TSTP Solution File: GEO118+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO118+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 20:34:57 EDT 2022
% Result : Theorem 156.78s 98.61s
% Output : Proof 156.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO118+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 05:52:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 156.78/98.61 % SZS status Theorem
% 156.78/98.61 % SZS output start Proof
% 156.78/98.61 tff(between_c_type, type, (
% 156.78/98.61 between_c: ( $i * $i * $i * $i ) > $o)).
% 156.78/98.61 tff(tptp_fun_Q_23_type, type, (
% 156.78/98.61 tptp_fun_Q_23: $i)).
% 156.78/98.61 tff(tptp_fun_P_24_type, type, (
% 156.78/98.61 tptp_fun_P_24: $i)).
% 156.78/98.61 tff(tptp_fun_C_16_type, type, (
% 156.78/98.61 tptp_fun_C_16: ( $i * $i * $i * $i ) > $i)).
% 156.78/98.61 tff(tptp_fun_O_25_type, type, (
% 156.78/98.61 tptp_fun_O_25: $i)).
% 156.78/98.61 tff(incident_c_type, type, (
% 156.78/98.61 incident_c: ( $i * $i ) > $o)).
% 156.78/98.61 tff(incident_o_type, type, (
% 156.78/98.61 incident_o: ( $i * $i ) > $o)).
% 156.78/98.61 tff(between_o_type, type, (
% 156.78/98.61 between_o: ( $i * $i * $i * $i ) > $o)).
% 156.78/98.61 tff(tptp_fun_P_17_type, type, (
% 156.78/98.61 tptp_fun_P_17: ( $i * $i ) > $i)).
% 156.78/98.61 tff(ordered_by_type, type, (
% 156.78/98.61 ordered_by: ( $i * $i * $i ) > $o)).
% 156.78/98.61 tff(inner_point_type, type, (
% 156.78/98.61 inner_point: ( $i * $i ) > $o)).
% 156.78/98.61 tff(end_point_type, type, (
% 156.78/98.61 end_point: ( $i * $i ) > $o)).
% 156.78/98.61 tff(part_of_type, type, (
% 156.78/98.61 part_of: ( $i * $i ) > $o)).
% 156.78/98.61 tff(tptp_fun_Cpp_12_type, type, (
% 156.78/98.61 tptp_fun_Cpp_12: ( $i * $i * $i * $i ) > $i)).
% 156.78/98.61 tff(1,plain,
% 156.78/98.61 (^[P: $i, Q: $i, R: $i, O: $i] : rewrite((~((~((~between_o(O, P, Q, R)) | (~((~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P)))) | (~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)))))) | (~(between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C))))))) <=> (~((~(between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C))))) | (~((~between_o(O, P, Q, R)) | (~((~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)) | (~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P)))))))))))),
% 156.78/98.61 inference(bind,[status(th)],[])).
% 156.78/98.61 tff(2,plain,
% 156.78/98.61 (![P: $i, Q: $i, R: $i, O: $i] : (~((~((~between_o(O, P, Q, R)) | (~((~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P)))) | (~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)))))) | (~(between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C))))))) <=> ![P: $i, Q: $i, R: $i, O: $i] : (~((~(between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C))))) | (~((~between_o(O, P, Q, R)) | (~((~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)) | (~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P))))))))))),
% 156.78/98.61 inference(quant_intro,[status(thm)],[1])).
% 156.78/98.61 tff(3,plain,
% 156.78/98.61 (^[P: $i, Q: $i, R: $i, O: $i] : refl((~((~((~between_o(O, P, Q, R)) | (~((~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P)))) | (~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)))))) | (~(between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C))))))) <=> (~((~((~between_o(O, P, Q, R)) | (~((~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P)))) | (~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)))))) | (~(between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C))))))))),
% 156.78/98.61 inference(bind,[status(th)],[])).
% 156.78/98.61 tff(4,plain,
% 156.78/98.61 (![P: $i, Q: $i, R: $i, O: $i] : (~((~((~between_o(O, P, Q, R)) | (~((~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P)))) | (~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)))))) | (~(between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C))))))) <=> ![P: $i, Q: $i, R: $i, O: $i] : (~((~((~between_o(O, P, Q, R)) | (~((~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P)))) | (~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)))))) | (~(between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C)))))))),
% 156.78/98.61 inference(quant_intro,[status(thm)],[3])).
