TSTP Solution File: GEO112+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO112+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:34:55 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO112+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 05:46:35 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(inner_point_type, type, (
% 0.13/0.40 inner_point: ( $i * $i ) > $o)).
% 0.13/0.40 tff(sum_type, type, (
% 0.13/0.40 sum: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_C2_7_type, type, (
% 0.13/0.40 tptp_fun_C2_7: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_Cpp_12_type, type, (
% 0.13/0.40 tptp_fun_Cpp_12: ( $i * $i * $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_C_16_type, type, (
% 0.13/0.40 tptp_fun_C_16: $i)).
% 0.13/0.40 tff(tptp_fun_P_15_type, type, (
% 0.13/0.40 tptp_fun_P_15: $i)).
% 0.13/0.40 tff(tptp_fun_Q_14_type, type, (
% 0.13/0.40 tptp_fun_Q_14: $i)).
% 0.13/0.40 tff(tptp_fun_R_13_type, type, (
% 0.13/0.40 tptp_fun_R_13: $i)).
% 0.13/0.40 tff(tptp_fun_C1_8_type, type, (
% 0.13/0.40 tptp_fun_C1_8: ( $i * $i ) > $i)).
% 0.13/0.40 tff(meet_type, type, (
% 0.13/0.40 meet: ( $i * $i * $i ) > $o)).
% 0.13/0.40 tff(end_point_type, type, (
% 0.13/0.40 end_point: ( $i * $i ) > $o)).
% 0.13/0.40 tff(part_of_type, type, (
% 0.13/0.40 part_of: ( $i * $i ) > $o)).
% 0.13/0.40 tff(between_c_type, type, (
% 0.13/0.40 between_c: ( $i * $i * $i * $i ) > $o)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (^[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))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (![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)))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (^[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))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (![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)))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (![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)))))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 (^[C: $i, P: $i, Q: $i, R: $i] : trans(monotonicity(rewrite(((~between_c(C, P, Q, R)) | ((~(P = R)) & part_of(tptp_fun_Cpp_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)))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![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)))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (^[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))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (![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)))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (![C: $i, P: $i, Q: $i, R: $i] : (between_c(C, P, Q, R) <=> ((~(P = R)) & ?[Cpp: $i] : (part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp)))) <=> ![C: $i, P: $i, Q: $i, R: $i] : (between_c(C, P, Q, R) <=> ((~(P = R)) & ?[Cpp: $i] : (part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (^[C: $i, P: $i, Q: $i, R: $i] : rewrite((between_c(C, P, Q, R) <=> ((~(P = R)) & ?[Cpp: $i] : (((part_of(Cpp, C) & end_point(P, Cpp)) & end_point(R, Cpp)) & inner_point(Q, Cpp)))) <=> (between_c(C, P, Q, R) <=> ((~(P = R)) & ?[Cpp: $i] : (part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (![C: $i, P: $i, Q: $i, R: $i] : (between_c(C, P, Q, R) <=> ((~(P = R)) & ?[Cpp: $i] : (((part_of(Cpp, C) & end_point(P, Cpp)) & end_point(R, Cpp)) & inner_point(Q, Cpp)))) <=> ![C: $i, P: $i, Q: $i, R: $i] : (between_c(C, P, Q, R) <=> ((~(P = R)) & ?[Cpp: $i] : (part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.13/0.40 tff(13,axiom,(![C: $i, P: $i, Q: $i, R: $i] : (between_c(C, P, Q, R) <=> ((~(P = R)) & ?[Cpp: $i] : (((part_of(Cpp, C) & end_point(P, Cpp)) & end_point(R, Cpp)) & inner_point(Q, Cpp))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004+1.ax','between_c_defn')).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (![C: $i, P: $i, Q: $i, R: $i] : (between_c(C, P, Q, R) <=> ((~(P = R)) & ?[Cpp: $i] : (part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (![C: $i, P: $i, Q: $i, R: $i] : (between_c(C, P, Q, R) <=> ((~(P = R)) & ?[Cpp: $i] : (part_of(Cpp, C) & end_point(P, Cpp) & end_point(R, Cpp) & inner_point(Q, Cpp))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.13/0.40 tff(16,plain,(
% 0.13/0.40 ![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))))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[15])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (![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)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (![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)))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (![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)))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[18, 5])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 ((~![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)))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (~((~((~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))))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (((~((~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))))))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(23,plain,
% 0.13/0.41 ((~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)))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.13/0.41 tff(24,plain,
% 0.13/0.41 ((~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | between_c(C, R, Q, P))) <=> (~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | between_c(C, R, Q, P)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(25,plain,
% 0.13/0.41 ((~![C: $i, P: $i, Q: $i, R: $i] : (between_c(C, P, Q, R) => between_c(C, R, Q, P))) <=> (~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | between_c(C, R, Q, P)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(26,axiom,(~![C: $i, P: $i, Q: $i, R: $i] : (between_c(C, P, Q, R) => between_c(C, R, Q, P))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','theorem_3_8_2')).
