TSTP Solution File: GEO111+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO111+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 : Fri Sep 16 20:34:55 EDT 2022
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEO111+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 05:49:19 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 tff(inner_point_type, type, (
% 0.21/0.43 inner_point: ( $i * $i ) > $o)).
% 0.21/0.43 tff(tptp_fun_Cpp_12_type, type, (
% 0.21/0.43 tptp_fun_Cpp_12: ( $i * $i * $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_C_16_type, type, (
% 0.21/0.43 tptp_fun_C_16: $i)).
% 0.21/0.43 tff(tptp_fun_P_15_type, type, (
% 0.21/0.43 tptp_fun_P_15: $i)).
% 0.21/0.43 tff(tptp_fun_Q_14_type, type, (
% 0.21/0.43 tptp_fun_Q_14: $i)).
% 0.21/0.43 tff(tptp_fun_R_13_type, type, (
% 0.21/0.43 tptp_fun_R_13: $i)).
% 0.21/0.43 tff(sum_type, type, (
% 0.21/0.43 sum: ( $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_C2_7_type, type, (
% 0.21/0.43 tptp_fun_C2_7: ( $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_C1_8_type, type, (
% 0.21/0.43 tptp_fun_C1_8: ( $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_Q_9_type, type, (
% 0.21/0.43 tptp_fun_Q_9: ( $i * $i ) > $i)).
% 0.21/0.43 tff(meet_type, type, (
% 0.21/0.43 meet: ( $i * $i * $i ) > $o)).
% 0.21/0.43 tff(end_point_type, type, (
% 0.21/0.43 end_point: ( $i * $i ) > $o)).
% 0.21/0.43 tff(part_of_type, type, (
% 0.21/0.43 part_of: ( $i * $i ) > $o)).
% 0.21/0.43 tff(between_c_type, type, (
% 0.21/0.43 between_c: ( $i * $i * $i * $i ) > $o)).
% 0.21/0.43 tff(incident_c_type, type, (
% 0.21/0.43 incident_c: ( $i * $i ) > $o)).
% 0.21/0.43 tff(tptp_fun_P_0_type, type, (
% 0.21/0.43 tptp_fun_P_0: ( $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_C2_2_type, type, (
% 0.21/0.43 tptp_fun_C2_2: ( $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_C1_3_type, type, (
% 0.21/0.43 tptp_fun_C1_3: ( $i * $i ) > $i)).
% 0.21/0.43 tff(1,plain,
% 0.21/0.43 (^[C: $i, P: $i, Q: $i, R: $i] : refl((~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_12(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_12(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_12(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_12(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_12(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_12(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_12(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_12(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))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(2,plain,
% 0.21/0.43 (![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_12(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_12(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_12(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_12(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_12(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_12(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_12(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_12(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)))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.43 tff(3,plain,
% 0.21/0.43 (^[C: $i, P: $i, Q: $i, R: $i] : rewrite((~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_12(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_12(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_12(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_12(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_12(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_12(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_12(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_12(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))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(4,plain,
% 0.21/0.43 (![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_12(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_12(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_12(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_12(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_12(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_12(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_12(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_12(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)))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.43 tff(5,plain,
% 0.21/0.43 (![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_12(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_12(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_12(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_12(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_12(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_12(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_12(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_12(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)))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[4, 2])).
% 0.21/0.43 tff(6,plain,
% 0.21/0.43 (^[C: $i, P: $i, Q: $i, R: $i] : trans(monotonicity(rewrite(((~between_c(C, P, Q, R)) | ((~(P = R)) & part_of(tptp_fun_Cpp_12(R, Q, P, C), C) & end_point(P, tptp_fun_Cpp_12(R, Q, P, C)) & end_point(R, tptp_fun_Cpp_12(R, Q, P, C)) & inner_point(Q, tptp_fun_Cpp_12(R, Q, P, C)))) <=> ((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_12(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_12(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_12(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_12(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_12(R, Q, P, C), C) & end_point(P, tptp_fun_Cpp_12(R, Q, P, C)) & end_point(R, tptp_fun_Cpp_12(R, Q, P, C)) & inner_point(Q, tptp_fun_Cpp_12(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_12(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_12(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_12(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_12(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_12(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_12(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_12(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_12(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_12(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_12(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_12(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_12(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_12(R, Q, P, C), C) & end_point(P, tptp_fun_Cpp_12(R, Q, P, C)) & end_point(R, tptp_fun_Cpp_12(R, Q, P, C)) & inner_point(Q, tptp_fun_Cpp_12(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_12(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_12(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_12(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_12(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)))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(7,plain,
% 0.21/0.44 (![C: $i, P: $i, Q: $i, R: $i] : (((~between_c(C, P, Q, R)) | ((~(P = R)) & part_of(tptp_fun_Cpp_12(R, Q, P, C), C) & end_point(P, tptp_fun_Cpp_12(R, Q, P, C)) & end_point(R, tptp_fun_Cpp_12(R, Q, P, C)) & inner_point(Q, tptp_fun_Cpp_12(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_12(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_12(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_12(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_12(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)))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.44 tff(8,plain,
% 0.21/0.44 (^[C: $i, P: $i, Q: $i, R: $i] : rewrite((((~between_c(C, P, Q, R)) | ((~(P = R)) & (part_of(tptp_fun_Cpp_12(R, Q, P, C), C) & end_point(P, tptp_fun_Cpp_12(R, Q, P, C)) & end_point(R, tptp_fun_Cpp_12(R, Q, P, C)) & inner_point(Q, tptp_fun_Cpp_12(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_12(R, Q, P, C), C) & end_point(P, tptp_fun_Cpp_12(R, Q, P, C)) & end_point(R, tptp_fun_Cpp_12(R, Q, P, C)) & inner_point(Q, tptp_fun_Cpp_12(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))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(9,plain,
% 0.21/0.44 (![C: $i, P: $i, Q: $i, R: $i] : (((~between_c(C, P, Q, R)) | ((~(P = R)) & (part_of(tptp_fun_Cpp_12(R, Q, P, C), C) & end_point(P, tptp_fun_Cpp_12(R, Q, P, C)) & end_point(R, tptp_fun_Cpp_12(R, Q, P, C)) & inner_point(Q, tptp_fun_Cpp_12(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_12(R, Q, P, C), C) & end_point(P, tptp_fun_Cpp_12(R, Q, P, C)) & end_point(R, tptp_fun_Cpp_12(R, Q, P, C)) & inner_point(Q, tptp_fun_Cpp_12(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)))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.44 tff(10,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(11,plain,
% 0.21/0.44 (^[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)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(12,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[11])).