% 156.78/98.61 tff(5,plain,
% 156.78/98.61 (^[P: $i, Q: $i, R: $i, O: $i] : rewrite((~((~((~between_o(O, P, Q, R)) | (~((~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P)))) | (~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)))))) | (~(between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C))))))) <=> (~((~((~between_o(O, P, Q, R)) | (~((~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P)))) | (~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)))))) | (~(between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C))))))))),
% 156.78/98.61 inference(bind,[status(th)],[])).
% 156.78/98.61 tff(6,plain,
% 156.78/98.61 (![P: $i, Q: $i, R: $i, O: $i] : (~((~((~between_o(O, P, Q, R)) | (~((~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P)))) | (~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)))))) | (~(between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C))))))) <=> ![P: $i, Q: $i, R: $i, O: $i] : (~((~((~between_o(O, P, Q, R)) | (~((~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P)))) | (~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)))))) | (~(between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C)))))))),
% 156.78/98.61 inference(quant_intro,[status(thm)],[5])).
% 156.78/98.61 tff(7,plain,
% 156.78/98.61 (![P: $i, Q: $i, R: $i, O: $i] : (~((~((~between_o(O, P, Q, R)) | (~((~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P)))) | (~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)))))) | (~(between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C))))))) <=> ![P: $i, Q: $i, R: $i, O: $i] : (~((~((~between_o(O, P, Q, R)) | (~((~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P)))) | (~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)))))) | (~(between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C)))))))),
% 156.78/98.61 inference(transitivity,[status(thm)],[6, 4])).
% 156.78/98.61 tff(8,plain,
% 156.78/98.61 (^[P: $i, Q: $i, R: $i, O: $i] : trans(monotonicity(rewrite(((~between_o(O, P, Q, R)) | (![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P))) & between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R))) <=> ((~between_o(O, P, Q, R)) | (~((~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P)))) | (~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)))))), rewrite((between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C)))) <=> (between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C))))), ((((~between_o(O, P, Q, R)) | (![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P))) & between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R))) & (between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C))))) <=> (((~between_o(O, P, Q, R)) | (~((~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P)))) | (~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R))))) & (between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C))))))), rewrite((((~between_o(O, P, Q, R)) | (~((~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P)))) | (~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R))))) & (between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C))))) <=> (~((~((~between_o(O, P, Q, R)) | (~((~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P)))) | (~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)))))) | (~(between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C)))))))), ((((~between_o(O, P, Q, R)) | (![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P))) & between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R))) & (between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C))))) <=> (~((~((~between_o(O, P, Q, R)) | (~((~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P)))) | (~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)))))) | (~(between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C)))))))))),
% 156.78/98.61 inference(bind,[status(th)],[])).
% 156.78/98.61 tff(9,plain,
% 156.78/98.61 (![P: $i, Q: $i, R: $i, O: $i] : (((~between_o(O, P, Q, R)) | (![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P))) & between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R))) & (between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C))))) <=> ![P: $i, Q: $i, R: $i, O: $i] : (~((~((~between_o(O, P, Q, R)) | (~((~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P)))) | (~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)))))) | (~(between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C)))))))),
% 156.78/98.61 inference(quant_intro,[status(thm)],[8])).
% 156.78/98.61 tff(10,plain,
% 156.78/98.61 (^[P: $i, Q: $i, R: $i, O: $i] : rewrite((((~between_o(O, P, Q, R)) | (![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P))) & between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R))) & (between_o(O, P, Q, R) | ![C: $i] : ((~(incident_o(tptp_fun_P_17(C, O), O) <=> incident_c(tptp_fun_P_17(C, O), C))) | (~between_c(C, P, Q, R))))) <=> (((~between_o(O, P, Q, R)) | (![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P))) & between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R))) & (between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C))))))),
% 156.78/98.61 inference(bind,[status(th)],[])).
% 156.78/98.61 tff(11,plain,
% 156.78/98.61 (![P: $i, Q: $i, R: $i, O: $i] : (((~between_o(O, P, Q, R)) | (![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P))) & between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R))) & (between_o(O, P, Q, R) | ![C: $i] : ((~(incident_o(tptp_fun_P_17(C, O), O) <=> incident_c(tptp_fun_P_17(C, O), C))) | (~between_c(C, P, Q, R))))) <=> ![P: $i, Q: $i, R: $i, O: $i] : (((~between_o(O, P, Q, R)) | (![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P))) & between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R))) & (between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C)))))),
% 156.78/98.61 inference(quant_intro,[status(thm)],[10])).
