%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO082+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:05:32 AM UTC 2025
% Result : Theorem 0.20s 0.52s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO082+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 14:15:41 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52 % SZS output start Proof
% 0.20/0.52 tff(incident_c_type, type, (
% 0.20/0.52 incident_c: ( $i * $i ) > $o)).
% 0.20/0.52 tff(tptp_fun_C2_11_type, type, (
% 0.20/0.52 tptp_fun_C2_11: $i)).
% 0.20/0.52 tff(tptp_fun_Q_1_type, type, (
% 0.20/0.52 tptp_fun_Q_1: ( $i * $i * $i ) > $i)).
% 0.20/0.52 tff(tptp_fun_C1_12_type, type, (
% 0.20/0.52 tptp_fun_C1_12: $i)).
% 0.20/0.52 tff(sum_type, type, (
% 0.20/0.52 sum: ( $i * $i ) > $i)).
% 0.20/0.52 tff(tptp_fun_Q_9_type, type, (
% 0.20/0.52 tptp_fun_Q_9: ( $i * $i ) > $i)).
% 0.20/0.52 tff(tptp_fun_P_5_type, type, (
% 0.20/0.52 tptp_fun_P_5: $i > $i)).
% 0.20/0.52 tff(tptp_fun_P_10_type, type, (
% 0.20/0.52 tptp_fun_P_10: ( $i * $i ) > $i)).
% 0.20/0.52 tff(part_of_type, type, (
% 0.20/0.52 part_of: ( $i * $i ) > $o)).
% 0.20/0.52 tff(tptp_fun_P_0_type, type, (
% 0.20/0.52 tptp_fun_P_0: ( $i * $i ) > $i)).
% 0.20/0.52 tff(1,plain,
% 0.20/0.52 (^[C: $i, C1: $i, C2: $i, Q: $i] : refl((~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(2,plain,
% 0.20/0.52 (![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> ![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.52 tff(3,plain,
% 0.20/0.52 (![C: $i, C1: $i, C2: $i] : ![Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> ![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.20/0.52 inference(pull_quant,[status(thm)],[])).
% 0.20/0.52 tff(4,plain,
% 0.20/0.52 (^[C: $i, C1: $i, C2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) <=> ![Q: $i] : ((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))), ((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) <=> (~![Q: $i] : ((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))))), pull_quant((~![Q: $i] : ((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) <=> ?[Q: $i] : (~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))))), ((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) <=> ?[Q: $i] : (~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))))), (((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))) <=> (?[Q: $i] : (~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))), pull_quant((?[Q: $i] : (~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))) <=> ?[Q: $i] : ((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))), (((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))) <=> ?[Q: $i] : ((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))), ((~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> (~?[Q: $i] : ((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))))), pull_quant((~?[Q: $i] : ((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> ![Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))), ((~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> ![Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(5,plain,
% 0.20/0.52 (![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> ![C: $i, C1: $i, C2: $i] : ![Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.52 tff(6,plain,
% 0.20/0.52 (![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> ![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[5, 3])).
% 0.20/0.52 tff(7,plain,
% 0.20/0.52 (![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> ![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[6, 2])).
% 0.20/0.52 tff(8,plain,
% 0.20/0.52 (^[C: $i, C1: $i, C2: $i] : rewrite((~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(9,plain,
% 0.20/0.52 (![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> ![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.52 tff(10,plain,
% 0.20/0.52 (![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> ![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[9, 7])).
% 0.20/0.52 tff(11,plain,
% 0.20/0.52 (^[C: $i, C1: $i, C2: $i] : trans(monotonicity(rewrite(((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) <=> ((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))), trans(monotonicity(trans(monotonicity(rewrite((incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))), ((~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))) <=> (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))), rewrite((~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))) <=> (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))), ((~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))) <=> (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))), (((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))) <=> ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))), rewrite(((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))) <=> ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))), (((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))) <=> ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))), ((((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))) <=> (((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))), rewrite((((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))) <=> (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))), ((((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))) <=> (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(12,plain,
% 0.20/0.52 (![C: $i, C1: $i, C2: $i] : (((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))) <=> ![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.52 tff(13,plain,
% 0.20/0.52 (![C: $i, C1: $i, C2: $i] : ((C = sum(C1, C2)) <=> ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) <=> ![C: $i, C1: $i, C2: $i] : ((C = sum(C1, C2)) <=> ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(14,axiom,(![C: $i, C1: $i, C2: $i] : ((C = sum(C1, C2)) <=> ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','sum_defn')).