% 0.21/0.44 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')).
% 0.21/0.44 tff(14,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.44 tff(15,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.21/0.44 tff(16,plain,(
% 0.21/0.44 ![C: $i, P: $i, Q: $i, R: $i] : (((~between_c(C, P, Q, R)) | ((~(P = R)) & (part_of(tptp_fun_Cpp_12(R, Q, P, C), C) & end_point(P, tptp_fun_Cpp_12(R, Q, P, C)) & end_point(R, tptp_fun_Cpp_12(R, Q, P, C)) & inner_point(Q, tptp_fun_Cpp_12(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))))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[15])).
% 0.21/0.44 tff(17,plain,
% 0.21/0.44 (![C: $i, P: $i, Q: $i, R: $i] : (((~between_c(C, P, Q, R)) | ((~(P = R)) & part_of(tptp_fun_Cpp_12(R, Q, P, C), C) & end_point(P, tptp_fun_Cpp_12(R, Q, P, C)) & end_point(R, tptp_fun_Cpp_12(R, Q, P, C)) & inner_point(Q, tptp_fun_Cpp_12(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)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.21/0.44 tff(18,plain,
% 0.21/0.44 (![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_12(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_12(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_12(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_12(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)))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.21/0.44 tff(19,plain,
% 0.21/0.44 (![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_12(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_12(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_12(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_12(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)))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[18, 5])).
% 0.21/0.44 tff(20,plain,
% 0.21/0.44 ((~![C: $i, P: $i, Q: $i, R: $i] : (~((~((~between_c(C, P, Q, R)) | (~((P = R) | (~part_of(tptp_fun_Cpp_12(R, Q, P, C), C)) | (~end_point(P, tptp_fun_Cpp_12(R, Q, P, C))) | (~end_point(R, tptp_fun_Cpp_12(R, Q, P, C))) | (~inner_point(Q, tptp_fun_Cpp_12(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!16, P!15, Q!14, R!13)) | (~((P!15 = R!13) | (~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | (~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))))) | (~((P!15 = R!13) | between_c(C!16, P!15, Q!14, R!13) | ![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp)))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(21,plain,
% 0.21/0.44 (~((~((~between_c(C!16, P!15, Q!14, R!13)) | (~((P!15 = R!13) | (~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | (~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))))) | (~((P!15 = R!13) | between_c(C!16, P!15, Q!14, R!13) | ![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.21/0.44 tff(22,plain,
% 0.21/0.44 (((~((~between_c(C!16, P!15, Q!14, R!13)) | (~((P!15 = R!13) | (~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | (~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))))) | (~((P!15 = R!13) | between_c(C!16, P!15, Q!14, R!13) | ![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp)))))) | ((~between_c(C!16, P!15, Q!14, R!13)) | (~((P!15 = R!13) | (~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | (~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(23,plain,
% 0.21/0.44 ((~between_c(C!16, P!15, Q!14, R!13)) | (~((P!15 = R!13) | (~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | (~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.21/0.44 tff(24,plain,
% 0.21/0.44 ((~![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)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(25,plain,
% 0.21/0.44 ((~![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)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(26,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/sandbox/benchmark/theBenchmark.p','theorem_3_8_1')).
% 0.21/0.44 tff(27,plain,
% 0.21/0.44 (~![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))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.44 tff(28,plain,
% 0.21/0.44 (~![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))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.21/0.44 tff(29,plain,
% 0.21/0.44 (~![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))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.21/0.44 tff(30,plain,
% 0.21/0.44 (~![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))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.21/0.44 tff(31,plain,
% 0.21/0.44 (~![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))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[30, 24])).
% 0.21/0.44 tff(32,plain,
% 0.21/0.44 (~![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))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.21/0.44 tff(33,plain,
% 0.21/0.44 (~![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))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[32, 24])).
