%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO087+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 05:05:33 AM UTC 2025
% Result : Theorem 0.39s 0.56s
% Output : Proof 0.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO087+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % 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 14:15:56 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.39/0.56 % SZS status Theorem
% 0.39/0.56 % SZS output start Proof
% 0.39/0.56 tff(incident_c_type, type, (
% 0.39/0.56 incident_c: ( $i * $i ) > $o)).
% 0.39/0.56 tff(tptp_fun_C2_11_type, type, (
% 0.39/0.56 tptp_fun_C2_11: $i)).
% 0.39/0.56 tff(tptp_fun_P_6_type, type, (
% 0.39/0.56 tptp_fun_P_6: $i > $i)).
% 0.39/0.56 tff(tptp_fun_C1_12_type, type, (
% 0.39/0.56 tptp_fun_C1_12: $i)).
% 0.39/0.56 tff(end_point_type, type, (
% 0.39/0.56 end_point: ( $i * $i ) > $o)).
% 0.39/0.56 tff(inner_point_type, type, (
% 0.39/0.56 inner_point: ( $i * $i ) > $o)).
% 0.39/0.56 tff(tptp_fun_P_13_type, type, (
% 0.39/0.56 tptp_fun_P_13: $i)).
% 0.39/0.56 tff(meet_type, type, (
% 0.39/0.56 meet: ( $i * $i * $i ) > $o)).
% 0.39/0.56 tff(tptp_fun_Q_4_type, type, (
% 0.39/0.56 tptp_fun_Q_4: ( $i * $i ) > $i)).
% 0.39/0.56 tff(part_of_type, type, (
% 0.39/0.56 part_of: ( $i * $i ) > $o)).
% 0.39/0.56 tff(tptp_fun_P_0_type, type, (
% 0.39/0.56 tptp_fun_P_0: ( $i * $i ) > $i)).
% 0.39/0.56 tff(1,plain,
% 0.39/0.56 (^[P: $i, C: $i] : refl((~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C))) <=> (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C))))),
% 0.39/0.56 inference(bind,[status(th)],[])).
% 0.39/0.56 tff(2,plain,
% 0.39/0.56 (![P: $i, C: $i] : (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C))) <=> ![P: $i, C: $i] : (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C)))),
% 0.39/0.56 inference(quant_intro,[status(thm)],[1])).
% 0.39/0.56 tff(3,plain,
% 0.39/0.56 (^[P: $i, C: $i] : trans(trans(monotonicity(rewrite((incident_c(P, C) & (~end_point(P, C))) <=> (~((~incident_c(P, C)) | end_point(P, C)))), ((inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C)))) <=> (inner_point(P, C) <=> (~((~incident_c(P, C)) | end_point(P, C)))))), rewrite((inner_point(P, C) <=> (~((~incident_c(P, C)) | end_point(P, C)))) <=> (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C)))), ((inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C)))) <=> (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C))))), rewrite((~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C))) <=> (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C)))), ((inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C)))) <=> (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C)))))),
% 0.39/0.56 inference(bind,[status(th)],[])).
% 0.39/0.56 tff(4,plain,
% 0.39/0.56 (![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C)))) <=> ![P: $i, C: $i] : (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C)))),
% 0.39/0.56 inference(quant_intro,[status(thm)],[3])).
% 0.39/0.56 tff(5,plain,
% 0.39/0.56 (![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C)))) <=> ![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C))))),
% 0.39/0.56 inference(rewrite,[status(thm)],[])).
% 0.39/0.56 tff(6,axiom,(![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','inner_point_defn')).
% 0.39/0.56 tff(7,plain,
% 0.39/0.56 (![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C))))),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.39/0.56 tff(8,plain,(
% 0.39/0.56 ![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C))))),
% 0.39/0.56 inference(skolemize,[status(sab)],[7])).