% 0.20/0.52 tff(15,plain,
% 0.20/0.52 (![C: $i, C1: $i, C2: $i] : ((C = sum(C1, C2)) <=> ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.52 tff(16,plain,(
% 0.20/0.52 ![C: $i, C1: $i, C2: $i] : (((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))),
% 0.20/0.52 inference(skolemize,[status(sab)],[15])).
% 0.20/0.52 tff(17,plain,
% 0.20/0.52 (![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.52 tff(18,plain,
% 0.20/0.52 (![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.20/0.52 tff(19,plain,
% 0.20/0.52 (((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (C2!11 = sum(C2!11, C2!11))) <=> ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (C2!11 = sum(C2!11, C2!11)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(20,plain,
% 0.20/0.52 ((~(~(C2!11 = sum(C2!11, C2!11)))) <=> (C2!11 = sum(C2!11, C2!11))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(21,plain,
% 0.20/0.52 (($false | (~(C2!11 = sum(C2!11, C2!11)))) <=> (~(C2!11 = sum(C2!11, C2!11)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(22,plain,
% 0.20/0.52 ((~((C2!11 = sum(C2!11, C2!11)) | (~(incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11) <=> (incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11) | incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11)))))) <=> (~(C2!11 = sum(C2!11, C2!11)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(23,plain,
% 0.20/0.52 ((~$true) <=> $false),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(24,plain,
% 0.20/0.52 (((~(C2!11 = sum(C2!11, C2!11))) | $true) <=> $true),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(25,plain,
% 0.20/0.52 ((incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) <=> incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11)) <=> $true),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(26,plain,
% 0.20/0.52 ((incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) | incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11)) <=> incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(27,plain,
% 0.20/0.52 ((incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) <=> (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) | incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11))) <=> (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) <=> incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[26])).
% 0.20/0.52 tff(28,plain,
% 0.20/0.52 ((incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) <=> (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) | incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11))) <=> $true),
% 0.20/0.52 inference(transitivity,[status(thm)],[27, 25])).
% 0.20/0.52 tff(29,plain,
% 0.20/0.52 (((~(C2!11 = sum(C2!11, C2!11))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) <=> (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) | incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11)))) <=> ((~(C2!11 = sum(C2!11, C2!11))) | $true)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[28])).
% 0.20/0.52 tff(30,plain,
% 0.20/0.52 (((~(C2!11 = sum(C2!11, C2!11))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) <=> (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) | incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11)))) <=> $true),
% 0.20/0.52 inference(transitivity,[status(thm)],[29, 24])).
% 0.20/0.52 tff(31,plain,
% 0.20/0.52 ((~((~(C2!11 = sum(C2!11, C2!11))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) <=> (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) | incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11))))) <=> (~$true)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[30])).
% 0.20/0.52 tff(32,plain,
% 0.20/0.52 ((~((~(C2!11 = sum(C2!11, C2!11))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) <=> (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) | incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11))))) <=> $false),
% 0.20/0.52 inference(transitivity,[status(thm)],[31, 23])).
% 0.20/0.52 tff(33,plain,
% 0.20/0.52 (((~((~(C2!11 = sum(C2!11, C2!11))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) <=> (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) | incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11))))) | (~((C2!11 = sum(C2!11, C2!11)) | (~(incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11) <=> (incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11) | incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11))))))) <=> ($false | (~(C2!11 = sum(C2!11, C2!11))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[32, 22])).
% 0.20/0.52 tff(34,plain,
% 0.20/0.52 (((~((~(C2!11 = sum(C2!11, C2!11))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) <=> (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) | incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11))))) | (~((C2!11 = sum(C2!11, C2!11)) | (~(incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11) <=> (incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11) | incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11))))))) <=> (~(C2!11 = sum(C2!11, C2!11)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[33, 21])).
% 0.20/0.52 tff(35,plain,
% 0.20/0.52 ((~((~((~(C2!11 = sum(C2!11, C2!11))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) <=> (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) | incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11))))) | (~((C2!11 = sum(C2!11, C2!11)) | (~(incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11) <=> (incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11) | incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11)))))))) <=> (~(~(C2!11 = sum(C2!11, C2!11))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[34])).