% 156.78/98.61 tff(12,plain,
% 156.78/98.61 (![P: $i, Q: $i, R: $i, O: $i] : (between_o(O, P, Q, R) <=> ?[C: $i] : (![P: $i] : (incident_o(P, O) <=> incident_c(P, C)) & between_c(C, P, Q, R))) <=> ![P: $i, Q: $i, R: $i, O: $i] : (between_o(O, P, Q, R) <=> ?[C: $i] : (![P: $i] : (incident_o(P, O) <=> incident_c(P, C)) & between_c(C, P, Q, R)))),
% 156.78/98.61 inference(rewrite,[status(thm)],[])).
% 156.78/98.61 tff(13,axiom,(![P: $i, Q: $i, R: $i, O: $i] : (between_o(O, P, Q, R) <=> ?[C: $i] : (![P: $i] : (incident_o(P, O) <=> incident_c(P, C)) & between_c(C, P, Q, R)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax','o3')).
% 156.78/98.61 tff(14,plain,
% 156.78/98.61 (![P: $i, Q: $i, R: $i, O: $i] : (between_o(O, P, Q, R) <=> ?[C: $i] : (![P: $i] : (incident_o(P, O) <=> incident_c(P, C)) & between_c(C, P, Q, R)))),
% 156.78/98.61 inference(modus_ponens,[status(thm)],[13, 12])).
% 156.78/98.61 tff(15,plain,(
% 156.78/98.61 ![P: $i, Q: $i, R: $i, O: $i] : (((~between_o(O, P, Q, R)) | (![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P))) & between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R))) & (between_o(O, P, Q, R) | ![C: $i] : ((~(incident_o(tptp_fun_P_17(C, O), O) <=> incident_c(tptp_fun_P_17(C, O), C))) | (~between_c(C, P, Q, R)))))),
% 156.78/98.61 inference(skolemize,[status(sab)],[14])).
% 156.78/98.61 tff(16,plain,
% 156.78/98.61 (![P: $i, Q: $i, R: $i, O: $i] : (((~between_o(O, P, Q, R)) | (![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P))) & between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R))) & (between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C)))))),
% 156.78/98.61 inference(modus_ponens,[status(thm)],[15, 11])).
% 156.78/98.61 tff(17,plain,
% 156.78/98.61 (![P: $i, Q: $i, R: $i, O: $i] : (~((~((~between_o(O, P, Q, R)) | (~((~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P)))) | (~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)))))) | (~(between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C)))))))),
% 156.78/98.61 inference(modus_ponens,[status(thm)],[16, 9])).
% 156.78/98.61 tff(18,plain,
% 156.78/98.61 (![P: $i, Q: $i, R: $i, O: $i] : (~((~((~between_o(O, P, Q, R)) | (~((~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P)))) | (~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)))))) | (~(between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C)))))))),
% 156.78/98.61 inference(modus_ponens,[status(thm)],[17, 7])).
% 156.78/98.61 tff(19,plain,
% 156.78/98.61 (![P: $i, Q: $i, R: $i, O: $i] : (~((~(between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C))))) | (~((~between_o(O, P, Q, R)) | (~((~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)) | (~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P))))))))))),
% 156.78/98.61 inference(modus_ponens,[status(thm)],[18, 2])).
% 156.78/98.61 tff(20,plain,
% 156.78/98.61 ((~![P: $i, Q: $i, R: $i, O: $i] : (~((~(between_o(O, P, Q, R) | ![C: $i] : ((~between_c(C, P, Q, R)) | ((~incident_o(tptp_fun_P_17(C, O), O)) <=> incident_c(tptp_fun_P_17(C, O), C))))) | (~((~between_o(O, P, Q, R)) | (~((~between_c(tptp_fun_C_16(O, R, Q, P), P, Q, R)) | (~![P: $i] : (incident_o(P, O) <=> incident_c(P, tptp_fun_C_16(O, R, Q, P))))))))))) | (~((~(between_o(O!25, Q!23, P!24, Q!23) | ![C: $i] : ((~between_c(C, Q!23, P!24, Q!23)) | ((~incident_o(tptp_fun_P_17(C, O!25), O!25)) <=> incident_c(tptp_fun_P_17(C, O!25), C))))) | (~((~between_o(O!25, Q!23, P!24, Q!23)) | (~((~between_c(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23)) | (~![P: $i] : (incident_o(P, O!25) <=> incident_c(P, tptp_fun_C_16(O!25, Q!23, P!24, Q!23))))))))))),
% 156.78/98.61 inference(quant_inst,[status(thm)],[])).
