%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU194+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:27:12 AM UTC 2025
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU194+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:15:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(in_type, type, (
% 0.19/0.42 in: ( $i * $i ) > $o)).
% 0.19/0.42 tff(relation_dom_type, type, (
% 0.19/0.42 relation_dom: $i > $i)).
% 0.19/0.42 tff(relation_dom_restriction_type, type, (
% 0.19/0.42 relation_dom_restriction: ( $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_A_8_type, type, (
% 0.19/0.42 tptp_fun_A_8: $i)).
% 0.19/0.42 tff(tptp_fun_B_7_type, type, (
% 0.19/0.42 tptp_fun_B_7: $i)).
% 0.19/0.42 tff(tptp_fun_D_0_type, type, (
% 0.19/0.42 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(set_intersection2_type, type, (
% 0.19/0.42 set_intersection2: ( $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_A_4_type, type, (
% 0.19/0.42 tptp_fun_A_4: $i)).
% 0.19/0.42 tff(relation_type, type, (
% 0.19/0.42 relation: $i > $o)).
% 0.19/0.42 tff(1,assumption,((~((~(relation_dom(relation_dom_restriction(B!7, A!8)) = set_intersection2(A!8, relation_dom(B!7)))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), A!4, relation_dom(relation_dom_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), A!4, relation_dom(relation_dom_restriction(B!7, A!8))), relation_dom(B!7)))) <=> in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), A!4, relation_dom(relation_dom_restriction(B!7, A!8))), relation_dom(relation_dom_restriction(B!7, A!8))))))) | (~((relation_dom(relation_dom_restriction(B!7, A!8)) = set_intersection2(A!8, relation_dom(B!7))) | (((~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), A!8)) | (~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(B!7)))) <=> in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(relation_dom_restriction(B!7, A!8))))))), introduced(assumption)).
% 0.19/0.42 tff(2,plain,
% 0.19/0.42 (^[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_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(3,plain,
% 0.19/0.42 (![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_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.42 tff(4,plain,
% 0.19/0.42 (![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_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 0.19/0.42 inference(pull_quant,[status(thm)],[])).
% 0.19/0.42 tff(5,plain,
% 0.19/0.42 (^[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_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(6,plain,
% 0.19/0.42 (![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_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.42 tff(7,plain,
% 0.19/0.42 (![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_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[6, 4])).
% 0.19/0.42 tff(8,plain,
% 0.19/0.42 (![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_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[7, 3])).
% 0.19/0.42 tff(9,plain,
% 0.19/0.42 (^[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_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(10,plain,
% 0.19/0.42 (![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_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.42 tff(11,plain,
% 0.19/0.42 (![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_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[10, 8])).
% 0.19/0.42 tff(12,plain,
% 0.19/0.42 (^[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_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B))))) <=> ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))) <=> (((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))), rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(13,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.42 tff(14,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 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')).
% 0.19/0.42 tff(16,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.42 tff(17,plain,(
% 0.19/0.42 ![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B))))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[16])).
% 0.19/0.42 tff(18,plain,
% 0.19/0.42 (![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_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.42 tff(19,plain,
% 0.19/0.42 (![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_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.19/0.42 tff(20,plain,
% 0.19/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~((~((~(relation_dom(relation_dom_restriction(B!7, A!8)) = set_intersection2(A!8, relation_dom(B!7)))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), A!4, relation_dom(relation_dom_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), A!4, relation_dom(relation_dom_restriction(B!7, A!8))), relation_dom(B!7)))) <=> in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), A!4, relation_dom(relation_dom_restriction(B!7, A!8))), relation_dom(relation_dom_restriction(B!7, A!8))))))) | (~((relation_dom(relation_dom_restriction(B!7, A!8)) = set_intersection2(A!8, relation_dom(B!7))) | (((~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), A!8)) | (~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(B!7)))) <=> in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(relation_dom_restriction(B!7, A!8))))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(21,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[20, 19, 1])).
% 0.19/0.43 tff(22,plain,(~((~((~(relation_dom(relation_dom_restriction(B!7, A!8)) = set_intersection2(A!8, relation_dom(B!7)))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), A!4, relation_dom(relation_dom_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), A!4, relation_dom(relation_dom_restriction(B!7, A!8))), relation_dom(B!7)))) <=> in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), A!4, relation_dom(relation_dom_restriction(B!7, A!8))), relation_dom(relation_dom_restriction(B!7, A!8))))))) | (~((relation_dom(relation_dom_restriction(B!7, A!8)) = set_intersection2(A!8, relation_dom(B!7))) | (((~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), A!8)) | (~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(B!7)))) <=> in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(relation_dom_restriction(B!7, A!8)))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(24,plain,
% 0.19/0.43 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.43 tff(25,plain,
% 0.19/0.43 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(26,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.19/0.43 tff(27,plain,
% 0.19/0.43 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.43 tff(28,plain,(
% 0.19/0.43 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.19/0.43 inference(skolemize,[status(sab)],[27])).
