inference(unit_resolution,[status(thm)],[181, 47, 56])).
% 7.81/8.00 tff(183,plain,
% 7.81/8.00 (relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12)),
% 7.81/8.00 inference(transitivity,[status(thm)],[182, 93, 33])).
% 7.81/8.00 tff(184,plain,
% 7.81/8.00 (set_intersection2(B!11, A!12) = set_intersection2(A!12, B!11)),
% 7.81/8.00 inference(symmetry,[status(thm)],[33])).
% 7.81/8.00 tff(185,plain,
% 7.81/8.00 (identity_relation(set_intersection2(B!11, A!12)) = identity_relation(set_intersection2(A!12, B!11))),
% 7.81/8.00 inference(monotonicity,[status(thm)],[184])).
% 7.81/8.00 tff(186,plain,
% 7.81/8.00 ((relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) <=> (relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(A!12, B!11)))),
% 7.81/8.00 inference(monotonicity,[status(thm)],[185])).
% 7.81/8.00 tff(187,plain,
% 7.81/8.00 ((relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(A!12, B!11))) <=> (relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))),
% 7.81/8.00 inference(symmetry,[status(thm)],[186])).
% 7.81/8.00 tff(188,plain,
% 7.81/8.00 ((~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(A!12, B!11)))) <=> (~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))))),
% 7.81/8.00 inference(monotonicity,[status(thm)],[187])).
% 7.81/8.00 tff(189,plain,
% 7.81/8.00 ((~![A: $i, B: $i] : (relation_composition(identity_relation(B), identity_relation(A)) = identity_relation(set_intersection2(A, B)))) <=> (~![A: $i, B: $i] : (relation_composition(identity_relation(B), identity_relation(A)) = identity_relation(set_intersection2(A, B))))),
% 7.81/8.00 inference(rewrite,[status(thm)],[])).
% 7.81/8.00 tff(190,axiom,(~![A: $i, B: $i] : (relation_composition(identity_relation(B), identity_relation(A)) = identity_relation(set_intersection2(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t43_funct_1')).
% 7.81/8.00 tff(191,plain,
% 7.81/8.00 (~![A: $i, B: $i] : (relation_composition(identity_relation(B), identity_relation(A)) = identity_relation(set_intersection2(A, B)))),
% 7.81/8.00 inference(modus_ponens,[status(thm)],[190, 189])).
% 7.81/8.00 tff(192,plain,
% 7.81/8.00 (~![A: $i, B: $i] : (relation_composition(identity_relation(B), identity_relation(A)) = identity_relation(set_intersection2(A, B)))),
% 7.81/8.00 inference(modus_ponens,[status(thm)],[191, 189])).
% 7.81/8.00 tff(193,plain,
% 7.81/8.00 (~![A: $i, B: $i] : (relation_composition(identity_relation(B), identity_relation(A)) = identity_relation(set_intersection2(A, B)))),
% 7.81/8.00 inference(modus_ponens,[status(thm)],[192, 189])).
% 7.81/8.00 tff(194,plain,
% 7.81/8.00 (~![A: $i, B: $i] : (relation_composition(identity_relation(B), identity_relation(A)) = identity_relation(set_intersection2(A, B)))),
% 7.81/8.00 inference(modus_ponens,[status(thm)],[193, 189])).
% 7.81/8.00 tff(195,plain,(
% 7.81/8.00 ~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(A!12, B!11)))),
% 7.81/8.00 inference(skolemize,[status(sab)],[194])).
% 7.81/8.00 tff(196,plain,
% 7.81/8.00 (~(relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12)))),
% 7.81/8.00 inference(modus_ponens,[status(thm)],[195, 188])).
% 7.81/8.00 tff(197,plain,
% 7.81/8.00 ((~((~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))))) | (~(relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))) = set_intersection2(B!11, A!12))) | (relation_composition(identity_relation(B!11), identity_relation(A!12)) = identity_relation(set_intersection2(B!11, A!12))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)))))),
% 7.81/8.01 inference(tautology,[status(thm)],[])).