% 0.21/0.45 tff(34,plain,(
% 0.21/0.45 ~((~between_c(C!16, P!15, Q!14, R!13)) | (incident_c(P!15, C!16) & incident_c(Q!14, C!16) & incident_c(R!13, C!16) & (~(P!15 = Q!14)) & (~(Q!14 = R!13)) & (~(P!15 = R!13))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[33])).
% 0.21/0.45 tff(35,plain,
% 0.21/0.45 (between_c(C!16, P!15, Q!14, R!13)),
% 0.21/0.45 inference(or_elim,[status(thm)],[34])).
% 0.21/0.45 tff(36,plain,
% 0.21/0.45 ((~((~between_c(C!16, P!15, Q!14, R!13)) | (~((P!15 = R!13) | (~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | (~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))))) | (~between_c(C!16, P!15, Q!14, R!13)) | (~((P!15 = R!13) | (~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | (~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(37,plain,
% 0.21/0.45 ((~((~between_c(C!16, P!15, Q!14, R!13)) | (~((P!15 = R!13) | (~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | (~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))))) | (~((P!15 = R!13) | (~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | (~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.21/0.45 tff(38,plain,
% 0.21/0.45 (~((P!15 = R!13) | (~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | (~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[37, 23])).
% 0.21/0.45 tff(39,plain,
% 0.21/0.45 (((P!15 = R!13) | (~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | (~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))) | inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(40,plain,
% 0.21/0.45 (inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.21/0.45 tff(41,plain,
% 0.21/0.45 (^[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))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(42,plain,
% 0.21/0.45 (![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)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[41])).
% 0.21/0.45 tff(43,plain,
% 0.21/0.45 (^[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))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(44,plain,
% 0.21/0.45 (![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)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.45 tff(45,plain,
% 0.21/0.45 (![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))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(46,plain,
% 0.21/0.45 (^[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)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(47,plain,
% 0.21/0.45 (![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))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.45 tff(48,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')).
% 0.21/0.45 tff(49,plain,
% 0.21/0.45 (![C: $i, P: $i] : ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.21/0.45 tff(50,plain,
% 0.21/0.45 (![C: $i, P: $i] : ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.21/0.45 tff(51,plain,(
% 0.21/0.45 ![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)))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[50])).
% 0.21/0.45 tff(52,plain,
% 0.21/0.45 (![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)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.21/0.45 tff(53,plain,
% 0.21/0.45 (![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)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[52, 42])).
% 0.21/0.45 tff(54,plain,
% 0.21/0.45 (((~![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!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~meet(Q!14, tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))) | (~(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16) = sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))))))) <=> ((~![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!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~meet(Q!14, tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))) | (~(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16) = sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(55,plain,
% 0.21/0.45 ((~![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!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~meet(Q!14, tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))) | (~(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16) = sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(56,plain,
% 0.21/0.45 ((~![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!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~meet(Q!14, tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))) | (~(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16) = sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.45 tff(57,plain,
% 0.21/0.45 (~((~meet(Q!14, tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))) | (~(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16) = sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[56, 53, 40])).
% 0.21/0.45 tff(58,plain,
% 0.21/0.45 (((~meet(Q!14, tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))) | (~(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16) = sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))))) | (tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16) = sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(59,plain,
% 0.21/0.45 (tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16) = sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.21/0.45 tff(60,plain,
% 0.21/0.45 ((R!13 = P!15) <=> (P!15 = R!13)),
% 0.21/0.45 inference(commutativity,[status(thm)],[])).
% 0.21/0.45 tff(61,plain,
% 0.21/0.45 ((P!15 = R!13) <=> (R!13 = P!15)),
% 0.21/0.45 inference(symmetry,[status(thm)],[60])).
% 0.21/0.45 tff(62,plain,
% 0.21/0.45 ((~(P!15 = R!13)) <=> (~(R!13 = P!15))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[61])).
% 0.21/0.45 tff(63,plain,
% 0.21/0.45 (((P!15 = R!13) | (~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | (~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))) | (~(P!15 = R!13))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(64,plain,
% 0.21/0.45 (~(P!15 = R!13)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[63, 38])).
% 0.21/0.45 tff(65,plain,
% 0.21/0.45 (~(R!13 = P!15)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[64, 62])).
% 0.21/0.45 tff(66,plain,
% 0.21/0.45 (sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) = tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)),
% 0.21/0.45 inference(symmetry,[status(thm)],[59])).
% 0.21/0.45 tff(67,plain,
% 0.21/0.45 (end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))) <=> end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[66])).
% 0.21/0.45 tff(68,plain,
% 0.21/0.45 (end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) <=> end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))),
% 0.21/0.45 inference(symmetry,[status(thm)],[67])).
% 0.21/0.45 tff(69,plain,
% 0.21/0.45 (((P!15 = R!13) | (~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | (~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))) | end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(70,plain,
% 0.21/0.45 (end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[69, 38])).
% 0.21/0.45 tff(71,plain,
% 0.21/0.45 (^[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))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(72,plain,
% 0.21/0.46 (![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)))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[71])).
% 0.21/0.46 tff(73,plain,
% 0.21/0.46 (^[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))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(74,plain,
% 0.21/0.46 (![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)))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[73])).
