%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU249+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:27:23 AM UTC 2025
% Result : Theorem 4.33s 4.48s
% Output : Proof 4.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU249+1 : TPTP v9.0.0. Released v3.3.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Jun 20 06:28:57 EDT 2025
% 0.14/0.34 % CPUTime :
% 4.33/4.48 % SZS status Theorem
% 4.33/4.48 % SZS output start Proof
% 4.33/4.48 tff(element_type, type, (
% 4.33/4.48 element: ( $i * $i ) > $o)).
% 4.33/4.48 tff(relation_rng_type, type, (
% 4.33/4.48 relation_rng: $i > $i)).
% 4.33/4.48 tff(tptp_fun_C_8_type, type, (
% 4.33/4.48 tptp_fun_C_8: $i)).
% 4.33/4.48 tff(tptp_fun_A_10_type, type, (
% 4.33/4.48 tptp_fun_A_10: $i)).
% 4.33/4.48 tff(empty_type, type, (
% 4.33/4.48 empty: $i > $o)).
% 4.33/4.48 tff(in_type, type, (
% 4.33/4.48 in: ( $i * $i ) > $o)).
% 4.33/4.48 tff(relation_dom_restriction_type, type, (
% 4.33/4.48 relation_dom_restriction: ( $i * $i ) > $i)).
% 4.33/4.48 tff(tptp_fun_B_9_type, type, (
% 4.33/4.48 tptp_fun_B_9: $i)).
% 4.33/4.48 tff(set_intersection2_type, type, (
% 4.33/4.48 set_intersection2: ( $i * $i ) > $i)).
% 4.33/4.48 tff(tptp_fun_D_1_type, type, (
% 4.33/4.48 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 4.33/4.48 tff(relation_dom_type, type, (
% 4.33/4.48 relation_dom: $i > $i)).
% 4.33/4.48 tff(relation_restriction_type, type, (
% 4.33/4.48 relation_restriction: ( $i * $i ) > $i)).
% 4.33/4.48 tff(relation_rng_restriction_type, type, (
% 4.33/4.48 relation_rng_restriction: ( $i * $i ) > $i)).
% 4.33/4.48 tff(powerset_type, type, (
% 4.33/4.48 powerset: $i > $i)).
% 4.33/4.48 tff(subset_type, type, (
% 4.33/4.48 subset: ( $i * $i ) > $o)).
% 4.33/4.48 tff(relation_type, type, (
% 4.33/4.48 relation: $i > $o)).
% 4.33/4.48 tff(relation_field_type, type, (
% 4.33/4.48 relation_field: $i > $i)).
% 4.33/4.48 tff(set_union2_type, type, (
% 4.33/4.48 set_union2: ( $i * $i ) > $i)).
% 4.33/4.48 tff(tptp_fun_D_0_type, type, (
% 4.33/4.48 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 4.33/4.48 tff(1,assumption,((~((~(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9) = set_intersection2(B!9, relation_rng(relation_dom_restriction(C!8, B!9))))) | (~(((~in(A!10, B!9)) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9))))) <=> in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))))) | (~((set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9) = set_intersection2(B!9, relation_rng(relation_dom_restriction(C!8, B!9)))) | (((~in(tptp_fun_D_1(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_rng(relation_dom_restriction(C!8, B!9)), B!9), B!9)) | (~in(tptp_fun_D_1(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_rng(relation_dom_restriction(C!8, B!9))))) <=> in(tptp_fun_D_1(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_rng(relation_dom_restriction(C!8, B!9)), B!9), set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))))), introduced(assumption)).
% 4.33/4.48 tff(2,plain,
% 4.33/4.48 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))))),
% 4.33/4.48 inference(bind,[status(th)],[])).
% 4.33/4.48 tff(3,plain,
% 4.33/4.48 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 4.33/4.48 inference(quant_intro,[status(thm)],[2])).
% 4.33/4.48 tff(4,plain,
% 4.33/4.48 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 4.33/4.48 inference(pull_quant,[status(thm)],[])).
% 4.33/4.48 tff(5,plain,
% 4.33/4.48 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))))),
% 4.33/4.48 inference(bind,[status(th)],[])).
% 4.33/4.48 tff(6,plain,
% 4.33/4.48 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 4.33/4.48 inference(quant_intro,[status(thm)],[5])).
% 4.33/4.48 tff(7,plain,
% 4.33/4.48 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 4.33/4.48 inference(transitivity,[status(thm)],[6, 4])).
% 4.33/4.48 tff(8,plain,
% 4.33/4.48 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 4.33/4.48 inference(transitivity,[status(thm)],[7, 3])).
% 4.33/4.48 tff(9,plain,
% 4.33/4.48 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))))),
% 4.33/4.48 inference(bind,[status(th)],[])).
% 4.33/4.48 tff(10,plain,
% 4.33/4.48 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 4.33/4.48 inference(quant_intro,[status(thm)],[9])).
% 4.33/4.48 tff(11,plain,
% 4.33/4.48 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 4.33/4.48 inference(transitivity,[status(thm)],[10, 8])).
% 4.33/4.48 tff(12,plain,
% 4.33/4.48 (^[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, A)) | (~in(D, B))) <=> in(D, C))))), rewrite(((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B))))) <=> ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B)))))) <=> (((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))), rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))))),
% 4.33/4.48 inference(bind,[status(th)],[])).
% 4.33/4.48 tff(13,plain,
% 4.33/4.48 (![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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 4.33/4.48 inference(quant_intro,[status(thm)],[12])).
% 4.33/4.48 tff(14,plain,
% 4.33/4.48 (![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))))),
% 4.33/4.48 inference(rewrite,[status(thm)],[])).
% 4.33/4.48 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')).
% 4.33/4.48 tff(16,plain,
% 4.33/4.48 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 4.33/4.48 inference(modus_ponens,[status(thm)],[15, 14])).
% 4.33/4.48 tff(17,plain,(
% 4.33/4.48 ![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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B))))))),
% 4.33/4.48 inference(skolemize,[status(sab)],[16])).
% 4.33/4.48 tff(18,plain,
% 4.33/4.48 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 4.33/4.48 inference(modus_ponens,[status(thm)],[17, 13])).
% 4.33/4.48 tff(19,plain,
% 4.33/4.48 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 4.33/4.48 inference(modus_ponens,[status(thm)],[18, 11])).
% 4.33/4.48 tff(20,plain,
% 4.33/4.48 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9) = set_intersection2(B!9, relation_rng(relation_dom_restriction(C!8, B!9))))) | (~(((~in(A!10, B!9)) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9))))) <=> in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))))) | (~((set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9) = set_intersection2(B!9, relation_rng(relation_dom_restriction(C!8, B!9)))) | (((~in(tptp_fun_D_1(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_rng(relation_dom_restriction(C!8, B!9)), B!9), B!9)) | (~in(tptp_fun_D_1(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_rng(relation_dom_restriction(C!8, B!9))))) <=> in(tptp_fun_D_1(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_rng(relation_dom_restriction(C!8, B!9)), B!9), set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))))))),
% 4.33/4.48 inference(quant_inst,[status(thm)],[])).
% 4.33/4.48 tff(21,plain,
% 4.33/4.48 ($false),
% 4.33/4.48 inference(unit_resolution,[status(thm)],[20, 19, 1])).
% 4.33/4.48 tff(22,plain,(~((~((~(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9) = set_intersection2(B!9, relation_rng(relation_dom_restriction(C!8, B!9))))) | (~(((~in(A!10, B!9)) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9))))) <=> in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))))) | (~((set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9) = set_intersection2(B!9, relation_rng(relation_dom_restriction(C!8, B!9)))) | (((~in(tptp_fun_D_1(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_rng(relation_dom_restriction(C!8, B!9)), B!9), B!9)) | (~in(tptp_fun_D_1(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_rng(relation_dom_restriction(C!8, B!9))))) <=> in(tptp_fun_D_1(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_rng(relation_dom_restriction(C!8, B!9)), B!9), set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9))))))), inference(lemma,lemma(discharge,[]))).
% 4.33/4.48 tff(23,plain,
% 4.33/4.48 (((~((~(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9) = set_intersection2(B!9, relation_rng(relation_dom_restriction(C!8, B!9))))) | (~(((~in(A!10, B!9)) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9))))) <=> in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))))) | (~((set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9) = set_intersection2(B!9, relation_rng(relation_dom_restriction(C!8, B!9)))) | (((~in(tptp_fun_D_1(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_rng(relation_dom_restriction(C!8, B!9)), B!9), B!9)) | (~in(tptp_fun_D_1(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_rng(relation_dom_restriction(C!8, B!9))))) <=> in(tptp_fun_D_1(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_rng(relation_dom_restriction(C!8, B!9)), B!9), set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))))) | ((~(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9) = set_intersection2(B!9, relation_rng(relation_dom_restriction(C!8, B!9))))) | (~(((~in(A!10, B!9)) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9))))) <=> in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))))),
% 4.33/4.48 inference(tautology,[status(thm)],[])).
% 4.33/4.48 tff(24,plain,
% 4.33/4.48 ((~(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9) = set_intersection2(B!9, relation_rng(relation_dom_restriction(C!8, B!9))))) | (~(((~in(A!10, B!9)) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9))))) <=> in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9))))),
% 4.33/4.48 inference(unit_resolution,[status(thm)],[23, 22])).
% 4.33/4.48 tff(25,plain,
% 4.33/4.48 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 4.33/4.48 inference(bind,[status(th)],[])).
% 4.33/4.48 tff(26,plain,
% 4.33/4.48 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 4.33/4.48 inference(quant_intro,[status(thm)],[25])).
% 4.33/4.48 tff(27,plain,
% 4.33/4.48 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 4.33/4.48 inference(rewrite,[status(thm)],[])).
% 4.33/4.48 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')).
% 4.33/4.48 tff(29,plain,
% 4.33/4.48 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 4.33/4.48 inference(modus_ponens,[status(thm)],[28, 27])).
% 4.33/4.48 tff(30,plain,(
% 4.33/4.48 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 4.33/4.48 inference(skolemize,[status(sab)],[29])).
% 4.33/4.48 tff(31,plain,
% 4.33/4.48 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 4.33/4.48 inference(modus_ponens,[status(thm)],[30, 26])).
% 4.33/4.48 tff(32,plain,
% 4.33/4.48 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9) = set_intersection2(B!9, relation_rng(relation_dom_restriction(C!8, B!9))))),
% 4.33/4.48 inference(quant_inst,[status(thm)],[])).
% 4.33/4.48 tff(33,plain,
% 4.33/4.48 (set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9) = set_intersection2(B!9, relation_rng(relation_dom_restriction(C!8, B!9)))),
% 4.33/4.48 inference(unit_resolution,[status(thm)],[32, 31])).
% 4.33/4.48 tff(34,plain,
% 4.33/4.48 ((~((~(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9) = set_intersection2(B!9, relation_rng(relation_dom_restriction(C!8, B!9))))) | (~(((~in(A!10, B!9)) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9))))) <=> in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))))) | (~(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9) = set_intersection2(B!9, relation_rng(relation_dom_restriction(C!8, B!9))))) | (~(((~in(A!10, B!9)) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9))))) <=> in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9))))),
% 4.33/4.48 inference(tautology,[status(thm)],[])).
% 4.33/4.48 tff(35,plain,
% 4.33/4.48 ((~((~(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9) = set_intersection2(B!9, relation_rng(relation_dom_restriction(C!8, B!9))))) | (~(((~in(A!10, B!9)) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9))))) <=> in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))))) | (~(((~in(A!10, B!9)) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9))))) <=> in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9))))),
% 4.33/4.48 inference(unit_resolution,[status(thm)],[34, 33])).
% 4.33/4.48 tff(36,plain,
% 4.33/4.48 (~(((~in(A!10, B!9)) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9))))) <=> in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))),
% 4.33/4.48 inference(unit_resolution,[status(thm)],[35, 24])).
% 4.33/4.48 tff(37,assumption,(in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))), introduced(assumption)).
% 4.33/4.48 tff(38,plain,
% 4.33/4.48 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 4.33/4.48 inference(bind,[status(th)],[])).
% 4.33/4.48 tff(39,plain,
% 4.33/4.48 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 4.33/4.48 inference(quant_intro,[status(thm)],[38])).
% 4.33/4.48 tff(40,plain,
% 4.33/4.48 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 4.33/4.48 inference(rewrite,[status(thm)],[])).
% 4.33/4.48 tff(41,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_subset')).
% 4.33/4.48 tff(42,plain,
% 4.33/4.48 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 4.33/4.48 inference(modus_ponens,[status(thm)],[41, 40])).
% 4.33/4.48 tff(43,plain,(
% 4.33/4.48 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 4.33/4.48 inference(skolemize,[status(sab)],[42])).
% 4.33/4.48 tff(44,plain,
% 4.33/4.48 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 4.33/4.48 inference(modus_ponens,[status(thm)],[43, 39])).
% 4.33/4.48 tff(45,plain,
% 4.33/4.48 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8))) <=> subset(relation_dom(relation_rng_restriction(B!9, C!8)), relation_dom(C!8)))),
% 4.33/4.48 inference(quant_inst,[status(thm)],[])).