% 7.81/8.01 tff(198,plain,
% 7.81/8.01 (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))),
% 7.81/8.01 inference(unit_resolution,[status(thm)],[197, 196, 183, 164])).
% 7.81/8.01 tff(199,plain,
% 7.81/8.01 (((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)))) | in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))),
% 7.81/8.01 inference(tautology,[status(thm)],[])).
% 7.81/8.01 tff(200,plain,
% 7.81/8.01 (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))),
% 7.81/8.01 inference(unit_resolution,[status(thm)],[199, 198])).
% 7.81/8.01 tff(201,plain,
% 7.81/8.01 (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11))),
% 7.81/8.01 inference(modus_ponens,[status(thm)],[200, 99])).
% 7.81/8.01 tff(202,plain,
% 7.81/8.01 ((((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11))) <=> in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11)))),
% 7.81/8.01 inference(tautology,[status(thm)],[])).
% 7.81/8.01 tff(203,plain,
% 7.81/8.01 ((((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11))) <=> in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(relation_dom(identity_relation(A!12)), B!11))) | (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11))))),
% 7.81/8.01 inference(unit_resolution,[status(thm)],[202, 201])).
% 7.81/8.01 tff(204,plain,
% 7.81/8.01 (~((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)))),
% 7.81/8.01 inference(unit_resolution,[status(thm)],[203, 97])).
% 7.81/8.01 tff(205,plain,
% 7.81/8.01 (((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11))) | in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)),
% 7.81/8.01 inference(tautology,[status(thm)],[])).
% 7.81/8.01 tff(206,plain,
% 7.81/8.01 (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)),
% 7.81/8.01 inference(unit_resolution,[status(thm)],[205, 204])).
% 7.81/8.01 tff(207,plain,
% 7.81/8.01 (((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12))) | ![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))),
% 7.81/8.01 inference(tautology,[status(thm)],[])).
% 7.81/8.01 tff(208,plain,
% 7.81/8.01 (![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))),
% 7.81/8.01 inference(unit_resolution,[status(thm)],[207, 88])).
% 7.81/8.01 tff(209,plain,
% 7.81/8.01 (((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | ((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) <=> ((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))),
% 7.81/8.01 inference(rewrite,[status(thm)],[])).
% 7.81/8.01 tff(210,plain,
% 7.81/8.01 ((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | ((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))),
% 7.81/8.01 inference(quant_inst,[status(thm)],[])).
% 7.81/8.01 tff(211,plain,
% 7.81/8.01 ((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)))),
% 7.81/8.01 inference(modus_ponens,[status(thm)],[210, 209])).
% 7.81/8.01 tff(212,plain,
% 7.81/8.01 ((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)))),
% 7.81/8.01 inference(unit_resolution,[status(thm)],[211, 208])).
% 7.81/8.01 tff(213,plain,
% 7.81/8.01 (apply(identity_relation(A!12), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))),
% 7.81/8.01 inference(unit_resolution,[status(thm)],[212, 206])).
% 7.81/8.01 tff(214,plain,
% 7.81/8.01 (((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), A!12)) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11))) | in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)),
% 7.81/8.01 inference(tautology,[status(thm)],[])).
% 7.81/8.01 tff(215,plain,
% 7.81/8.01 (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)),
% 7.81/8.01 inference(unit_resolution,[status(thm)],[214, 204])).
% 7.81/8.01 tff(216,plain,
% 7.81/8.01 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))) | (~(relation_dom(identity_relation(B!11)) = B!11)))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))) | (~(relation_dom(identity_relation(B!11)) = B!11)))))),
% 7.81/8.01 inference(rewrite,[status(thm)],[])).
