%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO112+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 0.19s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO112+1 : TPTP v9.0.0. Released v2.4.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 14:22:33 EDT 2025
% 0.19/0.34 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(inner_point_type, type, (
% 0.19/0.39 inner_point: ( $i * $i ) > $o)).
% 0.19/0.39 tff(sum_type, type, (
% 0.19/0.39 sum: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_C2_7_type, type, (
% 0.19/0.39 tptp_fun_C2_7: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_Cpp_11_type, type, (
% 0.19/0.39 tptp_fun_Cpp_11: ( $i * $i * $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_C_15_type, type, (
% 0.19/0.39 tptp_fun_C_15: $i)).
% 0.19/0.39 tff(tptp_fun_P_14_type, type, (
% 0.19/0.39 tptp_fun_P_14: $i)).
% 0.19/0.39 tff(tptp_fun_Q_13_type, type, (
% 0.19/0.39 tptp_fun_Q_13: $i)).
% 0.19/0.39 tff(tptp_fun_R_12_type, type, (
% 0.19/0.39 tptp_fun_R_12: $i)).
% 0.19/0.39 tff(tptp_fun_C1_8_type, type, (
% 0.19/0.39 tptp_fun_C1_8: ( $i * $i ) > $i)).
% 0.19/0.39 tff(meet_type, type, (
% 0.19/0.39 meet: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(part_of_type, type, (
% 0.19/0.39 part_of: ( $i * $i ) > $o)).
% 0.19/0.39 tff(end_point_type, type, (
% 0.19/0.39 end_point: ( $i * $i ) > $o)).
% 0.19/0.39 tff(between_c_type, type, (
% 0.19/0.39 between_c: ( $i * $i * $i * $i ) > $o)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[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))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (^[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))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (^[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)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (^[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))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (![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)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (^[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)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.39 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/sandbox/benchmark/Axioms/GEO004+1.ax','between_c_defn')).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.39 tff(16,plain,(
% 0.19/0.39 ![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))))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[15])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (![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)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 5])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (((~![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)))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 ((~((~((~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))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (((~![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)))))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[21])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (((~![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)))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[22, 20])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 ((~![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)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 ((~![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))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (~((~((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)))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[25, 19])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (((~((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)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 ((~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))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 ((~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | between_c(C, R, Q, P))) <=> (~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | between_c(C, R, Q, P)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 ((~![C: $i, P: $i, Q: $i, R: $i] : (between_c(C, P, Q, R) => between_c(C, R, Q, P))) <=> (~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | between_c(C, R, Q, P)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(31,axiom,(~![C: $i, P: $i, Q: $i, R: $i] : (between_c(C, P, Q, R) => between_c(C, R, Q, P))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','theorem_3_8_2')).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | between_c(C, R, Q, P))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | between_c(C, R, Q, P))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[32, 29])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | between_c(C, R, Q, P))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | between_c(C, R, Q, P))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[34, 29])).
% 0.19/0.40 tff(36,plain,(
% 0.19/0.40 ~((~between_c(C!15, P!14, Q!13, R!12)) | between_c(C!15, R!12, Q!13, P!14))),
% 0.19/0.40 inference(skolemize,[status(sab)],[35])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (between_c(C!15, P!14, Q!13, R!12)),
% 0.19/0.40 inference(or_elim,[status(thm)],[36])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 ((~((~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))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 ((~((~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))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (~((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)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[39, 28])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (((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))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (^[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))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (![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)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (^[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))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (![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)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (![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))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (![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))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.41 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/sandbox/benchmark/Axioms/GEO004+0.ax','c4')).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (![C: $i, P: $i] : ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (![C: $i, P: $i] : ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.19/0.41 tff(53,plain,(
% 0.19/0.41 ![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)))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[52])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (![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)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (![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)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[54, 44])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (((~![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))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 ((~![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))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 ((~![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)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (~((~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))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[58, 55, 42])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (((~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))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (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)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (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)),