% 156.78/98.61 tff(21,plain,
% 156.78/98.61 (~((~(between_o(O!25, Q!23, P!24, Q!23) | ![C: $i] : ((~between_c(C, Q!23, P!24, Q!23)) | ((~incident_o(tptp_fun_P_17(C, O!25), O!25)) <=> incident_c(tptp_fun_P_17(C, O!25), C))))) | (~((~between_o(O!25, Q!23, P!24, Q!23)) | (~((~between_c(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23)) | (~![P: $i] : (incident_o(P, O!25) <=> incident_c(P, tptp_fun_C_16(O!25, Q!23, P!24, Q!23)))))))))),
% 156.78/98.61 inference(unit_resolution,[status(thm)],[20, 19])).
% 156.78/98.61 tff(22,plain,
% 156.78/98.61 (((~(between_o(O!25, Q!23, P!24, Q!23) | ![C: $i] : ((~between_c(C, Q!23, P!24, Q!23)) | ((~incident_o(tptp_fun_P_17(C, O!25), O!25)) <=> incident_c(tptp_fun_P_17(C, O!25), C))))) | (~((~between_o(O!25, Q!23, P!24, Q!23)) | (~((~between_c(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23)) | (~![P: $i] : (incident_o(P, O!25) <=> incident_c(P, tptp_fun_C_16(O!25, Q!23, P!24, Q!23))))))))) | ((~between_o(O!25, Q!23, P!24, Q!23)) | (~((~between_c(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23)) | (~![P: $i] : (incident_o(P, O!25) <=> incident_c(P, tptp_fun_C_16(O!25, Q!23, P!24, Q!23)))))))),
% 156.78/98.61 inference(tautology,[status(thm)],[])).
% 156.78/98.61 tff(23,plain,
% 156.78/98.61 ((~between_o(O!25, Q!23, P!24, Q!23)) | (~((~between_c(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23)) | (~![P: $i] : (incident_o(P, O!25) <=> incident_c(P, tptp_fun_C_16(O!25, Q!23, P!24, Q!23))))))),
% 156.78/98.61 inference(unit_resolution,[status(thm)],[22, 21])).
% 156.78/98.61 tff(24,plain,
% 156.78/98.61 (^[O: $i, P: $i, Q: $i, R: $i] : refl((between_o(O, P, Q, R) <=> ((~((~ordered_by(O, R, Q)) | (~ordered_by(O, Q, P)))) | (~((~ordered_by(O, P, Q)) | (~ordered_by(O, Q, R)))))) <=> (between_o(O, P, Q, R) <=> ((~((~ordered_by(O, R, Q)) | (~ordered_by(O, Q, P)))) | (~((~ordered_by(O, P, Q)) | (~ordered_by(O, Q, R)))))))),
% 156.91/98.62 inference(bind,[status(th)],[])).
% 156.91/98.62 tff(25,plain,
% 156.91/98.62 (![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((~((~ordered_by(O, R, Q)) | (~ordered_by(O, Q, P)))) | (~((~ordered_by(O, P, Q)) | (~ordered_by(O, Q, R)))))) <=> ![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((~((~ordered_by(O, R, Q)) | (~ordered_by(O, Q, P)))) | (~((~ordered_by(O, P, Q)) | (~ordered_by(O, Q, R))))))),
% 156.91/98.62 inference(quant_intro,[status(thm)],[24])).
% 156.91/98.62 tff(26,plain,
% 156.91/98.62 (^[O: $i, P: $i, Q: $i, R: $i] : rewrite((between_o(O, P, Q, R) <=> ((ordered_by(O, R, Q) & ordered_by(O, Q, P)) | (ordered_by(O, P, Q) & ordered_by(O, Q, R)))) <=> (between_o(O, P, Q, R) <=> ((~((~ordered_by(O, R, Q)) | (~ordered_by(O, Q, P)))) | (~((~ordered_by(O, P, Q)) | (~ordered_by(O, Q, R)))))))),
% 156.91/98.62 inference(bind,[status(th)],[])).
% 156.91/98.62 tff(27,plain,
% 156.91/98.62 (![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((ordered_by(O, R, Q) & ordered_by(O, Q, P)) | (ordered_by(O, P, Q) & ordered_by(O, Q, R)))) <=> ![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((~((~ordered_by(O, R, Q)) | (~ordered_by(O, Q, P)))) | (~((~ordered_by(O, P, Q)) | (~ordered_by(O, Q, R))))))),
% 156.91/98.62 inference(quant_intro,[status(thm)],[26])).