% 4.33/4.48 tff(46,plain,
% 4.33/4.48 (element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8))) <=> subset(relation_dom(relation_rng_restriction(B!9, C!8)), relation_dom(C!8))),
% 4.33/4.48 inference(unit_resolution,[status(thm)],[45, 44])).
% 4.33/4.48 tff(47,plain,
% 4.33/4.48 ((~((in(A!10, relation_field(C!8)) & in(A!10, B!9)) | (~relation(C!8)) | (~in(A!10, relation_field(relation_restriction(C!8, B!9)))))) <=> (~((in(A!10, relation_field(C!8)) & in(A!10, B!9)) | (~relation(C!8)) | (~in(A!10, relation_field(relation_restriction(C!8, B!9))))))),
% 4.33/4.49 inference(rewrite,[status(thm)],[])).
% 4.33/4.49 tff(48,plain,
% 4.33/4.49 ((~![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))) <=> (~![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))))),
% 4.33/4.49 inference(rewrite,[status(thm)],[])).
% 4.33/4.49 tff(49,plain,
% 4.33/4.49 ((~![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B))))) <=> (~![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))))),
% 4.33/4.49 inference(rewrite,[status(thm)],[])).
% 4.33/4.49 tff(50,axiom,(~![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t19_wellord1')).
% 4.33/4.49 tff(51,plain,
% 4.33/4.49 (~![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 4.33/4.49 inference(modus_ponens,[status(thm)],[50, 49])).
% 4.33/4.49 tff(52,plain,
% 4.33/4.49 (~![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 4.33/4.49 inference(modus_ponens,[status(thm)],[51, 48])).
% 4.33/4.49 tff(53,plain,
% 4.33/4.49 (~![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 4.33/4.49 inference(modus_ponens,[status(thm)],[52, 48])).
% 4.33/4.49 tff(54,plain,
% 4.33/4.49 (~![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 4.33/4.49 inference(modus_ponens,[status(thm)],[53, 48])).
% 4.33/4.49 tff(55,plain,(
% 4.33/4.49 ~((in(A!10, relation_field(C!8)) & in(A!10, B!9)) | (~relation(C!8)) | (~in(A!10, relation_field(relation_restriction(C!8, B!9)))))),
% 4.33/4.49 inference(skolemize,[status(sab)],[54])).
% 4.33/4.49 tff(56,plain,
% 4.33/4.49 (~((in(A!10, relation_field(C!8)) & in(A!10, B!9)) | (~relation(C!8)) | (~in(A!10, relation_field(relation_restriction(C!8, B!9)))))),
% 4.33/4.49 inference(modus_ponens,[status(thm)],[55, 47])).
% 4.33/4.49 tff(57,plain,
% 4.33/4.49 (relation(C!8)),
% 4.33/4.49 inference(or_elim,[status(thm)],[56])).
% 4.33/4.49 tff(58,plain,
% 4.33/4.49 (^[A: $i, B: $i] : refl(((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B))) <=> ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B))))),
% 4.33/4.49 inference(bind,[status(th)],[])).
% 4.33/4.49 tff(59,plain,
% 4.33/4.49 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B))) <=> ![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B)))),
% 4.33/4.49 inference(quant_intro,[status(thm)],[58])).
% 4.33/4.49 tff(60,plain,
% 4.33/4.49 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B))) <=> ![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B)))),
% 4.33/4.49 inference(rewrite,[status(thm)],[])).
% 4.33/4.49 tff(61,plain,
% 4.33/4.49 (^[A: $i, B: $i] : rewrite((relation(B) => subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B))) <=> ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B))))),
% 4.33/4.49 inference(bind,[status(th)],[])).
% 4.33/4.49 tff(62,plain,
% 4.33/4.49 (![A: $i, B: $i] : (relation(B) => subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B))) <=> ![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B)))),
% 4.33/4.49 inference(quant_intro,[status(thm)],[61])).
% 4.33/4.49 tff(63,axiom,(![A: $i, B: $i] : (relation(B) => subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l29_wellord1')).
% 4.33/4.49 tff(64,plain,
% 4.33/4.49 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B)))),
% 4.33/4.49 inference(modus_ponens,[status(thm)],[63, 62])).
% 4.33/4.49 tff(65,plain,
% 4.33/4.49 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B)))),
% 4.33/4.49 inference(modus_ponens,[status(thm)],[64, 60])).
% 4.33/4.49 tff(66,plain,(
% 4.33/4.49 ![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B)))),
% 4.33/4.49 inference(skolemize,[status(sab)],[65])).
% 4.33/4.49 tff(67,plain,
% 4.33/4.49 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B)))),
% 4.33/4.49 inference(modus_ponens,[status(thm)],[66, 59])).
% 4.33/4.49 tff(68,plain,
% 4.33/4.49 (((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B)))) | ((~relation(C!8)) | subset(relation_dom(relation_rng_restriction(B!9, C!8)), relation_dom(C!8)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B)))) | (~relation(C!8)) | subset(relation_dom(relation_rng_restriction(B!9, C!8)), relation_dom(C!8)))),
% 4.33/4.49 inference(rewrite,[status(thm)],[])).
% 4.33/4.49 tff(69,plain,
% 4.33/4.49 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B)))) | ((~relation(C!8)) | subset(relation_dom(relation_rng_restriction(B!9, C!8)), relation_dom(C!8)))),
% 4.33/4.49 inference(quant_inst,[status(thm)],[])).
% 4.33/4.49 tff(70,plain,
% 4.33/4.49 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_rng_restriction(A, B)), relation_dom(B)))) | (~relation(C!8)) | subset(relation_dom(relation_rng_restriction(B!9, C!8)), relation_dom(C!8))),
% 4.33/4.49 inference(modus_ponens,[status(thm)],[69, 68])).
% 4.33/4.49 tff(71,plain,
% 4.33/4.49 (subset(relation_dom(relation_rng_restriction(B!9, C!8)), relation_dom(C!8))),
% 4.33/4.49 inference(unit_resolution,[status(thm)],[70, 67, 57])).
% 4.33/4.49 tff(72,plain,
% 4.33/4.49 ((~(element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8))) <=> subset(relation_dom(relation_rng_restriction(B!9, C!8)), relation_dom(C!8)))) | element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8))) | (~subset(relation_dom(relation_rng_restriction(B!9, C!8)), relation_dom(C!8)))),
% 4.33/4.49 inference(tautology,[status(thm)],[])).
% 4.33/4.49 tff(73,plain,
% 4.33/4.49 ((~(element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8))) <=> subset(relation_dom(relation_rng_restriction(B!9, C!8)), relation_dom(C!8)))) | element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8)))),
% 4.33/4.49 inference(unit_resolution,[status(thm)],[72, 71])).
% 4.33/4.49 tff(74,plain,
% 4.33/4.49 (element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8)))),
% 4.33/4.49 inference(unit_resolution,[status(thm)],[73, 46])).
% 4.33/4.49 tff(75,plain,
% 4.33/4.49 (^[A: $i, B: $i, C: $i] : refl(((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 4.33/4.49 inference(bind,[status(th)],[])).
% 4.33/4.49 tff(76,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 4.33/4.49 inference(quant_intro,[status(thm)],[75])).
% 4.33/4.49 tff(77,plain,
% 4.33/4.49 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C)) & empty(C)) <=> (~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> (~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 4.33/4.49 inference(bind,[status(th)],[])).
% 4.33/4.49 tff(78,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 4.33/4.49 inference(quant_intro,[status(thm)],[77])).
% 4.33/4.49 tff(79,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 4.33/4.49 inference(rewrite,[status(thm)],[])).
% 4.33/4.49 tff(80,plain,
% 4.33/4.49 (^[A: $i, B: $i, C: $i] : rewrite((~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> (~(in(A, B) & element(B, powerset(C)) & empty(C))))),
% 4.33/4.49 inference(bind,[status(th)],[])).
% 4.33/4.49 tff(81,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 4.33/4.49 inference(quant_intro,[status(thm)],[80])).
% 4.33/4.49 tff(82,axiom,(![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t5_subset')).
% 4.33/4.49 tff(83,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 4.33/4.49 inference(modus_ponens,[status(thm)],[82, 81])).
% 4.33/4.49 tff(84,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 4.33/4.49 inference(modus_ponens,[status(thm)],[83, 79])).
% 4.33/4.49 tff(85,plain,(
% 4.33/4.49 ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 4.33/4.49 inference(skolemize,[status(sab)],[84])).
% 4.33/4.49 tff(86,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 4.33/4.49 inference(modus_ponens,[status(thm)],[85, 78])).
% 4.33/4.49 tff(87,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 4.33/4.49 inference(modus_ponens,[status(thm)],[86, 76])).
% 4.33/4.49 tff(88,plain,
% 4.33/4.49 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8)))) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))) | (~empty(relation_dom(C!8))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8)))) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))) | (~empty(relation_dom(C!8))))),
% 4.33/4.49 inference(rewrite,[status(thm)],[])).
% 4.33/4.49 tff(89,plain,
% 4.33/4.49 (((~empty(relation_dom(C!8))) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))) | (~element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8))))) <=> ((~element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8)))) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))) | (~empty(relation_dom(C!8))))),
% 4.33/4.49 inference(rewrite,[status(thm)],[])).
% 4.33/4.49 tff(90,plain,
% 4.33/4.49 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(relation_dom(C!8))) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))) | (~element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8)))) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))) | (~empty(relation_dom(C!8)))))),
% 4.33/4.49 inference(monotonicity,[status(thm)],[89])).
% 4.33/4.49 tff(91,plain,
% 4.33/4.49 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(relation_dom(C!8))) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))) | (~element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8)))) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))) | (~empty(relation_dom(C!8))))),
% 4.33/4.49 inference(transitivity,[status(thm)],[90, 88])).
% 4.33/4.49 tff(92,plain,
% 4.33/4.49 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(relation_dom(C!8))) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))) | (~element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8)))))),
% 4.33/4.49 inference(quant_inst,[status(thm)],[])).
% 4.33/4.49 tff(93,plain,
% 4.33/4.49 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8)))) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))) | (~empty(relation_dom(C!8)))),
% 4.33/4.49 inference(modus_ponens,[status(thm)],[92, 91])).
% 4.33/4.49 tff(94,plain,
% 4.33/4.49 (~empty(relation_dom(C!8))),
% 4.33/4.49 inference(unit_resolution,[status(thm)],[93, 87, 74, 37])).
% 4.33/4.49 tff(95,plain,
% 4.33/4.49 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))))),
% 4.33/4.49 inference(bind,[status(th)],[])).
% 4.33/4.49 tff(96,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 4.33/4.49 inference(quant_intro,[status(thm)],[95])).
% 4.33/4.49 tff(97,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 4.33/4.49 inference(pull_quant,[status(thm)],[])).
% 4.33/4.49 tff(98,plain,
% 4.33/4.49 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))))),
% 4.33/4.49 inference(bind,[status(th)],[])).
% 4.33/4.49 tff(99,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 4.33/4.49 inference(quant_intro,[status(thm)],[98])).
% 4.33/4.49 tff(100,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 4.33/4.49 inference(transitivity,[status(thm)],[99, 97])).
% 4.33/4.49 tff(101,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 4.33/4.49 inference(transitivity,[status(thm)],[100, 96])).
% 4.33/4.49 tff(102,plain,
% 4.33/4.49 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))))),
% 4.33/4.49 inference(bind,[status(th)],[])).
% 4.33/4.49 tff(103,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 4.33/4.49 inference(quant_intro,[status(thm)],[102])).
% 4.33/4.49 tff(104,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 4.33/4.49 inference(transitivity,[status(thm)],[103, 101])).
% 4.33/4.49 tff(105,plain,
% 4.33/4.49 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))), trans(monotonicity(rewrite((~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))) <=> (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))), rewrite(((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))))),
% 4.33/4.49 inference(bind,[status(th)],[])).
% 4.33/4.49 tff(106,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 4.33/4.49 inference(quant_intro,[status(thm)],[105])).
% 4.33/4.49 tff(107,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 4.33/4.49 inference(rewrite,[status(thm)],[])).
% 4.33/4.49 tff(108,plain,
% 4.33/4.49 (^[A: $i, B: $i, C: $i] : rewrite(((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))))),
% 4.33/4.49 inference(bind,[status(th)],[])).
% 4.33/4.49 tff(109,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 4.33/4.49 inference(quant_intro,[status(thm)],[108])).
% 4.33/4.49 tff(110,axiom,(![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_xboole_0')).
% 4.33/4.49 tff(111,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 4.33/4.49 inference(modus_ponens,[status(thm)],[110, 109])).
% 4.33/4.49 tff(112,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 4.33/4.49 inference(modus_ponens,[status(thm)],[111, 107])).
% 4.33/4.49 tff(113,plain,(
% 4.33/4.49 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))),
% 4.33/4.49 inference(skolemize,[status(sab)],[112])).
% 4.33/4.49 tff(114,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 4.33/4.49 inference(modus_ponens,[status(thm)],[113, 106])).
% 4.33/4.49 tff(115,plain,
% 4.33/4.49 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 4.33/4.49 inference(modus_ponens,[status(thm)],[114, 104])).