% 0.39/0.56 tff(9,plain,
% 0.39/0.56 (![P: $i, C: $i] : (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C)))),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.39/0.56 tff(10,plain,
% 0.39/0.56 (![P: $i, C: $i] : (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C)))),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.39/0.56 tff(11,plain,
% 0.39/0.56 ((~![P: $i, C: $i] : (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C)))) | (~(((~incident_c(tptp_fun_P_6(C1!12), C1!12)) | end_point(tptp_fun_P_6(C1!12), C1!12)) <=> inner_point(tptp_fun_P_6(C1!12), C1!12)))),
% 0.39/0.56 inference(quant_inst,[status(thm)],[])).
% 0.39/0.56 tff(12,plain,
% 0.39/0.56 (~(((~incident_c(tptp_fun_P_6(C1!12), C1!12)) | end_point(tptp_fun_P_6(C1!12), C1!12)) <=> inner_point(tptp_fun_P_6(C1!12), C1!12))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.39/0.56 tff(13,plain,
% 0.39/0.56 (![C: $i] : ?[P: $i] : inner_point(P, C) <=> ![C: $i] : ?[P: $i] : inner_point(P, C)),
% 0.39/0.56 inference(rewrite,[status(thm)],[])).
% 0.39/0.56 tff(14,axiom,(![C: $i] : ?[P: $i] : inner_point(P, C)), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','c3')).
% 0.39/0.56 tff(15,plain,
% 0.39/0.56 (![C: $i] : ?[P: $i] : inner_point(P, C)),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.39/0.56 tff(16,plain,(
% 0.39/0.56 ![C: $i] : inner_point(tptp_fun_P_6(C), C)),
% 0.39/0.56 inference(skolemize,[status(sab)],[15])).
% 0.39/0.56 tff(17,plain,
% 0.39/0.56 ((~![C: $i] : inner_point(tptp_fun_P_6(C), C)) | inner_point(tptp_fun_P_6(C1!12), C1!12)),
% 0.39/0.56 inference(quant_inst,[status(thm)],[])).
% 0.39/0.56 tff(18,plain,
% 0.39/0.56 (inner_point(tptp_fun_P_6(C1!12), C1!12)),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.39/0.56 tff(19,plain,
% 0.39/0.56 ((((~incident_c(tptp_fun_P_6(C1!12), C1!12)) | end_point(tptp_fun_P_6(C1!12), C1!12)) <=> inner_point(tptp_fun_P_6(C1!12), C1!12)) | (~((~incident_c(tptp_fun_P_6(C1!12), C1!12)) | end_point(tptp_fun_P_6(C1!12), C1!12))) | (~inner_point(tptp_fun_P_6(C1!12), C1!12))),
% 0.39/0.56 inference(tautology,[status(thm)],[])).
% 0.39/0.56 tff(20,plain,
% 0.39/0.56 ((((~incident_c(tptp_fun_P_6(C1!12), C1!12)) | end_point(tptp_fun_P_6(C1!12), C1!12)) <=> inner_point(tptp_fun_P_6(C1!12), C1!12)) | (~((~incident_c(tptp_fun_P_6(C1!12), C1!12)) | end_point(tptp_fun_P_6(C1!12), C1!12)))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.39/0.56 tff(21,plain,
% 0.39/0.56 (~((~incident_c(tptp_fun_P_6(C1!12), C1!12)) | end_point(tptp_fun_P_6(C1!12), C1!12))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[20, 12])).
% 0.39/0.56 tff(22,plain,
% 0.39/0.56 (((~incident_c(tptp_fun_P_6(C1!12), C1!12)) | end_point(tptp_fun_P_6(C1!12), C1!12)) | (~end_point(tptp_fun_P_6(C1!12), C1!12))),
% 0.39/0.56 inference(tautology,[status(thm)],[])).