% 7.81/8.01 tff(217,plain,
% 7.81/8.01 (((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))) | (~(relation_dom(identity_relation(B!11)) = B!11))))) <=> ((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))) | (~(relation_dom(identity_relation(B!11)) = B!11)))))),
% 7.81/8.01 inference(rewrite,[status(thm)],[])).
% 7.81/8.01 tff(218,plain,
% 7.81/8.01 ((~((~((identity_relation(B!11) = identity_relation(B!11)) | (~(relation_dom(identity_relation(B!11)) = B!11)) | (~((~in(tptp_fun_C_10(identity_relation(B!11), B!11), B!11)) | (apply(identity_relation(B!11), tptp_fun_C_10(identity_relation(B!11), B!11)) = tptp_fun_C_10(identity_relation(B!11), B!11)))))) | (~((~(identity_relation(B!11) = identity_relation(B!11))) | (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))))))))) <=> (~((~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))) | (~(relation_dom(identity_relation(B!11)) = B!11))))),
% 7.81/8.01 inference(rewrite,[status(thm)],[])).
% 7.81/8.01 tff(219,plain,
% 7.81/8.01 (((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~((identity_relation(B!11) = identity_relation(B!11)) | (~(relation_dom(identity_relation(B!11)) = B!11)) | (~((~in(tptp_fun_C_10(identity_relation(B!11), B!11), B!11)) | (apply(identity_relation(B!11), tptp_fun_C_10(identity_relation(B!11), B!11)) = tptp_fun_C_10(identity_relation(B!11), B!11)))))) | (~((~(identity_relation(B!11) = identity_relation(B!11))) | (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C)))))))))) <=> ((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))) | (~(relation_dom(identity_relation(B!11)) = B!11)))))),
% 7.81/8.01 inference(monotonicity,[status(thm)],[218])).
% 7.81/8.01 tff(220,plain,
% 7.81/8.01 (((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~((identity_relation(B!11) = identity_relation(B!11)) | (~(relation_dom(identity_relation(B!11)) = B!11)) | (~((~in(tptp_fun_C_10(identity_relation(B!11), B!11), B!11)) | (apply(identity_relation(B!11), tptp_fun_C_10(identity_relation(B!11), B!11)) = tptp_fun_C_10(identity_relation(B!11), B!11)))))) | (~((~(identity_relation(B!11) = identity_relation(B!11))) | (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C)))))))))) <=> ((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))) | (~(relation_dom(identity_relation(B!11)) = B!11)))))),
% 7.81/8.01 inference(transitivity,[status(thm)],[219, 217])).
% 7.81/8.01 tff(221,plain,
% 7.81/8.01 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~((identity_relation(B!11) = identity_relation(B!11)) | (~(relation_dom(identity_relation(B!11)) = B!11)) | (~((~in(tptp_fun_C_10(identity_relation(B!11), B!11), B!11)) | (apply(identity_relation(B!11), tptp_fun_C_10(identity_relation(B!11), B!11)) = tptp_fun_C_10(identity_relation(B!11), B!11)))))) | (~((~(identity_relation(B!11) = identity_relation(B!11))) | (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))) | (~(relation_dom(identity_relation(B!11)) = B!11))))))),
% 7.81/8.01 inference(monotonicity,[status(thm)],[220])).
% 7.81/8.01 tff(222,plain,
% 7.81/8.01 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~((identity_relation(B!11) = identity_relation(B!11)) | (~(relation_dom(identity_relation(B!11)) = B!11)) | (~((~in(tptp_fun_C_10(identity_relation(B!11), B!11), B!11)) | (apply(identity_relation(B!11), tptp_fun_C_10(identity_relation(B!11), B!11)) = tptp_fun_C_10(identity_relation(B!11), B!11)))))) | (~((~(identity_relation(B!11) = identity_relation(B!11))) | (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))) | (~(relation_dom(identity_relation(B!11)) = B!11)))))),
% 7.81/8.01 inference(transitivity,[status(thm)],[221, 216])).