% 0.20/0.52 tff(36,plain,
% 0.20/0.52 ((~((~((~(C2!11 = sum(C2!11, C2!11))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) <=> (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) | incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11))))) | (~((C2!11 = sum(C2!11, C2!11)) | (~(incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11) <=> (incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11) | incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11)))))))) <=> (C2!11 = sum(C2!11, C2!11))),
% 0.20/0.52 inference(transitivity,[status(thm)],[35, 20])).
% 0.20/0.52 tff(37,plain,
% 0.20/0.52 (((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (~((~((~(C2!11 = sum(C2!11, C2!11))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) <=> (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) | incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11))))) | (~((C2!11 = sum(C2!11, C2!11)) | (~(incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11) <=> (incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11) | incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11))))))))) <=> ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (C2!11 = sum(C2!11, C2!11)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[36])).
% 0.20/0.52 tff(38,plain,
% 0.20/0.52 (((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (~((~((~(C2!11 = sum(C2!11, C2!11))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) <=> (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) | incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11))))) | (~((C2!11 = sum(C2!11, C2!11)) | (~(incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11) <=> (incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11) | incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11))))))))) <=> ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (C2!11 = sum(C2!11, C2!11)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[37, 19])).
% 0.20/0.52 tff(39,plain,
% 0.20/0.52 ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (~((~((~(C2!11 = sum(C2!11, C2!11))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) <=> (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11) | incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C2!11), C2!11), C2!11), C2!11), C2!11))))) | (~((C2!11 = sum(C2!11, C2!11)) | (~(incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11) <=> (incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11) | incident_c(tptp_fun_Q_1(C2!11, C2!11, C2!11), C2!11))))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(40,plain,
% 0.20/0.52 ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (C2!11 = sum(C2!11, C2!11))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.53 tff(41,plain,
% 0.20/0.53 (C2!11 = sum(C2!11, C2!11)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[40, 18])).
% 0.20/0.53 tff(42,plain,
% 0.20/0.53 (incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C2!11) <=> incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[41])).
% 0.20/0.53 tff(43,plain,
% 0.20/0.53 (incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11)) <=> incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C2!11)),
% 0.20/0.53 inference(symmetry,[status(thm)],[42])).
% 0.20/0.53 tff(44,plain,
% 0.20/0.53 ((~incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11))) <=> (~incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C2!11))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[43])).
% 0.20/0.53 tff(45,assumption,(~incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12)), introduced(assumption)).
% 0.20/0.53 tff(46,plain,
% 0.20/0.53 (((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (~((~((~(C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), C1!12) <=> incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), sum(C2!11, C2!11))))) | (~((C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12) <=> incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11))))))))) <=> ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (~((~((~(C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), C1!12) <=> incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), sum(C2!11, C2!11))))) | (~((C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12) <=> incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11)))))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(47,plain,
% 0.20/0.53 ((~((~((~(C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), C1!12) <=> (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), sum(C2!11, C2!11)))))) | (~((C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12) <=> (incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11))))))))) <=> (~((~((~(C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), C1!12) <=> incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), sum(C2!11, C2!11))))) | (~((C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12) <=> incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11))))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(48,plain,
% 0.20/0.53 (((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (~((~((~(C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), C1!12) <=> (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), sum(C2!11, C2!11)))))) | (~((C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12) <=> (incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11)))))))))) <=> ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (~((~((~(C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), C1!12) <=> incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), sum(C2!11, C2!11))))) | (~((C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12) <=> incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11)))))))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[47])).
% 0.20/0.53 tff(49,plain,
% 0.20/0.53 (((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (~((~((~(C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), C1!12) <=> (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), sum(C2!11, C2!11)))))) | (~((C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12) <=> (incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11)))))))))) <=> ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (~((~((~(C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), C1!12) <=> incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), sum(C2!11, C2!11))))) | (~((C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12) <=> incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11)))))))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[48, 46])).
% 0.20/0.53 tff(50,plain,
% 0.20/0.53 ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (~((~((~(C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), C1!12) <=> (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), sum(C2!11, C2!11)))))) | (~((C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12) <=> (incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11)))))))))),
% 0.37/0.53 inference(quant_inst,[status(thm)],[])).