% 0.21/0.46 tff(75,plain,
% 0.21/0.46 (![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))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(76,plain,
% 0.21/0.46 (^[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)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(77,plain,
% 0.21/0.46 (![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))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[76])).
% 0.21/0.46 tff(78,axiom,(![C: $i, P: $i] : (end_point(P, C) => ?[Q: $i] : (end_point(Q, C) & (~(P = Q))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax','c6')).
% 0.21/0.46 tff(79,plain,
% 0.21/0.46 (![C: $i, P: $i] : ((~end_point(P, C)) | ?[Q: $i] : (end_point(Q, C) & (~(P = Q))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.46 tff(80,plain,
% 0.21/0.46 (![C: $i, P: $i] : ((~end_point(P, C)) | ?[Q: $i] : (end_point(Q, C) & (~(P = Q))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.21/0.46 tff(81,plain,(
% 0.21/0.46 ![C: $i, P: $i] : ((~end_point(P, C)) | (end_point(tptp_fun_Q_9(P, C), C) & (~(P = tptp_fun_Q_9(P, C)))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[80])).
% 0.21/0.46 tff(82,plain,
% 0.21/0.46 (![C: $i, P: $i] : ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.21/0.46 tff(83,plain,
% 0.21/0.46 (![C: $i, P: $i] : ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[82, 72])).
% 0.21/0.46 tff(84,plain,
% 0.21/0.46 (((~![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(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (P!15 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))))) <=> ((~![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(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (P!15 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(85,plain,
% 0.21/0.46 ((~![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(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (P!15 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(86,plain,
% 0.21/0.46 ((~![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(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (P!15 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.21/0.46 tff(87,plain,
% 0.21/0.46 (~((~end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (P!15 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[86, 83, 70])).
% 0.21/0.46 tff(88,plain,
% 0.21/0.46 (((~end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (P!15 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))) | end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(89,plain,
% 0.21/0.46 (end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.21/0.46 tff(90,plain,
% 0.21/0.46 (end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[89, 68])).
% 0.21/0.46 tff(91,plain,
% 0.21/0.46 ((tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) = P!15) <=> (P!15 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))),
% 0.21/0.46 inference(commutativity,[status(thm)],[])).
% 0.21/0.46 tff(92,plain,
% 0.21/0.46 ((P!15 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) <=> (tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) = P!15)),
% 0.21/0.46 inference(symmetry,[status(thm)],[91])).
% 0.21/0.46 tff(93,plain,
% 0.21/0.46 ((~(P!15 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))) <=> (~(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) = P!15))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[92])).
% 0.21/0.46 tff(94,plain,
% 0.21/0.46 (((~end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (P!15 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))) | (~(P!15 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(95,plain,
% 0.21/0.46 (~(P!15 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[94, 87])).
% 0.21/0.46 tff(96,plain,
% 0.21/0.46 (~(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) = P!15)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[95, 93])).
% 0.21/0.46 tff(97,plain,
% 0.21/0.46 (end_point(R!13, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))) <=> end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[66])).
% 0.21/0.46 tff(98,plain,
% 0.21/0.46 (end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) <=> end_point(R!13, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))),
% 0.21/0.46 inference(symmetry,[status(thm)],[97])).
% 0.21/0.46 tff(99,plain,
% 0.21/0.46 (((P!15 = R!13) | (~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | (~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))) | end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(100,plain,
% 0.21/0.46 (end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[99, 38])).
% 0.21/0.46 tff(101,plain,
% 0.21/0.46 (end_point(R!13, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[100, 98])).
% 0.21/0.46 tff(102,plain,
% 0.21/0.46 (end_point(P!15, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))) <=> end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[66])).
% 0.21/0.46 tff(103,plain,
% 0.21/0.46 (end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) <=> end_point(P!15, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))),
% 0.21/0.46 inference(symmetry,[status(thm)],[102])).
% 0.21/0.46 tff(104,plain,
% 0.21/0.46 (end_point(P!15, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[70, 103])).
% 0.21/0.46 tff(105,plain,
% 0.21/0.46 (^[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))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(106,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[105])).
% 0.21/0.46 tff(107,plain,
% 0.21/0.46 (^[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)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(108,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[107])).
% 0.21/0.46 tff(109,plain,
% 0.21/0.46 (![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))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(110,plain,
% 0.21/0.46 (^[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))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(111,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[110])).
% 0.21/0.47 tff(112,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/sandbox/benchmark/Axioms/GEO004+0.ax','c5')).
% 0.21/0.47 tff(113,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.47 tff(114,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.21/0.47 tff(115,plain,(
% 0.21/0.47 ![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))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[114])).
% 0.21/0.47 tff(116,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.21/0.47 tff(117,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[116, 106])).
