%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO111+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:05:36 AM UTC 2025
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO111+1 : TPTP v9.0.0. Released v2.4.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 14:24:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(inner_point_type, type, (
% 0.20/0.40 inner_point: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_Cpp_11_type, type, (
% 0.20/0.40 tptp_fun_Cpp_11: ( $i * $i * $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_C_15_type, type, (
% 0.20/0.40 tptp_fun_C_15: $i)).
% 0.20/0.40 tff(tptp_fun_P_14_type, type, (
% 0.20/0.40 tptp_fun_P_14: $i)).
% 0.20/0.40 tff(tptp_fun_Q_13_type, type, (
% 0.20/0.40 tptp_fun_Q_13: $i)).
% 0.20/0.40 tff(tptp_fun_R_12_type, type, (
% 0.20/0.40 tptp_fun_R_12: $i)).
% 0.20/0.40 tff(end_point_type, type, (
% 0.20/0.40 end_point: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_Q_9_type, type, (
% 0.20/0.40 tptp_fun_Q_9: ( $i * $i ) > $i)).
% 0.20/0.40 tff(sum_type, type, (
% 0.20/0.40 sum: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_C2_7_type, type, (
% 0.20/0.40 tptp_fun_C2_7: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_C1_8_type, type, (
% 0.20/0.40 tptp_fun_C1_8: ( $i * $i ) > $i)).
% 0.20/0.40 tff(meet_type, type, (
% 0.20/0.40 meet: ( $i * $i * $i ) > $o)).
% 0.20/0.40 tff(part_of_type, type, (
% 0.20/0.40 part_of: ( $i * $i ) > $o)).
% 0.20/0.40 tff(between_c_type, type, (
% 0.20/0.40 between_c: ( $i * $i * $i * $i ) > $o)).
% 0.20/0.40 tff(incident_c_type, type, (
% 0.20/0.40 incident_c: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_C1_3_type, type, (
% 0.20/0.40 tptp_fun_C1_3: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_C2_2_type, type, (
% 0.20/0.40 tptp_fun_C2_2: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_P_0_type, type, (
% 0.20/0.40 tptp_fun_P_0: ( $i * $i ) > $i)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[C: $i, P: $i, Q: $i, R: $i] : refl((~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp))))))) <=> (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp))))))) <=> ![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (^[C: $i, P: $i, Q: $i, R: $i] : rewrite((~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp))))))) <=> (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp))))))) <=> ![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp))))))) <=> ![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp)))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (^[C: $i, P: $i, Q: $i, R: $i] : trans(monotonicity(rewrite(((~between_c(C, P, Q, R)) | ((~(P = R)) & part_of(tptp_fun_Cpp_11(R, Q, P, C), C) & end_point(P, tptp_fun_Cpp_11(R, Q, P, C)) & end_point(R, tptp_fun_Cpp_11(R, Q, P, C)) & inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C)))) <=> ((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))), rewrite(((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : (~(part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp)))) <=> ((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp))))), ((((~between_c(C, P, Q, R)) | ((~(P = R)) & part_of(tptp_fun_Cpp_11(R, Q, P, C), C) & end_point(P, tptp_fun_Cpp_11(R, Q, P, C)) & end_point(R, tptp_fun_Cpp_11(R, Q, P, C)) & inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C)))) & ((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : (~(part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp))))) <=> (((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C)))))) & ((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp))))))), rewrite((((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C)))))) & ((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp))))) <=> (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp)))))))), ((((~between_c(C, P, Q, R)) | ((~(P = R)) & part_of(tptp_fun_Cpp_11(R, Q, P, C), C) & end_point(P, tptp_fun_Cpp_11(R, Q, P, C)) & end_point(R, tptp_fun_Cpp_11(R, Q, P, C)) & inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C)))) & ((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : (~(part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp))))) <=> (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![C: $i, P: $i, Q: $i, R: $i] : (((~between_c(C, P, Q, R)) | ((~(P = R)) & part_of(tptp_fun_Cpp_11(R, Q, P, C), C) & end_point(P, tptp_fun_Cpp_11(R, Q, P, C)) & end_point(R, tptp_fun_Cpp_11(R, Q, P, C)) & inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C)))) & ((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : (~(part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp))))) <=> ![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (^[C: $i, P: $i, Q: $i, R: $i] : rewrite((((~between_c(C, P, Q, R)) | ((~(P = R)) & (part_of(tptp_fun_Cpp_11(R, Q, P, C), C) & end_point(P, tptp_fun_Cpp_11(R, Q, P, C)) & end_point(R, tptp_fun_Cpp_11(R, Q, P, C)) & inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))) & (between_c(C, P, Q, R) | ((P = R) | ![Cpp: $i] : (~(part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp)))))) <=> (((~between_c(C, P, Q, R)) | ((~(P = R)) & part_of(tptp_fun_Cpp_11(R, Q, P, C), C) & end_point(P, tptp_fun_Cpp_11(R, Q, P, C)) & end_point(R, tptp_fun_Cpp_11(R, Q, P, C)) & inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C)))) & ((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : (~(part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (![C: $i, P: $i, Q: $i, R: $i] : (((~between_c(C, P, Q, R)) | ((~(P = R)) & (part_of(tptp_fun_Cpp_11(R, Q, P, C), C) & end_point(P, tptp_fun_Cpp_11(R, Q, P, C)) & end_point(R, tptp_fun_Cpp_11(R, Q, P, C)) & inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))) & (between_c(C, P, Q, R) | ((P = R) | ![Cpp: $i] : (~(part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp)))))) <=> ![C: $i, P: $i, Q: $i, R: $i] : (((~between_c(C, P, Q, R)) | ((~(P = R)) & part_of(tptp_fun_Cpp_11(R, Q, P, C), C) & end_point(P, tptp_fun_Cpp_11(R, Q, P, C)) & end_point(R, tptp_fun_Cpp_11(R, Q, P, C)) & inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C)))) & ((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : (~(part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (![C: $i, P: $i, Q: $i, R: $i] : (between_c(C, P, Q, R) <=> ((~(P = R)) & ?[Cpp: $i] : (part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp)))) <=> ![C: $i, P: $i, Q: $i, R: $i] : (between_c(C, P, Q, R) <=> ((~(P = R)) & ?[Cpp: $i] : (part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (^[C: $i, P: $i, Q: $i, R: $i] : rewrite((between_c(C, P, Q, R) <=> ((~(P = R)) & ?[Cpp: $i] : (((part_of(Cpp, C) & end_point(P, Cpp)) & end_point(R, Cpp)) & inner_point(Q, Cpp)))) <=> (between_c(C, P, Q, R) <=> ((~(P = R)) & ?[Cpp: $i] : (part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (![C: $i, P: $i, Q: $i, R: $i] : (between_c(C, P, Q, R) <=> ((~(P = R)) & ?[Cpp: $i] : (((part_of(Cpp, C) & end_point(P, Cpp)) & end_point(R, Cpp)) & inner_point(Q, Cpp)))) <=> ![C: $i, P: $i, Q: $i, R: $i] : (between_c(C, P, Q, R) <=> ((~(P = R)) & ?[Cpp: $i] : (part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.40 tff(13,axiom,(![C: $i, P: $i, Q: $i, R: $i] : (between_c(C, P, Q, R) <=> ((~(P = R)) & ?[Cpp: $i] : (((part_of(Cpp, C) & end_point(P, Cpp)) & end_point(R, Cpp)) & inner_point(Q, Cpp))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+1.ax','between_c_defn')).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (![C: $i, P: $i, Q: $i, R: $i] : (between_c(C, P, Q, R) <=> ((~(P = R)) & ?[Cpp: $i] : (part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (![C: $i, P: $i, Q: $i, R: $i] : (between_c(C, P, Q, R) <=> ((~(P = R)) & ?[Cpp: $i] : (part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.20/0.40 tff(16,plain,(