% 7.81/8.01 tff(223,plain,
% 7.81/8.01 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~((identity_relation(B!11) = identity_relation(B!11)) | (~(relation_dom(identity_relation(B!11)) = B!11)) | (~((~in(tptp_fun_C_10(identity_relation(B!11), B!11), B!11)) | (apply(identity_relation(B!11), tptp_fun_C_10(identity_relation(B!11), B!11)) = tptp_fun_C_10(identity_relation(B!11), B!11)))))) | (~((~(identity_relation(B!11) = identity_relation(B!11))) | (~((~(relation_dom(identity_relation(B!11)) = B!11)) | (~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))))))))))),
% 7.81/8.01 inference(quant_inst,[status(thm)],[])).
% 7.81/8.01 tff(224,plain,
% 7.81/8.01 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (~((~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))) | (~(relation_dom(identity_relation(B!11)) = B!11))))),
% 7.81/8.01 inference(modus_ponens,[status(thm)],[223, 222])).
% 7.81/8.01 tff(225,plain,
% 7.81/8.01 (~((~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))) | (~(relation_dom(identity_relation(B!11)) = B!11)))),
% 7.81/8.01 inference(unit_resolution,[status(thm)],[224, 78, 105, 103])).
% 7.81/8.01 tff(226,plain,
% 7.81/8.01 (((~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))) | (~(relation_dom(identity_relation(B!11)) = B!11))) | ![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))),
% 7.81/8.01 inference(tautology,[status(thm)],[])).
% 7.81/8.01 tff(227,plain,
% 7.81/8.01 (![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))),
% 7.81/8.01 inference(unit_resolution,[status(thm)],[226, 225])).
% 7.81/8.01 tff(228,plain,
% 7.81/8.01 (((~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))) | ((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) <=> ((~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))),
% 7.81/8.01 inference(rewrite,[status(thm)],[])).
% 7.81/8.01 tff(229,plain,
% 7.81/8.01 ((~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))) | ((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))),
% 7.81/8.01 inference(quant_inst,[status(thm)],[])).
% 7.81/8.01 tff(230,plain,
% 7.81/8.01 ((~![C: $i] : ((~in(C, B!11)) | (apply(identity_relation(B!11), C) = C))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)))),
% 7.81/8.01 inference(modus_ponens,[status(thm)],[229, 228])).
% 7.81/8.01 tff(231,plain,
% 7.81/8.01 ((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), B!11)) | (apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)))),
% 7.81/8.01 inference(unit_resolution,[status(thm)],[230, 227])).
% 7.81/8.01 tff(232,plain,
% 7.81/8.01 (apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))),
% 7.81/8.01 inference(unit_resolution,[status(thm)],[231, 215])).
% 7.81/8.01 tff(233,plain,
% 7.81/8.01 (apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)))) = apply(identity_relation(A!12), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)))),
% 7.81/8.01 inference(monotonicity,[status(thm)],[232])).
% 7.81/8.01 tff(234,plain,
% 7.81/8.01 (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12)))) <=> in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))),
% 7.81/8.01 inference(monotonicity,[status(thm)],[183])).
% 7.81/8.01 tff(235,plain,
% 7.81/8.01 (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12)) <=> in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))))),
% 7.81/8.01 inference(symmetry,[status(thm)],[234])).
% 7.81/8.01 tff(236,plain,
% 7.81/8.01 (in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))))),
% 7.81/8.01 inference(modus_ponens,[status(thm)],[200, 235])).
% 7.81/8.01 tff(237,plain,
% 7.81/8.01 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))), (((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))), rewrite(((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))), (((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))))),
% 7.81/8.01 inference(bind,[status(th)],[])).
% 7.81/8.01 tff(238,plain,
% 7.81/8.01 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))),
% 7.81/8.01 inference(quant_intro,[status(thm)],[237])).