% 156.91/98.62 tff(28,plain,
% 156.91/98.62 (![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((ordered_by(O, R, Q) & ordered_by(O, Q, P)) | (ordered_by(O, P, Q) & ordered_by(O, Q, R)))) <=> ![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((ordered_by(O, R, Q) & ordered_by(O, Q, P)) | (ordered_by(O, P, Q) & ordered_by(O, Q, R))))),
% 156.91/98.62 inference(rewrite,[status(thm)],[])).
% 156.91/98.62 tff(29,plain,
% 156.91/98.62 (^[O: $i, P: $i, Q: $i, R: $i] : rewrite((between_o(O, P, Q, R) <=> ((ordered_by(O, P, Q) & ordered_by(O, Q, R)) | (ordered_by(O, R, Q) & ordered_by(O, Q, P)))) <=> (between_o(O, P, Q, R) <=> ((ordered_by(O, R, Q) & ordered_by(O, Q, P)) | (ordered_by(O, P, Q) & ordered_by(O, Q, R)))))),
% 156.91/98.62 inference(bind,[status(th)],[])).
% 156.91/98.62 tff(30,plain,
% 156.91/98.62 (![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((ordered_by(O, P, Q) & ordered_by(O, Q, R)) | (ordered_by(O, R, Q) & ordered_by(O, Q, P)))) <=> ![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((ordered_by(O, R, Q) & ordered_by(O, Q, P)) | (ordered_by(O, P, Q) & ordered_by(O, Q, R))))),
% 156.91/98.62 inference(quant_intro,[status(thm)],[29])).
% 156.91/98.62 tff(31,axiom,(![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((ordered_by(O, P, Q) & ordered_by(O, Q, R)) | (ordered_by(O, R, Q) & ordered_by(O, Q, P))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax','between_o_defn')).
% 156.91/98.62 tff(32,plain,
% 156.91/98.62 (![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((ordered_by(O, R, Q) & ordered_by(O, Q, P)) | (ordered_by(O, P, Q) & ordered_by(O, Q, R))))),
% 156.91/98.62 inference(modus_ponens,[status(thm)],[31, 30])).
% 156.91/98.62 tff(33,plain,
% 156.91/98.62 (![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((ordered_by(O, R, Q) & ordered_by(O, Q, P)) | (ordered_by(O, P, Q) & ordered_by(O, Q, R))))),
% 156.91/98.62 inference(modus_ponens,[status(thm)],[32, 28])).
% 156.91/98.62 tff(34,plain,(
% 156.91/98.62 ![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((ordered_by(O, R, Q) & ordered_by(O, Q, P)) | (ordered_by(O, P, Q) & ordered_by(O, Q, R))))),
% 156.91/98.62 inference(skolemize,[status(sab)],[33])).
% 156.91/98.62 tff(35,plain,
% 156.91/98.62 (![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((~((~ordered_by(O, R, Q)) | (~ordered_by(O, Q, P)))) | (~((~ordered_by(O, P, Q)) | (~ordered_by(O, Q, R))))))),
% 156.91/98.62 inference(modus_ponens,[status(thm)],[34, 27])).
% 156.91/98.62 tff(36,plain,
% 156.91/98.62 (![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((~((~ordered_by(O, R, Q)) | (~ordered_by(O, Q, P)))) | (~((~ordered_by(O, P, Q)) | (~ordered_by(O, Q, R))))))),
% 156.91/98.62 inference(modus_ponens,[status(thm)],[35, 25])).
% 156.91/98.62 tff(37,plain,
% 156.91/98.62 (((~![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((~((~ordered_by(O, R, Q)) | (~ordered_by(O, Q, P)))) | (~((~ordered_by(O, P, Q)) | (~ordered_by(O, Q, R))))))) | (between_o(O!25, Q!23, P!24, Q!23) <=> (~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23)))))) <=> ((~![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((~((~ordered_by(O, R, Q)) | (~ordered_by(O, Q, P)))) | (~((~ordered_by(O, P, Q)) | (~ordered_by(O, Q, R))))))) | (between_o(O!25, Q!23, P!24, Q!23) <=> (~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23))))))),
% 156.91/98.62 inference(rewrite,[status(thm)],[])).
% 156.91/98.62 tff(38,plain,
% 156.91/98.62 ((between_o(O!25, Q!23, P!24, Q!23) <=> ((~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23)))) | (~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23)))))) <=> (between_o(O!25, Q!23, P!24, Q!23) <=> (~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23)))))),
% 156.91/98.62 inference(rewrite,[status(thm)],[])).