% 0.39/0.56 tff(23,plain,
% 0.39/0.56 (~end_point(tptp_fun_P_6(C1!12), C1!12)),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.39/0.56 tff(24,plain,
% 0.39/0.56 (((~end_point(tptp_fun_P_6(C1!12), C1!12)) | (~end_point(tptp_fun_P_6(C1!12), C2!11))) | end_point(tptp_fun_P_6(C1!12), C1!12)),
% 0.39/0.56 inference(tautology,[status(thm)],[])).
% 0.39/0.56 tff(25,plain,
% 0.39/0.56 ((~end_point(tptp_fun_P_6(C1!12), C1!12)) | (~end_point(tptp_fun_P_6(C1!12), C2!11))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.39/0.56 tff(26,plain,
% 0.39/0.56 (((~incident_c(tptp_fun_P_6(C1!12), C1!12)) | end_point(tptp_fun_P_6(C1!12), C1!12)) | incident_c(tptp_fun_P_6(C1!12), C1!12)),
% 0.39/0.56 inference(tautology,[status(thm)],[])).
% 0.39/0.56 tff(27,plain,
% 0.39/0.56 (incident_c(tptp_fun_P_6(C1!12), C1!12)),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[26, 21])).
% 0.39/0.56 tff(28,plain,
% 0.39/0.56 (^[P: $i, C: $i, C1: $i] : rewrite((~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))))))),
% 0.39/0.56 inference(bind,[status(th)],[])).
% 0.39/0.56 tff(29,plain,
% 0.39/0.56 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> ![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))),
% 0.39/0.57 inference(quant_intro,[status(thm)],[28])).
% 0.39/0.57 tff(30,plain,
% 0.39/0.57 (^[P: $i, C: $i, C1: $i] : refl((~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))))),
% 0.39/0.57 inference(bind,[status(th)],[])).
% 0.39/0.57 tff(31,plain,
% 0.39/0.57 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> ![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 0.39/0.57 inference(quant_intro,[status(thm)],[30])).
% 0.39/0.57 tff(32,plain,
% 0.39/0.57 (^[P: $i, C: $i, C1: $i] : rewrite((~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))))),
% 0.39/0.57 inference(bind,[status(th)],[])).
% 0.39/0.57 tff(33,plain,
% 0.39/0.57 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> ![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 0.39/0.57 inference(quant_intro,[status(thm)],[32])).
% 0.39/0.57 tff(34,plain,
% 0.39/0.57 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> ![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 0.39/0.57 inference(transitivity,[status(thm)],[33, 31])).
% 0.39/0.57 tff(35,plain,
% 0.39/0.57 (^[P: $i, C: $i, C1: $i] : trans(monotonicity(rewrite(((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) <=> ((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))), trans(monotonicity(rewrite((~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))) <=> (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))), ((meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))) <=> (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))), rewrite((meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))) <=> (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))), ((meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))) <=> (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))), ((((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))))) <=> (((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))), rewrite((((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) <=> (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))), ((((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))))) <=> (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))))),
% 0.39/0.57 inference(bind,[status(th)],[])).
% 0.39/0.57 tff(36,plain,
% 0.39/0.57 (![P: $i, C: $i, C1: $i] : (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))))) <=> ![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 0.39/0.57 inference(quant_intro,[status(thm)],[35])).
% 0.39/0.57 tff(37,plain,
% 0.39/0.57 (^[P: $i, C: $i, C1: $i] : rewrite((((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | ((~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))))) <=> (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))))))),
% 0.39/0.57 inference(bind,[status(th)],[])).
% 0.39/0.57 tff(38,plain,
% 0.39/0.57 (![P: $i, C: $i, C1: $i] : (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | ((~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))))) <=> ![P: $i, C: $i, C1: $i] : (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))))),
% 0.39/0.57 inference(quant_intro,[status(thm)],[37])).
% 0.39/0.57 tff(39,plain,
% 0.39/0.57 (![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) <=> ![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1)))))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(40,plain,
% 0.39/0.57 (^[P: $i, C: $i, C1: $i] : rewrite((meet(P, C, C1) <=> ((incident_c(P, C) & incident_c(P, C1)) & ![Q: $i] : ((incident_c(Q, C) & incident_c(Q, C1)) => (end_point(Q, C) & end_point(Q, C1))))) <=> (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))))),
% 0.39/0.57 inference(bind,[status(th)],[])).