% 0.20/0.40 ![C: $i, P: $i, Q: $i, R: $i] : (((~between_c(C, P, Q, R)) | ((~(P = R)) & (part_of(tptp_fun_Cpp_11(R, Q, P, C), C) & end_point(P, tptp_fun_Cpp_11(R, Q, P, C)) & end_point(R, tptp_fun_Cpp_11(R, Q, P, C)) & inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))) & (between_c(C, P, Q, R) | ((P = R) | ![Cpp: $i] : (~(part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp))))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[15])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![C: $i, P: $i, Q: $i, R: $i] : (((~between_c(C, P, Q, R)) | ((~(P = R)) & part_of(tptp_fun_Cpp_11(R, Q, P, C), C) & end_point(P, tptp_fun_Cpp_11(R, Q, P, C)) & end_point(R, tptp_fun_Cpp_11(R, Q, P, C)) & inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C)))) & ((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : (~(part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[18, 5])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (((~![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp)))))))) | (~((~((P!14 = R!12) | between_c(C!15, P!14, Q!13, R!12) | ![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp))))) | (~((~between_c(C!15, P!14, Q!13, R!12)) | (~((P!14 = R!12) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15))))))))) <=> ((~![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp)))))))) | (~((~((P!14 = R!12) | between_c(C!15, P!14, Q!13, R!12) | ![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp))))) | (~((~between_c(C!15, P!14, Q!13, R!12)) | (~((P!14 = R!12) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 ((~((~((~between_c(C!15, P!14, Q!13, R!12)) | (~((P!14 = R!12) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))))) | (~((P!14 = R!12) | between_c(C!15, P!14, Q!13, R!12) | ![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp))))))) <=> (~((~((P!14 = R!12) | between_c(C!15, P!14, Q!13, R!12) | ![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp))))) | (~((~between_c(C!15, P!14, Q!13, R!12)) | (~((P!14 = R!12) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (((~![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp)))))))) | (~((~((~between_c(C!15, P!14, Q!13, R!12)) | (~((P!14 = R!12) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))))) | (~((P!14 = R!12) | between_c(C!15, P!14, Q!13, R!12) | ![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp)))))))) <=> ((~![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp)))))))) | (~((~((P!14 = R!12) | between_c(C!15, P!14, Q!13, R!12) | ![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp))))) | (~((~between_c(C!15, P!14, Q!13, R!12)) | (~((P!14 = R!12) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)))))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[21])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (((~![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp)))))))) | (~((~((~between_c(C!15, P!14, Q!13, R!12)) | (~((P!14 = R!12) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))))) | (~((P!14 = R!12) | between_c(C!15, P!14, Q!13, R!12) | ![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp)))))))) <=> ((~![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp)))))))) | (~((~((P!14 = R!12) | between_c(C!15, P!14, Q!13, R!12) | ![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp))))) | (~((~between_c(C!15, P!14, Q!13, R!12)) | (~((P!14 = R!12) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[22, 20])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 ((~![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp)))))))) | (~((~((~between_c(C!15, P!14, Q!13, R!12)) | (~((P!14 = R!12) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))))) | (~((P!14 = R!12) | between_c(C!15, P!14, Q!13, R!12) | ![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp)))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 ((~![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_11(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_11(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_11(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_11(R, Q, P, C))))))) | (~((P = R) | between_c(C, P, Q, R) | ![Cpp: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp)))))))) | (~((~((P!14 = R!12) | between_c(C!15, P!14, Q!13, R!12) | ![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp))))) | (~((~between_c(C!15, P!14, Q!13, R!12)) | (~((P!14 = R!12) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (~((~((P!14 = R!12) | between_c(C!15, P!14, Q!13, R!12) | ![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp))))) | (~((~between_c(C!15, P!14, Q!13, R!12)) | (~((P!14 = R!12) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[25, 19])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (((~((P!14 = R!12) | between_c(C!15, P!14, Q!13, R!12) | ![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp))))) | (~((~between_c(C!15, P!14, Q!13, R!12)) | (~((P!14 = R!12) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15))))))) | ((~between_c(C!15, P!14, Q!13, R!12)) | (~((P!14 = R!12) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 ((~between_c(C!15, P!14, Q!13, R!12)) | (~((P!14 = R!12) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 ((~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | (incident_c(P, C) & incident_c(Q, C) & incident_c(R, C) & (~(P = Q)) & (~(Q = R)) & (~(P = R))))) <=> (~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | (incident_c(P, C) & incident_c(Q, C) & incident_c(R, C) & (~(P = Q)) & (~(Q = R)) & (~(P = R)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 ((~![C: $i, P: $i, Q: $i, R: $i] : (between_c(C, P, Q, R) => (((((incident_c(P, C) & incident_c(Q, C)) & incident_c(R, C)) & (~(P = Q))) & (~(Q = R))) & (~(P = R))))) <=> (~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | (incident_c(P, C) & incident_c(Q, C) & incident_c(R, C) & (~(P = Q)) & (~(Q = R)) & (~(P = R)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(31,axiom,(~![C: $i, P: $i, Q: $i, R: $i] : (between_c(C, P, Q, R) => (((((incident_c(P, C) & incident_c(Q, C)) & incident_c(R, C)) & (~(P = Q))) & (~(Q = R))) & (~(P = R))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','theorem_3_8_1')).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | (incident_c(P, C) & incident_c(Q, C) & incident_c(R, C) & (~(P = Q)) & (~(Q = R)) & (~(P = R))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | (incident_c(P, C) & incident_c(Q, C) & incident_c(R, C) & (~(P = Q)) & (~(Q = R)) & (~(P = R))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[32, 29])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | (incident_c(P, C) & incident_c(Q, C) & incident_c(R, C) & (~(P = Q)) & (~(Q = R)) & (~(P = R))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | (incident_c(P, C) & incident_c(Q, C) & incident_c(R, C) & (~(P = Q)) & (~(Q = R)) & (~(P = R))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[34, 29])).