% 4.33/4.49 tff(116,plain,
% 4.33/4.49 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))))),
% 4.33/4.49 inference(rewrite,[status(thm)],[])).
% 4.33/4.49 tff(117,plain,
% 4.33/4.49 ((~(~(in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))))) <=> (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8))))),
% 4.33/4.49 inference(rewrite,[status(thm)],[])).
% 4.33/4.49 tff(118,plain,
% 4.33/4.49 (((~(in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8))))) | $false) <=> (~(in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))))),
% 4.33/4.49 inference(rewrite,[status(thm)],[])).
% 4.33/4.49 tff(119,plain,
% 4.33/4.49 ((~$true) <=> $false),
% 4.33/4.49 inference(rewrite,[status(thm)],[])).
% 4.33/4.49 tff(120,plain,
% 4.33/4.49 (($true | (~(in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_rng(C!8)) | in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_dom(C!8)))))) <=> $true),
% 4.33/4.49 inference(rewrite,[status(thm)],[])).
% 4.33/4.49 tff(121,plain,
% 4.33/4.49 ((~(in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_rng(C!8)) | in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_dom(C!8))))) <=> (~(in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_rng(C!8)) | in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_dom(C!8)))))),
% 4.33/4.49 inference(rewrite,[status(thm)],[])).
% 4.33/4.49 tff(122,plain,
% 4.33/4.49 ((in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_rng(C!8)) | in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_dom(C!8)))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_rng(C!8)) | in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_dom(C!8))))),
% 4.33/4.49 inference(rewrite,[status(thm)],[])).
% 4.33/4.49 tff(123,plain,
% 4.33/4.49 ((~(in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_rng(C!8)) | in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_dom(C!8))))) <=> (~(in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_rng(C!8)) | in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_dom(C!8)))))),
% 4.33/4.49 inference(monotonicity,[status(thm)],[122])).
% 4.33/4.49 tff(124,plain,
% 4.33/4.49 ((~(in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_rng(C!8)) | in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_dom(C!8))))) <=> (~(in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_rng(C!8)) | in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_dom(C!8)))))),
% 4.33/4.49 inference(transitivity,[status(thm)],[123, 121])).
% 4.33/4.49 tff(125,plain,
% 4.33/4.49 ((set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8))) <=> $true),
% 4.33/4.49 inference(rewrite,[status(thm)],[])).
% 4.33/4.49 tff(126,plain,
% 4.33/4.49 (((set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8))) | (~(in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_rng(C!8)) | in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_dom(C!8)))))) <=> ($true | (~(in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_rng(C!8)) | in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_dom(C!8))))))),
% 4.33/4.49 inference(monotonicity,[status(thm)],[125, 124])).
% 4.33/4.49 tff(127,plain,
% 4.33/4.49 (((set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8))) | (~(in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_rng(C!8)) | in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_dom(C!8)))))) <=> $true),
% 4.33/4.49 inference(transitivity,[status(thm)],[126, 120])).
% 4.33/4.49 tff(128,plain,
% 4.33/4.49 ((~((set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8))) | (~(in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_rng(C!8)) | in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_dom(C!8))))))) <=> (~$true)),
% 4.33/4.49 inference(monotonicity,[status(thm)],[127])).
% 4.33/4.49 tff(129,plain,
% 4.33/4.49 ((~((set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8))) | (~(in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_rng(C!8)) | in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_dom(C!8))))))) <=> $false),
% 4.33/4.49 inference(transitivity,[status(thm)],[128, 119])).
% 4.33/4.49 tff(130,plain,
% 4.33/4.49 ((~(in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8))))) <=> (~(in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))))),
% 4.33/4.49 inference(rewrite,[status(thm)],[])).
% 4.33/4.49 tff(131,plain,
% 4.33/4.49 (($false | (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8))))) <=> (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8))))),
% 4.33/4.49 inference(rewrite,[status(thm)],[])).
% 4.33/4.49 tff(132,plain,
% 4.33/4.49 ((in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))),
% 4.33/4.49 inference(rewrite,[status(thm)],[])).
% 4.33/4.49 tff(133,plain,
% 4.33/4.49 ((in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))) <=> (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8))))),
% 4.33/4.49 inference(monotonicity,[status(thm)],[132])).
% 4.33/4.49 tff(134,plain,
% 4.33/4.49 ((~(set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8)))) <=> (~$true)),
% 4.33/4.49 inference(monotonicity,[status(thm)],[125])).
% 4.33/4.49 tff(135,plain,
% 4.33/4.49 ((~(set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8)))) <=> $false),
% 4.33/4.49 inference(transitivity,[status(thm)],[134, 119])).
% 4.33/4.49 tff(136,plain,
% 4.33/4.49 (((~(set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8)))) | (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8))))) <=> ($false | (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))))),
% 4.33/4.49 inference(monotonicity,[status(thm)],[135, 133])).
% 4.33/4.49 tff(137,plain,
% 4.33/4.49 (((~(set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8)))) | (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8))))) <=> (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8))))),
% 4.33/4.49 inference(transitivity,[status(thm)],[136, 131])).
% 4.33/4.49 tff(138,plain,
% 4.33/4.49 ((~((~(set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8)))) | (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))))) <=> (~(in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))))),
% 4.33/4.49 inference(monotonicity,[status(thm)],[137])).
% 4.33/4.49 tff(139,plain,
% 4.33/4.49 ((~((~(set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8)))) | (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))))) <=> (~(in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))))),
% 4.33/4.49 inference(transitivity,[status(thm)],[138, 130])).
% 4.33/4.49 tff(140,plain,
% 4.33/4.49 (((~((~(set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8)))) | (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))))) | (~((set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8))) | (~(in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_rng(C!8)) | in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_dom(C!8)))))))) <=> ((~(in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8))))) | $false)),
% 4.33/4.50 inference(monotonicity,[status(thm)],[139, 129])).
% 4.33/4.50 tff(141,plain,
% 4.33/4.50 (((~((~(set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8)))) | (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))))) | (~((set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8))) | (~(in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_rng(C!8)) | in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_dom(C!8)))))))) <=> (~(in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))))),
% 4.33/4.50 inference(transitivity,[status(thm)],[140, 118])).
% 4.33/4.50 tff(142,plain,
% 4.33/4.50 ((~((~((~(set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8)))) | (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))))) | (~((set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8))) | (~(in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_rng(C!8)) | in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_dom(C!8))))))))) <=> (~(~(in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8))))))),
% 4.33/4.50 inference(monotonicity,[status(thm)],[141])).
% 4.33/4.50 tff(143,plain,
% 4.33/4.50 ((~((~((~(set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8)))) | (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))))) | (~((set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8))) | (~(in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_rng(C!8)) | in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_dom(C!8))))))))) <=> (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8))))),
% 4.33/4.50 inference(transitivity,[status(thm)],[142, 117])).
% 4.33/4.50 tff(144,plain,
% 4.33/4.50 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8)))) | (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))))) | (~((set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8))) | (~(in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_rng(C!8)) | in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_dom(C!8)))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))))),
% 4.33/4.50 inference(monotonicity,[status(thm)],[143])).
% 4.33/4.50 tff(145,plain,
% 4.33/4.50 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8)))) | (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))))) | (~((set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8))) | (~(in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_rng(C!8)) | in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_dom(C!8)))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))))),
% 4.33/4.50 inference(transitivity,[status(thm)],[144, 116])).
% 4.33/4.50 tff(146,plain,
% 4.33/4.50 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8)))) | (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))))) | (~((set_union2(relation_dom(C!8), relation_rng(C!8)) = set_union2(relation_dom(C!8), relation_rng(C!8))) | (~(in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_rng(C!8)) | in(tptp_fun_D_0(set_union2(relation_dom(C!8), relation_rng(C!8)), relation_rng(C!8), relation_dom(C!8)), relation_dom(C!8)))))))))),
% 4.33/4.50 inference(quant_inst,[status(thm)],[])).
% 4.33/4.50 tff(147,plain,
% 4.33/4.50 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8))))),
% 4.33/4.50 inference(modus_ponens,[status(thm)],[146, 145])).
% 4.33/4.50 tff(148,plain,
% 4.33/4.50 (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))),
% 4.33/4.50 inference(unit_resolution,[status(thm)],[147, 115])).
% 4.33/4.50 tff(149,plain,
% 4.33/4.50 (^[A: $i] : refl(((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 4.33/4.50 inference(bind,[status(th)],[])).
% 4.33/4.50 tff(150,plain,
% 4.33/4.50 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 4.33/4.50 inference(quant_intro,[status(thm)],[149])).
% 4.33/4.50 tff(151,plain,
% 4.33/4.50 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 4.33/4.50 inference(rewrite,[status(thm)],[])).
% 4.33/4.50 tff(152,plain,
% 4.33/4.50 (^[A: $i] : rewrite((relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 4.33/4.50 inference(bind,[status(th)],[])).
% 4.33/4.50 tff(153,plain,
% 4.33/4.50 (![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 4.33/4.50 inference(quant_intro,[status(thm)],[152])).
% 4.33/4.50 tff(154,axiom,(![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d6_relat_1')).
% 4.33/4.50 tff(155,plain,
% 4.33/4.50 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 4.33/4.50 inference(modus_ponens,[status(thm)],[154, 153])).
% 4.33/4.50 tff(156,plain,
% 4.33/4.50 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 4.33/4.50 inference(modus_ponens,[status(thm)],[155, 151])).
% 4.33/4.50 tff(157,plain,(
% 4.33/4.50 ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 4.33/4.50 inference(skolemize,[status(sab)],[156])).
% 4.33/4.50 tff(158,plain,
% 4.33/4.50 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 4.33/4.50 inference(modus_ponens,[status(thm)],[157, 150])).
% 4.33/4.50 tff(159,plain,
% 4.33/4.50 (((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(C!8)) | (relation_field(C!8) = set_union2(relation_dom(C!8), relation_rng(C!8))))) <=> ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(C!8)) | (relation_field(C!8) = set_union2(relation_dom(C!8), relation_rng(C!8))))),
% 4.33/4.50 inference(rewrite,[status(thm)],[])).
% 4.33/4.50 tff(160,plain,
% 4.33/4.50 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(C!8)) | (relation_field(C!8) = set_union2(relation_dom(C!8), relation_rng(C!8))))),
% 4.33/4.50 inference(quant_inst,[status(thm)],[])).
% 4.33/4.50 tff(161,plain,
% 4.33/4.50 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(C!8)) | (relation_field(C!8) = set_union2(relation_dom(C!8), relation_rng(C!8)))),
% 4.33/4.50 inference(modus_ponens,[status(thm)],[160, 159])).
% 4.33/4.50 tff(162,plain,
% 4.33/4.50 (relation_field(C!8) = set_union2(relation_dom(C!8), relation_rng(C!8))),
% 4.33/4.50 inference(unit_resolution,[status(thm)],[161, 158, 57])).
% 4.33/4.50 tff(163,plain,
% 4.33/4.50 (set_union2(relation_dom(C!8), relation_rng(C!8)) = relation_field(C!8)),
% 4.33/4.50 inference(symmetry,[status(thm)],[162])).
% 4.33/4.50 tff(164,plain,
% 4.33/4.50 (in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> in(A!10, relation_field(C!8))),
% 4.33/4.50 inference(monotonicity,[status(thm)],[163])).
% 4.33/4.50 tff(165,plain,
% 4.33/4.50 (in(A!10, relation_field(C!8)) <=> in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8)))),
% 4.33/4.50 inference(symmetry,[status(thm)],[164])).
% 4.33/4.50 tff(166,plain,
% 4.33/4.50 ((~in(A!10, relation_field(C!8))) <=> (~in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))))),
% 4.33/4.50 inference(monotonicity,[status(thm)],[165])).
% 4.33/4.50 tff(167,assumption,(~in(A!10, B!9)), introduced(assumption)).
% 4.33/4.50 tff(168,plain,
% 4.33/4.50 (((~in(A!10, B!9)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8))))) | in(A!10, B!9)),
% 4.33/4.50 inference(tautology,[status(thm)],[])).
% 4.33/4.50 tff(169,plain,
% 4.33/4.50 ((~in(A!10, B!9)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8))))),
% 4.33/4.50 inference(unit_resolution,[status(thm)],[168, 167])).
% 4.33/4.50 tff(170,assumption,((~((~(relation_dom(relation_restriction(C!8, B!9)) = set_intersection2(B!9, relation_dom(relation_rng_restriction(B!9, C!8))))) | (~(((~in(A!10, B!9)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8))))) <=> in(A!10, relation_dom(relation_restriction(C!8, B!9))))))) | (~((relation_dom(relation_restriction(C!8, B!9)) = set_intersection2(B!9, relation_dom(relation_rng_restriction(B!9, C!8)))) | (((~in(tptp_fun_D_1(relation_dom(relation_restriction(C!8, B!9)), relation_dom(relation_rng_restriction(B!9, C!8)), B!9), B!9)) | (~in(tptp_fun_D_1(relation_dom(relation_restriction(C!8, B!9)), relation_dom(relation_rng_restriction(B!9, C!8)), B!9), relation_dom(relation_rng_restriction(B!9, C!8))))) <=> in(tptp_fun_D_1(relation_dom(relation_restriction(C!8, B!9)), relation_dom(relation_rng_restriction(B!9, C!8)), B!9), relation_dom(relation_restriction(C!8, B!9))))))), introduced(assumption)).