% 0.39/0.57 tff(41,plain,
% 0.39/0.57 (![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> ((incident_c(P, C) & incident_c(P, C1)) & ![Q: $i] : ((incident_c(Q, C) & incident_c(Q, C1)) => (end_point(Q, C) & end_point(Q, C1))))) <=> ![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1)))))),
% 0.39/0.57 inference(quant_intro,[status(thm)],[40])).
% 0.39/0.57 tff(42,axiom,(![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> ((incident_c(P, C) & incident_c(P, C1)) & ![Q: $i] : ((incident_c(Q, C) & incident_c(Q, C1)) => (end_point(Q, C) & end_point(Q, C1)))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','meet_defn')).
% 0.39/0.57 tff(43,plain,
% 0.39/0.57 (![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1)))))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.39/0.57 tff(44,plain,
% 0.39/0.57 (![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1)))))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.39/0.57 tff(45,plain,(
% 0.39/0.57 ![P: $i, C: $i, C1: $i] : (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | ((~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))))))),
% 0.39/0.57 inference(skolemize,[status(sab)],[44])).
% 0.39/0.57 tff(46,plain,
% 0.39/0.57 (![P: $i, C: $i, C1: $i] : (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.39/0.57 tff(47,plain,
% 0.39/0.57 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[46, 36])).
% 0.39/0.57 tff(48,plain,
% 0.39/0.57 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[47, 34])).
% 0.39/0.57 tff(49,plain,
% 0.39/0.57 (![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[48, 29])).
% 0.39/0.57 tff(50,plain,
% 0.39/0.57 (((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!13, C1!12, C2!11) | (~incident_c(P!13, C2!11)) | (~incident_c(P!13, C1!12)) | (~((~incident_c(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~incident_c(tptp_fun_Q_4(C2!11, C1!12), C2!11)) | (~((~end_point(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~end_point(tptp_fun_Q_4(C2!11, C1!12), C2!11)))))))) | (~((~meet(P!13, C1!12, C2!11)) | (~((~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12))))))))))))) <=> ((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!13, C1!12, C2!11) | (~incident_c(P!13, C2!11)) | (~incident_c(P!13, C1!12)) | (~((~incident_c(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~incident_c(tptp_fun_Q_4(C2!11, C1!12), C2!11)) | (~((~end_point(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~end_point(tptp_fun_Q_4(C2!11, C1!12), C2!11)))))))) | (~((~meet(P!13, C1!12, C2!11)) | (~((~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12)))))))))))))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(51,plain,
% 0.39/0.57 ((~((~(meet(P!13, C1!12, C2!11) | (~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~((~incident_c(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~incident_c(tptp_fun_Q_4(C2!11, C1!12), C2!11)) | (~((~end_point(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~end_point(tptp_fun_Q_4(C2!11, C1!12), C2!11)))))))) | (~((~meet(P!13, C1!12, C2!11)) | (~((~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~![Q: $i] : ((~incident_c(Q, C2!11)) | (~incident_c(Q, C1!12)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12)))))))))))) <=> (~((~(meet(P!13, C1!12, C2!11) | (~incident_c(P!13, C2!11)) | (~incident_c(P!13, C1!12)) | (~((~incident_c(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~incident_c(tptp_fun_Q_4(C2!11, C1!12), C2!11)) | (~((~end_point(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~end_point(tptp_fun_Q_4(C2!11, C1!12), C2!11)))))))) | (~((~meet(P!13, C1!12, C2!11)) | (~((~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12))))))))))))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(52,plain,
% 0.39/0.57 (((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!13, C1!12, C2!11) | (~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~((~incident_c(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~incident_c(tptp_fun_Q_4(C2!11, C1!12), C2!11)) | (~((~end_point(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~end_point(tptp_fun_Q_4(C2!11, C1!12), C2!11)))))))) | (~((~meet(P!13, C1!12, C2!11)) | (~((~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~![Q: $i] : ((~incident_c(Q, C2!11)) | (~incident_c(Q, C1!12)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12))))))))))))) <=> ((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!13, C1!12, C2!11) | (~incident_c(P!13, C2!11)) | (~incident_c(P!13, C1!12)) | (~((~incident_c(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~incident_c(tptp_fun_Q_4(C2!11, C1!12), C2!11)) | (~((~end_point(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~end_point(tptp_fun_Q_4(C2!11, C1!12), C2!11)))))))) | (~((~meet(P!13, C1!12, C2!11)) | (~((~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12)))))))))))))),
% 0.39/0.57 inference(monotonicity,[status(thm)],[51])).