% 0.20/0.41 tff(36,plain,(
% 0.20/0.41 ~((~between_c(C!15, P!14, Q!13, R!12)) | (incident_c(P!14, C!15) & incident_c(Q!13, C!15) & incident_c(R!12, C!15) & (~(P!14 = Q!13)) & (~(Q!13 = R!12)) & (~(P!14 = R!12))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[35])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (between_c(C!15, P!14, Q!13, R!12)),
% 0.20/0.41 inference(or_elim,[status(thm)],[36])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 ((~((~between_c(C!15, P!14, Q!13, R!12)) | (~((P!14 = R!12) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)))))) | (~between_c(C!15, P!14, Q!13, R!12)) | (~((P!14 = R!12) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 ((~((~between_c(C!15, P!14, Q!13, R!12)) | (~((P!14 = R!12) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)))))) | (~((P!14 = R!12) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (~((P!14 = R!12) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[39, 28])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (((P!14 = R!12) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15))) | inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (^[C: $i, P: $i] : refl(((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))))))) <=> ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))))))) <=> ![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (^[C: $i, P: $i] : rewrite(((~inner_point(P, C)) | (meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)) & (C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))))) <=> ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (![C: $i, P: $i] : ((~inner_point(P, C)) | (meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)) & (C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))))) <=> ![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (![C: $i, P: $i] : ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2)))) <=> ![C: $i, P: $i] : ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (^[C: $i, P: $i] : rewrite((inner_point(P, C) => ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2)))) <=> ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (![C: $i, P: $i] : (inner_point(P, C) => ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2)))) <=> ![C: $i, P: $i] : ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.42 tff(50,axiom,(![C: $i, P: $i] : (inner_point(P, C) => ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','c4')).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (![C: $i, P: $i] : ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (![C: $i, P: $i] : ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.20/0.42 tff(53,plain,(
% 0.20/0.42 ![C: $i, P: $i] : ((~inner_point(P, C)) | (meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)) & (C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[52])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[54, 44])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 (((~![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))) | ((~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~meet(Q!13, tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))) | (~(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15) = sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))))))) <=> ((~![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~meet(Q!13, tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))) | (~(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15) = sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 ((~![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))) | ((~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~meet(Q!13, tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))) | (~(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15) = sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 ((~![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~meet(Q!13, tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))) | (~(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15) = sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (~((~meet(Q!13, tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))) | (~(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15) = sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[58, 55, 42])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (((~meet(Q!13, tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))) | (~(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15) = sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))))) | (tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15) = sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15) = sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) = tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)),
% 0.20/0.42 inference(symmetry,[status(thm)],[61])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (end_point(R!12, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))) <=> end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[62])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) <=> end_point(R!12, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))),
% 0.20/0.42 inference(symmetry,[status(thm)],[63])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (((P!14 = R!12) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15))) | end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[65, 40])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (end_point(R!12, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[66, 64])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))) <=> end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[62])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 (end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) <=> end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))),
% 0.20/0.42 inference(symmetry,[status(thm)],[68])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 (^[C: $i, P: $i] : refl(((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C))))) <=> ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (![C: $i, P: $i] : ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C))))) <=> ![C: $i, P: $i] : ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 (^[C: $i, P: $i] : rewrite(((~end_point(P, C)) | (end_point(tptp_fun_Q_9(P, C), C) & (~(P = tptp_fun_Q_9(P, C))))) <=> ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 (![C: $i, P: $i] : ((~end_point(P, C)) | (end_point(tptp_fun_Q_9(P, C), C) & (~(P = tptp_fun_Q_9(P, C))))) <=> ![C: $i, P: $i] : ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (![C: $i, P: $i] : ((~end_point(P, C)) | ?[Q: $i] : (end_point(Q, C) & (~(P = Q)))) <=> ![C: $i, P: $i] : ((~end_point(P, C)) | ?[Q: $i] : (end_point(Q, C) & (~(P = Q))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.43 (^[C: $i, P: $i] : rewrite((end_point(P, C) => ?[Q: $i] : (end_point(Q, C) & (~(P = Q)))) <=> ((~end_point(P, C)) | ?[Q: $i] : (end_point(Q, C) & (~(P = Q)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (![C: $i, P: $i] : (end_point(P, C) => ?[Q: $i] : (end_point(Q, C) & (~(P = Q)))) <=> ![C: $i, P: $i] : ((~end_point(P, C)) | ?[Q: $i] : (end_point(Q, C) & (~(P = Q))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.43 tff(77,axiom,(![C: $i, P: $i] : (end_point(P, C) => ?[Q: $i] : (end_point(Q, C) & (~(P = Q))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','c6')).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (![C: $i, P: $i] : ((~end_point(P, C)) | ?[Q: $i] : (end_point(Q, C) & (~(P = Q))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 (![C: $i, P: $i] : ((~end_point(P, C)) | ?[Q: $i] : (end_point(Q, C) & (~(P = Q))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.20/0.43 tff(80,plain,(