% 0.37/0.53 tff(51,plain,
% 0.37/0.53 ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (~((~((~(C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), C1!12) <=> incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), sum(C2!11, C2!11))))) | (~((C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12) <=> incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11))))))))),
% 0.37/0.53 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.37/0.53 tff(52,plain,
% 0.37/0.53 (~((~((~(C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), C1!12) <=> incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), sum(C2!11, C2!11))))) | (~((C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12) <=> incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11)))))))),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[51, 18])).
% 0.37/0.53 tff(53,plain,
% 0.37/0.53 (((~((~(C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), C1!12) <=> incident_c(tptp_fun_Q_9(tptp_fun_Q_9(tptp_fun_P_5(C1!12), C1!12), C1!12), sum(C2!11, C2!11))))) | (~((C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12) <=> incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11))))))) | ((C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12) <=> incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11)))))),
% 0.37/0.53 inference(tautology,[status(thm)],[])).
% 0.37/0.53 tff(54,plain,
% 0.37/0.53 ((C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12) <=> incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11))))),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.37/0.53 tff(55,plain,
% 0.37/0.53 (sum(C2!11, C2!11) = C2!11),
% 0.37/0.53 inference(symmetry,[status(thm)],[41])).
% 0.37/0.53 tff(56,plain,
% 0.37/0.53 (((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) <=> ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(57,plain,
% 0.37/0.53 ((~(~(sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))))) <=> (sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(58,plain,
% 0.37/0.53 (($false | (~(sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))))) <=> (~(sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(59,plain,
% 0.37/0.53 ((~((sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11)) <=> (incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11))))))) <=> (~(sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(60,plain,
% 0.37/0.53 (((~(sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | $true) <=> $true),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(61,plain,
% 0.37/0.53 ((incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) <=> incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11))) <=> $true),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(62,plain,
% 0.37/0.53 ((incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11))) <=> incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(63,plain,
% 0.37/0.53 ((incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) <=> (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)))) <=> (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) <=> incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)))),
% 0.37/0.53 inference(monotonicity,[status(thm)],[62])).
% 0.37/0.53 tff(64,plain,
% 0.37/0.53 ((incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) <=> (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)))) <=> $true),
% 0.37/0.53 inference(transitivity,[status(thm)],[63, 61])).
% 0.37/0.53 tff(65,plain,
% 0.37/0.53 (((~(sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) <=> (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11))))) <=> ((~(sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | $true)),
% 0.37/0.53 inference(monotonicity,[status(thm)],[64])).
% 0.37/0.53 tff(66,plain,
% 0.37/0.53 (((~(sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) <=> (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11))))) <=> $true),
% 0.37/0.53 inference(transitivity,[status(thm)],[65, 60])).
% 0.37/0.53 tff(67,plain,
% 0.37/0.53 ((~((~(sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) <=> (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)))))) <=> (~$true)),
% 0.37/0.53 inference(monotonicity,[status(thm)],[66])).
% 0.37/0.53 tff(68,plain,
% 0.37/0.53 ((~((~(sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) <=> (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)))))) <=> $false),
% 0.37/0.53 inference(transitivity,[status(thm)],[67, 23])).
% 0.37/0.53 tff(69,plain,
% 0.37/0.53 (((~((~(sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) <=> (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)))))) | (~((sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11)) <=> (incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11)))))))) <=> ($false | (~(sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))))),
% 0.37/0.53 inference(monotonicity,[status(thm)],[68, 59])).
% 0.37/0.53 tff(70,plain,
% 0.37/0.53 (((~((~(sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) <=> (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)))))) | (~((sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11)) <=> (incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11)))))))) <=> (~(sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))))),
% 0.37/0.53 inference(transitivity,[status(thm)],[69, 58])).
% 0.37/0.53 tff(71,plain,
% 0.37/0.53 ((~((~((~(sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) <=> (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)))))) | (~((sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11)) <=> (incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11))))))))) <=> (~(~(sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))))),
% 0.37/0.53 inference(monotonicity,[status(thm)],[70])).
% 0.37/0.53 tff(72,plain,
% 0.37/0.53 ((~((~((~(sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) <=> (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)))))) | (~((sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11)) <=> (incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11))))))))) <=> (sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))),
% 0.37/0.53 inference(transitivity,[status(thm)],[71, 57])).