% 0.39/0.57 tff(53,plain,
% 0.39/0.57 (((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!13, C1!12, C2!11) | (~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~((~incident_c(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~incident_c(tptp_fun_Q_4(C2!11, C1!12), C2!11)) | (~((~end_point(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~end_point(tptp_fun_Q_4(C2!11, C1!12), C2!11)))))))) | (~((~meet(P!13, C1!12, C2!11)) | (~((~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~![Q: $i] : ((~incident_c(Q, C2!11)) | (~incident_c(Q, C1!12)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12))))))))))))) <=> ((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!13, C1!12, C2!11) | (~incident_c(P!13, C2!11)) | (~incident_c(P!13, C1!12)) | (~((~incident_c(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~incident_c(tptp_fun_Q_4(C2!11, C1!12), C2!11)) | (~((~end_point(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~end_point(tptp_fun_Q_4(C2!11, C1!12), C2!11)))))))) | (~((~meet(P!13, C1!12, C2!11)) | (~((~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12)))))))))))))),
% 0.39/0.57 inference(transitivity,[status(thm)],[52, 50])).
% 0.39/0.57 tff(54,plain,
% 0.39/0.57 ((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!13, C1!12, C2!11) | (~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~((~incident_c(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~incident_c(tptp_fun_Q_4(C2!11, C1!12), C2!11)) | (~((~end_point(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~end_point(tptp_fun_Q_4(C2!11, C1!12), C2!11)))))))) | (~((~meet(P!13, C1!12, C2!11)) | (~((~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~![Q: $i] : ((~incident_c(Q, C2!11)) | (~incident_c(Q, C1!12)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12))))))))))))),
% 0.39/0.57 inference(quant_inst,[status(thm)],[])).
% 0.39/0.57 tff(55,plain,
% 0.39/0.57 ((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!13, C1!12, C2!11) | (~incident_c(P!13, C2!11)) | (~incident_c(P!13, C1!12)) | (~((~incident_c(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~incident_c(tptp_fun_Q_4(C2!11, C1!12), C2!11)) | (~((~end_point(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~end_point(tptp_fun_Q_4(C2!11, C1!12), C2!11)))))))) | (~((~meet(P!13, C1!12, C2!11)) | (~((~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12))))))))))))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.39/0.57 tff(56,plain,
% 0.39/0.57 (~((~(meet(P!13, C1!12, C2!11) | (~incident_c(P!13, C2!11)) | (~incident_c(P!13, C1!12)) | (~((~incident_c(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~incident_c(tptp_fun_Q_4(C2!11, C1!12), C2!11)) | (~((~end_point(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~end_point(tptp_fun_Q_4(C2!11, C1!12), C2!11)))))))) | (~((~meet(P!13, C1!12, C2!11)) | (~((~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12)))))))))))),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[55, 49])).