% 0.20/0.43 ![C: $i, P: $i] : ((~end_point(P, C)) | (end_point(tptp_fun_Q_9(P, C), C) & (~(P = tptp_fun_Q_9(P, C)))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[79])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (![C: $i, P: $i] : ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 (![C: $i, P: $i] : ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (((~![C: $i, P: $i] : ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C)))))) | ((~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (R!12 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))))) <=> ((~![C: $i, P: $i] : ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C)))))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (R!12 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 ((~![C: $i, P: $i] : ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C)))))) | ((~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (R!12 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 ((~![C: $i, P: $i] : ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C)))))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (R!12 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 (~((~end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (R!12 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[85, 82, 66])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (((~end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (R!12 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))) | end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[88, 69])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 ((tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) = R!12) <=> (R!12 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))),
% 0.20/0.43 inference(commutativity,[status(thm)],[])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 ((R!12 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) <=> (tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) = R!12)),
% 0.20/0.43 inference(symmetry,[status(thm)],[90])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 ((~(R!12 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))) <=> (~(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) = R!12))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[91])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (((~end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (R!12 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))) | (~(R!12 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 (~(R!12 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[93, 86])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (~(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) = R!12)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[94, 92])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (end_point(P!14, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))) <=> end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[62])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) <=> end_point(P!14, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))),
% 0.20/0.43 inference(symmetry,[status(thm)],[96])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (((P!14 = R!12) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15))) | end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[98, 40])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (end_point(P!14, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[99, 97])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (((P!14 = R!12) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15))) | (~(P!14 = R!12))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 (~(P!14 = R!12)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[101, 40])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 (^[C: $i, P: $i, Q: $i, R: $i] : refl(((Q = R) | (P = R) | (P = Q) | (~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C))) <=> ((Q = R) | (P = R) | (P = Q) | (~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (![C: $i, P: $i, Q: $i, R: $i] : ((Q = R) | (P = R) | (P = Q) | (~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C))) <=> ![C: $i, P: $i, Q: $i, R: $i] : ((Q = R) | (P = R) | (P = Q) | (~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 (^[C: $i, P: $i, Q: $i, R: $i] : trans(monotonicity(trans(monotonicity(rewrite((end_point(P, C) & end_point(Q, C) & end_point(R, C)) <=> (~((~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C))))), ((~(end_point(P, C) & end_point(Q, C) & end_point(R, C))) <=> (~(~((~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C))))))), rewrite((~(~((~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C))))) <=> ((~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C)))), ((~(end_point(P, C) & end_point(Q, C) & end_point(R, C))) <=> ((~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C))))), (((Q = R) | (P = R) | (P = Q) | (~(end_point(P, C) & end_point(Q, C) & end_point(R, C)))) <=> ((Q = R) | (P = R) | (P = Q) | ((~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C)))))), rewrite(((Q = R) | (P = R) | (P = Q) | ((~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C)))) <=> ((Q = R) | (P = R) | (P = Q) | (~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C)))), (((Q = R) | (P = R) | (P = Q) | (~(end_point(P, C) & end_point(Q, C) & end_point(R, C)))) <=> ((Q = R) | (P = R) | (P = Q) | (~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (![C: $i, P: $i, Q: $i, R: $i] : ((Q = R) | (P = R) | (P = Q) | (~(end_point(P, C) & end_point(Q, C) & end_point(R, C)))) <=> ![C: $i, P: $i, Q: $i, R: $i] : ((Q = R) | (P = R) | (P = Q) | (~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[105])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 (![C: $i, P: $i, Q: $i, R: $i] : ((Q = R) | (P = R) | (P = Q) | (~(end_point(P, C) & end_point(Q, C) & end_point(R, C)))) <=> ![C: $i, P: $i, Q: $i, R: $i] : ((Q = R) | (P = R) | (P = Q) | (~(end_point(P, C) & end_point(Q, C) & end_point(R, C))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 (^[C: $i, P: $i, Q: $i, R: $i] : trans(monotonicity(rewrite(((end_point(P, C) & end_point(Q, C)) & end_point(R, C)) <=> (end_point(P, C) & end_point(Q, C) & end_point(R, C))), trans(monotonicity(rewrite(((P = Q) | (P = R)) <=> ((P = R) | (P = Q))), ((((P = Q) | (P = R)) | (Q = R)) <=> (((P = R) | (P = Q)) | (Q = R)))), rewrite((((P = R) | (P = Q)) | (Q = R)) <=> ((Q = R) | (P = R) | (P = Q))), ((((P = Q) | (P = R)) | (Q = R)) <=> ((Q = R) | (P = R) | (P = Q)))), ((((end_point(P, C) & end_point(Q, C)) & end_point(R, C)) => (((P = Q) | (P = R)) | (Q = R))) <=> ((end_point(P, C) & end_point(Q, C) & end_point(R, C)) => ((Q = R) | (P = R) | (P = Q))))), rewrite(((end_point(P, C) & end_point(Q, C) & end_point(R, C)) => ((Q = R) | (P = R) | (P = Q))) <=> ((Q = R) | (P = R) | (P = Q) | (~(end_point(P, C) & end_point(Q, C) & end_point(R, C))))), ((((end_point(P, C) & end_point(Q, C)) & end_point(R, C)) => (((P = Q) | (P = R)) | (Q = R))) <=> ((Q = R) | (P = R) | (P = Q) | (~(end_point(P, C) & end_point(Q, C) & end_point(R, C))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 (![C: $i, P: $i, Q: $i, R: $i] : (((end_point(P, C) & end_point(Q, C)) & end_point(R, C)) => (((P = Q) | (P = R)) | (Q = R))) <=> ![C: $i, P: $i, Q: $i, R: $i] : ((Q = R) | (P = R) | (P = Q) | (~(end_point(P, C) & end_point(Q, C) & end_point(R, C))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[108])).