% 0.19/0.43 tff(29,plain,
% 0.19/0.43 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.43 tff(30,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(relation_dom(B!7), A!8) = set_intersection2(A!8, relation_dom(B!7)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(31,plain,
% 0.19/0.43 (set_intersection2(relation_dom(B!7), A!8) = set_intersection2(A!8, relation_dom(B!7))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.19/0.43 tff(32,plain,
% 0.19/0.43 (set_intersection2(A!8, relation_dom(B!7)) = set_intersection2(relation_dom(B!7), A!8)),
% 0.19/0.43 inference(symmetry,[status(thm)],[31])).
% 0.19/0.43 tff(33,assumption,(relation_dom(relation_dom_restriction(B!7, A!8)) = set_intersection2(A!8, relation_dom(B!7))), introduced(assumption)).
% 0.19/0.43 tff(34,plain,
% 0.19/0.43 (relation_dom(relation_dom_restriction(B!7, A!8)) = set_intersection2(relation_dom(B!7), A!8)),
% 0.19/0.43 inference(transitivity,[status(thm)],[33, 32])).
% 0.19/0.43 tff(35,plain,
% 0.19/0.43 ((~![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))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(36,plain,
% 0.19/0.43 ((~![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))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(37,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')).
% 0.19/0.43 tff(38,plain,
% 0.19/0.43 (~![A: $i, B: $i] : ((~relation(B)) | (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.43 tff(39,plain,
% 0.19/0.43 (~![A: $i, B: $i] : ((~relation(B)) | (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.19/0.43 tff(40,plain,
% 0.19/0.43 (~![A: $i, B: $i] : ((~relation(B)) | (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.19/0.43 tff(41,plain,
% 0.19/0.43 (~![A: $i, B: $i] : ((~relation(B)) | (relation_dom(relation_dom_restriction(B, A)) = set_intersection2(relation_dom(B), A)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[40, 35])).
% 0.19/0.43 tff(42,plain,(
% 0.19/0.43 ~((~relation(B!7)) | (relation_dom(relation_dom_restriction(B!7, A!8)) = set_intersection2(relation_dom(B!7), A!8)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[41])).
% 0.19/0.43 tff(43,plain,
% 0.19/0.43 (~(relation_dom(relation_dom_restriction(B!7, A!8)) = set_intersection2(relation_dom(B!7), A!8))),
% 0.19/0.43 inference(or_elim,[status(thm)],[42])).
% 0.19/0.43 tff(44,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[43, 34])).
% 0.19/0.43 tff(45,plain,(~(relation_dom(relation_dom_restriction(B!7, A!8)) = set_intersection2(A!8, relation_dom(B!7)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(46,assumption,(((~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), A!8)) | (~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(B!7)))) <=> in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(relation_dom_restriction(B!7, A!8)))), introduced(assumption)).
% 0.19/0.43 tff(47,plain,
% 0.19/0.43 (relation(B!7)),
% 0.19/0.43 inference(or_elim,[status(thm)],[42])).
% 0.19/0.43 tff(48,plain,
% 0.19/0.43 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_dom(C)))) <=> in(A, relation_dom(relation_dom_restriction(C, B)))))) <=> ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_dom(C)))) <=> in(A, relation_dom(relation_dom_restriction(C, B)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(49,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_dom(C)))) <=> in(A, relation_dom(relation_dom_restriction(C, B)))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_dom(C)))) <=> in(A, relation_dom(relation_dom_restriction(C, B))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.43 tff(50,plain,
% 0.19/0.43 (^[A: $i, B: $i, C: $i] : rewrite(((~relation(C)) | (in(A, relation_dom(relation_dom_restriction(C, B))) <=> (in(A, B) & in(A, relation_dom(C))))) <=> ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_dom(C)))) <=> in(A, relation_dom(relation_dom_restriction(C, B)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(51,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_dom(relation_dom_restriction(C, B))) <=> (in(A, B) & in(A, relation_dom(C))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_dom(C)))) <=> in(A, relation_dom(relation_dom_restriction(C, B))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.43 tff(52,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_dom(relation_dom_restriction(C, B))) <=> (in(A, B) & in(A, relation_dom(C))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_dom(relation_dom_restriction(C, B))) <=> (in(A, B) & in(A, relation_dom(C)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(53,plain,
% 0.19/0.43 (^[A: $i, B: $i, C: $i] : rewrite((relation(C) => (in(A, relation_dom(relation_dom_restriction(C, B))) <=> (in(A, B) & in(A, relation_dom(C))))) <=> ((~relation(C)) | (in(A, relation_dom(relation_dom_restriction(C, B))) <=> (in(A, B) & in(A, relation_dom(C))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(54,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_dom(relation_dom_restriction(C, B))) <=> (in(A, B) & in(A, relation_dom(C))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_dom(relation_dom_restriction(C, B))) <=> (in(A, B) & in(A, relation_dom(C)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.43 tff(55,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_dom(relation_dom_restriction(C, B))) <=> (in(A, B) & in(A, relation_dom(C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t86_relat_1')).