% 0.39/0.57 tff(57,plain,
% 0.39/0.57 (((~(meet(P!13, C1!12, C2!11) | (~incident_c(P!13, C2!11)) | (~incident_c(P!13, C1!12)) | (~((~incident_c(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~incident_c(tptp_fun_Q_4(C2!11, C1!12), C2!11)) | (~((~end_point(tptp_fun_Q_4(C2!11, C1!12), C1!12)) | (~end_point(tptp_fun_Q_4(C2!11, C1!12), C2!11)))))))) | (~((~meet(P!13, C1!12, C2!11)) | (~((~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12))))))))))) | ((~meet(P!13, C1!12, C2!11)) | (~((~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12)))))))))),
% 0.39/0.57 inference(tautology,[status(thm)],[])).
% 0.39/0.57 tff(58,plain,
% 0.39/0.57 ((~meet(P!13, C1!12, C2!11)) | (~((~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12))))))))),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.39/0.57 tff(59,plain,
% 0.39/0.57 ((~![C1: $i, C2: $i] : ((~part_of(C1, C2)) | (~?[P: $i] : meet(P, C1, C2)))) <=> (~![C1: $i, C2: $i] : ((~part_of(C1, C2)) | (~?[P: $i] : meet(P, C1, C2))))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(60,plain,
% 0.39/0.57 ((~![C1: $i, C2: $i] : (part_of(C1, C2) => (~?[P: $i] : meet(P, C1, C2)))) <=> (~![C1: $i, C2: $i] : ((~part_of(C1, C2)) | (~?[P: $i] : meet(P, C1, C2))))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(61,axiom,(~![C1: $i, C2: $i] : (part_of(C1, C2) => (~?[P: $i] : meet(P, C1, C2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary_2_9')).
% 0.39/0.57 tff(62,plain,
% 0.39/0.57 (~![C1: $i, C2: $i] : ((~part_of(C1, C2)) | (~?[P: $i] : meet(P, C1, C2)))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.39/0.57 tff(63,plain,
% 0.39/0.57 (~![C1: $i, C2: $i] : ((~part_of(C1, C2)) | (~?[P: $i] : meet(P, C1, C2)))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[62, 59])).
% 0.39/0.57 tff(64,plain,
% 0.39/0.57 (~![C1: $i, C2: $i] : ((~part_of(C1, C2)) | (~?[P: $i] : meet(P, C1, C2)))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.39/0.57 tff(65,plain,
% 0.39/0.57 (~![C1: $i, C2: $i] : ((~part_of(C1, C2)) | (~?[P: $i] : meet(P, C1, C2)))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[64, 59])).
% 0.39/0.57 tff(66,plain,
% 0.39/0.57 (meet(P!13, C1!12, C2!11)),
% 0.39/0.57 inference(and_elim,[status(thm)],[65])).
% 0.39/0.57 tff(67,plain,
% 0.39/0.57 ((~((~meet(P!13, C1!12, C2!11)) | (~((~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12)))))))))) | (~meet(P!13, C1!12, C2!11)) | (~((~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12))))))))),
% 0.39/0.57 inference(tautology,[status(thm)],[])).
% 0.39/0.57 tff(68,plain,
% 0.39/0.57 ((~((~meet(P!13, C1!12, C2!11)) | (~((~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12)))))))))) | (~((~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12))))))))),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.39/0.57 tff(69,plain,
% 0.39/0.57 (~((~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12)))))))),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[68, 58])).
% 0.39/0.57 tff(70,plain,
% 0.39/0.57 (((~incident_c(P!13, C1!12)) | (~incident_c(P!13, C2!11)) | (~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12))))))) | ![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12)))))),
% 0.39/0.57 inference(tautology,[status(thm)],[])).