% 0.20/0.43 tff(110,axiom,(![C: $i, P: $i, Q: $i, R: $i] : (((end_point(P, C) & end_point(Q, C)) & end_point(R, C)) => (((P = Q) | (P = R)) | (Q = R)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','c5')).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 (![C: $i, P: $i, Q: $i, R: $i] : ((Q = R) | (P = R) | (P = Q) | (~(end_point(P, C) & end_point(Q, C) & end_point(R, C))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 (![C: $i, P: $i, Q: $i, R: $i] : ((Q = R) | (P = R) | (P = Q) | (~(end_point(P, C) & end_point(Q, C) & end_point(R, C))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.20/0.43 tff(113,plain,(
% 0.20/0.43 ![C: $i, P: $i, Q: $i, R: $i] : ((Q = R) | (P = R) | (P = Q) | (~(end_point(P, C) & end_point(Q, C) & end_point(R, C))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[112])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 (![C: $i, P: $i, Q: $i, R: $i] : ((Q = R) | (P = R) | (P = Q) | (~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 (![C: $i, P: $i, Q: $i, R: $i] : ((Q = R) | (P = R) | (P = Q) | (~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[114, 104])).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 (((~![C: $i, P: $i, Q: $i, R: $i] : ((Q = R) | (P = R) | (P = Q) | (~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C)))) | ((P!14 = R!12) | (~end_point(R!12, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (~end_point(P!14, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) = R!12) | (~end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (P!14 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) <=> ((~![C: $i, P: $i, Q: $i, R: $i] : ((Q = R) | (P = R) | (P = Q) | (~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C)))) | (P!14 = R!12) | (~end_point(R!12, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (~end_point(P!14, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) = R!12) | (~end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (P!14 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(117,plain,
% 0.20/0.44 (((tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) = R!12) | (P!14 = R!12) | (P!14 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (~end_point(P!14, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (~end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))))) <=> ((P!14 = R!12) | (~end_point(R!12, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (~end_point(P!14, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) = R!12) | (~end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (P!14 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 (((~![C: $i, P: $i, Q: $i, R: $i] : ((Q = R) | (P = R) | (P = Q) | (~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C)))) | ((tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) = R!12) | (P!14 = R!12) | (P!14 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (~end_point(P!14, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (~end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))))) <=> ((~![C: $i, P: $i, Q: $i, R: $i] : ((Q = R) | (P = R) | (P = Q) | (~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C)))) | ((P!14 = R!12) | (~end_point(R!12, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (~end_point(P!14, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) = R!12) | (~end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (P!14 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[117])).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 (((~![C: $i, P: $i, Q: $i, R: $i] : ((Q = R) | (P = R) | (P = Q) | (~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C)))) | ((tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) = R!12) | (P!14 = R!12) | (P!14 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (~end_point(P!14, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (~end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))))) <=> ((~![C: $i, P: $i, Q: $i, R: $i] : ((Q = R) | (P = R) | (P = Q) | (~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C)))) | (P!14 = R!12) | (~end_point(R!12, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (~end_point(P!14, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) = R!12) | (~end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (P!14 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[118, 116])).
% 0.20/0.44 tff(120,plain,
% 0.20/0.44 ((~![C: $i, P: $i, Q: $i, R: $i] : ((Q = R) | (P = R) | (P = Q) | (~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C)))) | ((tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) = R!12) | (P!14 = R!12) | (P!14 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (~end_point(P!14, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (~end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(121,plain,
% 0.20/0.44 ((~![C: $i, P: $i, Q: $i, R: $i] : ((Q = R) | (P = R) | (P = Q) | (~end_point(R, C)) | (~end_point(P, C)) | (~end_point(Q, C)))) | (P!14 = R!12) | (~end_point(R!12, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (~end_point(P!14, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) = R!12) | (~end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (P!14 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.20/0.44 tff(122,plain,
% 0.20/0.44 ((~end_point(R!12, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (~end_point(P!14, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) = R!12) | (~end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (P!14 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[121, 115, 102])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 (P!14 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[122, 100, 95, 89, 67])).
% 0.20/0.44 tff(124,assumption,(P!14 = Q!13), introduced(assumption)).
% 0.20/0.44 tff(125,plain,
% 0.20/0.44 (Q!13 = P!14),
% 0.20/0.44 inference(symmetry,[status(thm)],[124])).
% 0.20/0.44 tff(126,plain,
% 0.20/0.44 (Q!13 = tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.44 inference(transitivity,[status(thm)],[125, 123])).
% 0.20/0.44 tff(127,plain,
% 0.20/0.44 (end_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) <=> end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[126])).
% 0.20/0.44 tff(128,plain,
% 0.20/0.44 (end_point(tptp_fun_Q_9(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) <=> end_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.44 inference(symmetry,[status(thm)],[127])).
% 0.20/0.44 tff(129,plain,
% 0.20/0.44 (end_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[88, 128])).
% 0.20/0.44 tff(130,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(131,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[130])).
% 0.20/0.44 tff(132,plain,
% 0.20/0.44 (^[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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(133,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[132])).
% 0.20/0.44 tff(134,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(135,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')).
% 0.20/0.44 tff(136,plain,
% 0.20/0.44 (![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.44 tff(137,plain,(
% 0.20/0.44 ![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[136])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 (![P: $i, C: $i] : (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 (![P: $i, C: $i] : (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.20/0.45 tff(140,plain,
% 0.20/0.45 ((~![P: $i, C: $i] : (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C)))) | (~(((~incident_c(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | end_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) <=> inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(141,plain,
% 0.20/0.45 (~(((~incident_c(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | end_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) <=> inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.20/0.45 tff(142,plain,
% 0.20/0.45 ((((~incident_c(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | end_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) <=> inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | end_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(143,plain,
% 0.20/0.45 ((((~incident_c(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | end_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) <=> inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | end_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[142, 42])).
% 0.20/0.45 tff(144,plain,
% 0.20/0.45 (~((~incident_c(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | end_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[143, 141])).
% 0.20/0.45 tff(145,plain,
% 0.20/0.45 (((~incident_c(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | end_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(146,plain,
% 0.20/0.45 (~end_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.20/0.45 tff(147,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[146, 129])).