% 4.33/4.50 tff(171,plain,
% 4.33/4.50 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(relation_dom(relation_restriction(C!8, B!9)) = set_intersection2(B!9, relation_dom(relation_rng_restriction(B!9, C!8))))) | (~(((~in(A!10, B!9)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8))))) <=> in(A!10, relation_dom(relation_restriction(C!8, B!9))))))) | (~((relation_dom(relation_restriction(C!8, B!9)) = set_intersection2(B!9, relation_dom(relation_rng_restriction(B!9, C!8)))) | (((~in(tptp_fun_D_1(relation_dom(relation_restriction(C!8, B!9)), relation_dom(relation_rng_restriction(B!9, C!8)), B!9), B!9)) | (~in(tptp_fun_D_1(relation_dom(relation_restriction(C!8, B!9)), relation_dom(relation_rng_restriction(B!9, C!8)), B!9), relation_dom(relation_rng_restriction(B!9, C!8))))) <=> in(tptp_fun_D_1(relation_dom(relation_restriction(C!8, B!9)), relation_dom(relation_rng_restriction(B!9, C!8)), B!9), relation_dom(relation_restriction(C!8, B!9))))))))),
% 4.33/4.50 inference(quant_inst,[status(thm)],[])).
% 4.33/4.50 tff(172,plain,
% 4.33/4.50 ($false),
% 4.33/4.50 inference(unit_resolution,[status(thm)],[171, 19, 170])).
% 4.33/4.50 tff(173,plain,(~((~((~(relation_dom(relation_restriction(C!8, B!9)) = set_intersection2(B!9, relation_dom(relation_rng_restriction(B!9, C!8))))) | (~(((~in(A!10, B!9)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8))))) <=> in(A!10, relation_dom(relation_restriction(C!8, B!9))))))) | (~((relation_dom(relation_restriction(C!8, B!9)) = set_intersection2(B!9, relation_dom(relation_rng_restriction(B!9, C!8)))) | (((~in(tptp_fun_D_1(relation_dom(relation_restriction(C!8, B!9)), relation_dom(relation_rng_restriction(B!9, C!8)), B!9), B!9)) | (~in(tptp_fun_D_1(relation_dom(relation_restriction(C!8, B!9)), relation_dom(relation_rng_restriction(B!9, C!8)), B!9), relation_dom(relation_rng_restriction(B!9, C!8))))) <=> in(tptp_fun_D_1(relation_dom(relation_restriction(C!8, B!9)), relation_dom(relation_rng_restriction(B!9, C!8)), B!9), relation_dom(relation_restriction(C!8, B!9)))))))), inference(lemma,lemma(discharge,[]))).
% 4.33/4.50 tff(174,plain,
% 4.33/4.50 (((~((~(relation_dom(relation_restriction(C!8, B!9)) = set_intersection2(B!9, relation_dom(relation_rng_restriction(B!9, C!8))))) | (~(((~in(A!10, B!9)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8))))) <=> in(A!10, relation_dom(relation_restriction(C!8, B!9))))))) | (~((relation_dom(relation_restriction(C!8, B!9)) = set_intersection2(B!9, relation_dom(relation_rng_restriction(B!9, C!8)))) | (((~in(tptp_fun_D_1(relation_dom(relation_restriction(C!8, B!9)), relation_dom(relation_rng_restriction(B!9, C!8)), B!9), B!9)) | (~in(tptp_fun_D_1(relation_dom(relation_restriction(C!8, B!9)), relation_dom(relation_rng_restriction(B!9, C!8)), B!9), relation_dom(relation_rng_restriction(B!9, C!8))))) <=> in(tptp_fun_D_1(relation_dom(relation_restriction(C!8, B!9)), relation_dom(relation_rng_restriction(B!9, C!8)), B!9), relation_dom(relation_restriction(C!8, B!9))))))) | ((~(relation_dom(relation_restriction(C!8, B!9)) = set_intersection2(B!9, relation_dom(relation_rng_restriction(B!9, C!8))))) | (~(((~in(A!10, B!9)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8))))) <=> in(A!10, relation_dom(relation_restriction(C!8, B!9))))))),
% 4.33/4.50 inference(tautology,[status(thm)],[])).
% 4.33/4.50 tff(175,plain,
% 4.33/4.50 ((~(relation_dom(relation_restriction(C!8, B!9)) = set_intersection2(B!9, relation_dom(relation_rng_restriction(B!9, C!8))))) | (~(((~in(A!10, B!9)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8))))) <=> in(A!10, relation_dom(relation_restriction(C!8, B!9)))))),
% 4.33/4.50 inference(unit_resolution,[status(thm)],[174, 173])).
% 4.33/4.50 tff(176,plain,
% 4.33/4.50 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(relation_dom(relation_rng_restriction(B!9, C!8)), B!9) = set_intersection2(B!9, relation_dom(relation_rng_restriction(B!9, C!8))))),
% 4.33/4.50 inference(quant_inst,[status(thm)],[])).
% 4.33/4.50 tff(177,plain,
% 4.33/4.50 (set_intersection2(relation_dom(relation_rng_restriction(B!9, C!8)), B!9) = set_intersection2(B!9, relation_dom(relation_rng_restriction(B!9, C!8)))),
% 4.33/4.50 inference(unit_resolution,[status(thm)],[176, 31])).
% 4.33/4.50 tff(178,plain,
% 4.33/4.50 (^[A: $i, B: $i] : refl(((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 4.33/4.50 inference(bind,[status(th)],[])).
% 4.33/4.50 tff(179,plain,
% 4.33/4.50 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 4.33/4.50 inference(quant_intro,[status(thm)],[178])).
% 4.33/4.50 tff(180,plain,
% 4.33/4.50 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 4.33/4.50 inference(rewrite,[status(thm)],[])).
% 4.33/4.50 tff(181,plain,
% 4.33/4.50 (^[A: $i, B: $i] : rewrite((relation(B) => relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 4.33/4.50 inference(bind,[status(th)],[])).
% 4.33/4.50 tff(182,plain,
% 4.33/4.50 (![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 4.33/4.50 inference(quant_intro,[status(thm)],[181])).
% 4.33/4.50 tff(183,axiom,(![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k8_relat_1')).
% 4.33/4.50 tff(184,plain,
% 4.33/4.50 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 4.33/4.50 inference(modus_ponens,[status(thm)],[183, 182])).
% 4.33/4.50 tff(185,plain,
% 4.33/4.50 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 4.33/4.50 inference(modus_ponens,[status(thm)],[184, 180])).
% 4.33/4.50 tff(186,plain,(
% 4.33/4.50 ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 4.33/4.50 inference(skolemize,[status(sab)],[185])).
% 4.33/4.50 tff(187,plain,
% 4.33/4.50 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 4.33/4.50 inference(modus_ponens,[status(thm)],[186, 179])).
% 4.33/4.50 tff(188,plain,
% 4.33/4.50 (((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(C!8)) | relation(relation_rng_restriction(B!9, C!8)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(C!8)) | relation(relation_rng_restriction(B!9, C!8)))),
% 4.33/4.50 inference(rewrite,[status(thm)],[])).
% 4.33/4.50 tff(189,plain,
% 4.33/4.50 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(C!8)) | relation(relation_rng_restriction(B!9, C!8)))),
% 4.33/4.50 inference(quant_inst,[status(thm)],[])).
% 4.33/4.50 tff(190,plain,
% 4.33/4.50 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(C!8)) | relation(relation_rng_restriction(B!9, C!8))),
% 4.33/4.50 inference(modus_ponens,[status(thm)],[189, 188])).
% 4.33/4.50 tff(191,plain,
% 4.33/4.50 (relation(relation_rng_restriction(B!9, C!8))),
% 4.33/4.50 inference(unit_resolution,[status(thm)],[190, 187, 57])).
% 4.33/4.50 tff(192,plain,
% 4.33/4.50 (^[A: $i, B: $i] : refl(((~relation(B)) | (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A))) <=> ((~relation(B)) | (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A))))),
% 4.33/4.50 inference(bind,[status(th)],[])).
% 4.33/4.50 tff(193,plain,
% 4.33/4.50 (![A: $i, B: $i] : ((~relation(B)) | (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A)))),
% 4.33/4.50 inference(quant_intro,[status(thm)],[192])).
% 4.33/4.50 tff(194,plain,
% 4.33/4.50 (![A: $i, B: $i] : ((~relation(B)) | (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A)))),
% 4.33/4.50 inference(rewrite,[status(thm)],[])).
% 4.33/4.50 tff(195,plain,
% 4.33/4.50 (^[A: $i, B: $i] : rewrite((relation(B) => (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A))) <=> ((~relation(B)) | (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A))))),
% 4.33/4.50 inference(bind,[status(th)],[])).
% 4.33/4.50 tff(196,plain,
% 4.33/4.50 (![A: $i, B: $i] : (relation(B) => (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A)))),
% 4.33/4.50 inference(quant_intro,[status(thm)],[195])).
% 4.33/4.50 tff(197,axiom,(![A: $i, B: $i] : (relation(B) => (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t90_relat_1')).
% 4.33/4.50 tff(198,plain,
% 4.33/4.50 (![A: $i, B: $i] : ((~relation(B)) | (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A)))),
% 4.33/4.50 inference(modus_ponens,[status(thm)],[197, 196])).
% 4.33/4.50 tff(199,plain,
% 4.33/4.50 (![A: $i, B: $i] : ((~relation(B)) | (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A)))),
% 4.33/4.50 inference(modus_ponens,[status(thm)],[198, 194])).
% 4.33/4.50 tff(200,plain,(
% 4.33/4.50 ![A: $i, B: $i] : ((~relation(B)) | (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A)))),
% 4.33/4.50 inference(skolemize,[status(sab)],[199])).
% 4.33/4.50 tff(201,plain,
% 4.33/4.50 (![A: $i, B: $i] : ((~relation(B)) | (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A)))),
% 4.33/4.50 inference(modus_ponens,[status(thm)],[200, 193])).
% 4.33/4.50 tff(202,plain,
% 4.33/4.50 (((~![A: $i, B: $i] : ((~relation(B)) | (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A)))) | ((~relation(relation_rng_restriction(B!9, C!8))) | (relation_dom(relation_dom_restriction(relation_rng_restriction(B!9, C!8), B!9)) = set_intersection2(relation_dom(relation_rng_restriction(B!9, C!8)), B!9)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A)))) | (~relation(relation_rng_restriction(B!9, C!8))) | (relation_dom(relation_dom_restriction(relation_rng_restriction(B!9, C!8), B!9)) = set_intersection2(relation_dom(relation_rng_restriction(B!9, C!8)), B!9)))),
% 4.33/4.50 inference(rewrite,[status(thm)],[])).
% 4.33/4.50 tff(203,plain,
% 4.33/4.50 ((~![A: $i, B: $i] : ((~relation(B)) | (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A)))) | ((~relation(relation_rng_restriction(B!9, C!8))) | (relation_dom(relation_dom_restriction(relation_rng_restriction(B!9, C!8), B!9)) = set_intersection2(relation_dom(relation_rng_restriction(B!9, C!8)), B!9)))),
% 4.33/4.50 inference(quant_inst,[status(thm)],[])).
% 4.33/4.50 tff(204,plain,
% 4.33/4.50 ((~![A: $i, B: $i] : ((~relation(B)) | (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A)))) | (~relation(relation_rng_restriction(B!9, C!8))) | (relation_dom(relation_dom_restriction(relation_rng_restriction(B!9, C!8), B!9)) = set_intersection2(relation_dom(relation_rng_restriction(B!9, C!8)), B!9))),
% 4.33/4.50 inference(modus_ponens,[status(thm)],[203, 202])).
% 4.33/4.50 tff(205,plain,
% 4.33/4.50 (relation_dom(relation_dom_restriction(relation_rng_restriction(B!9, C!8), B!9)) = set_intersection2(relation_dom(relation_rng_restriction(B!9, C!8)), B!9)),
% 4.33/4.50 inference(unit_resolution,[status(thm)],[204, 201, 191])).
% 4.33/4.50 tff(206,plain,
% 4.33/4.50 (^[A: $i, B: $i] : refl(((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))) <=> ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))))),
% 4.33/4.50 inference(bind,[status(th)],[])).
% 4.33/4.50 tff(207,plain,
% 4.33/4.50 (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 4.33/4.50 inference(quant_intro,[status(thm)],[206])).
% 4.33/4.50 tff(208,plain,
% 4.33/4.50 (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 4.33/4.50 inference(rewrite,[status(thm)],[])).
% 4.33/4.50 tff(209,plain,
% 4.33/4.50 (^[A: $i, B: $i] : rewrite((relation(B) => (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))) <=> ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))))),
% 4.33/4.50 inference(bind,[status(th)],[])).
% 4.33/4.50 tff(210,plain,
% 4.33/4.50 (![A: $i, B: $i] : (relation(B) => (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 4.33/4.50 inference(quant_intro,[status(thm)],[209])).