% 0.21/0.47 tff(118,plain,
% 0.21/0.47 (((~![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)))) | ((R!13 = P!15) | (~end_point(P!15, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (~end_point(R!13, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) = P!15) | (~end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (R!13 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) <=> ((~![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)))) | (R!13 = P!15) | (~end_point(P!15, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (~end_point(R!13, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) = P!15) | (~end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (R!13 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(119,plain,
% 0.21/0.47 (((tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) = P!15) | (R!13 = P!15) | (R!13 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~end_point(P!15, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (~end_point(R!13, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (~end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))))) <=> ((R!13 = P!15) | (~end_point(P!15, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (~end_point(R!13, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) = P!15) | (~end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (R!13 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(120,plain,
% 0.21/0.47 (((~![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(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) = P!15) | (R!13 = P!15) | (R!13 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~end_point(P!15, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (~end_point(R!13, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (~end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))))) <=> ((~![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)))) | ((R!13 = P!15) | (~end_point(P!15, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (~end_point(R!13, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) = P!15) | (~end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (R!13 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[119])).
% 0.21/0.47 tff(121,plain,
% 0.21/0.47 (((~![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(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) = P!15) | (R!13 = P!15) | (R!13 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~end_point(P!15, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (~end_point(R!13, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (~end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))))) <=> ((~![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)))) | (R!13 = P!15) | (~end_point(P!15, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (~end_point(R!13, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) = P!15) | (~end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (R!13 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[120, 118])).
% 0.21/0.47 tff(122,plain,
% 0.21/0.47 ((~![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(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) = P!15) | (R!13 = P!15) | (R!13 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~end_point(P!15, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (~end_point(R!13, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (~end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(123,plain,
% 0.21/0.47 ((~![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)))) | (R!13 = P!15) | (~end_point(P!15, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (~end_point(R!13, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) = P!15) | (~end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (R!13 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.21/0.48 tff(124,plain,
% 0.21/0.48 ((R!13 = P!15) | (~end_point(P!15, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (~end_point(R!13, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) = P!15) | (~end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (R!13 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[123, 117])).
% 0.21/0.48 tff(125,plain,
% 0.21/0.48 (R!13 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[124, 104, 101, 96, 90, 65])).
% 0.21/0.48 tff(126,assumption,(P!15 = Q!14), introduced(assumption)).
% 0.21/0.48 tff(127,plain,
% 0.21/0.48 (Q!14 = P!15),
% 0.21/0.48 inference(symmetry,[status(thm)],[126])).
% 0.21/0.48 tff(128,plain,
% 0.21/0.48 (end_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) <=> end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[127])).
% 0.21/0.48 tff(129,plain,
% 0.21/0.48 (end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) <=> end_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.48 inference(symmetry,[status(thm)],[128])).
% 0.21/0.48 tff(130,plain,
% 0.21/0.48 (end_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[70, 129])).
% 0.21/0.48 tff(131,plain,
% 0.21/0.48 (^[P: $i, C: $i] : refl((inner_point(P, C) <=> (~((~incident_c(P, C)) | end_point(P, C)))) <=> (inner_point(P, C) <=> (~((~incident_c(P, C)) | end_point(P, C)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(132,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[131])).
% 0.21/0.48 tff(133,plain,
% 0.21/0.48 (^[P: $i, C: $i] : rewrite((inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C)))) <=> (inner_point(P, C) <=> (~((~incident_c(P, C)) | end_point(P, C)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(134,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[133])).
% 0.21/0.48 tff(135,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(136,axiom,(![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax','inner_point_defn')).
% 0.21/0.48 tff(137,plain,
% 0.21/0.48 (![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.21/0.48 tff(138,plain,(
% 0.21/0.48 ![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[137])).
% 0.21/0.48 tff(139,plain,
% 0.21/0.48 (![P: $i, C: $i] : (inner_point(P, C) <=> (~((~incident_c(P, C)) | end_point(P, C))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.21/0.48 tff(140,plain,
% 0.21/0.48 (![P: $i, C: $i] : (inner_point(P, C) <=> (~((~incident_c(P, C)) | end_point(P, C))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.21/0.48 tff(141,plain,
% 0.21/0.48 ((~![P: $i, C: $i] : (inner_point(P, C) <=> (~((~incident_c(P, C)) | end_point(P, C))))) | (inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) <=> (~((~incident_c(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | end_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(142,plain,
% 0.21/0.48 (inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) <=> (~((~incident_c(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | end_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.21/0.48 tff(143,plain,
% 0.21/0.48 ((~(inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) <=> (~((~incident_c(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | end_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))))) | (~inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~incident_c(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | end_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(144,plain,
% 0.21/0.48 ((~(inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) <=> (~((~incident_c(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | end_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))))) | (~((~incident_c(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | end_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[143, 40])).
% 0.21/0.48 tff(145,plain,
% 0.21/0.48 (~((~incident_c(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | end_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[144, 142])).
% 0.21/0.48 tff(146,plain,
% 0.21/0.48 (((~incident_c(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | end_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~end_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(147,plain,
% 0.21/0.48 (~end_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.21/0.48 tff(148,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[147, 130])).
% 0.21/0.48 tff(149,plain,(~(P!15 = Q!14)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(150,plain,
% 0.21/0.48 (^[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))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(151,plain,
% 0.21/0.48 (![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)))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[150])).
% 0.21/0.48 tff(152,plain,
% 0.21/0.48 (^[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))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(153,plain,
% 0.21/0.48 (![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)))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[152])).
% 0.21/0.48 tff(154,plain,
% 0.21/0.48 (![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)))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[153, 151])).