% 0.20/0.45 tff(148,plain,(~(P!14 = Q!13)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(149,plain,
% 0.20/0.45 (^[P: $i, C: $i] : rewrite((~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(150,plain,
% 0.20/0.45 (![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> ![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[149])).
% 0.20/0.45 tff(151,plain,
% 0.20/0.45 (^[P: $i, C: $i] : refl((~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(152,plain,
% 0.20/0.45 (![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> ![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[151])).
% 0.20/0.45 tff(153,plain,
% 0.20/0.45 (^[P: $i, C: $i] : rewrite((~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(154,plain,
% 0.20/0.45 (![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> ![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[153])).
% 0.20/0.45 tff(155,plain,
% 0.20/0.45 (![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> ![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[154, 152])).
% 0.20/0.45 tff(156,plain,
% 0.20/0.45 (^[P: $i, C: $i] : trans(monotonicity(rewrite(((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) <=> ((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))), trans(monotonicity(rewrite((~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P)))))) <=> (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))), ((end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P))))))) <=> (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))), rewrite((end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))) <=> (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))), ((end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P))))))) <=> (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))), ((((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P)))))))) <=> (((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))), rewrite((((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) <=> (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))), ((((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P)))))))) <=> (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(157,plain,
% 0.20/0.45 (![P: $i, C: $i] : (((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[156])).
% 0.20/0.45 tff(158,plain,
% 0.20/0.45 (^[P: $i, C: $i] : rewrite((((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | ((~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> (((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(159,plain,
% 0.20/0.45 (![P: $i, C: $i] : (((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | ((~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> ![P: $i, C: $i] : (((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[158])).
% 0.20/0.45 tff(160,plain,
% 0.20/0.45 (![P: $i, C: $i] : (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) <=> ![P: $i, C: $i] : (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(161,plain,
% 0.20/0.45 (^[P: $i, C: $i] : rewrite((end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : ((((part_of(C1, C) & part_of(C2, C)) & incident_c(P, C1)) & incident_c(P, C2)) => (part_of(C1, C2) | part_of(C2, C1))))) <=> (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(162,plain,
% 0.20/0.45 (![P: $i, C: $i] : (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : ((((part_of(C1, C) & part_of(C2, C)) & incident_c(P, C1)) & incident_c(P, C2)) => (part_of(C1, C2) | part_of(C2, C1))))) <=> ![P: $i, C: $i] : (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[161])).
% 0.20/0.45 tff(163,axiom,(![P: $i, C: $i] : (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : ((((part_of(C1, C) & part_of(C2, C)) & incident_c(P, C1)) & incident_c(P, C2)) => (part_of(C1, C2) | part_of(C2, C1)))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','end_point_defn')).
% 0.20/0.45 tff(164,plain,
% 0.20/0.45 (![P: $i, C: $i] : (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.20/0.45 tff(165,plain,
% 0.20/0.45 (![P: $i, C: $i] : (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.20/0.45 tff(166,plain,(
% 0.20/0.45 ![P: $i, C: $i] : (((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | ((~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[165])).
% 0.20/0.45 tff(167,plain,
% 0.20/0.45 (![P: $i, C: $i] : (((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[166, 159])).
% 0.20/0.45 tff(168,plain,
% 0.20/0.45 (![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[167, 157])).
% 0.20/0.45 tff(169,plain,
% 0.20/0.45 (![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[168, 155])).
% 0.20/0.45 tff(170,plain,
% 0.20/0.45 (![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[169, 150])).
% 0.20/0.45 tff(171,plain,
% 0.20/0.45 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))) | (~incident_c(R!12, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)) | part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)))))) | (~((~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, C1)) | (~incident_c(R!12, C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))) | (~incident_c(R!12, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)) | part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)))))) | (~((~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, C1)) | (~incident_c(R!12, C2)))))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(172,plain,
% 0.20/0.45 ((~((~(end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~(part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))) | (~incident_c(R!12, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))))))) | (~((~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, C1)) | (~incident_c(R!12, C2)))))))))) <=> (~((~(end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))) | (~incident_c(R!12, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)) | part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)))))) | (~((~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, C1)) | (~incident_c(R!12, C2))))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(173,plain,
% 0.20/0.46 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~(part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))) | (~incident_c(R!12, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))))))) | (~((~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, C1)) | (~incident_c(R!12, C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))) | (~incident_c(R!12, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)) | part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)))))) | (~((~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, C1)) | (~incident_c(R!12, C2)))))))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[172])).
% 0.20/0.46 tff(174,plain,
% 0.20/0.46 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~(part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))) | (~incident_c(R!12, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))))))) | (~((~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, C1)) | (~incident_c(R!12, C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))) | (~incident_c(R!12, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)) | part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)))))) | (~((~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, C1)) | (~incident_c(R!12, C2)))))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[173, 171])).
% 0.20/0.46 tff(175,plain,
% 0.20/0.46 ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~(part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))) | (~incident_c(R!12, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))))))) | (~((~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, C1)) | (~incident_c(R!12, C2))))))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(176,plain,
% 0.20/0.46 ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))) | (~incident_c(R!12, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)) | part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)))))) | (~((~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, C1)) | (~incident_c(R!12, C2))))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.20/0.46 tff(177,plain,
% 0.20/0.46 (~((~(end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))) | (~incident_c(R!12, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)) | part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)))))) | (~((~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, C1)) | (~incident_c(R!12, C2)))))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[176, 170])).
% 0.20/0.46 tff(178,plain,
% 0.20/0.46 (((~(end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))) | (~incident_c(R!12, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)) | part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), R!12)))))) | (~((~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, C1)) | (~incident_c(R!12, C2))))))))) | ((~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, C1)) | (~incident_c(R!12, C2)))))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(179,plain,
% 0.20/0.46 ((~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, C1)) | (~incident_c(R!12, C2))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.20/0.46 tff(180,plain,
% 0.20/0.46 ((~((~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, C1)) | (~incident_c(R!12, C2)))))))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, C1)) | (~incident_c(R!12, C2))))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(181,plain,
% 0.20/0.47 ((~((~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, C1)) | (~incident_c(R!12, C2)))))))) | (~((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, C1)) | (~incident_c(R!12, C2))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[180, 66])).