% 156.91/98.62 tff(39,plain,
% 156.91/98.62 (((~![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((~((~ordered_by(O, R, Q)) | (~ordered_by(O, Q, P)))) | (~((~ordered_by(O, P, Q)) | (~ordered_by(O, Q, R))))))) | (between_o(O!25, Q!23, P!24, Q!23) <=> ((~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23)))) | (~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23))))))) <=> ((~![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((~((~ordered_by(O, R, Q)) | (~ordered_by(O, Q, P)))) | (~((~ordered_by(O, P, Q)) | (~ordered_by(O, Q, R))))))) | (between_o(O!25, Q!23, P!24, Q!23) <=> (~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23))))))),
% 156.91/98.62 inference(monotonicity,[status(thm)],[38])).
% 156.91/98.62 tff(40,plain,
% 156.91/98.62 (((~![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((~((~ordered_by(O, R, Q)) | (~ordered_by(O, Q, P)))) | (~((~ordered_by(O, P, Q)) | (~ordered_by(O, Q, R))))))) | (between_o(O!25, Q!23, P!24, Q!23) <=> ((~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23)))) | (~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23))))))) <=> ((~![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((~((~ordered_by(O, R, Q)) | (~ordered_by(O, Q, P)))) | (~((~ordered_by(O, P, Q)) | (~ordered_by(O, Q, R))))))) | (between_o(O!25, Q!23, P!24, Q!23) <=> (~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23))))))),
% 156.91/98.62 inference(transitivity,[status(thm)],[39, 37])).
% 156.91/98.62 tff(41,plain,
% 156.91/98.62 ((~![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((~((~ordered_by(O, R, Q)) | (~ordered_by(O, Q, P)))) | (~((~ordered_by(O, P, Q)) | (~ordered_by(O, Q, R))))))) | (between_o(O!25, Q!23, P!24, Q!23) <=> ((~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23)))) | (~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23))))))),
% 156.91/98.62 inference(quant_inst,[status(thm)],[])).
% 156.91/98.62 tff(42,plain,
% 156.91/98.62 ((~![O: $i, P: $i, Q: $i, R: $i] : (between_o(O, P, Q, R) <=> ((~((~ordered_by(O, R, Q)) | (~ordered_by(O, Q, P)))) | (~((~ordered_by(O, P, Q)) | (~ordered_by(O, Q, R))))))) | (between_o(O!25, Q!23, P!24, Q!23) <=> (~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23)))))),
% 156.91/98.62 inference(modus_ponens,[status(thm)],[41, 40])).
% 156.91/98.62 tff(43,plain,
% 156.91/98.62 (between_o(O!25, Q!23, P!24, Q!23) <=> (~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23))))),
% 156.91/98.62 inference(unit_resolution,[status(thm)],[42, 36])).
% 156.91/98.62 tff(44,plain,
% 156.91/98.62 ((~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23)))) <=> (~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23))))),
% 156.91/98.62 inference(rewrite,[status(thm)],[])).
% 156.91/98.62 tff(45,plain,
% 156.91/98.62 ((~![O: $i, P: $i, Q: $i] : ((~ordered_by(O, Q, P)) | (~ordered_by(O, P, Q)))) <=> (~![O: $i, P: $i, Q: $i] : ((~ordered_by(O, Q, P)) | (~ordered_by(O, P, Q))))),
% 156.91/98.62 inference(rewrite,[status(thm)],[])).
% 156.91/98.62 tff(46,plain,
% 156.91/98.62 ((~![O: $i, P: $i, Q: $i] : (ordered_by(O, P, Q) => (~ordered_by(O, Q, P)))) <=> (~![O: $i, P: $i, Q: $i] : ((~ordered_by(O, Q, P)) | (~ordered_by(O, P, Q))))),
% 156.91/98.62 inference(rewrite,[status(thm)],[])).
% 156.91/98.62 tff(47,axiom,(~![O: $i, P: $i, Q: $i] : (ordered_by(O, P, Q) => (~ordered_by(O, Q, P)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','theorem_4_5')).
% 156.91/98.62 tff(48,plain,
% 156.91/98.62 (~![O: $i, P: $i, Q: $i] : ((~ordered_by(O, Q, P)) | (~ordered_by(O, P, Q)))),
% 156.91/98.62 inference(modus_ponens,[status(thm)],[47, 46])).
% 156.91/98.62 tff(49,plain,
% 156.91/98.62 (~![O: $i, P: $i, Q: $i] : ((~ordered_by(O, Q, P)) | (~ordered_by(O, P, Q)))),
% 156.91/98.62 inference(modus_ponens,[status(thm)],[48, 45])).