% 0.37/0.53 tff(73,plain,
% 0.37/0.53 (((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (~((~((~(sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) <=> (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)))))) | (~((sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11)) <=> (incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11)))))))))) <=> ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))))),
% 0.37/0.53 inference(monotonicity,[status(thm)],[72])).
% 0.37/0.53 tff(74,plain,
% 0.37/0.53 (((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (~((~((~(sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) <=> (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)))))) | (~((sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11)) <=> (incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11)))))))))) <=> ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))))),
% 0.37/0.54 inference(transitivity,[status(thm)],[73, 56])).
% 0.37/0.54 tff(75,plain,
% 0.37/0.54 ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (~((~((~(sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))) | (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) <=> (incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)) | incident_c(tptp_fun_P_10(C2!11, C1!12), sum(C2!11, C2!11)))))) | (~((sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11)) <=> (incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), sum(C2!11, C2!11)), sum(C2!11, C2!11)))))))))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(76,plain,
% 0.37/0.54 ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.37/0.54 tff(77,plain,
% 0.37/0.54 (sum(C2!11, C2!11) = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[76, 18])).
% 0.37/0.54 tff(78,plain,
% 0.37/0.54 (sum(sum(C2!11, C2!11), sum(C2!11, C2!11)) = sum(C2!11, C2!11)),
% 0.37/0.54 inference(symmetry,[status(thm)],[77])).
% 0.37/0.54 tff(79,plain,
% 0.37/0.54 (sum(sum(C2!11, C2!11), sum(C2!11, C2!11)) = C2!11),
% 0.37/0.54 inference(transitivity,[status(thm)],[78, 55])).
% 0.37/0.54 tff(80,plain,
% 0.37/0.54 ((C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) <=> (C1!12 = C2!11)),
% 0.37/0.54 inference(monotonicity,[status(thm)],[79])).
% 0.37/0.54 tff(81,plain,
% 0.37/0.54 ((C1!12 = C2!11) <=> (C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))),
% 0.37/0.54 inference(symmetry,[status(thm)],[80])).
% 0.37/0.54 tff(82,plain,
% 0.37/0.54 ((~(C1!12 = C2!11)) <=> (~(C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))))),
% 0.37/0.54 inference(monotonicity,[status(thm)],[81])).
% 0.37/0.54 tff(83,plain,
% 0.37/0.54 ((~![C1: $i, C2: $i] : ((~(part_of(C1, C2) & part_of(C2, C1))) | (C1 = C2))) <=> (~![C1: $i, C2: $i] : ((~(part_of(C1, C2) & part_of(C2, C1))) | (C1 = C2)))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(84,plain,
% 0.37/0.54 ((~![C1: $i, C2: $i] : ((part_of(C1, C2) & part_of(C2, C1)) => (C1 = C2))) <=> (~![C1: $i, C2: $i] : ((~(part_of(C1, C2) & part_of(C2, C1))) | (C1 = C2)))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(85,axiom,(~![C1: $i, C2: $i] : ((part_of(C1, C2) & part_of(C2, C1)) => (C1 = C2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','part_of_antisymmetry')).
% 0.37/0.54 tff(86,plain,
% 0.37/0.54 (~![C1: $i, C2: $i] : ((~(part_of(C1, C2) & part_of(C2, C1))) | (C1 = C2))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.37/0.54 tff(87,plain,
% 0.37/0.54 (~![C1: $i, C2: $i] : ((~(part_of(C1, C2) & part_of(C2, C1))) | (C1 = C2))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[86, 83])).
% 0.37/0.54 tff(88,plain,
% 0.37/0.54 (~![C1: $i, C2: $i] : ((~(part_of(C1, C2) & part_of(C2, C1))) | (C1 = C2))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.37/0.54 tff(89,plain,
% 0.37/0.54 (~![C1: $i, C2: $i] : ((~(part_of(C1, C2) & part_of(C2, C1))) | (C1 = C2))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[88, 83])).
% 0.37/0.54 tff(90,plain,(
% 0.37/0.54 ~((~(part_of(C1!12, C2!11) & part_of(C2!11, C1!12))) | (C1!12 = C2!11))),
% 0.37/0.54 inference(skolemize,[status(sab)],[89])).
% 0.37/0.54 tff(91,plain,
% 0.37/0.54 (~(C1!12 = C2!11)),
% 0.37/0.54 inference(or_elim,[status(thm)],[90])).