% 0.21/0.48 tff(155,plain,
% 0.21/0.48 (^[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)))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(156,plain,
% 0.21/0.48 (![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)))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[155])).
% 0.21/0.48 tff(157,plain,
% 0.21/0.48 (![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)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(158,plain,
% 0.21/0.48 (^[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))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(159,plain,
% 0.21/0.48 (![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)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[158])).
% 0.21/0.48 tff(160,axiom,(![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : (incident_c(P, C1) => incident_c(P, C)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax','part_of_defn')).
% 0.21/0.48 tff(161,plain,
% 0.21/0.48 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.21/0.48 tff(162,plain,
% 0.21/0.48 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.21/0.48 tff(163,plain,(
% 0.21/0.48 ![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)))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[162])).
% 0.21/0.48 tff(164,plain,
% 0.21/0.48 (![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)))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[163, 156])).
% 0.21/0.48 tff(165,plain,
% 0.21/0.48 (![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)))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[164, 154])).
% 0.21/0.48 tff(166,plain,
% 0.21/0.48 ((~![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_12(R!13, Q!14, P!15, C!16), C!16)) | ![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16)))) | (~(part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16) | (~((~incident_c(tptp_fun_P_0(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(tptp_fun_P_0(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16), C!16)))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(167,plain,
% 0.21/0.48 (~((~((~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | ![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16)))) | (~(part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16) | (~((~incident_c(tptp_fun_P_0(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(tptp_fun_P_0(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16), C!16))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.21/0.48 tff(168,plain,
% 0.21/0.48 (((~((~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | ![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16)))) | (~(part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16) | (~((~incident_c(tptp_fun_P_0(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(tptp_fun_P_0(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16), C!16)))))) | ((~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | ![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(169,plain,
% 0.21/0.48 ((~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | ![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.21/0.48 tff(170,plain,
% 0.21/0.48 (((P!15 = R!13) | (~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | (~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))) | part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(171,plain,
% 0.21/0.48 (part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[170, 38])).
% 0.21/0.49 tff(172,plain,
% 0.21/0.49 ((~((~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | ![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16)))) | (~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | ![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(173,plain,
% 0.21/0.49 ((~((~part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)) | ![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16)))) | ![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.21/0.49 tff(174,plain,
% 0.21/0.49 (![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[173, 169])).
% 0.21/0.49 tff(175,plain,
% 0.21/0.49 (^[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)))))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(176,plain,
% 0.21/0.49 (![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))))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[175])).
% 0.21/0.49 tff(177,plain,
% 0.21/0.49 (^[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))))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(178,plain,
% 0.21/0.49 (![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)))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[177])).
% 0.21/0.49 tff(179,plain,
% 0.21/0.49 (^[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))))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(180,plain,
% 0.21/0.49 (![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)))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[179])).
% 0.21/0.49 tff(181,plain,
% 0.21/0.49 (![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)))))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[180, 178])).
% 0.21/0.49 tff(182,plain,
% 0.21/0.49 (^[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)))))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(183,plain,
% 0.21/0.49 (![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)))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[182])).
% 0.21/0.49 tff(184,plain,
% 0.21/0.49 (^[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)))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(185,plain,
% 0.21/0.49 (![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))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[184])).
% 0.21/0.49 tff(186,plain,
% 0.21/0.49 (![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))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(187,plain,
% 0.21/0.49 (^[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)))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(188,plain,
% 0.21/0.49 (![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))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[187])).
% 0.21/0.49 tff(189,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/sandbox/benchmark/Axioms/GEO004+0.ax','end_point_defn')).
% 0.21/0.49 tff(190,plain,
% 0.21/0.49 (![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))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.21/0.49 tff(191,plain,
% 0.21/0.49 (![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))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[190, 186])).
% 0.21/0.49 tff(192,plain,(
% 0.21/0.49 ![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)))))))))),
% 0.21/0.49 inference(skolemize,[status(sab)],[191])).
% 0.21/0.49 tff(193,plain,
% 0.21/0.49 (![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))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[192, 185])).
% 0.21/0.49 tff(194,plain,
% 0.21/0.49 (![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)))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[193, 183])).
% 0.21/0.49 tff(195,plain,
% 0.21/0.49 (![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)))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[194, 181])).
% 0.21/0.49 tff(196,plain,
% 0.21/0.49 (![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))))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[195, 176])).
% 0.21/0.49 tff(197,plain,
% 0.21/0.49 ((~![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!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) | (~incident_c(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~(part_of(tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13), tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13)) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13), tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13)) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(R!13, tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13))) | (~incident_c(R!13, tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13))))))) | (~((~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~incident_c(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(R!13, C1)) | (~incident_c(R!13, C2))))))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(198,plain,
% 0.21/0.50 (~((~(end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) | (~incident_c(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~(part_of(tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13), tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13)) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13), tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13)) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(R!13, tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13))) | (~incident_c(R!13, tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13))))))) | (~((~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~incident_c(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(R!13, C1)) | (~incident_c(R!13, C2)))))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.21/0.50 tff(199,plain,
% 0.21/0.50 (((~(end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) | (~incident_c(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~(part_of(tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13), tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13)) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13), tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13)) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(R!13, tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13))) | (~incident_c(R!13, tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), R!13))))))) | (~((~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~incident_c(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(R!13, C1)) | (~incident_c(R!13, C2))))))))) | ((~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~incident_c(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(R!13, C1)) | (~incident_c(R!13, C2)))))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(200,plain,
% 0.21/0.50 ((~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~incident_c(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(R!13, C1)) | (~incident_c(R!13, C2))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[199, 198])).