% 0.13/0.41 tff(27,plain,
% 0.13/0.41 (~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | between_c(C, R, Q, P))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.41 tff(28,plain,
% 0.13/0.41 (~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | between_c(C, R, Q, P))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.13/0.41 tff(29,plain,
% 0.13/0.41 (~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | between_c(C, R, Q, P))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.13/0.41 tff(30,plain,
% 0.13/0.41 (~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | between_c(C, R, Q, P))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.13/0.41 tff(31,plain,
% 0.13/0.41 (~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | between_c(C, R, Q, P))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[30, 24])).
% 0.13/0.41 tff(32,plain,
% 0.13/0.41 (~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | between_c(C, R, Q, P))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.13/0.41 tff(33,plain,
% 0.13/0.41 (~![C: $i, P: $i, Q: $i, R: $i] : ((~between_c(C, P, Q, R)) | between_c(C, R, Q, P))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[32, 24])).
% 0.13/0.41 tff(34,plain,(
% 0.13/0.41 ~((~between_c(C!16, P!15, Q!14, R!13)) | between_c(C!16, R!13, Q!14, P!15))),
% 0.13/0.41 inference(skolemize,[status(sab)],[33])).
% 0.13/0.41 tff(35,plain,
% 0.13/0.41 (between_c(C!16, P!15, Q!14, R!13)),
% 0.13/0.41 inference(or_elim,[status(thm)],[34])).
% 0.13/0.41 tff(36,plain,
% 0.13/0.41 ((~((~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)))))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(37,plain,
% 0.13/0.41 ((~((~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)))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.13/0.41 tff(38,plain,
% 0.13/0.41 (~((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))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[37, 23])).
% 0.13/0.41 tff(39,plain,
% 0.13/0.41 (((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))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(40,plain,
% 0.13/0.41 (inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.13/0.41 tff(41,plain,
% 0.13/0.41 (^[C: $i, P: $i] : refl(((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))))))) <=> ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(42,plain,
% 0.13/0.41 (![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))))))) <=> ![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[41])).
% 0.13/0.41 tff(43,plain,
% 0.13/0.41 (^[C: $i, P: $i] : rewrite(((~inner_point(P, C)) | (meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)) & (C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))))) <=> ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(44,plain,
% 0.13/0.41 (![C: $i, P: $i] : ((~inner_point(P, C)) | (meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)) & (C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))))) <=> ![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[43])).
% 0.13/0.41 tff(45,plain,
% 0.13/0.41 (![C: $i, P: $i] : ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2)))) <=> ![C: $i, P: $i] : ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(46,plain,
% 0.13/0.41 (^[C: $i, P: $i] : rewrite((inner_point(P, C) => ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2)))) <=> ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(47,plain,
% 0.13/0.41 (![C: $i, P: $i] : (inner_point(P, C) => ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2)))) <=> ![C: $i, P: $i] : ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[46])).
% 0.13/0.41 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')).