% 4.33/4.50 tff(211,axiom,(![A: $i, B: $i] : (relation(B) => (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t17_wellord1')).
% 4.33/4.50 tff(212,plain,
% 4.33/4.50 (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 4.33/4.50 inference(modus_ponens,[status(thm)],[211, 210])).
% 4.33/4.50 tff(213,plain,
% 4.33/4.50 (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 4.33/4.50 inference(modus_ponens,[status(thm)],[212, 208])).
% 4.33/4.50 tff(214,plain,(
% 4.33/4.50 ![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 4.33/4.50 inference(skolemize,[status(sab)],[213])).
% 4.33/4.50 tff(215,plain,
% 4.33/4.50 (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 4.33/4.50 inference(modus_ponens,[status(thm)],[214, 207])).
% 4.33/4.50 tff(216,plain,
% 4.33/4.50 (((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))) | ((~relation(C!8)) | (relation_restriction(C!8, B!9) = relation_dom_restriction(relation_rng_restriction(B!9, C!8), B!9)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))) | (~relation(C!8)) | (relation_restriction(C!8, B!9) = relation_dom_restriction(relation_rng_restriction(B!9, C!8), B!9)))),
% 4.33/4.50 inference(rewrite,[status(thm)],[])).
% 4.33/4.50 tff(217,plain,
% 4.33/4.50 ((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))) | ((~relation(C!8)) | (relation_restriction(C!8, B!9) = relation_dom_restriction(relation_rng_restriction(B!9, C!8), B!9)))),
% 4.33/4.50 inference(quant_inst,[status(thm)],[])).
% 4.33/4.50 tff(218,plain,
% 4.33/4.50 ((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))) | (~relation(C!8)) | (relation_restriction(C!8, B!9) = relation_dom_restriction(relation_rng_restriction(B!9, C!8), B!9))),
% 4.33/4.50 inference(modus_ponens,[status(thm)],[217, 216])).
% 4.33/4.50 tff(219,plain,
% 4.33/4.50 (relation_restriction(C!8, B!9) = relation_dom_restriction(relation_rng_restriction(B!9, C!8), B!9)),
% 4.33/4.50 inference(unit_resolution,[status(thm)],[218, 215, 57])).
% 4.33/4.50 tff(220,plain,
% 4.33/4.50 (relation_dom_restriction(relation_rng_restriction(B!9, C!8), B!9) = relation_restriction(C!8, B!9)),
% 4.33/4.50 inference(symmetry,[status(thm)],[219])).
% 4.33/4.50 tff(221,plain,
% 4.33/4.50 (relation_dom(relation_dom_restriction(relation_rng_restriction(B!9, C!8), B!9)) = relation_dom(relation_restriction(C!8, B!9))),
% 4.33/4.50 inference(monotonicity,[status(thm)],[220])).
% 4.33/4.50 tff(222,plain,
% 4.33/4.50 (relation_dom(relation_restriction(C!8, B!9)) = relation_dom(relation_dom_restriction(relation_rng_restriction(B!9, C!8), B!9))),
% 4.33/4.50 inference(symmetry,[status(thm)],[221])).
% 4.33/4.50 tff(223,plain,
% 4.33/4.50 (relation_dom(relation_restriction(C!8, B!9)) = set_intersection2(B!9, relation_dom(relation_rng_restriction(B!9, C!8)))),
% 4.33/4.50 inference(transitivity,[status(thm)],[222, 205, 177])).
% 4.33/4.50 tff(224,plain,
% 4.33/4.50 ((~((~(relation_dom(relation_restriction(C!8, B!9)) = set_intersection2(B!9, relation_dom(relation_rng_restriction(B!9, C!8))))) | (~(((~in(A!10, B!9)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8))))) <=> in(A!10, relation_dom(relation_restriction(C!8, B!9))))))) | (~(relation_dom(relation_restriction(C!8, B!9)) = set_intersection2(B!9, relation_dom(relation_rng_restriction(B!9, C!8))))) | (~(((~in(A!10, B!9)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8))))) <=> in(A!10, relation_dom(relation_restriction(C!8, B!9)))))),
% 4.33/4.50 inference(tautology,[status(thm)],[])).
% 4.33/4.50 tff(225,plain,
% 4.33/4.50 ((~((~(relation_dom(relation_restriction(C!8, B!9)) = set_intersection2(B!9, relation_dom(relation_rng_restriction(B!9, C!8))))) | (~(((~in(A!10, B!9)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8))))) <=> in(A!10, relation_dom(relation_restriction(C!8, B!9))))))) | (~(((~in(A!10, B!9)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8))))) <=> in(A!10, relation_dom(relation_restriction(C!8, B!9)))))),
% 4.33/4.50 inference(unit_resolution,[status(thm)],[224, 223])).
% 4.33/4.50 tff(226,plain,
% 4.33/4.50 (~(((~in(A!10, B!9)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8))))) <=> in(A!10, relation_dom(relation_restriction(C!8, B!9))))),
% 4.33/4.50 inference(unit_resolution,[status(thm)],[225, 175])).
% 4.33/4.50 tff(227,plain,
% 4.33/4.50 ((((~in(A!10, B!9)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8))))) <=> in(A!10, relation_dom(relation_restriction(C!8, B!9)))) | (~((~in(A!10, B!9)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))))) | (~in(A!10, relation_dom(relation_restriction(C!8, B!9))))),
% 4.33/4.50 inference(tautology,[status(thm)],[])).
% 4.33/4.50 tff(228,plain,
% 4.33/4.50 ((~((~in(A!10, B!9)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))))) | (~in(A!10, relation_dom(relation_restriction(C!8, B!9))))),
% 4.33/4.50 inference(unit_resolution,[status(thm)],[227, 226])).
% 4.33/4.50 tff(229,plain,
% 4.33/4.50 (~in(A!10, relation_dom(relation_restriction(C!8, B!9)))),
% 4.33/4.50 inference(unit_resolution,[status(thm)],[228, 169])).
% 4.33/4.50 tff(230,plain,
% 4.33/4.50 (((~in(A!10, B!9)) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9))))) | in(A!10, B!9)),
% 4.33/4.50 inference(tautology,[status(thm)],[])).
% 4.33/4.50 tff(231,plain,
% 4.33/4.50 ((~in(A!10, B!9)) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9))))),
% 4.33/4.50 inference(unit_resolution,[status(thm)],[230, 167])).
% 4.33/4.50 tff(232,plain,
% 4.33/4.50 ((((~in(A!10, B!9)) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9))))) <=> in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9))) | (~((~in(A!10, B!9)) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))))) | (~in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))),
% 4.33/4.50 inference(tautology,[status(thm)],[])).
% 4.33/4.50 tff(233,plain,
% 4.33/4.50 (~in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9))),
% 4.33/4.50 inference(unit_resolution,[status(thm)],[232, 231, 36])).
% 4.33/4.50 tff(234,plain,
% 4.33/4.50 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))) = set_union2(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_dom(relation_restriction(C!8, B!9))))) | (in(A!10, set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9)))) <=> (in(A!10, relation_dom(relation_restriction(C!8, B!9))) | in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))))) | (~((set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))) = set_union2(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_dom(relation_restriction(C!8, B!9)))) | (~(in(tptp_fun_D_0(set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))), relation_dom(relation_restriction(C!8, B!9)), set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)), set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9)))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))), relation_dom(relation_restriction(C!8, B!9)), set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)), relation_dom(relation_restriction(C!8, B!9))) | in(tptp_fun_D_0(set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))), relation_dom(relation_restriction(C!8, B!9)), set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)), set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))))))))),
% 4.33/4.51 inference(quant_inst,[status(thm)],[])).
% 4.33/4.51 tff(235,plain,
% 4.33/4.51 (~((~((~(set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))) = set_union2(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_dom(relation_restriction(C!8, B!9))))) | (in(A!10, set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9)))) <=> (in(A!10, relation_dom(relation_restriction(C!8, B!9))) | in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))))) | (~((set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))) = set_union2(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_dom(relation_restriction(C!8, B!9)))) | (~(in(tptp_fun_D_0(set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))), relation_dom(relation_restriction(C!8, B!9)), set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)), set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9)))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))), relation_dom(relation_restriction(C!8, B!9)), set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)), relation_dom(relation_restriction(C!8, B!9))) | in(tptp_fun_D_0(set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))), relation_dom(relation_restriction(C!8, B!9)), set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)), set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9))))))))),
% 4.33/4.51 inference(unit_resolution,[status(thm)],[234, 115])).
% 4.33/4.51 tff(236,plain,
% 4.33/4.51 (((~((~(set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))) = set_union2(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_dom(relation_restriction(C!8, B!9))))) | (in(A!10, set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9)))) <=> (in(A!10, relation_dom(relation_restriction(C!8, B!9))) | in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))))) | (~((set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))) = set_union2(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_dom(relation_restriction(C!8, B!9)))) | (~(in(tptp_fun_D_0(set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))), relation_dom(relation_restriction(C!8, B!9)), set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)), set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9)))) <=> (in(tptp_fun_D_0(set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))), relation_dom(relation_restriction(C!8, B!9)), set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)), relation_dom(relation_restriction(C!8, B!9))) | in(tptp_fun_D_0(set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))), relation_dom(relation_restriction(C!8, B!9)), set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)), set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))))))) | ((~(set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))) = set_union2(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_dom(relation_restriction(C!8, B!9))))) | (in(A!10, set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9)))) <=> (in(A!10, relation_dom(relation_restriction(C!8, B!9))) | in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))))),
% 4.33/4.51 inference(tautology,[status(thm)],[])).
% 4.33/4.51 tff(237,plain,
% 4.33/4.51 ((~(set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))) = set_union2(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_dom(relation_restriction(C!8, B!9))))) | (in(A!10, set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9)))) <=> (in(A!10, relation_dom(relation_restriction(C!8, B!9))) | in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9))))),
% 4.33/4.51 inference(unit_resolution,[status(thm)],[236, 235])).
% 4.33/4.51 tff(238,plain,
% 4.33/4.51 (^[A: $i, B: $i] : refl(((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A)))) <=> ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A)))))),
% 4.33/4.51 inference(bind,[status(th)],[])).
% 4.33/4.51 tff(239,plain,
% 4.33/4.51 (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 4.33/4.51 inference(quant_intro,[status(thm)],[238])).
% 4.33/4.51 tff(240,plain,
% 4.33/4.51 (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 4.33/4.51 inference(rewrite,[status(thm)],[])).
% 4.33/4.51 tff(241,plain,
% 4.33/4.51 (^[A: $i, B: $i] : rewrite((relation(B) => (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A)))) <=> ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A)))))),
% 4.33/4.51 inference(bind,[status(th)],[])).
% 4.33/4.51 tff(242,plain,
% 4.33/4.51 (![A: $i, B: $i] : (relation(B) => (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 4.33/4.51 inference(quant_intro,[status(thm)],[241])).
% 4.33/4.51 tff(243,axiom,(![A: $i, B: $i] : (relation(B) => (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t18_wellord1')).
% 4.33/4.51 tff(244,plain,
% 4.33/4.51 (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[243, 242])).
% 4.33/4.51 tff(245,plain,
% 4.33/4.51 (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[244, 240])).
% 4.33/4.51 tff(246,plain,(
% 4.33/4.51 ![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 4.33/4.51 inference(skolemize,[status(sab)],[245])).
% 4.33/4.51 tff(247,plain,
% 4.33/4.51 (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[246, 239])).
% 4.33/4.51 tff(248,plain,
% 4.33/4.51 (((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))) | ((~relation(C!8)) | (relation_restriction(C!8, B!9) = relation_rng_restriction(B!9, relation_dom_restriction(C!8, B!9))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))) | (~relation(C!8)) | (relation_restriction(C!8, B!9) = relation_rng_restriction(B!9, relation_dom_restriction(C!8, B!9))))),
% 4.33/4.51 inference(rewrite,[status(thm)],[])).
% 4.33/4.51 tff(249,plain,
% 4.33/4.51 ((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))) | ((~relation(C!8)) | (relation_restriction(C!8, B!9) = relation_rng_restriction(B!9, relation_dom_restriction(C!8, B!9))))),
% 4.33/4.51 inference(quant_inst,[status(thm)],[])).
% 4.33/4.51 tff(250,plain,
% 4.33/4.51 ((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))) | (~relation(C!8)) | (relation_restriction(C!8, B!9) = relation_rng_restriction(B!9, relation_dom_restriction(C!8, B!9)))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[249, 248])).
% 4.33/4.51 tff(251,plain,
% 4.33/4.51 (relation_restriction(C!8, B!9) = relation_rng_restriction(B!9, relation_dom_restriction(C!8, B!9))),
% 4.33/4.51 inference(unit_resolution,[status(thm)],[250, 247, 57])).
% 4.33/4.51 tff(252,plain,
% 4.33/4.51 (relation_rng(relation_restriction(C!8, B!9)) = relation_rng(relation_rng_restriction(B!9, relation_dom_restriction(C!8, B!9)))),
% 4.33/4.51 inference(monotonicity,[status(thm)],[251])).