% 7.81/8.01 tff(239,plain,
% 7.81/8.01 (^[A: $i, B: $i, C: $i] : refl(((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))),
% 7.81/8.01 inference(bind,[status(th)],[])).
% 7.81/8.01 tff(240,plain,
% 7.81/8.01 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 7.81/8.01 inference(quant_intro,[status(thm)],[239])).
% 7.81/8.01 tff(241,plain,
% 7.81/8.01 (![A: $i, B: $i] : ![C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 7.81/8.01 inference(pull_quant,[status(thm)],[])).
% 7.81/8.01 tff(242,plain,
% 7.81/8.01 (^[A: $i, B: $i] : pull_quant(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))),
% 7.81/8.01 inference(bind,[status(th)],[])).
% 7.81/8.01 tff(243,plain,
% 7.81/8.01 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ![C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 7.81/8.01 inference(quant_intro,[status(thm)],[242])).
% 7.81/8.01 tff(244,plain,
% 7.81/8.01 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 7.81/8.01 inference(transitivity,[status(thm)],[243, 241])).
% 7.81/8.01 tff(245,plain,
% 7.81/8.01 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 7.81/8.01 inference(transitivity,[status(thm)],[244, 240])).
% 7.81/8.01 tff(246,plain,
% 7.81/8.01 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))),
% 7.81/8.01 inference(bind,[status(th)],[])).
% 7.81/8.01 tff(247,plain,
% 7.81/8.01 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 7.81/8.01 inference(quant_intro,[status(thm)],[246])).
% 7.81/8.01 tff(248,plain,
% 7.81/8.01 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 7.81/8.01 inference(transitivity,[status(thm)],[247, 245])).
% 7.81/8.01 tff(249,plain,
% 7.81/8.01 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(C) & function(C)) <=> (~((~relation(C)) | (~function(C))))), ((~(relation(C) & function(C))) <=> (~(~((~relation(C)) | (~function(C))))))), rewrite((~(~((~relation(C)) | (~function(C))))) <=> ((~relation(C)) | (~function(C)))), ((~(relation(C) & function(C))) <=> ((~relation(C)) | (~function(C))))), (((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | ((~relation(C)) | (~function(C)))))), rewrite(((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | ((~relation(C)) | (~function(C)))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))), (((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))), (![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))) <=> ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C))))) <=> (((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))), rewrite((((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))))),
% 7.81/8.01 inference(bind,[status(th)],[])).
% 7.81/8.01 tff(250,plain,
% 7.81/8.01 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 7.81/8.01 inference(quant_intro,[status(thm)],[249])).
% 7.81/8.01 tff(251,plain,
% 7.81/8.01 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))))),
% 7.81/8.01 inference(rewrite,[status(thm)],[])).
% 7.81/8.01 tff(252,plain,
% 7.81/8.01 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A)))) <=> ((~in(A, relation_dom(relation_composition(C, B)))) | (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))), (((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))) <=> ((relation(C) & function(C)) => ((~in(A, relation_dom(relation_composition(C, B)))) | (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))))), rewrite(((relation(C) & function(C)) => ((~in(A, relation_dom(relation_composition(C, B)))) | (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C))))), (((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C))))))), (![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))) <=> ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A)))))) <=> ((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C))))))), rewrite(((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A)))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))))))),
% 7.81/8.01 inference(bind,[status(th)],[])).
% 7.81/8.01 tff(253,plain,
% 7.81/8.01 (![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A)))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))))),
% 7.81/8.01 inference(quant_intro,[status(thm)],[252])).
% 7.81/8.01 tff(254,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t22_funct_1')).
% 7.81/8.01 tff(255,plain,
% 7.81/8.01 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))))),
% 7.81/8.01 inference(modus_ponens,[status(thm)],[254, 253])).
% 7.81/8.01 tff(256,plain,
% 7.81/8.01 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))))),
% 7.81/8.01 inference(modus_ponens,[status(thm)],[255, 251])).