% 0.13/0.41 tff(49,plain,
% 0.13/0.41 (![C: $i, P: $i] : ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 (![C: $i, P: $i] : ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.13/0.41 tff(51,plain,(
% 0.13/0.41 ![C: $i, P: $i] : ((~inner_point(P, C)) | (meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)) & (C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[50])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 (![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 (![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[52, 42])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 (((~![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))) | ((~inner_point(Q!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))))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 ((~![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))) | ((~inner_point(Q!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))))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(56,plain,
% 0.13/0.41 ((~![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))) | (~inner_point(Q!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)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.13/0.41 tff(57,plain,
% 0.13/0.41 (~((~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))))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[56, 53, 40])).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 (((~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))))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(59,plain,
% 0.18/0.42 (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)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.18/0.42 tff(60,plain,
% 0.18/0.42 (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)),
% 0.18/0.42 inference(symmetry,[status(thm)],[59])).
% 0.18/0.42 tff(61,plain,
% 0.18/0.42 (inner_point(Q!14, 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))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[60])).
% 0.18/0.42 tff(62,plain,
% 0.18/0.42 (inner_point(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)) <=> inner_point(Q!14, 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))))),
% 0.18/0.42 inference(symmetry,[status(thm)],[61])).
% 0.18/0.42 tff(63,plain,
% 0.18/0.42 (inner_point(Q!14, 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))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[40, 62])).
% 0.18/0.42 tff(64,plain,
% 0.18/0.42 (part_of(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!16) <=> part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)),
% 0.18/0.42 inference(monotonicity,[status(thm)],[60])).
% 0.18/0.42 tff(65,plain,
% 0.18/0.42 (part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16) <=> part_of(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!16)),
% 0.18/0.42 inference(symmetry,[status(thm)],[64])).
% 0.18/0.42 tff(66,plain,
% 0.18/0.42 (((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)),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(67,plain,
% 0.18/0.42 (part_of(tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16), C!16)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[66, 38])).
% 0.18/0.42 tff(68,plain,
% 0.18/0.42 (part_of(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!16)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[67, 65])).
% 0.18/0.42 tff(69,plain,
% 0.18/0.42 (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))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[60])).
% 0.18/0.42 tff(70,plain,
% 0.18/0.42 (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))))),
% 0.18/0.42 inference(symmetry,[status(thm)],[69])).
% 0.18/0.42 tff(71,plain,
% 0.18/0.42 (((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))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(72,plain,
% 0.18/0.42 (end_point(P!15, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[71, 38])).
% 0.18/0.42 tff(73,plain,
% 0.18/0.42 (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))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[72, 70])).
% 0.18/0.42 tff(74,plain,
% 0.18/0.42 (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))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[60])).
% 0.18/0.42 tff(75,plain,
% 0.18/0.42 (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))))),
% 0.18/0.42 inference(symmetry,[status(thm)],[74])).
% 0.18/0.42 tff(76,plain,
% 0.18/0.42 (((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))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(77,plain,
% 0.18/0.42 (end_point(R!13, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[76, 38])).
% 0.18/0.42 tff(78,plain,
% 0.18/0.42 (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))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[77, 75])).
% 0.18/0.42 tff(79,plain,
% 0.18/0.42 (((~![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, R!13, Q!14, P!15)) | (~((R!13 = P!15) | (~part_of(tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16), C!16)) | (~end_point(R!13, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~end_point(P!15, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))))))) | (~((R!13 = P!15) | between_c(C!16, R!13, Q!14, P!15) | ![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, 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)))))))) | (~((~((~between_c(C!16, R!13, Q!14, P!15)) | (~((R!13 = P!15) | (~part_of(tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16), C!16)) | (~end_point(R!13, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~end_point(P!15, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))))))) | (~((R!13 = P!15) | between_c(C!16, R!13, Q!14, P!15) | ![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp))))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(80,plain,
% 0.18/0.42 ((~((~((~between_c(C!16, R!13, Q!14, P!15)) | (~((R!13 = P!15) | (~part_of(tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16), C!16)) | (~end_point(R!13, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~end_point(P!15, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))))))) | (~((R!13 = P!15) | between_c(C!16, R!13, Q!14, P!15) | ![Cpp: $i] : ((~end_point(P!15, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(R!13, Cpp)) | (~inner_point(Q!14, Cpp))))))) <=> (~((~((~between_c(C!16, R!13, Q!14, P!15)) | (~((R!13 = P!15) | (~part_of(tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16), C!16)) | (~end_point(R!13, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~end_point(P!15, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))))))) | (~((R!13 = P!15) | between_c(C!16, R!13, Q!14, P!15) | ![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp)))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(81,plain,
% 0.18/0.42 (((~![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, R!13, Q!14, P!15)) | (~((R!13 = P!15) | (~part_of(tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16), C!16)) | (~end_point(R!13, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~end_point(P!15, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))))))) | (~((R!13 = P!15) | between_c(C!16, R!13, Q!14, P!15) | ![Cpp: $i] : ((~end_point(P!15, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(R!13, Cpp)) | (~inner_point(Q!14, 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)))))))) | (~((~((~between_c(C!16, R!13, Q!14, P!15)) | (~((R!13 = P!15) | (~part_of(tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16), C!16)) | (~end_point(R!13, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~end_point(P!15, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))))))) | (~((R!13 = P!15) | between_c(C!16, R!13, Q!14, P!15) | ![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp))))))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[80])).