% 4.33/4.51 tff(253,plain,
% 4.33/4.51 (relation_rng(relation_rng_restriction(B!9, relation_dom_restriction(C!8, B!9))) = relation_rng(relation_restriction(C!8, B!9))),
% 4.33/4.51 inference(symmetry,[status(thm)],[252])).
% 4.33/4.51 tff(254,plain,
% 4.33/4.51 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 4.33/4.51 inference(bind,[status(th)],[])).
% 4.33/4.51 tff(255,plain,
% 4.33/4.51 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 4.33/4.51 inference(quant_intro,[status(thm)],[254])).
% 4.33/4.51 tff(256,plain,
% 4.33/4.51 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 4.33/4.51 inference(rewrite,[status(thm)],[])).
% 4.33/4.51 tff(257,plain,
% 4.33/4.51 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 4.33/4.51 inference(bind,[status(th)],[])).
% 4.33/4.51 tff(258,plain,
% 4.33/4.51 (![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 4.33/4.51 inference(quant_intro,[status(thm)],[257])).
% 4.33/4.51 tff(259,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k7_relat_1')).
% 4.33/4.51 tff(260,plain,
% 4.33/4.51 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[259, 258])).
% 4.33/4.51 tff(261,plain,
% 4.33/4.51 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[260, 256])).
% 4.33/4.51 tff(262,plain,(
% 4.33/4.51 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 4.33/4.51 inference(skolemize,[status(sab)],[261])).
% 4.33/4.51 tff(263,plain,
% 4.33/4.51 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[262, 255])).
% 4.33/4.51 tff(264,plain,
% 4.33/4.51 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(C!8)) | relation(relation_dom_restriction(C!8, B!9)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(C!8)) | relation(relation_dom_restriction(C!8, B!9)))),
% 4.33/4.51 inference(rewrite,[status(thm)],[])).
% 4.33/4.51 tff(265,plain,
% 4.33/4.51 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(C!8)) | relation(relation_dom_restriction(C!8, B!9)))),
% 4.33/4.51 inference(quant_inst,[status(thm)],[])).
% 4.33/4.51 tff(266,plain,
% 4.33/4.51 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(C!8)) | relation(relation_dom_restriction(C!8, B!9))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[265, 264])).
% 4.33/4.51 tff(267,plain,
% 4.33/4.51 (relation(relation_dom_restriction(C!8, B!9))),
% 4.33/4.51 inference(unit_resolution,[status(thm)],[266, 263, 57])).
% 4.33/4.51 tff(268,plain,
% 4.33/4.51 (^[A: $i, B: $i] : refl(((~relation(B)) | (relation_rng(relation_rng_restriction(A, B)) = set_intersection2(relation_rng(B), A))) <=> ((~relation(B)) | (relation_rng(relation_rng_restriction(A, B)) = set_intersection2(relation_rng(B), A))))),
% 4.33/4.51 inference(bind,[status(th)],[])).
% 4.33/4.51 tff(269,plain,
% 4.33/4.51 (![A: $i, B: $i] : ((~relation(B)) | (relation_rng(relation_rng_restriction(A, B)) = set_intersection2(relation_rng(B), A))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_rng(relation_rng_restriction(A, B)) = set_intersection2(relation_rng(B), A)))),
% 4.33/4.51 inference(quant_intro,[status(thm)],[268])).
% 4.33/4.51 tff(270,plain,
% 4.33/4.51 (![A: $i, B: $i] : ((~relation(B)) | (relation_rng(relation_rng_restriction(A, B)) = set_intersection2(relation_rng(B), A))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_rng(relation_rng_restriction(A, B)) = set_intersection2(relation_rng(B), A)))),
% 4.33/4.51 inference(rewrite,[status(thm)],[])).
% 4.33/4.51 tff(271,plain,
% 4.33/4.51 (^[A: $i, B: $i] : rewrite((relation(B) => (relation_rng(relation_rng_restriction(A, B)) = set_intersection2(relation_rng(B), A))) <=> ((~relation(B)) | (relation_rng(relation_rng_restriction(A, B)) = set_intersection2(relation_rng(B), A))))),
% 4.33/4.51 inference(bind,[status(th)],[])).
% 4.33/4.51 tff(272,plain,
% 4.33/4.51 (![A: $i, B: $i] : (relation(B) => (relation_rng(relation_rng_restriction(A, B)) = set_intersection2(relation_rng(B), A))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_rng(relation_rng_restriction(A, B)) = set_intersection2(relation_rng(B), A)))),
% 4.33/4.51 inference(quant_intro,[status(thm)],[271])).
% 4.33/4.51 tff(273,axiom,(![A: $i, B: $i] : (relation(B) => (relation_rng(relation_rng_restriction(A, B)) = set_intersection2(relation_rng(B), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t119_relat_1')).
% 4.33/4.51 tff(274,plain,
% 4.33/4.51 (![A: $i, B: $i] : ((~relation(B)) | (relation_rng(relation_rng_restriction(A, B)) = set_intersection2(relation_rng(B), A)))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[273, 272])).
% 4.33/4.51 tff(275,plain,
% 4.33/4.51 (![A: $i, B: $i] : ((~relation(B)) | (relation_rng(relation_rng_restriction(A, B)) = set_intersection2(relation_rng(B), A)))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[274, 270])).
% 4.33/4.51 tff(276,plain,(
% 4.33/4.51 ![A: $i, B: $i] : ((~relation(B)) | (relation_rng(relation_rng_restriction(A, B)) = set_intersection2(relation_rng(B), A)))),
% 4.33/4.51 inference(skolemize,[status(sab)],[275])).
% 4.33/4.51 tff(277,plain,
% 4.33/4.51 (![A: $i, B: $i] : ((~relation(B)) | (relation_rng(relation_rng_restriction(A, B)) = set_intersection2(relation_rng(B), A)))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[276, 269])).
% 4.33/4.51 tff(278,plain,
% 4.33/4.51 (((~![A: $i, B: $i] : ((~relation(B)) | (relation_rng(relation_rng_restriction(A, B)) = set_intersection2(relation_rng(B), A)))) | ((~relation(relation_dom_restriction(C!8, B!9))) | (relation_rng(relation_rng_restriction(B!9, relation_dom_restriction(C!8, B!9))) = set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (relation_rng(relation_rng_restriction(A, B)) = set_intersection2(relation_rng(B), A)))) | (~relation(relation_dom_restriction(C!8, B!9))) | (relation_rng(relation_rng_restriction(B!9, relation_dom_restriction(C!8, B!9))) = set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))),
% 4.33/4.51 inference(rewrite,[status(thm)],[])).
% 4.33/4.51 tff(279,plain,
% 4.33/4.51 ((~![A: $i, B: $i] : ((~relation(B)) | (relation_rng(relation_rng_restriction(A, B)) = set_intersection2(relation_rng(B), A)))) | ((~relation(relation_dom_restriction(C!8, B!9))) | (relation_rng(relation_rng_restriction(B!9, relation_dom_restriction(C!8, B!9))) = set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))),
% 4.33/4.51 inference(quant_inst,[status(thm)],[])).
% 4.33/4.51 tff(280,plain,
% 4.33/4.51 ((~![A: $i, B: $i] : ((~relation(B)) | (relation_rng(relation_rng_restriction(A, B)) = set_intersection2(relation_rng(B), A)))) | (~relation(relation_dom_restriction(C!8, B!9))) | (relation_rng(relation_rng_restriction(B!9, relation_dom_restriction(C!8, B!9))) = set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[279, 278])).
% 4.33/4.51 tff(281,plain,
% 4.33/4.51 ((~relation(relation_dom_restriction(C!8, B!9))) | (relation_rng(relation_rng_restriction(B!9, relation_dom_restriction(C!8, B!9))) = set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9))),
% 4.33/4.51 inference(unit_resolution,[status(thm)],[280, 277])).
% 4.33/4.51 tff(282,plain,
% 4.33/4.51 (relation_rng(relation_rng_restriction(B!9, relation_dom_restriction(C!8, B!9))) = set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)),
% 4.33/4.51 inference(unit_resolution,[status(thm)],[281, 267])).
% 4.33/4.51 tff(283,plain,
% 4.33/4.51 (set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9) = relation_rng(relation_rng_restriction(B!9, relation_dom_restriction(C!8, B!9)))),
% 4.33/4.51 inference(symmetry,[status(thm)],[282])).
% 4.33/4.51 tff(284,plain,
% 4.33/4.51 (set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9) = relation_rng(relation_restriction(C!8, B!9))),
% 4.33/4.51 inference(transitivity,[status(thm)],[283, 253])).
% 4.33/4.51 tff(285,plain,
% 4.33/4.51 (set_union2(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_dom(relation_restriction(C!8, B!9))) = set_union2(relation_rng(relation_restriction(C!8, B!9)), relation_dom(relation_restriction(C!8, B!9)))),
% 4.33/4.51 inference(monotonicity,[status(thm)],[284])).
% 4.33/4.51 tff(286,plain,
% 4.33/4.51 (set_union2(relation_rng(relation_restriction(C!8, B!9)), relation_dom(relation_restriction(C!8, B!9))) = set_union2(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_dom(relation_restriction(C!8, B!9)))),
% 4.33/4.51 inference(symmetry,[status(thm)],[285])).
% 4.33/4.51 tff(287,plain,
% 4.33/4.51 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 4.33/4.51 inference(bind,[status(th)],[])).
% 4.33/4.51 tff(288,plain,
% 4.33/4.51 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 4.33/4.51 inference(quant_intro,[status(thm)],[287])).
% 4.33/4.51 tff(289,plain,
% 4.33/4.51 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 4.33/4.51 inference(rewrite,[status(thm)],[])).
% 4.33/4.51 tff(290,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 4.33/4.51 tff(291,plain,
% 4.33/4.51 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[290, 289])).
% 4.33/4.51 tff(292,plain,(
% 4.33/4.51 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 4.33/4.51 inference(skolemize,[status(sab)],[291])).
% 4.33/4.51 tff(293,plain,
% 4.33/4.51 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[292, 288])).
% 4.33/4.51 tff(294,plain,
% 4.33/4.51 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))) = set_union2(relation_rng(relation_restriction(C!8, B!9)), relation_dom(relation_restriction(C!8, B!9))))),
% 4.33/4.51 inference(quant_inst,[status(thm)],[])).
% 4.33/4.51 tff(295,plain,
% 4.33/4.51 (set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))) = set_union2(relation_rng(relation_restriction(C!8, B!9)), relation_dom(relation_restriction(C!8, B!9)))),
% 4.33/4.51 inference(unit_resolution,[status(thm)],[294, 293])).
% 4.33/4.51 tff(296,plain,
% 4.33/4.51 (set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))) = set_union2(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_dom(relation_restriction(C!8, B!9)))),
% 4.33/4.51 inference(transitivity,[status(thm)],[295, 286])).
% 4.33/4.51 tff(297,plain,
% 4.33/4.51 ((~((~(set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))) = set_union2(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_dom(relation_restriction(C!8, B!9))))) | (in(A!10, set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9)))) <=> (in(A!10, relation_dom(relation_restriction(C!8, B!9))) | in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))))) | (~(set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))) = set_union2(set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9), relation_dom(relation_restriction(C!8, B!9))))) | (in(A!10, set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9)))) <=> (in(A!10, relation_dom(relation_restriction(C!8, B!9))) | in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9))))),
% 4.33/4.51 inference(tautology,[status(thm)],[])).
% 4.33/4.51 tff(298,plain,
% 4.33/4.51 (in(A!10, set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9)))) <=> (in(A!10, relation_dom(relation_restriction(C!8, B!9))) | in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))),
% 4.33/4.51 inference(unit_resolution,[status(thm)],[297, 296, 237])).
% 4.33/4.51 tff(299,plain,
% 4.33/4.51 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 4.33/4.51 inference(bind,[status(th)],[])).
% 4.33/4.51 tff(300,plain,
% 4.33/4.51 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 4.33/4.51 inference(quant_intro,[status(thm)],[299])).
% 4.33/4.51 tff(301,plain,
% 4.33/4.51 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 4.33/4.51 inference(rewrite,[status(thm)],[])).
% 4.33/4.51 tff(302,plain,
% 4.33/4.51 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 4.33/4.51 inference(bind,[status(th)],[])).
% 4.33/4.51 tff(303,plain,
% 4.33/4.51 (![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 4.33/4.51 inference(quant_intro,[status(thm)],[302])).
% 4.33/4.51 tff(304,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_wellord1')).
% 4.33/4.51 tff(305,plain,
% 4.33/4.51 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[304, 303])).
% 4.33/4.51 tff(306,plain,
% 4.33/4.51 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[305, 301])).
% 4.33/4.51 tff(307,plain,(
% 4.33/4.51 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 4.33/4.51 inference(skolemize,[status(sab)],[306])).
% 4.33/4.51 tff(308,plain,
% 4.33/4.51 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[307, 300])).
% 4.33/4.51 tff(309,plain,
% 4.33/4.51 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(C!8)) | relation(relation_restriction(C!8, B!9)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(C!8)) | relation(relation_restriction(C!8, B!9)))),
% 4.33/4.51 inference(rewrite,[status(thm)],[])).