% 156.91/98.62 tff(50,plain,
% 156.91/98.62 (~![O: $i, P: $i, Q: $i] : ((~ordered_by(O, Q, P)) | (~ordered_by(O, P, Q)))),
% 156.91/98.62 inference(modus_ponens,[status(thm)],[49, 45])).
% 156.91/98.62 tff(51,plain,
% 156.91/98.62 (~![O: $i, P: $i, Q: $i] : ((~ordered_by(O, Q, P)) | (~ordered_by(O, P, Q)))),
% 156.91/98.62 inference(modus_ponens,[status(thm)],[50, 45])).
% 156.91/98.62 tff(52,plain,
% 156.91/98.62 (~![O: $i, P: $i, Q: $i] : ((~ordered_by(O, Q, P)) | (~ordered_by(O, P, Q)))),
% 156.91/98.62 inference(modus_ponens,[status(thm)],[51, 45])).
% 156.91/98.62 tff(53,plain,
% 156.91/98.62 (~![O: $i, P: $i, Q: $i] : ((~ordered_by(O, Q, P)) | (~ordered_by(O, P, Q)))),
% 156.91/98.62 inference(modus_ponens,[status(thm)],[52, 45])).
% 156.91/98.62 tff(54,plain,
% 156.91/98.62 (~![O: $i, P: $i, Q: $i] : ((~ordered_by(O, Q, P)) | (~ordered_by(O, P, Q)))),
% 156.91/98.62 inference(modus_ponens,[status(thm)],[53, 45])).
% 156.91/98.62 tff(55,plain,(
% 156.91/98.62 ~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23)))),
% 156.91/98.62 inference(skolemize,[status(sab)],[54])).
% 156.91/98.62 tff(56,plain,
% 156.91/98.62 (~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23)))),
% 156.91/98.62 inference(modus_ponens,[status(thm)],[55, 44])).
% 156.91/98.62 tff(57,plain,
% 156.91/98.62 (ordered_by(O!25, P!24, Q!23)),
% 156.91/98.62 inference(or_elim,[status(thm)],[56])).
% 156.91/98.62 tff(58,plain,
% 156.91/98.62 (ordered_by(O!25, Q!23, P!24)),
% 156.91/98.62 inference(or_elim,[status(thm)],[56])).
% 156.91/98.62 tff(59,plain,
% 156.91/98.62 ((~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23)))) | (~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23))),
% 156.91/98.62 inference(tautology,[status(thm)],[])).
% 156.91/98.62 tff(60,plain,
% 156.91/98.62 (~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23)))),
% 156.91/98.62 inference(unit_resolution,[status(thm)],[59, 58, 57])).
% 156.91/98.62 tff(61,plain,
% 156.91/98.62 ((~(between_o(O!25, Q!23, P!24, Q!23) <=> (~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23)))))) | between_o(O!25, Q!23, P!24, Q!23) | ((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23)))),
% 156.91/98.62 inference(tautology,[status(thm)],[])).
% 156.91/98.62 tff(62,plain,
% 156.91/98.62 ((~(between_o(O!25, Q!23, P!24, Q!23) <=> (~((~ordered_by(O!25, Q!23, P!24)) | (~ordered_by(O!25, P!24, Q!23)))))) | between_o(O!25, Q!23, P!24, Q!23)),
% 156.91/98.62 inference(unit_resolution,[status(thm)],[61, 60])).
% 156.91/98.62 tff(63,plain,
% 156.91/98.62 (between_o(O!25, Q!23, P!24, Q!23)),
% 156.91/98.62 inference(unit_resolution,[status(thm)],[62, 43])).
% 156.91/98.62 tff(64,plain,
% 156.91/98.62 ((~((~between_o(O!25, Q!23, P!24, Q!23)) | (~((~between_c(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23)) | (~![P: $i] : (incident_o(P, O!25) <=> incident_c(P, tptp_fun_C_16(O!25, Q!23, P!24, Q!23)))))))) | (~between_o(O!25, Q!23, P!24, Q!23)) | (~((~between_c(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23)) | (~![P: $i] : (incident_o(P, O!25) <=> incident_c(P, tptp_fun_C_16(O!25, Q!23, P!24, Q!23))))))),
% 156.91/98.62 inference(tautology,[status(thm)],[])).
% 156.91/98.62 tff(65,plain,
% 156.91/98.62 ((~((~between_o(O!25, Q!23, P!24, Q!23)) | (~((~between_c(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23)) | (~![P: $i] : (incident_o(P, O!25) <=> incident_c(P, tptp_fun_C_16(O!25, Q!23, P!24, Q!23)))))))) | (~((~between_c(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23)) | (~![P: $i] : (incident_o(P, O!25) <=> incident_c(P, tptp_fun_C_16(O!25, Q!23, P!24, Q!23))))))),
% 156.91/98.62 inference(unit_resolution,[status(thm)],[64, 63])).