% 0.37/0.54 tff(92,plain,
% 0.37/0.54 (~(C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[91, 82])).
% 0.37/0.54 tff(93,plain,
% 0.37/0.54 ((~((C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12) <=> incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11)))))) | (C1!12 = sum(sum(C2!11, C2!11), sum(C2!11, C2!11))) | (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12) <=> incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11))))),
% 0.37/0.54 inference(tautology,[status(thm)],[])).
% 0.37/0.54 tff(94,plain,
% 0.37/0.54 (~(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12) <=> incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11)))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[93, 92, 54])).
% 0.37/0.54 tff(95,plain,
% 0.37/0.54 ((incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12) <=> incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11))) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11))),
% 0.37/0.54 inference(tautology,[status(thm)],[])).
% 0.37/0.54 tff(96,plain,
% 0.37/0.54 (incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.37/0.54 tff(97,plain,
% 0.37/0.54 (incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[96, 45])).
% 0.37/0.54 tff(98,plain,
% 0.37/0.54 (incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C2!11)),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[97, 43])).
% 0.37/0.54 tff(99,plain,
% 0.37/0.54 (^[C: $i, C1: $i] : refl((~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))))),
% 0.37/0.54 inference(bind,[status(th)],[])).
% 0.37/0.54 tff(100,plain,
% 0.37/0.54 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> ![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.37/0.54 inference(quant_intro,[status(thm)],[99])).
% 0.37/0.54 tff(101,plain,
% 0.37/0.54 (^[C: $i, C1: $i] : rewrite((~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))))),
% 0.37/0.54 inference(bind,[status(th)],[])).
% 0.37/0.54 tff(102,plain,
% 0.37/0.54 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> ![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.37/0.54 inference(quant_intro,[status(thm)],[101])).
% 0.37/0.54 tff(103,plain,
% 0.37/0.54 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> ![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.37/0.54 inference(transitivity,[status(thm)],[102, 100])).
% 0.37/0.54 tff(104,plain,
% 0.37/0.54 (^[C: $i, C1: $i] : trans(monotonicity(rewrite(((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) <=> ((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))), rewrite((part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))) <=> (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))), ((((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))) <=> (((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))), rewrite((((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))) <=> (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))), ((((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))) <=> (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))))),
% 0.37/0.54 inference(bind,[status(th)],[])).
% 0.37/0.54 tff(105,plain,
% 0.37/0.54 (![C: $i, C1: $i] : (((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))) <=> ![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.37/0.54 inference(quant_intro,[status(thm)],[104])).
% 0.37/0.54 tff(106,plain,
% 0.37/0.54 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) <=> ![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(107,plain,
% 0.37/0.54 (^[C: $i, C1: $i] : rewrite((part_of(C1, C) <=> ![P: $i] : (incident_c(P, C1) => incident_c(P, C))) <=> (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))))),
% 0.37/0.54 inference(bind,[status(th)],[])).
% 0.37/0.54 tff(108,plain,
% 0.37/0.54 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : (incident_c(P, C1) => incident_c(P, C))) <=> ![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.37/0.54 inference(quant_intro,[status(thm)],[107])).
% 0.37/0.54 tff(109,axiom,(![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : (incident_c(P, C1) => incident_c(P, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','part_of_defn')).
% 0.37/0.54 tff(110,plain,
% 0.37/0.54 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.37/0.54 tff(111,plain,
% 0.37/0.54 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.37/0.54 tff(112,plain,(
% 0.37/0.54 ![C: $i, C1: $i] : (((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))),
% 0.37/0.54 inference(skolemize,[status(sab)],[111])).
% 0.37/0.54 tff(113,plain,
% 0.37/0.54 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.37/0.54 tff(114,plain,
% 0.37/0.54 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[113, 103])).