% 0.19/0.41 inference(symmetry,[status(thm)],[61])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (inner_point(Q!13, 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)))) <=> inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[62])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (inner_point(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)) <=> inner_point(Q!13, 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))))),
% 0.19/0.41 inference(symmetry,[status(thm)],[63])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (inner_point(Q!13, 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))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[42, 64])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (part_of(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!15) <=> part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[62])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15) <=> part_of(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!15)),
% 0.19/0.41 inference(symmetry,[status(thm)],[66])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (((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)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (part_of(tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15), C!15)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[68, 40])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (part_of(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!15)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[69, 67])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (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))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[62])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (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))))),
% 0.19/0.41 inference(symmetry,[status(thm)],[71])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (((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))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (end_point(R!12, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[73, 40])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (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))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[74, 72])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (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))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[62])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (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))))),
% 0.19/0.41 inference(symmetry,[status(thm)],[76])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (((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))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (end_point(P!14, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[78, 40])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (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))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[79, 77])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (((~![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)))))))) | (~((~((R!12 = P!14) | between_c(C!15, R!12, Q!13, P!14) | ![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, R!12, Q!13, P!14)) | (~((R!12 = P!14) | (~inner_point(Q!13, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~part_of(tptp_fun_Cpp_11(P!14, Q!13, R!12, 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)))))))) | (~((~((R!12 = P!14) | between_c(C!15, R!12, Q!13, P!14) | ![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, R!12, Q!13, P!14)) | (~((R!12 = P!14) | (~inner_point(Q!13, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~part_of(tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15), C!15)))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 ((~((~((~between_c(C!15, R!12, Q!13, P!14)) | (~((R!12 = P!14) | (~part_of(tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15), C!15)) | (~end_point(R!12, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~inner_point(Q!13, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))))))) | (~((R!12 = P!14) | between_c(C!15, R!12, Q!13, P!14) | ![Cpp: $i] : ((~end_point(P!14, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(R!12, Cpp)) | (~inner_point(Q!13, Cpp))))))) <=> (~((~((R!12 = P!14) | between_c(C!15, R!12, Q!13, P!14) | ![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, R!12, Q!13, P!14)) | (~((R!12 = P!14) | (~inner_point(Q!13, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~part_of(tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15), C!15))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (((~![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, R!12, Q!13, P!14)) | (~((R!12 = P!14) | (~part_of(tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15), C!15)) | (~end_point(R!12, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~inner_point(Q!13, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))))))) | (~((R!12 = P!14) | between_c(C!15, R!12, Q!13, P!14) | ![Cpp: $i] : ((~end_point(P!14, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(R!12, 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)))))))) | (~((~((R!12 = P!14) | between_c(C!15, R!12, Q!13, P!14) | ![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, R!12, Q!13, P!14)) | (~((R!12 = P!14) | (~inner_point(Q!13, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~part_of(tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15), C!15)))))))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[82])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 (((~![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, R!12, Q!13, P!14)) | (~((R!12 = P!14) | (~part_of(tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15), C!15)) | (~end_point(R!12, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~inner_point(Q!13, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))))))) | (~((R!12 = P!14) | between_c(C!15, R!12, Q!13, P!14) | ![Cpp: $i] : ((~end_point(P!14, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(R!12, 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)))))))) | (~((~((R!12 = P!14) | between_c(C!15, R!12, Q!13, P!14) | ![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, R!12, Q!13, P!14)) | (~((R!12 = P!14) | (~inner_point(Q!13, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~part_of(tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15), C!15)))))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[83, 81])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 ((~![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, R!12, Q!13, P!14)) | (~((R!12 = P!14) | (~part_of(tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15), C!15)) | (~end_point(R!12, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~inner_point(Q!13, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))))))) | (~((R!12 = P!14) | between_c(C!15, R!12, Q!13, P!14) | ![Cpp: $i] : ((~end_point(P!14, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(R!12, Cpp)) | (~inner_point(Q!13, Cpp)))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 ((~![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)))))))) | (~((~((R!12 = P!14) | between_c(C!15, R!12, Q!13, P!14) | ![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, R!12, Q!13, P!14)) | (~((R!12 = P!14) | (~inner_point(Q!13, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~part_of(tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15), C!15))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 (~((~((R!12 = P!14) | between_c(C!15, R!12, Q!13, P!14) | ![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, R!12, Q!13, P!14)) | (~((R!12 = P!14) | (~inner_point(Q!13, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~part_of(tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15), C!15)))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[86, 19])).