% 0.18/0.43 tff(82,plain,
% 0.18/0.43 (((~![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)))))))) | (~((~((~between_c(C!16, R!13, Q!14, P!15)) | (~((R!13 = P!15) | (~part_of(tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16), C!16)) | (~end_point(R!13, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~end_point(P!15, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))))))) | (~((R!13 = P!15) | between_c(C!16, R!13, Q!14, P!15) | ![Cpp: $i] : ((~end_point(P!15, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(R!13, Cpp)) | (~inner_point(Q!14, 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)))))))) | (~((~((~between_c(C!16, R!13, Q!14, P!15)) | (~((R!13 = P!15) | (~part_of(tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16), C!16)) | (~end_point(R!13, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~end_point(P!15, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))))))) | (~((R!13 = P!15) | between_c(C!16, R!13, Q!14, P!15) | ![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp))))))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[81, 79])).
% 0.18/0.43 tff(83,plain,
% 0.18/0.43 ((~![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)))))))) | (~((~((~between_c(C!16, R!13, Q!14, P!15)) | (~((R!13 = P!15) | (~part_of(tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16), C!16)) | (~end_point(R!13, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~end_point(P!15, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))))))) | (~((R!13 = P!15) | between_c(C!16, R!13, Q!14, P!15) | ![Cpp: $i] : ((~end_point(P!15, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(R!13, Cpp)) | (~inner_point(Q!14, Cpp)))))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(84,plain,
% 0.18/0.43 ((~![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)))))))) | (~((~((~between_c(C!16, R!13, Q!14, P!15)) | (~((R!13 = P!15) | (~part_of(tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16), C!16)) | (~end_point(R!13, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~end_point(P!15, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))))))) | (~((R!13 = P!15) | between_c(C!16, R!13, Q!14, P!15) | ![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp)))))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.18/0.43 tff(85,plain,
% 0.18/0.43 (~((~((~between_c(C!16, R!13, Q!14, P!15)) | (~((R!13 = P!15) | (~part_of(tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16), C!16)) | (~end_point(R!13, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~end_point(P!15, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))))))) | (~((R!13 = P!15) | between_c(C!16, R!13, Q!14, P!15) | ![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp))))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[84, 19])).
% 0.18/0.43 tff(86,plain,
% 0.18/0.43 (((~((~between_c(C!16, R!13, Q!14, P!15)) | (~((R!13 = P!15) | (~part_of(tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16), C!16)) | (~end_point(R!13, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~end_point(P!15, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))) | (~inner_point(Q!14, tptp_fun_Cpp_12(P!15, Q!14, R!13, C!16))))))) | (~((R!13 = P!15) | between_c(C!16, R!13, Q!14, P!15) | ![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp)))))) | ((R!13 = P!15) | between_c(C!16, R!13, Q!14, P!15) | ![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp))))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(87,plain,
% 0.18/0.43 ((R!13 = P!15) | between_c(C!16, R!13, Q!14, P!15) | ![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.18/0.43 tff(88,plain,
% 0.18/0.43 ((R!13 = P!15) <=> (P!15 = R!13)),
% 0.18/0.43 inference(commutativity,[status(thm)],[])).