% 0.39/0.57 tff(71,plain,
% 0.39/0.57 (![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12)))))),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.39/0.57 tff(72,plain,
% 0.39/0.57 (((~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12)))))) | ((~incident_c(tptp_fun_P_6(C1!12), C1!12)) | (~incident_c(tptp_fun_P_6(C1!12), C2!11)) | (~((~end_point(tptp_fun_P_6(C1!12), C1!12)) | (~end_point(tptp_fun_P_6(C1!12), C2!11)))))) <=> ((~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12)))))) | (~incident_c(tptp_fun_P_6(C1!12), C1!12)) | (~incident_c(tptp_fun_P_6(C1!12), C2!11)) | (~((~end_point(tptp_fun_P_6(C1!12), C1!12)) | (~end_point(tptp_fun_P_6(C1!12), C2!11)))))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(73,plain,
% 0.39/0.57 (((~incident_c(tptp_fun_P_6(C1!12), C1!12)) | (~incident_c(tptp_fun_P_6(C1!12), C2!11)) | (~((~end_point(tptp_fun_P_6(C1!12), C2!11)) | (~end_point(tptp_fun_P_6(C1!12), C1!12))))) <=> ((~incident_c(tptp_fun_P_6(C1!12), C1!12)) | (~incident_c(tptp_fun_P_6(C1!12), C2!11)) | (~((~end_point(tptp_fun_P_6(C1!12), C1!12)) | (~end_point(tptp_fun_P_6(C1!12), C2!11)))))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(74,plain,
% 0.39/0.57 (((~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12)))))) | ((~incident_c(tptp_fun_P_6(C1!12), C1!12)) | (~incident_c(tptp_fun_P_6(C1!12), C2!11)) | (~((~end_point(tptp_fun_P_6(C1!12), C2!11)) | (~end_point(tptp_fun_P_6(C1!12), C1!12)))))) <=> ((~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12)))))) | ((~incident_c(tptp_fun_P_6(C1!12), C1!12)) | (~incident_c(tptp_fun_P_6(C1!12), C2!11)) | (~((~end_point(tptp_fun_P_6(C1!12), C1!12)) | (~end_point(tptp_fun_P_6(C1!12), C2!11))))))),
% 0.39/0.57 inference(monotonicity,[status(thm)],[73])).
% 0.39/0.58 tff(75,plain,
% 0.39/0.58 (((~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12)))))) | ((~incident_c(tptp_fun_P_6(C1!12), C1!12)) | (~incident_c(tptp_fun_P_6(C1!12), C2!11)) | (~((~end_point(tptp_fun_P_6(C1!12), C2!11)) | (~end_point(tptp_fun_P_6(C1!12), C1!12)))))) <=> ((~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12)))))) | (~incident_c(tptp_fun_P_6(C1!12), C1!12)) | (~incident_c(tptp_fun_P_6(C1!12), C2!11)) | (~((~end_point(tptp_fun_P_6(C1!12), C1!12)) | (~end_point(tptp_fun_P_6(C1!12), C2!11)))))),
% 0.39/0.58 inference(transitivity,[status(thm)],[74, 72])).
% 0.39/0.58 tff(76,plain,
% 0.39/0.58 ((~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12)))))) | ((~incident_c(tptp_fun_P_6(C1!12), C1!12)) | (~incident_c(tptp_fun_P_6(C1!12), C2!11)) | (~((~end_point(tptp_fun_P_6(C1!12), C2!11)) | (~end_point(tptp_fun_P_6(C1!12), C1!12)))))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(77,plain,
% 0.39/0.58 ((~![Q: $i] : ((~incident_c(Q, C1!12)) | (~incident_c(Q, C2!11)) | (~((~end_point(Q, C2!11)) | (~end_point(Q, C1!12)))))) | (~incident_c(tptp_fun_P_6(C1!12), C1!12)) | (~incident_c(tptp_fun_P_6(C1!12), C2!11)) | (~((~end_point(tptp_fun_P_6(C1!12), C1!12)) | (~end_point(tptp_fun_P_6(C1!12), C2!11))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.39/0.58 tff(78,plain,
% 0.39/0.58 (~incident_c(tptp_fun_P_6(C1!12), C2!11)),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[77, 71, 27, 25])).
% 0.39/0.58 tff(79,plain,
% 0.39/0.58 (^[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))))))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(80,plain,
% 0.39/0.58 (![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)))))))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[79])).