% 0.19/0.43 tff(56,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_dom(relation_dom_restriction(C, B))) <=> (in(A, B) & in(A, relation_dom(C)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.43 tff(57,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_dom(relation_dom_restriction(C, B))) <=> (in(A, B) & in(A, relation_dom(C)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.19/0.43 tff(58,plain,(
% 0.19/0.43 ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_dom(relation_dom_restriction(C, B))) <=> (in(A, B) & in(A, relation_dom(C)))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[57])).
% 0.19/0.43 tff(59,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_dom(C)))) <=> in(A, relation_dom(relation_dom_restriction(C, B))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.19/0.43 tff(60,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_dom(C)))) <=> in(A, relation_dom(relation_dom_restriction(C, B))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_dom(C)))) <=> in(A, relation_dom(relation_dom_restriction(C, B))))))) | ((~relation(B!7)) | (~(((~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), A!8)) | (~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(B!7)))) <=> in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(relation_dom_restriction(B!7, A!8))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_dom(C)))) <=> in(A, relation_dom(relation_dom_restriction(C, B))))))) | (~relation(B!7)) | (~(((~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), A!8)) | (~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(B!7)))) <=> in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(relation_dom_restriction(B!7, A!8))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_dom(C)))) <=> in(A, relation_dom(relation_dom_restriction(C, B))))))) | ((~relation(B!7)) | (~(((~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), A!8)) | (~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(B!7)))) <=> in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(relation_dom_restriction(B!7, A!8))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(63,plain,
% 0.19/0.43 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, B)) | (~in(A, relation_dom(C)))) <=> in(A, relation_dom(relation_dom_restriction(C, B))))))) | (~relation(B!7)) | (~(((~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), A!8)) | (~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(B!7)))) <=> in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(relation_dom_restriction(B!7, A!8)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[63, 60, 47, 46])).
% 0.19/0.43 tff(65,plain,(~(((~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), A!8)) | (~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(B!7)))) <=> in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(relation_dom_restriction(B!7, A!8))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(66,plain,
% 0.19/0.43 ((~((relation_dom(relation_dom_restriction(B!7, A!8)) = set_intersection2(A!8, relation_dom(B!7))) | (((~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), A!8)) | (~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(B!7)))) <=> in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(relation_dom_restriction(B!7, A!8)))))) | (relation_dom(relation_dom_restriction(B!7, A!8)) = set_intersection2(A!8, relation_dom(B!7))) | (((~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), A!8)) | (~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(B!7)))) <=> in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(relation_dom_restriction(B!7, A!8))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(67,plain,
% 0.19/0.43 (~((relation_dom(relation_dom_restriction(B!7, A!8)) = set_intersection2(A!8, relation_dom(B!7))) | (((~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), A!8)) | (~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(B!7)))) <=> in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(relation_dom_restriction(B!7, A!8)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[66, 65, 45])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 (((~((~(relation_dom(relation_dom_restriction(B!7, A!8)) = set_intersection2(A!8, relation_dom(B!7)))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), A!4, relation_dom(relation_dom_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), A!4, relation_dom(relation_dom_restriction(B!7, A!8))), relation_dom(B!7)))) <=> in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), A!4, relation_dom(relation_dom_restriction(B!7, A!8))), relation_dom(relation_dom_restriction(B!7, A!8))))))) | (~((relation_dom(relation_dom_restriction(B!7, A!8)) = set_intersection2(A!8, relation_dom(B!7))) | (((~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), A!8)) | (~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(B!7)))) <=> in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(relation_dom_restriction(B!7, A!8))))))) | ((relation_dom(relation_dom_restriction(B!7, A!8)) = set_intersection2(A!8, relation_dom(B!7))) | (((~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), A!8)) | (~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(B!7)))) <=> in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(relation_dom_restriction(B!7, A!8)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(69,plain,
% 0.19/0.43 ((~((~(relation_dom(relation_dom_restriction(B!7, A!8)) = set_intersection2(A!8, relation_dom(B!7)))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), A!4, relation_dom(relation_dom_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), A!4, relation_dom(relation_dom_restriction(B!7, A!8))), relation_dom(B!7)))) <=> in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), A!4, relation_dom(relation_dom_restriction(B!7, A!8))), relation_dom(relation_dom_restriction(B!7, A!8))))))) | (~((relation_dom(relation_dom_restriction(B!7, A!8)) = set_intersection2(A!8, relation_dom(B!7))) | (((~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), A!8)) | (~in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(B!7)))) <=> in(tptp_fun_D_0(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7), A!8), relation_dom(relation_dom_restriction(B!7, A!8))))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.19/0.44 tff(70,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[69, 22])).
% 0.19/0.44 % SZS output end Proof
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------