% 0.37/0.54 tff(115,plain,
% 0.37/0.54 ((~![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))) | (~((~((~part_of(C2!11, C1!12)) | ![P: $i] : ((~incident_c(P, C2!11)) | incident_c(P, C1!12)))) | (~(part_of(C2!11, C1!12) | (~((~incident_c(tptp_fun_P_0(C2!11, C1!12), C2!11)) | incident_c(tptp_fun_P_0(C2!11, C1!12), C1!12)))))))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(116,plain,
% 0.37/0.54 (~((~((~part_of(C2!11, C1!12)) | ![P: $i] : ((~incident_c(P, C2!11)) | incident_c(P, C1!12)))) | (~(part_of(C2!11, C1!12) | (~((~incident_c(tptp_fun_P_0(C2!11, C1!12), C2!11)) | incident_c(tptp_fun_P_0(C2!11, C1!12), C1!12))))))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.37/0.54 tff(117,plain,
% 0.37/0.54 (((~((~part_of(C2!11, C1!12)) | ![P: $i] : ((~incident_c(P, C2!11)) | incident_c(P, C1!12)))) | (~(part_of(C2!11, C1!12) | (~((~incident_c(tptp_fun_P_0(C2!11, C1!12), C2!11)) | incident_c(tptp_fun_P_0(C2!11, C1!12), C1!12)))))) | ((~part_of(C2!11, C1!12)) | ![P: $i] : ((~incident_c(P, C2!11)) | incident_c(P, C1!12)))),
% 0.37/0.54 inference(tautology,[status(thm)],[])).
% 0.37/0.54 tff(118,plain,
% 0.37/0.54 ((~part_of(C2!11, C1!12)) | ![P: $i] : ((~incident_c(P, C2!11)) | incident_c(P, C1!12))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.37/0.54 tff(119,plain,
% 0.37/0.54 (part_of(C1!12, C2!11) & part_of(C2!11, C1!12)),
% 0.37/0.54 inference(or_elim,[status(thm)],[90])).
% 0.37/0.54 tff(120,plain,
% 0.37/0.54 (part_of(C2!11, C1!12)),
% 0.37/0.54 inference(and_elim,[status(thm)],[119])).
% 0.37/0.54 tff(121,plain,
% 0.37/0.54 ((~((~part_of(C2!11, C1!12)) | ![P: $i] : ((~incident_c(P, C2!11)) | incident_c(P, C1!12)))) | (~part_of(C2!11, C1!12)) | ![P: $i] : ((~incident_c(P, C2!11)) | incident_c(P, C1!12))),
% 0.37/0.54 inference(tautology,[status(thm)],[])).
% 0.37/0.54 tff(122,plain,
% 0.37/0.54 ((~((~part_of(C2!11, C1!12)) | ![P: $i] : ((~incident_c(P, C2!11)) | incident_c(P, C1!12)))) | ![P: $i] : ((~incident_c(P, C2!11)) | incident_c(P, C1!12))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.37/0.54 tff(123,plain,
% 0.37/0.54 (![P: $i] : ((~incident_c(P, C2!11)) | incident_c(P, C1!12))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[122, 118])).
% 0.37/0.54 tff(124,plain,
% 0.37/0.54 (((~![P: $i] : ((~incident_c(P, C2!11)) | incident_c(P, C1!12))) | ((~incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C2!11)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12))) <=> ((~![P: $i] : ((~incident_c(P, C2!11)) | incident_c(P, C1!12))) | (~incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C2!11)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(125,plain,
% 0.37/0.54 ((~![P: $i] : ((~incident_c(P, C2!11)) | incident_c(P, C1!12))) | ((~incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C2!11)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(126,plain,
% 0.37/0.54 ((~![P: $i] : ((~incident_c(P, C2!11)) | incident_c(P, C1!12))) | (~incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C2!11)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12)),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.37/0.54 tff(127,plain,
% 0.37/0.54 ((~incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C2!11)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12)),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[126, 123])).
% 0.37/0.54 tff(128,plain,
% 0.37/0.54 (~incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C2!11)),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[127, 45])).
% 0.37/0.54 tff(129,plain,
% 0.37/0.54 ($false),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[128, 98])).
% 0.37/0.54 tff(130,plain,(incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12)), inference(lemma,lemma(discharge,[]))).
% 0.37/0.54 tff(131,plain,
% 0.37/0.54 ((incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12) <=> incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11))) | (~incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12)) | (~incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11)))),
% 0.37/0.54 inference(tautology,[status(thm)],[])).
% 0.37/0.54 tff(132,plain,
% 0.37/0.54 ((~incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12)) | (~incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11)))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[131, 94])).
% 0.37/0.54 tff(133,plain,
% 0.37/0.54 (~incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), sum(C2!11, C2!11))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[132, 130])).