% 0.21/0.50 tff(201,plain,
% 0.21/0.50 ((~((~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~incident_c(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(R!13, C1)) | (~incident_c(R!13, C2)))))))) | (~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~incident_c(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(R!13, C1)) | (~incident_c(R!13, C2))))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(202,plain,
% 0.21/0.50 ((~((~end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~incident_c(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(R!13, C1)) | (~incident_c(R!13, C2)))))))) | (~((~incident_c(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(R!13, C1)) | (~incident_c(R!13, C2))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[201, 100])).
% 0.21/0.50 tff(203,plain,
% 0.21/0.50 (~((~incident_c(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(R!13, C1)) | (~incident_c(R!13, C2)))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[202, 200])).
% 0.21/0.50 tff(204,plain,
% 0.21/0.50 (((~incident_c(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(R!13, C1)) | (~incident_c(R!13, C2))))) | incident_c(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(205,plain,
% 0.21/0.50 (incident_c(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[204, 203])).
% 0.21/0.50 tff(206,plain,
% 0.21/0.50 (((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16))) | ((~incident_c(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(R!13, C!16))) <=> ((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16))) | (~incident_c(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(R!13, C!16))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(207,plain,
% 0.21/0.50 ((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16))) | ((~incident_c(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(R!13, C!16))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(208,plain,
% 0.21/0.50 ((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16))) | (~incident_c(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(R!13, C!16)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.21/0.50 tff(209,plain,
% 0.21/0.50 (incident_c(R!13, C!16)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[208, 205, 174])).
% 0.21/0.50 tff(210,plain,
% 0.21/0.50 (((~incident_c(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | end_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(211,plain,
% 0.21/0.50 (incident_c(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[210, 145])).
% 0.21/0.50 tff(212,plain,
% 0.21/0.50 (((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16))) | ((~incident_c(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(Q!14, C!16))) <=> ((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16))) | (~incident_c(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(Q!14, C!16))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(213,plain,
% 0.21/0.50 ((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16))) | ((~incident_c(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(Q!14, C!16))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(214,plain,
% 0.21/0.50 ((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16))) | (~incident_c(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(Q!14, C!16)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.21/0.50 tff(215,plain,
% 0.21/0.50 (incident_c(Q!14, C!16)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[214, 211, 174])).
% 0.21/0.50 tff(216,plain,
% 0.21/0.50 ((~![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!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) | (~incident_c(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~(part_of(tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15), tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15)) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15), tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15)) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(P!15, tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15))) | (~incident_c(P!15, tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15))))))) | (~((~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~incident_c(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(P!15, C1)) | (~incident_c(P!15, C2))))))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(217,plain,
% 0.21/0.50 (~((~(end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) | (~incident_c(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~(part_of(tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15), tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15)) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15), tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15)) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(P!15, tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15))) | (~incident_c(P!15, tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15))))))) | (~((~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~incident_c(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(P!15, C1)) | (~incident_c(P!15, C2)))))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[216, 196])).
% 0.21/0.50 tff(218,plain,
% 0.21/0.50 (((~(end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) | (~incident_c(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~(part_of(tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15), tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15)) | part_of(tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15), tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15)) | (~part_of(tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15), tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(P!15, tptp_fun_C1_3(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15))) | (~incident_c(P!15, tptp_fun_C2_2(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), P!15))))))) | (~((~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~incident_c(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(P!15, C1)) | (~incident_c(P!15, C2))))))))) | ((~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~incident_c(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(P!15, C1)) | (~incident_c(P!15, C2)))))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(219,plain,
% 0.21/0.50 ((~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~incident_c(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(P!15, C1)) | (~incident_c(P!15, C2))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[218, 217])).
% 0.21/0.50 tff(220,plain,
% 0.21/0.50 ((~((~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~incident_c(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(P!15, C1)) | (~incident_c(P!15, C2)))))))) | (~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~incident_c(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(P!15, C1)) | (~incident_c(P!15, C2))))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(221,plain,
% 0.21/0.50 ((~((~end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~((~incident_c(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(P!15, C1)) | (~incident_c(P!15, C2)))))))) | (~((~incident_c(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(P!15, C1)) | (~incident_c(P!15, C2))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[220, 70])).
% 0.21/0.50 tff(222,plain,
% 0.21/0.50 (~((~incident_c(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(P!15, C1)) | (~incident_c(P!15, C2)))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[221, 219])).
% 0.21/0.50 tff(223,plain,
% 0.21/0.50 (((~incident_c(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~part_of(C2, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | (~incident_c(P!15, C1)) | (~incident_c(P!15, C2))))) | incident_c(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(224,plain,
% 0.21/0.50 (incident_c(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[223, 222])).