% 0.20/0.47 tff(182,plain,
% 0.20/0.47 (~((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, C1)) | (~incident_c(R!12, C2)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[181, 179])).
% 0.20/0.47 tff(183,plain,
% 0.20/0.47 (((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(R!12, C1)) | (~incident_c(R!12, C2))))) | incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(184,plain,
% 0.20/0.47 (incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.20/0.47 tff(185,plain,
% 0.20/0.47 (^[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))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(186,plain,
% 0.20/0.47 (![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)))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[185])).
% 0.20/0.47 tff(187,plain,
% 0.20/0.47 (^[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))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(188,plain,
% 0.20/0.47 (![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)))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[187])).
% 0.20/0.47 tff(189,plain,
% 0.20/0.47 (![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)))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[188, 186])).
% 0.20/0.47 tff(190,plain,
% 0.20/0.47 (^[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)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(191,plain,
% 0.20/0.47 (![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)))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[190])).
% 0.20/0.47 tff(192,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(193,plain,
% 0.20/0.47 (^[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))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(194,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[193])).
% 0.20/0.47 tff(195,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')).
% 0.20/0.47 tff(196,plain,
% 0.20/0.47 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.20/0.47 tff(197,plain,
% 0.20/0.47 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.20/0.47 tff(198,plain,(
% 0.20/0.47 ![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)))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[197])).
% 0.20/0.47 tff(199,plain,
% 0.20/0.47 (![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)))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[198, 191])).
% 0.20/0.47 tff(200,plain,
% 0.20/0.47 (![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)))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[199, 189])).
% 0.20/0.47 tff(201,plain,
% 0.20/0.47 ((~![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(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)) | ![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15)))) | (~(part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15) | (~((~incident_c(tptp_fun_P_0(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(tptp_fun_P_0(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15), C!15)))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(202,plain,
% 0.20/0.47 (~((~((~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)) | ![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15)))) | (~(part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15) | (~((~incident_c(tptp_fun_P_0(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(tptp_fun_P_0(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15), C!15))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[201, 200])).
% 0.20/0.47 tff(203,plain,
% 0.20/0.47 (((~((~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)) | ![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15)))) | (~(part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15) | (~((~incident_c(tptp_fun_P_0(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(tptp_fun_P_0(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15), C!15)))))) | ((~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)) | ![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(204,plain,
% 0.20/0.47 ((~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)) | ![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.20/0.47 tff(205,plain,
% 0.20/0.47 (((P!14 = R!12) | (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15))) | part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(206,plain,
% 0.20/0.47 (part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[205, 40])).
% 0.20/0.47 tff(207,plain,
% 0.20/0.47 ((~((~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)) | ![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15)))) | (~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)) | ![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(208,plain,
% 0.20/0.47 ((~((~part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)) | ![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15)))) | ![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[207, 206])).
% 0.20/0.47 tff(209,plain,
% 0.20/0.47 (![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[208, 204])).
% 0.20/0.47 tff(210,plain,
% 0.20/0.47 (((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15))) | ((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(R!12, C!15))) <=> ((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15))) | (~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(R!12, C!15))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(211,plain,
% 0.20/0.47 ((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15))) | ((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(R!12, C!15))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(212,plain,
% 0.20/0.47 ((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15))) | (~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(R!12, C!15)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.20/0.47 tff(213,plain,
% 0.20/0.47 (incident_c(R!12, C!15)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[212, 209, 184])).
% 0.20/0.47 tff(214,plain,
% 0.20/0.47 (((~incident_c(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | end_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(215,plain,
% 0.20/0.47 (incident_c(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[214, 144])).
% 0.20/0.47 tff(216,plain,
% 0.20/0.47 (((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15))) | ((~incident_c(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(Q!13, C!15))) <=> ((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15))) | (~incident_c(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(Q!13, C!15))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(217,plain,
% 0.20/0.47 ((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15))) | ((~incident_c(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(Q!13, C!15))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(218,plain,
% 0.20/0.47 ((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15))) | (~incident_c(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(Q!13, C!15)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.20/0.47 tff(219,plain,
% 0.20/0.47 (incident_c(Q!13, C!15)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[218, 209, 215])).
% 0.20/0.47 tff(220,plain,
% 0.20/0.47 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))) | (~incident_c(P!14, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)) | part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)))))) | (~((~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, C1)) | (~incident_c(P!14, C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))) | (~incident_c(P!14, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)) | part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)))))) | (~((~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, C1)) | (~incident_c(P!14, C2)))))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(221,plain,
% 0.20/0.47 ((~((~(end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~(part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))) | (~incident_c(P!14, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))))))) | (~((~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, C1)) | (~incident_c(P!14, C2)))))))))) <=> (~((~(end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))) | (~incident_c(P!14, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)) | part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)))))) | (~((~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, C1)) | (~incident_c(P!14, C2))))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(222,plain,
% 0.20/0.47 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~(part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))) | (~incident_c(P!14, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))))))) | (~((~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, C1)) | (~incident_c(P!14, C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))) | (~incident_c(P!14, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)) | part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)))))) | (~((~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, C1)) | (~incident_c(P!14, C2)))))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[221])).
% 0.20/0.48 tff(223,plain,
% 0.20/0.48 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~(part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))) | (~incident_c(P!14, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))))))) | (~((~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, C1)) | (~incident_c(P!14, C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))) | (~incident_c(P!14, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)) | part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)))))) | (~((~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, C1)) | (~incident_c(P!14, C2)))))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[222, 220])).
% 0.20/0.48 tff(224,plain,
% 0.20/0.48 ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~(part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))) | (~incident_c(P!14, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))))))) | (~((~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, C1)) | (~incident_c(P!14, C2))))))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(225,plain,
% 0.20/0.48 ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))) | (~incident_c(P!14, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)) | part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)))))) | (~((~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, C1)) | (~incident_c(P!14, C2))))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.20/0.48 tff(226,plain,
% 0.20/0.48 (~((~(end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))) | (~incident_c(P!14, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)) | part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)))))) | (~((~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, C1)) | (~incident_c(P!14, C2)))))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[225, 170])).