% 0.37/0.54 tff(134,plain,
% 0.37/0.54 (~incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C2!11)),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[133, 44])).
% 0.37/0.54 tff(135,plain,
% 0.37/0.54 ((~![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))) | (~((~((~part_of(C1!12, C2!11)) | ![P: $i] : ((~incident_c(P, C1!12)) | incident_c(P, C2!11)))) | (~(part_of(C1!12, C2!11) | (~((~incident_c(tptp_fun_P_0(C1!12, C2!11), C1!12)) | incident_c(tptp_fun_P_0(C1!12, C2!11), C2!11)))))))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(136,plain,
% 0.37/0.54 (~((~((~part_of(C1!12, C2!11)) | ![P: $i] : ((~incident_c(P, C1!12)) | incident_c(P, C2!11)))) | (~(part_of(C1!12, C2!11) | (~((~incident_c(tptp_fun_P_0(C1!12, C2!11), C1!12)) | incident_c(tptp_fun_P_0(C1!12, C2!11), C2!11))))))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[135, 114])).
% 0.37/0.54 tff(137,plain,
% 0.37/0.54 (((~((~part_of(C1!12, C2!11)) | ![P: $i] : ((~incident_c(P, C1!12)) | incident_c(P, C2!11)))) | (~(part_of(C1!12, C2!11) | (~((~incident_c(tptp_fun_P_0(C1!12, C2!11), C1!12)) | incident_c(tptp_fun_P_0(C1!12, C2!11), C2!11)))))) | ((~part_of(C1!12, C2!11)) | ![P: $i] : ((~incident_c(P, C1!12)) | incident_c(P, C2!11)))),
% 0.37/0.54 inference(tautology,[status(thm)],[])).
% 0.37/0.54 tff(138,plain,
% 0.37/0.54 ((~part_of(C1!12, C2!11)) | ![P: $i] : ((~incident_c(P, C1!12)) | incident_c(P, C2!11))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.37/0.54 tff(139,plain,
% 0.37/0.54 (part_of(C1!12, C2!11)),
% 0.37/0.54 inference(and_elim,[status(thm)],[119])).
% 0.37/0.54 tff(140,plain,
% 0.37/0.54 ((~((~part_of(C1!12, C2!11)) | ![P: $i] : ((~incident_c(P, C1!12)) | incident_c(P, C2!11)))) | (~part_of(C1!12, C2!11)) | ![P: $i] : ((~incident_c(P, C1!12)) | incident_c(P, C2!11))),
% 0.37/0.54 inference(tautology,[status(thm)],[])).
% 0.37/0.54 tff(141,plain,
% 0.37/0.54 ((~((~part_of(C1!12, C2!11)) | ![P: $i] : ((~incident_c(P, C1!12)) | incident_c(P, C2!11)))) | ![P: $i] : ((~incident_c(P, C1!12)) | incident_c(P, C2!11))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.37/0.54 tff(142,plain,
% 0.37/0.54 (![P: $i] : ((~incident_c(P, C1!12)) | incident_c(P, C2!11))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[141, 138])).
% 0.37/0.54 tff(143,plain,
% 0.37/0.54 (((~![P: $i] : ((~incident_c(P, C1!12)) | incident_c(P, C2!11))) | ((~incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C2!11))) <=> ((~![P: $i] : ((~incident_c(P, C1!12)) | incident_c(P, C2!11))) | (~incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C2!11))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(144,plain,
% 0.37/0.54 ((~![P: $i] : ((~incident_c(P, C1!12)) | incident_c(P, C2!11))) | ((~incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C2!11))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(145,plain,
% 0.37/0.54 ((~![P: $i] : ((~incident_c(P, C1!12)) | incident_c(P, C2!11))) | (~incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C2!11)),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.37/0.54 tff(146,plain,
% 0.37/0.54 ((~incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C1!12)) | incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C2!11)),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[145, 142])).
% 0.37/0.54 tff(147,plain,
% 0.37/0.54 (incident_c(tptp_fun_Q_1(sum(C2!11, C2!11), sum(C2!11, C2!11), C1!12), C2!11)),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[146, 130])).
% 0.37/0.54 tff(148,plain,
% 0.37/0.54 ($false),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[147, 134])).
% 0.37/0.54 % SZS output end Proof
% 0.39/0.55 % E exiting
%------------------------------------------------------------------------------