% 0.18/0.43 tff(89,plain,
% 0.18/0.43 ((P!15 = R!13) <=> (R!13 = P!15)),
% 0.18/0.43 inference(symmetry,[status(thm)],[88])).
% 0.18/0.43 tff(90,plain,
% 0.18/0.43 ((~(P!15 = R!13)) <=> (~(R!13 = P!15))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[89])).
% 0.18/0.43 tff(91,plain,
% 0.18/0.43 (((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))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(92,plain,
% 0.18/0.43 (~(P!15 = R!13)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[91, 38])).
% 0.18/0.43 tff(93,plain,
% 0.18/0.43 (~(R!13 = P!15)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[92, 90])).
% 0.18/0.43 tff(94,plain,
% 0.18/0.43 (~between_c(C!16, R!13, Q!14, P!15)),
% 0.18/0.43 inference(or_elim,[status(thm)],[34])).
% 0.18/0.43 tff(95,plain,
% 0.18/0.43 ((~((R!13 = P!15) | between_c(C!16, R!13, Q!14, P!15) | ![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp))))) | (R!13 = P!15) | between_c(C!16, R!13, Q!14, P!15) | ![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp)))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(96,plain,
% 0.18/0.43 ((~((R!13 = P!15) | between_c(C!16, R!13, Q!14, P!15) | ![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp))))) | (R!13 = P!15) | ![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.18/0.43 tff(97,plain,
% 0.18/0.43 (![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[96, 93, 87])).
% 0.18/0.43 tff(98,plain,
% 0.18/0.43 (((~![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp)))) | ((~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))))) | (~part_of(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!16)) | (~inner_point(Q!14, 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))))))) <=> ((~![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp)))) | (~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))))) | (~part_of(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!16)) | (~inner_point(Q!14, 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))))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(99,plain,
% 0.18/0.43 (((~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))))) | (~part_of(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!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))))) | (~inner_point(Q!14, 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, 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))))) | (~part_of(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!16)) | (~inner_point(Q!14, 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))))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(100,plain,
% 0.18/0.43 (((~![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp)))) | ((~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))))) | (~part_of(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!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))))) | (~inner_point(Q!14, 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))))))) <=> ((~![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp)))) | ((~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))))) | (~part_of(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!16)) | (~inner_point(Q!14, 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)))))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[99])).
% 0.18/0.44 tff(101,plain,
% 0.18/0.44 (((~![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp)))) | ((~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))))) | (~part_of(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!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))))) | (~inner_point(Q!14, 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))))))) <=> ((~![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp)))) | (~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))))) | (~part_of(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!16)) | (~inner_point(Q!14, 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))))))),
% 0.18/0.44 inference(transitivity,[status(thm)],[100, 98])).
% 0.18/0.44 tff(102,plain,
% 0.18/0.44 ((~![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp)))) | ((~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))))) | (~part_of(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!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))))) | (~inner_point(Q!14, 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))))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(103,plain,
% 0.18/0.44 ((~![Cpp: $i] : ((~end_point(R!13, Cpp)) | (~part_of(Cpp, C!16)) | (~end_point(P!15, Cpp)) | (~inner_point(Q!14, Cpp)))) | (~end_point(P!15, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (~end_point(R!13, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (~part_of(sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))), C!16)) | (~inner_point(Q!14, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.18/0.44 tff(104,plain,
% 0.18/0.44 ((~end_point(P!15, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (~end_point(R!13, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))))) | (~part_of(sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16))), C!16)) | (~inner_point(Q!14, sum(tptp_fun_C1_8(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)), tptp_fun_C2_7(Q!14, tptp_fun_Cpp_12(R!13, Q!14, P!15, C!16)))))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[103, 97])).
% 0.18/0.44 tff(105,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[104, 78, 73, 68, 63])).
% 0.18/0.44 % SZS output end Proof
%------------------------------------------------------------------------------