% 0.39/0.58 tff(81,plain,
% 0.39/0.58 (^[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))))))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(82,plain,
% 0.39/0.58 (![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)))))))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[81])).
% 0.39/0.58 tff(83,plain,
% 0.39/0.58 (![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)))))))),
% 0.39/0.58 inference(transitivity,[status(thm)],[82, 80])).
% 0.39/0.58 tff(84,plain,
% 0.39/0.58 (^[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)))))))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(85,plain,
% 0.39/0.58 (![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)))))))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[84])).
% 0.39/0.58 tff(86,plain,
% 0.39/0.58 (![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)))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(87,plain,
% 0.39/0.58 (^[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))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(88,plain,
% 0.39/0.58 (![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)))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[87])).
% 0.39/0.58 tff(89,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')).
% 0.39/0.58 tff(90,plain,
% 0.39/0.58 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.39/0.58 tff(91,plain,
% 0.39/0.58 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.39/0.58 tff(92,plain,(
% 0.39/0.58 ![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)))))),
% 0.39/0.58 inference(skolemize,[status(sab)],[91])).
% 0.39/0.58 tff(93,plain,
% 0.39/0.58 (![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)))))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.39/0.58 tff(94,plain,
% 0.39/0.58 (![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)))))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[93, 83])).
% 0.39/0.58 tff(95,plain,
% 0.39/0.58 ((~![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)))))))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(96,plain,
% 0.39/0.58 (~((~((~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))))))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.39/0.58 tff(97,plain,
% 0.39/0.58 (((~((~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)))),
% 0.39/0.58 inference(tautology,[status(thm)],[])).
% 0.39/0.58 tff(98,plain,
% 0.39/0.58 ((~part_of(C1!12, C2!11)) | ![P: $i] : ((~incident_c(P, C1!12)) | incident_c(P, C2!11))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.39/0.58 tff(99,plain,
% 0.39/0.58 (part_of(C1!12, C2!11)),
% 0.39/0.58 inference(and_elim,[status(thm)],[65])).
% 0.39/0.58 tff(100,plain,
% 0.39/0.58 ((~((~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))),
% 0.39/0.58 inference(tautology,[status(thm)],[])).
% 0.39/0.58 tff(101,plain,
% 0.39/0.58 ((~((~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))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.39/0.58 tff(102,plain,
% 0.39/0.58 (![P: $i] : ((~incident_c(P, C1!12)) | incident_c(P, C2!11))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[101, 98])).
% 0.39/0.58 tff(103,plain,
% 0.39/0.58 (((~![P: $i] : ((~incident_c(P, C1!12)) | incident_c(P, C2!11))) | ((~incident_c(tptp_fun_P_6(C1!12), C1!12)) | incident_c(tptp_fun_P_6(C1!12), C2!11))) <=> ((~![P: $i] : ((~incident_c(P, C1!12)) | incident_c(P, C2!11))) | (~incident_c(tptp_fun_P_6(C1!12), C1!12)) | incident_c(tptp_fun_P_6(C1!12), C2!11))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(104,plain,
% 0.39/0.58 ((~![P: $i] : ((~incident_c(P, C1!12)) | incident_c(P, C2!11))) | ((~incident_c(tptp_fun_P_6(C1!12), C1!12)) | incident_c(tptp_fun_P_6(C1!12), C2!11))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(105,plain,
% 0.39/0.58 ((~![P: $i] : ((~incident_c(P, C1!12)) | incident_c(P, C2!11))) | (~incident_c(tptp_fun_P_6(C1!12), C1!12)) | incident_c(tptp_fun_P_6(C1!12), C2!11)),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.39/0.58 tff(106,plain,
% 0.39/0.58 ($false),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[105, 102, 27, 78])).
% 0.39/0.58 % SZS output end Proof
% 0.39/0.58 % E exiting
%------------------------------------------------------------------------------