% 0.20/0.48 tff(227,plain,
% 0.20/0.48 (((~(end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) | (~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))) | (~incident_c(P!14, tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)) | part_of(tptp_fun_C2_2(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14), tptp_fun_C1_3(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), P!14)))))) | (~((~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, C1)) | (~incident_c(P!14, C2))))))))) | ((~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, C1)) | (~incident_c(P!14, C2)))))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(228,plain,
% 0.20/0.48 ((~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, C1)) | (~incident_c(P!14, C2))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.20/0.48 tff(229,plain,
% 0.20/0.48 ((~((~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, C1)) | (~incident_c(P!14, C2)))))))) | (~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, C1)) | (~incident_c(P!14, C2))))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(230,plain,
% 0.20/0.48 ((~((~end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, C1)) | (~incident_c(P!14, C2)))))))) | (~((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, C1)) | (~incident_c(P!14, C2))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[229, 99])).
% 0.20/0.48 tff(231,plain,
% 0.20/0.48 (~((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, C1)) | (~incident_c(P!14, C2)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[230, 228])).
% 0.20/0.48 tff(232,plain,
% 0.20/0.48 (((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~part_of(C2, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~incident_c(P!14, C1)) | (~incident_c(P!14, C2))))) | incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(233,plain,
% 0.20/0.48 (incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[232, 231])).
% 0.20/0.48 tff(234,plain,
% 0.20/0.48 (((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15))) | ((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P!14, C!15))) <=> ((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15))) | (~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P!14, C!15))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(235,plain,
% 0.20/0.48 ((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15))) | ((~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P!14, C!15))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(236,plain,
% 0.20/0.48 ((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P, C!15))) | (~incident_c(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | incident_c(P!14, C!15)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.20/0.48 tff(237,plain,
% 0.20/0.48 (incident_c(P!14, C!15)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[236, 209, 233])).
% 0.20/0.48 tff(238,plain,
% 0.20/0.48 ((~(~((P!14 = Q!13) | (Q!13 = R!12) | (P!14 = R!12) | (~incident_c(P!14, C!15)) | (~incident_c(Q!13, C!15)) | (~incident_c(R!12, C!15))))) <=> ((P!14 = Q!13) | (Q!13 = R!12) | (P!14 = R!12) | (~incident_c(P!14, C!15)) | (~incident_c(Q!13, C!15)) | (~incident_c(R!12, C!15)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(239,plain,
% 0.20/0.48 ((incident_c(P!14, C!15) & incident_c(Q!13, C!15) & incident_c(R!12, C!15) & (~(P!14 = Q!13)) & (~(Q!13 = R!12)) & (~(P!14 = R!12))) <=> (~((P!14 = Q!13) | (Q!13 = R!12) | (P!14 = R!12) | (~incident_c(P!14, C!15)) | (~incident_c(Q!13, C!15)) | (~incident_c(R!12, C!15))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(240,plain,
% 0.20/0.48 ((~(incident_c(P!14, C!15) & incident_c(Q!13, C!15) & incident_c(R!12, C!15) & (~(P!14 = Q!13)) & (~(Q!13 = R!12)) & (~(P!14 = R!12)))) <=> (~(~((P!14 = Q!13) | (Q!13 = R!12) | (P!14 = R!12) | (~incident_c(P!14, C!15)) | (~incident_c(Q!13, C!15)) | (~incident_c(R!12, C!15)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[239])).
% 0.20/0.48 tff(241,plain,
% 0.20/0.48 ((~(incident_c(P!14, C!15) & incident_c(Q!13, C!15) & incident_c(R!12, C!15) & (~(P!14 = Q!13)) & (~(Q!13 = R!12)) & (~(P!14 = R!12)))) <=> ((P!14 = Q!13) | (Q!13 = R!12) | (P!14 = R!12) | (~incident_c(P!14, C!15)) | (~incident_c(Q!13, C!15)) | (~incident_c(R!12, C!15)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[240, 238])).
% 0.20/0.48 tff(242,plain,
% 0.20/0.48 (~(incident_c(P!14, C!15) & incident_c(Q!13, C!15) & incident_c(R!12, C!15) & (~(P!14 = Q!13)) & (~(Q!13 = R!12)) & (~(P!14 = R!12)))),
% 0.20/0.48 inference(or_elim,[status(thm)],[36])).
% 0.20/0.48 tff(243,plain,
% 0.20/0.48 ((P!14 = Q!13) | (Q!13 = R!12) | (P!14 = R!12) | (~incident_c(P!14, C!15)) | (~incident_c(Q!13, C!15)) | (~incident_c(R!12, C!15))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.20/0.48 tff(244,plain,
% 0.20/0.48 ((P!14 = Q!13) | (Q!13 = R!12)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[243, 102, 237, 219, 213])).
% 0.20/0.48 tff(245,plain,
% 0.20/0.48 (Q!13 = R!12),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[244, 148])).
% 0.20/0.48 tff(246,plain,
% 0.20/0.48 (inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) <=> inner_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[245])).
% 0.20/0.48 tff(247,plain,
% 0.20/0.48 (inner_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) <=> inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.48 inference(symmetry,[status(thm)],[246])).
% 0.20/0.48 tff(248,plain,
% 0.20/0.48 ((~inner_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) <=> (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[247])).
% 0.20/0.48 tff(249,plain,
% 0.20/0.48 ((~![P: $i, C: $i] : (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C)))) | (~(((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) <=> inner_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(250,plain,
% 0.20/0.48 (~(((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) <=> inner_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[249, 139])).
% 0.20/0.48 tff(251,plain,
% 0.20/0.48 (((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(252,plain,
% 0.20/0.49 ((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[251, 66])).
% 0.20/0.49 tff(253,plain,
% 0.20/0.49 ((((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) <=> inner_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))) | (~inner_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(254,plain,
% 0.20/0.49 ((((~incident_c(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) <=> inner_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))) | (~inner_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[253, 252])).
% 0.20/0.49 tff(255,plain,
% 0.20/0.49 (~inner_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[254, 250])).
% 0.20/0.49 tff(256,plain,
% 0.20/0.49 (~inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[255, 248])).
% 0.20/0.49 tff(257,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[42, 256])).
% 0.20/0.49 % SZS output end Proof
% 0.20/0.49 % E exiting
%------------------------------------------------------------------------------