% 0.21/0.50 tff(225,plain,
% 0.21/0.50 (((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16))) | ((~incident_c(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P!15, C!16))) <=> ((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16))) | (~incident_c(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P!15, C!16))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(226,plain,
% 0.21/0.51 ((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16))) | ((~incident_c(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P!15, C!16))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(227,plain,
% 0.21/0.51 ((~![P: $i] : ((~incident_c(P, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P, C!16))) | (~incident_c(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))) | incident_c(P!15, C!16)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.21/0.51 tff(228,plain,
% 0.21/0.51 (incident_c(P!15, C!16)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[227, 224, 174])).
% 0.21/0.51 tff(229,plain,
% 0.21/0.51 ((~(~((P!15 = Q!14) | (Q!14 = R!13) | (P!15 = R!13) | (~incident_c(P!15, C!16)) | (~incident_c(Q!14, C!16)) | (~incident_c(R!13, C!16))))) <=> ((P!15 = Q!14) | (Q!14 = R!13) | (P!15 = R!13) | (~incident_c(P!15, C!16)) | (~incident_c(Q!14, C!16)) | (~incident_c(R!13, C!16)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(230,plain,
% 0.21/0.51 ((incident_c(P!15, C!16) & incident_c(Q!14, C!16) & incident_c(R!13, C!16) & (~(P!15 = Q!14)) & (~(Q!14 = R!13)) & (~(P!15 = R!13))) <=> (~((P!15 = Q!14) | (Q!14 = R!13) | (P!15 = R!13) | (~incident_c(P!15, C!16)) | (~incident_c(Q!14, C!16)) | (~incident_c(R!13, C!16))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(231,plain,
% 0.21/0.51 ((~(incident_c(P!15, C!16) & incident_c(Q!14, C!16) & incident_c(R!13, C!16) & (~(P!15 = Q!14)) & (~(Q!14 = R!13)) & (~(P!15 = R!13)))) <=> (~(~((P!15 = Q!14) | (Q!14 = R!13) | (P!15 = R!13) | (~incident_c(P!15, C!16)) | (~incident_c(Q!14, C!16)) | (~incident_c(R!13, C!16)))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[230])).
% 0.21/0.51 tff(232,plain,
% 0.21/0.51 ((~(incident_c(P!15, C!16) & incident_c(Q!14, C!16) & incident_c(R!13, C!16) & (~(P!15 = Q!14)) & (~(Q!14 = R!13)) & (~(P!15 = R!13)))) <=> ((P!15 = Q!14) | (Q!14 = R!13) | (P!15 = R!13) | (~incident_c(P!15, C!16)) | (~incident_c(Q!14, C!16)) | (~incident_c(R!13, C!16)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[231, 229])).
% 0.21/0.51 tff(233,plain,
% 0.21/0.51 (~(incident_c(P!15, C!16) & incident_c(Q!14, C!16) & incident_c(R!13, C!16) & (~(P!15 = Q!14)) & (~(Q!14 = R!13)) & (~(P!15 = R!13)))),
% 0.21/0.51 inference(or_elim,[status(thm)],[34])).
% 0.21/0.51 tff(234,plain,
% 0.21/0.51 ((P!15 = Q!14) | (Q!14 = R!13) | (P!15 = R!13) | (~incident_c(P!15, C!16)) | (~incident_c(Q!14, C!16)) | (~incident_c(R!13, C!16))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.21/0.51 tff(235,plain,
% 0.21/0.51 ((P!15 = Q!14) | (Q!14 = R!13)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[234, 64, 228, 215, 209])).
% 0.21/0.51 tff(236,plain,
% 0.21/0.51 (Q!14 = R!13),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[235, 149])).
% 0.21/0.51 tff(237,plain,
% 0.21/0.51 (Q!14 = tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.51 inference(transitivity,[status(thm)],[236, 125])).
% 0.21/0.51 tff(238,plain,
% 0.21/0.51 (inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) <=> inner_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[237, 59])).
% 0.21/0.51 tff(239,plain,
% 0.21/0.51 (inner_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))) <=> inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.51 inference(symmetry,[status(thm)],[238])).
% 0.21/0.51 tff(240,plain,
% 0.21/0.51 ((~inner_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) <=> (~inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[239])).
% 0.21/0.51 tff(241,plain,
% 0.21/0.51 ((~![P: $i, C: $i] : (inner_point(P, C) <=> (~((~incident_c(P, C)) | end_point(P, C))))) | (inner_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))) <=> (~((~incident_c(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(242,plain,
% 0.21/0.51 (inner_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))) <=> (~((~incident_c(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[241, 140])).
% 0.21/0.51 tff(243,plain,
% 0.21/0.51 (((~incident_c(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (~end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(244,plain,
% 0.21/0.51 ((~incident_c(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[243, 90])).
% 0.21/0.51 tff(245,plain,
% 0.21/0.51 ((~(inner_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))) <=> (~((~incident_c(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))))))) | (~inner_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (~((~incident_c(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | end_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(246,plain,
% 0.21/0.51 (~inner_point(tptp_fun_Q_9(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[245, 244, 242])).
% 0.21/0.51 tff(247,plain,
% 0.21/0.51 (~inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[246, 240])).
% 0.21/0.51 tff(248,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[40, 247])).
% 0.21/0.51 % SZS output end Proof
%------------------------------------------------------------------------------