% 7.81/8.01 tff(257,plain,(
% 7.81/8.01 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~(relation(C) & function(C)))))),
% 7.81/8.01 inference(skolemize,[status(sab)],[256])).
% 7.81/8.01 tff(258,plain,
% 7.81/8.01 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 7.81/8.01 inference(modus_ponens,[status(thm)],[257, 250])).
% 7.81/8.01 tff(259,plain,
% 7.81/8.01 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 7.81/8.01 inference(modus_ponens,[status(thm)],[258, 248])).
% 7.81/8.01 tff(260,plain,
% 7.81/8.01 (![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))),
% 7.81/8.01 inference(modus_ponens,[status(thm)],[259, 238])).
% 7.81/8.01 tff(261,plain,
% 7.81/8.01 (((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))))))) <=> ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))))))),
% 7.81/8.01 inference(rewrite,[status(thm)],[])).
% 7.81/8.01 tff(262,plain,
% 7.81/8.01 (((apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))))) | (~relation(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~function(identity_relation(B!11)))) <=> ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))))))),
% 7.81/8.01 inference(rewrite,[status(thm)],[])).
% 7.81/8.01 tff(263,plain,
% 7.81/8.01 (((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))) | ((apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))))) | (~relation(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~function(identity_relation(B!11))))) <=> ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12)))))))),
% 7.81/8.02 inference(monotonicity,[status(thm)],[262])).
% 7.81/8.02 tff(264,plain,
% 7.81/8.02 (((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))) | ((apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))))) | (~relation(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~function(identity_relation(B!11))))) <=> ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))))))),
% 7.81/8.02 inference(transitivity,[status(thm)],[263, 261])).
% 7.81/8.02 tff(265,plain,
% 7.81/8.02 ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))) | ((apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12))))) | (~relation(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(A!12))) | (~function(identity_relation(B!11))))),
% 7.81/8.02 inference(quant_inst,[status(thm)],[])).
% 7.81/8.02 tff(266,plain,
% 7.81/8.02 ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)))) | (~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(B!11))) | (~function(identity_relation(B!11))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12)))))),
% 7.81/8.02 inference(modus_ponens,[status(thm)],[265, 264])).
% 7.81/8.02 tff(267,plain,
% 7.81/8.02 ((apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))) | (~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), relation_dom(relation_composition(identity_relation(B!11), identity_relation(A!12)))))),
% 7.81/8.02 inference(unit_resolution,[status(thm)],[266, 260, 56, 47, 105, 103])).
% 7.81/8.02 tff(268,plain,
% 7.81/8.02 (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = apply(identity_relation(A!12), apply(identity_relation(B!11), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))),
% 7.81/8.02 inference(unit_resolution,[status(thm)],[267, 236])).
% 7.81/8.02 tff(269,plain,
% 7.81/8.02 (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))),
% 7.81/8.02 inference(transitivity,[status(thm)],[268, 233, 213])).
% 7.81/8.02 tff(270,plain,
% 7.81/8.02 (((~in(tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)), set_intersection2(B!11, A!12))) | (apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)))) | (~(apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))))),
% 7.81/8.02 inference(tautology,[status(thm)],[])).
% 7.81/8.02 tff(271,plain,
% 7.81/8.02 (~(apply(relation_composition(identity_relation(B!11), identity_relation(A!12)), tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12))) = tptp_fun_C_10(relation_composition(identity_relation(B!11), identity_relation(A!12)), set_intersection2(B!11, A!12)))),
% 7.81/8.02 inference(unit_resolution,[status(thm)],[270, 198])).
% 7.87/8.05 tff(272,plain,
% 7.87/8.05 ($false),
% 7.87/8.05 inference(unit_resolution,[status(thm)],[271, 269])).
% 7.87/8.05 % SZS output end Proof
% 7.87/8.05 % E exiting
%------------------------------------------------------------------------------