% 4.33/4.51 tff(310,plain,
% 4.33/4.51 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(C!8)) | relation(relation_restriction(C!8, B!9)))),
% 4.33/4.51 inference(quant_inst,[status(thm)],[])).
% 4.33/4.51 tff(311,plain,
% 4.33/4.51 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(C!8)) | relation(relation_restriction(C!8, B!9))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[310, 309])).
% 4.33/4.51 tff(312,plain,
% 4.33/4.51 (relation(relation_restriction(C!8, B!9))),
% 4.33/4.51 inference(unit_resolution,[status(thm)],[311, 308, 57])).
% 4.33/4.51 tff(313,plain,
% 4.33/4.51 (((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(relation_restriction(C!8, B!9))) | (relation_field(relation_restriction(C!8, B!9)) = set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9)))))) <=> ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(relation_restriction(C!8, B!9))) | (relation_field(relation_restriction(C!8, B!9)) = set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9)))))),
% 4.33/4.51 inference(rewrite,[status(thm)],[])).
% 4.33/4.51 tff(314,plain,
% 4.33/4.51 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(relation_restriction(C!8, B!9))) | (relation_field(relation_restriction(C!8, B!9)) = set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9)))))),
% 4.33/4.51 inference(quant_inst,[status(thm)],[])).
% 4.33/4.51 tff(315,plain,
% 4.33/4.51 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(relation_restriction(C!8, B!9))) | (relation_field(relation_restriction(C!8, B!9)) = set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[314, 313])).
% 4.33/4.51 tff(316,plain,
% 4.33/4.51 ((~relation(relation_restriction(C!8, B!9))) | (relation_field(relation_restriction(C!8, B!9)) = set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))))),
% 4.33/4.51 inference(unit_resolution,[status(thm)],[315, 158])).
% 4.33/4.51 tff(317,plain,
% 4.33/4.51 (relation_field(relation_restriction(C!8, B!9)) = set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9)))),
% 4.33/4.51 inference(unit_resolution,[status(thm)],[316, 312])).
% 4.33/4.51 tff(318,plain,
% 4.33/4.51 (set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))) = relation_field(relation_restriction(C!8, B!9))),
% 4.33/4.51 inference(symmetry,[status(thm)],[317])).
% 4.33/4.51 tff(319,plain,
% 4.33/4.51 (in(A!10, set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9)))) <=> in(A!10, relation_field(relation_restriction(C!8, B!9)))),
% 4.33/4.51 inference(monotonicity,[status(thm)],[318])).
% 4.33/4.51 tff(320,plain,
% 4.33/4.51 (in(A!10, relation_field(relation_restriction(C!8, B!9))) <=> in(A!10, set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))))),
% 4.33/4.51 inference(symmetry,[status(thm)],[319])).
% 4.33/4.51 tff(321,plain,
% 4.33/4.51 (in(A!10, relation_field(relation_restriction(C!8, B!9)))),
% 4.33/4.51 inference(or_elim,[status(thm)],[56])).
% 4.33/4.51 tff(322,plain,
% 4.33/4.51 (in(A!10, set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[321, 320])).
% 4.33/4.51 tff(323,plain,
% 4.33/4.51 ((~(in(A!10, set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9)))) <=> (in(A!10, relation_dom(relation_restriction(C!8, B!9))) | in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9))))) | (~in(A!10, set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9))))) | (in(A!10, relation_dom(relation_restriction(C!8, B!9))) | in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))),
% 4.33/4.51 inference(tautology,[status(thm)],[])).
% 4.33/4.51 tff(324,plain,
% 4.33/4.51 ((~(in(A!10, set_union2(relation_dom(relation_restriction(C!8, B!9)), relation_rng(relation_restriction(C!8, B!9)))) <=> (in(A!10, relation_dom(relation_restriction(C!8, B!9))) | in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9))))) | (in(A!10, relation_dom(relation_restriction(C!8, B!9))) | in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))),
% 4.33/4.51 inference(unit_resolution,[status(thm)],[323, 322])).
% 4.33/4.51 tff(325,plain,
% 4.33/4.51 (in(A!10, relation_dom(relation_restriction(C!8, B!9))) | in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9))),
% 4.33/4.51 inference(unit_resolution,[status(thm)],[324, 298])).
% 4.33/4.51 tff(326,plain,
% 4.33/4.51 ((~(in(A!10, relation_dom(relation_restriction(C!8, B!9))) | in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9)))) | in(A!10, relation_dom(relation_restriction(C!8, B!9))) | in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9))),
% 4.33/4.51 inference(tautology,[status(thm)],[])).
% 4.33/4.51 tff(327,plain,
% 4.33/4.51 (in(A!10, relation_dom(relation_restriction(C!8, B!9))) | in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9))),
% 4.33/4.51 inference(unit_resolution,[status(thm)],[326, 325])).
% 4.33/4.51 tff(328,plain,
% 4.33/4.51 ($false),
% 4.33/4.51 inference(unit_resolution,[status(thm)],[327, 233, 229])).
% 4.33/4.51 tff(329,plain,(in(A!10, B!9)), inference(lemma,lemma(discharge,[]))).
% 4.33/4.51 tff(330,plain,
% 4.33/4.51 ((~(~((~in(A!10, relation_field(C!8))) | (~in(A!10, B!9))))) <=> ((~in(A!10, relation_field(C!8))) | (~in(A!10, B!9)))),
% 4.33/4.51 inference(rewrite,[status(thm)],[])).
% 4.33/4.51 tff(331,plain,
% 4.33/4.51 ((in(A!10, relation_field(C!8)) & in(A!10, B!9)) <=> (~((~in(A!10, relation_field(C!8))) | (~in(A!10, B!9))))),
% 4.33/4.51 inference(rewrite,[status(thm)],[])).
% 4.33/4.51 tff(332,plain,
% 4.33/4.51 ((~(in(A!10, relation_field(C!8)) & in(A!10, B!9))) <=> (~(~((~in(A!10, relation_field(C!8))) | (~in(A!10, B!9)))))),
% 4.33/4.51 inference(monotonicity,[status(thm)],[331])).
% 4.33/4.51 tff(333,plain,
% 4.33/4.51 ((~(in(A!10, relation_field(C!8)) & in(A!10, B!9))) <=> ((~in(A!10, relation_field(C!8))) | (~in(A!10, B!9)))),
% 4.33/4.51 inference(transitivity,[status(thm)],[332, 330])).
% 4.33/4.51 tff(334,plain,
% 4.33/4.51 (~(in(A!10, relation_field(C!8)) & in(A!10, B!9))),
% 4.33/4.51 inference(or_elim,[status(thm)],[56])).
% 4.33/4.51 tff(335,plain,
% 4.33/4.51 ((~in(A!10, relation_field(C!8))) | (~in(A!10, B!9))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[334, 333])).
% 4.33/4.51 tff(336,plain,
% 4.33/4.51 (~in(A!10, relation_field(C!8))),
% 4.33/4.51 inference(unit_resolution,[status(thm)],[335, 329])).
% 4.33/4.51 tff(337,plain,
% 4.33/4.51 (~in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8)))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[336, 166])).
% 4.33/4.51 tff(338,plain,
% 4.33/4.51 ((~(in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) <=> (in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8))))) | in(A!10, set_union2(relation_dom(C!8), relation_rng(C!8))) | (~(in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8))))),
% 4.33/4.51 inference(tautology,[status(thm)],[])).
% 4.33/4.51 tff(339,plain,
% 4.33/4.51 (~(in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8)))),
% 4.33/4.51 inference(unit_resolution,[status(thm)],[338, 337, 148])).
% 4.33/4.51 tff(340,plain,
% 4.33/4.51 ((in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8))) | (~in(A!10, relation_dom(C!8)))),
% 4.33/4.51 inference(tautology,[status(thm)],[])).
% 4.33/4.51 tff(341,plain,
% 4.33/4.51 (~in(A!10, relation_dom(C!8))),
% 4.33/4.51 inference(unit_resolution,[status(thm)],[340, 339])).
% 4.33/4.51 tff(342,plain,
% 4.33/4.51 (^[A: $i, B: $i] : refl((empty(B) | in(A, B) | (~element(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 4.33/4.51 inference(bind,[status(th)],[])).
% 4.33/4.51 tff(343,plain,
% 4.33/4.51 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 4.33/4.51 inference(quant_intro,[status(thm)],[342])).
% 4.33/4.51 tff(344,plain,
% 4.33/4.51 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 4.33/4.51 inference(rewrite,[status(thm)],[])).
% 4.33/4.51 tff(345,plain,
% 4.33/4.51 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 4.33/4.51 inference(bind,[status(th)],[])).
% 4.33/4.51 tff(346,plain,
% 4.33/4.51 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 4.33/4.51 inference(quant_intro,[status(thm)],[345])).
% 4.33/4.51 tff(347,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 4.33/4.51 tff(348,plain,
% 4.33/4.51 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[347, 346])).
% 4.33/4.51 tff(349,plain,
% 4.33/4.51 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[348, 344])).
% 4.33/4.51 tff(350,plain,(
% 4.33/4.51 ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 4.33/4.51 inference(skolemize,[status(sab)],[349])).
% 4.33/4.51 tff(351,plain,
% 4.33/4.51 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[350, 343])).
% 4.33/4.51 tff(352,plain,
% 4.33/4.51 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(relation_dom(C!8)) | in(A!10, relation_dom(C!8)) | (~element(A!10, relation_dom(C!8))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(relation_dom(C!8)) | in(A!10, relation_dom(C!8)) | (~element(A!10, relation_dom(C!8))))),
% 4.33/4.51 inference(rewrite,[status(thm)],[])).
% 4.33/4.51 tff(353,plain,
% 4.33/4.51 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(relation_dom(C!8)) | in(A!10, relation_dom(C!8)) | (~element(A!10, relation_dom(C!8))))),
% 4.33/4.51 inference(quant_inst,[status(thm)],[])).
% 4.33/4.51 tff(354,plain,
% 4.33/4.51 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(relation_dom(C!8)) | in(A!10, relation_dom(C!8)) | (~element(A!10, relation_dom(C!8)))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[353, 352])).
% 4.33/4.51 tff(355,plain,
% 4.33/4.51 (empty(relation_dom(C!8)) | (~element(A!10, relation_dom(C!8)))),
% 4.33/4.51 inference(unit_resolution,[status(thm)],[354, 351, 341])).
% 4.33/4.51 tff(356,plain,
% 4.33/4.51 (~element(A!10, relation_dom(C!8))),
% 4.33/4.51 inference(unit_resolution,[status(thm)],[355, 94])).
% 4.33/4.51 tff(357,plain,
% 4.33/4.51 (^[A: $i, B: $i, C: $i] : refl((element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 4.33/4.51 inference(bind,[status(th)],[])).
% 4.33/4.51 tff(358,plain,
% 4.33/4.51 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 4.33/4.51 inference(quant_intro,[status(thm)],[357])).
% 4.33/4.51 tff(359,plain,
% 4.33/4.51 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C))) <=> (~((~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)))) <=> (~(~((~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)))) <=> ((~in(A, B)) | (~element(B, powerset(C)))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)))), rewrite((((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 4.33/4.51 inference(bind,[status(th)],[])).
% 4.33/4.51 tff(360,plain,
% 4.33/4.51 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 4.33/4.51 inference(quant_intro,[status(thm)],[359])).
% 4.33/4.51 tff(361,plain,
% 4.33/4.51 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 4.33/4.51 inference(rewrite,[status(thm)],[])).
% 4.33/4.51 tff(362,plain,
% 4.33/4.51 (^[A: $i, B: $i, C: $i] : rewrite(((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)))),
% 4.33/4.51 inference(bind,[status(th)],[])).
% 4.33/4.51 tff(363,plain,
% 4.33/4.51 (![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 4.33/4.51 inference(quant_intro,[status(thm)],[362])).
% 4.33/4.51 tff(364,axiom,(![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t4_subset')).
% 4.33/4.51 tff(365,plain,
% 4.33/4.51 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[364, 363])).
% 4.33/4.51 tff(366,plain,
% 4.33/4.51 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[365, 361])).
% 4.33/4.51 tff(367,plain,(
% 4.33/4.51 ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 4.33/4.51 inference(skolemize,[status(sab)],[366])).
% 4.33/4.51 tff(368,plain,
% 4.33/4.51 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[367, 360])).
% 4.33/4.51 tff(369,plain,
% 4.33/4.51 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 4.33/4.51 inference(modus_ponens,[status(thm)],[368, 358])).
% 4.33/4.51 tff(370,plain,
% 4.33/4.51 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8)))) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))) | element(A!10, relation_dom(C!8)))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8)))) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))) | element(A!10, relation_dom(C!8)))),
% 4.33/4.51 inference(rewrite,[status(thm)],[])).
% 4.33/4.51 tff(371,plain,
% 4.33/4.51 ((element(A!10, relation_dom(C!8)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))) | (~element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8))))) <=> ((~element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8)))) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))) | element(A!10, relation_dom(C!8)))),
% 4.33/4.51 inference(rewrite,[status(thm)],[])).