% 0.21/0.43 tff(88,plain,
% 0.21/0.43 (((~((R!12 = P!14) | between_c(C!15, R!12, Q!13, P!14) | ![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, R!12, Q!13, P!14)) | (~((R!12 = P!14) | (~inner_point(Q!13, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~end_point(P!14, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~end_point(R!12, tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15))) | (~part_of(tptp_fun_Cpp_11(P!14, Q!13, R!12, C!15), C!15))))))) | ((R!12 = P!14) | between_c(C!15, R!12, Q!13, P!14) | ![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 ((R!12 = P!14) | between_c(C!15, R!12, Q!13, P!14) | ![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.21/0.43 tff(90,plain,
% 0.21/0.43 ((R!12 = P!14) <=> (P!14 = R!12)),
% 0.21/0.43 inference(commutativity,[status(thm)],[])).
% 0.21/0.43 tff(91,plain,
% 0.21/0.43 ((P!14 = R!12) <=> (R!12 = P!14)),
% 0.21/0.43 inference(symmetry,[status(thm)],[90])).
% 0.21/0.43 tff(92,plain,
% 0.21/0.43 ((~(P!14 = R!12)) <=> (~(R!12 = P!14))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[91])).
% 0.21/0.43 tff(93,plain,
% 0.21/0.43 (((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))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(94,plain,
% 0.21/0.43 (~(P!14 = R!12)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[93, 40])).
% 0.21/0.43 tff(95,plain,
% 0.21/0.43 (~(R!12 = P!14)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[94, 92])).
% 0.21/0.43 tff(96,plain,
% 0.21/0.43 (~between_c(C!15, R!12, Q!13, P!14)),
% 0.21/0.43 inference(or_elim,[status(thm)],[36])).
% 0.21/0.43 tff(97,plain,
% 0.21/0.43 ((~((R!12 = P!14) | between_c(C!15, R!12, Q!13, P!14) | ![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp))))) | (R!12 = P!14) | between_c(C!15, R!12, Q!13, P!14) | ![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(98,plain,
% 0.21/0.43 ((~((R!12 = P!14) | between_c(C!15, R!12, Q!13, P!14) | ![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp))))) | (R!12 = P!14) | ![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.21/0.43 tff(99,plain,
% 0.21/0.43 (![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[98, 95, 89])).
% 0.21/0.43 tff(100,plain,
% 0.21/0.43 (((~![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp)))) | ((~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))))) | (~part_of(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!15)) | (~inner_point(Q!13, 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))))))) <=> ((~![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp)))) | (~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))))) | (~part_of(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!15)) | (~inner_point(Q!13, 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))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(101,plain,
% 0.21/0.43 (((~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))))) | (~part_of(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!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))))) | (~inner_point(Q!13, 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, 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))))) | (~part_of(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!15)) | (~inner_point(Q!13, 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))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(102,plain,
% 0.21/0.43 (((~![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp)))) | ((~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))))) | (~part_of(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!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))))) | (~inner_point(Q!13, 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))))))) <=> ((~![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp)))) | ((~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))))) | (~part_of(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!15)) | (~inner_point(Q!13, 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)))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[101])).
% 0.21/0.43 tff(103,plain,
% 0.21/0.43 (((~![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp)))) | ((~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))))) | (~part_of(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!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))))) | (~inner_point(Q!13, 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))))))) <=> ((~![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp)))) | (~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))))) | (~part_of(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!15)) | (~inner_point(Q!13, 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))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[102, 100])).
% 0.21/0.43 tff(104,plain,
% 0.21/0.43 ((~![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp)))) | ((~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))))) | (~part_of(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!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))))) | (~inner_point(Q!13, 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))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(105,plain,
% 0.21/0.43 ((~![Cpp: $i] : ((~end_point(R!12, Cpp)) | (~part_of(Cpp, C!15)) | (~end_point(P!14, Cpp)) | (~inner_point(Q!13, Cpp)))) | (~end_point(R!12, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (~end_point(P!14, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (~part_of(sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))), C!15)) | (~inner_point(Q!13, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.21/0.43 tff(106,plain,
% 0.21/0.43 ((~end_point(R!12, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (~end_point(P!14, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))))) | (~part_of(sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15))), C!15)) | (~inner_point(Q!13, sum(tptp_fun_C1_8(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)), tptp_fun_C2_7(Q!13, tptp_fun_Cpp_11(R!12, Q!13, P!14, C!15)))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[105, 99])).
% 0.21/0.43 tff(107,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[106, 80, 75, 70, 65])).
% 0.21/0.44 % SZS output end Proof
% 0.21/0.44 % E exiting
%------------------------------------------------------------------------------