% 4.33/4.51 tff(372,plain,
% 4.33/4.51 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(A!10, relation_dom(C!8)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))) | (~element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8)))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8)))) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))) | element(A!10, relation_dom(C!8))))),
% 4.33/4.51 inference(monotonicity,[status(thm)],[371])).
% 4.33/4.51 tff(373,plain,
% 4.33/4.51 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(A!10, relation_dom(C!8)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))) | (~element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8)))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8)))) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))) | element(A!10, relation_dom(C!8)))),
% 4.33/4.51 inference(transitivity,[status(thm)],[372, 370])).
% 4.33/4.51 tff(374,plain,
% 4.33/4.51 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(A!10, relation_dom(C!8)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))) | (~element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8)))))),
% 4.33/4.51 inference(quant_inst,[status(thm)],[])).
% 4.33/4.51 tff(375,plain,
% 4.33/4.51 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(relation_dom(relation_rng_restriction(B!9, C!8)), powerset(relation_dom(C!8)))) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))) | element(A!10, relation_dom(C!8))),
% 4.33/4.52 inference(modus_ponens,[status(thm)],[374, 373])).
% 4.33/4.52 tff(376,plain,
% 4.33/4.52 ($false),
% 4.33/4.52 inference(unit_resolution,[status(thm)],[375, 369, 74, 37, 356])).
% 4.33/4.52 tff(377,plain,(~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))), inference(lemma,lemma(discharge,[]))).
% 4.33/4.52 tff(378,plain,
% 4.33/4.52 (((~in(A!10, B!9)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8))))) | in(A!10, relation_dom(relation_rng_restriction(B!9, C!8)))),
% 4.33/4.52 inference(tautology,[status(thm)],[])).
% 4.33/4.52 tff(379,plain,
% 4.33/4.52 ((~in(A!10, B!9)) | (~in(A!10, relation_dom(relation_rng_restriction(B!9, C!8))))),
% 4.33/4.52 inference(unit_resolution,[status(thm)],[378, 377])).
% 4.33/4.52 tff(380,plain,
% 4.33/4.52 (~in(A!10, relation_dom(relation_restriction(C!8, B!9)))),
% 4.33/4.52 inference(unit_resolution,[status(thm)],[228, 379])).
% 4.33/4.52 tff(381,plain,
% 4.33/4.52 (in(A!10, set_intersection2(relation_rng(relation_dom_restriction(C!8, B!9)), B!9))),
% 4.33/4.52 inference(unit_resolution,[status(thm)],[327, 380])).
% 4.33/4.52 tff(382,plain,
% 4.33/4.52 (~((~in(A!10, B!9)) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))))),
% 4.33/4.52 inference(unit_resolution,[status(thm)],[232, 381, 36])).
% 4.33/4.52 tff(383,plain,
% 4.33/4.52 (((~in(A!10, B!9)) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9))))) | in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))),
% 4.33/4.52 inference(tautology,[status(thm)],[])).
% 4.33/4.52 tff(384,plain,
% 4.33/4.52 (in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))),
% 4.33/4.52 inference(unit_resolution,[status(thm)],[383, 382])).
% 4.33/4.52 tff(385,plain,
% 4.33/4.52 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8))) <=> subset(relation_rng(relation_dom_restriction(C!8, B!9)), relation_rng(C!8)))),
% 4.33/4.52 inference(quant_inst,[status(thm)],[])).
% 4.33/4.52 tff(386,plain,
% 4.33/4.52 (element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8))) <=> subset(relation_rng(relation_dom_restriction(C!8, B!9)), relation_rng(C!8))),
% 4.33/4.52 inference(unit_resolution,[status(thm)],[385, 44])).
% 4.33/4.52 tff(387,plain,
% 4.33/4.52 (^[A: $i, B: $i] : refl(((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))) <=> ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))))),
% 4.33/4.52 inference(bind,[status(th)],[])).
% 4.33/4.52 tff(388,plain,
% 4.33/4.52 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))) <=> ![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 4.33/4.52 inference(quant_intro,[status(thm)],[387])).
% 4.33/4.52 tff(389,plain,
% 4.33/4.52 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))) <=> ![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 4.33/4.52 inference(rewrite,[status(thm)],[])).
% 4.33/4.52 tff(390,plain,
% 4.33/4.52 (^[A: $i, B: $i] : rewrite((relation(B) => subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))) <=> ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))))),
% 4.33/4.52 inference(bind,[status(th)],[])).
% 4.33/4.52 tff(391,plain,
% 4.33/4.52 (![A: $i, B: $i] : (relation(B) => subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))) <=> ![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 4.33/4.52 inference(quant_intro,[status(thm)],[390])).
% 4.33/4.52 tff(392,axiom,(![A: $i, B: $i] : (relation(B) => subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t99_relat_1')).
% 4.33/4.52 tff(393,plain,
% 4.33/4.52 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 4.33/4.52 inference(modus_ponens,[status(thm)],[392, 391])).
% 4.33/4.52 tff(394,plain,
% 4.33/4.52 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 4.33/4.52 inference(modus_ponens,[status(thm)],[393, 389])).
% 4.33/4.52 tff(395,plain,(
% 4.33/4.52 ![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 4.33/4.52 inference(skolemize,[status(sab)],[394])).
% 4.33/4.52 tff(396,plain,
% 4.33/4.52 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 4.33/4.52 inference(modus_ponens,[status(thm)],[395, 388])).
% 4.33/4.52 tff(397,plain,
% 4.33/4.52 (((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))) | ((~relation(C!8)) | subset(relation_rng(relation_dom_restriction(C!8, B!9)), relation_rng(C!8)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))) | (~relation(C!8)) | subset(relation_rng(relation_dom_restriction(C!8, B!9)), relation_rng(C!8)))),
% 4.33/4.52 inference(rewrite,[status(thm)],[])).
% 4.33/4.52 tff(398,plain,
% 4.33/4.52 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))) | ((~relation(C!8)) | subset(relation_rng(relation_dom_restriction(C!8, B!9)), relation_rng(C!8)))),
% 4.33/4.52 inference(quant_inst,[status(thm)],[])).
% 4.33/4.52 tff(399,plain,
% 4.33/4.52 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))) | (~relation(C!8)) | subset(relation_rng(relation_dom_restriction(C!8, B!9)), relation_rng(C!8))),
% 4.33/4.52 inference(modus_ponens,[status(thm)],[398, 397])).
% 4.33/4.52 tff(400,plain,
% 4.33/4.52 (subset(relation_rng(relation_dom_restriction(C!8, B!9)), relation_rng(C!8))),
% 4.33/4.52 inference(unit_resolution,[status(thm)],[399, 57, 396])).
% 4.33/4.52 tff(401,plain,
% 4.33/4.52 ((~(element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8))) <=> subset(relation_rng(relation_dom_restriction(C!8, B!9)), relation_rng(C!8)))) | element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8))) | (~subset(relation_rng(relation_dom_restriction(C!8, B!9)), relation_rng(C!8)))),
% 4.33/4.52 inference(tautology,[status(thm)],[])).
% 4.33/4.52 tff(402,plain,
% 4.33/4.52 ((~(element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8))) <=> subset(relation_rng(relation_dom_restriction(C!8, B!9)), relation_rng(C!8)))) | element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8)))),
% 4.33/4.52 inference(unit_resolution,[status(thm)],[401, 400])).
% 4.33/4.52 tff(403,plain,
% 4.33/4.52 (element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8)))),
% 4.33/4.52 inference(unit_resolution,[status(thm)],[402, 386])).
% 4.33/4.52 tff(404,plain,
% 4.33/4.52 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8)))) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))) | (~empty(relation_rng(C!8))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8)))) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))) | (~empty(relation_rng(C!8))))),
% 4.33/4.52 inference(rewrite,[status(thm)],[])).
% 4.33/4.52 tff(405,plain,
% 4.33/4.52 (((~empty(relation_rng(C!8))) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))) | (~element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8))))) <=> ((~element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8)))) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))) | (~empty(relation_rng(C!8))))),
% 4.33/4.52 inference(rewrite,[status(thm)],[])).
% 4.33/4.52 tff(406,plain,
% 4.33/4.52 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(relation_rng(C!8))) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))) | (~element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8)))) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))) | (~empty(relation_rng(C!8)))))),
% 4.33/4.52 inference(monotonicity,[status(thm)],[405])).
% 4.33/4.52 tff(407,plain,
% 4.33/4.52 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(relation_rng(C!8))) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))) | (~element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8)))) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))) | (~empty(relation_rng(C!8))))),
% 4.33/4.52 inference(transitivity,[status(thm)],[406, 404])).
% 4.33/4.52 tff(408,plain,
% 4.33/4.52 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(relation_rng(C!8))) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))) | (~element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8)))))),
% 4.33/4.52 inference(quant_inst,[status(thm)],[])).
% 4.33/4.52 tff(409,plain,
% 4.33/4.52 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8)))) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))) | (~empty(relation_rng(C!8)))),
% 4.33/4.52 inference(modus_ponens,[status(thm)],[408, 407])).
% 4.33/4.52 tff(410,plain,
% 4.33/4.52 (~empty(relation_rng(C!8))),
% 4.33/4.52 inference(unit_resolution,[status(thm)],[409, 87, 403, 384])).
% 4.33/4.52 tff(411,plain,
% 4.33/4.52 ((in(A!10, relation_rng(C!8)) | in(A!10, relation_dom(C!8))) | (~in(A!10, relation_rng(C!8)))),
% 4.33/4.52 inference(tautology,[status(thm)],[])).
% 4.33/4.52 tff(412,plain,
% 4.33/4.52 (~in(A!10, relation_rng(C!8))),
% 4.33/4.52 inference(unit_resolution,[status(thm)],[411, 339])).
% 4.33/4.52 tff(413,plain,
% 4.33/4.52 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(relation_rng(C!8)) | in(A!10, relation_rng(C!8)) | (~element(A!10, relation_rng(C!8))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(relation_rng(C!8)) | in(A!10, relation_rng(C!8)) | (~element(A!10, relation_rng(C!8))))),
% 4.33/4.52 inference(rewrite,[status(thm)],[])).
% 4.33/4.52 tff(414,plain,
% 4.33/4.52 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(relation_rng(C!8)) | in(A!10, relation_rng(C!8)) | (~element(A!10, relation_rng(C!8))))),
% 4.33/4.52 inference(quant_inst,[status(thm)],[])).
% 4.33/4.52 tff(415,plain,
% 4.33/4.52 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(relation_rng(C!8)) | in(A!10, relation_rng(C!8)) | (~element(A!10, relation_rng(C!8)))),
% 4.33/4.52 inference(modus_ponens,[status(thm)],[414, 413])).
% 4.33/4.52 tff(416,plain,
% 4.33/4.52 (empty(relation_rng(C!8)) | (~element(A!10, relation_rng(C!8)))),
% 4.33/4.52 inference(unit_resolution,[status(thm)],[415, 351, 412])).
% 4.33/4.52 tff(417,plain,
% 4.33/4.52 (~element(A!10, relation_rng(C!8))),
% 4.33/4.52 inference(unit_resolution,[status(thm)],[416, 410])).
% 4.33/4.52 tff(418,plain,
% 4.33/4.52 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8)))) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))) | element(A!10, relation_rng(C!8)))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8)))) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))) | element(A!10, relation_rng(C!8)))),
% 4.33/4.52 inference(rewrite,[status(thm)],[])).
% 4.33/4.52 tff(419,plain,
% 4.33/4.52 ((element(A!10, relation_rng(C!8)) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))) | (~element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8))))) <=> ((~element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8)))) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))) | element(A!10, relation_rng(C!8)))),
% 4.33/4.52 inference(rewrite,[status(thm)],[])).
% 4.33/4.52 tff(420,plain,
% 4.33/4.52 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(A!10, relation_rng(C!8)) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))) | (~element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8)))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8)))) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))) | element(A!10, relation_rng(C!8))))),
% 4.33/4.53 inference(monotonicity,[status(thm)],[419])).
% 4.33/4.53 tff(421,plain,
% 4.33/4.53 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(A!10, relation_rng(C!8)) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))) | (~element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8)))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8)))) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))) | element(A!10, relation_rng(C!8)))),
% 4.33/4.53 inference(transitivity,[status(thm)],[420, 418])).
% 4.33/4.53 tff(422,plain,
% 4.33/4.53 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(A!10, relation_rng(C!8)) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))) | (~element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8)))))),
% 4.33/4.53 inference(quant_inst,[status(thm)],[])).
% 4.33/4.53 tff(423,plain,
% 4.33/4.53 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(relation_rng(relation_dom_restriction(C!8, B!9)), powerset(relation_rng(C!8)))) | (~in(A!10, relation_rng(relation_dom_restriction(C!8, B!9)))) | element(A!10, relation_rng(C!8))),
% 4.33/4.53 inference(modus_ponens,[status(thm)],[422, 421])).
% 4.33/4.53 tff(424,plain,
% 4.33/4.53 ($false),
% 4.33/4.53 inference(unit_resolution,[status(thm)],[423, 369, 403, 384, 417])).
% 4.33/4.53 % SZS output end Proof
% 4.33/4.53 % E exiting
%------------------------------------------------------------------------------