% 156.91/98.62 tff(66,plain,
% 156.91/98.62 (~((~between_c(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23)) | (~![P: $i] : (incident_o(P, O!25) <=> incident_c(P, tptp_fun_C_16(O!25, Q!23, P!24, Q!23)))))),
% 156.91/98.62 inference(unit_resolution,[status(thm)],[65, 23])).
% 156.91/98.62 tff(67,plain,
% 156.91/98.62 (((~between_c(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23)) | (~![P: $i] : (incident_o(P, O!25) <=> incident_c(P, tptp_fun_C_16(O!25, Q!23, P!24, Q!23))))) | between_c(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23)),
% 156.91/98.62 inference(tautology,[status(thm)],[])).
% 156.91/98.62 tff(68,plain,
% 156.91/98.62 (between_c(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23)),
% 156.91/98.62 inference(unit_resolution,[status(thm)],[67, 66])).
% 156.91/98.62 tff(69,plain,
% 156.91/98.62 (^[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))))))))),
% 156.91/98.62 inference(bind,[status(th)],[])).
% 156.91/98.62 tff(70,plain,
% 156.91/98.62 (![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)))))))),
% 156.91/98.62 inference(quant_intro,[status(thm)],[69])).
% 156.91/98.62 tff(71,plain,
% 156.91/98.62 (^[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))))))))),
% 156.91/98.62 inference(bind,[status(th)],[])).
% 156.91/98.62 tff(72,plain,
% 156.91/98.62 (![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)))))))),
% 156.91/98.62 inference(quant_intro,[status(thm)],[71])).
% 156.91/98.62 tff(73,plain,
% 156.91/98.62 (![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)))))))),
% 156.91/98.62 inference(transitivity,[status(thm)],[72, 70])).
% 156.91/98.62 tff(74,plain,
% 156.91/98.62 (^[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)))))))))),
% 156.91/98.62 inference(bind,[status(th)],[])).
% 156.91/98.62 tff(75,plain,
% 156.91/98.62 (![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)))))))),
% 156.91/98.62 inference(quant_intro,[status(thm)],[74])).
% 156.91/98.62 tff(76,plain,
% 156.91/98.62 (^[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))))))),
% 156.91/98.62 inference(bind,[status(th)],[])).
% 156.91/98.62 tff(77,plain,
% 156.91/98.62 (![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)))))),
% 156.91/98.62 inference(quant_intro,[status(thm)],[76])).
% 156.91/98.62 tff(78,plain,
% 156.91/98.62 (![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))))),
% 156.91/98.62 inference(rewrite,[status(thm)],[])).
% 156.91/98.62 tff(79,plain,
% 156.91/98.62 (^[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)))))),
% 156.91/98.62 inference(bind,[status(th)],[])).
% 156.91/98.62 tff(80,plain,
% 156.91/98.62 (![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))))),
% 156.91/98.62 inference(quant_intro,[status(thm)],[79])).
% 156.91/98.62 tff(81,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')).
% 156.91/98.62 tff(82,plain,
% 156.91/98.62 (![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))))),
% 156.91/98.62 inference(modus_ponens,[status(thm)],[81, 80])).
% 156.91/98.62 tff(83,plain,
% 156.91/98.62 (![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))))),
% 156.91/98.62 inference(modus_ponens,[status(thm)],[82, 78])).
% 156.91/98.62 tff(84,plain,(
% 156.91/98.62 ![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))))))),
% 156.91/98.62 inference(skolemize,[status(sab)],[83])).
% 156.91/98.62 tff(85,plain,
% 156.91/98.62 (![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)))))),
% 156.91/98.62 inference(modus_ponens,[status(thm)],[84, 77])).
% 156.91/98.62 tff(86,plain,
% 156.91/98.62 (![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)))))))),
% 156.91/98.62 inference(modus_ponens,[status(thm)],[85, 75])).
% 156.91/98.62 tff(87,plain,
% 156.91/98.62 (![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)))))))),
% 156.91/98.62 inference(modus_ponens,[status(thm)],[86, 73])).
% 156.91/98.62 tff(88,plain,
% 156.91/98.62 (((~![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(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23))) <=> ((~![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(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23)))),
% 156.91/98.62 inference(rewrite,[status(thm)],[])).
% 156.91/98.62 tff(89,plain,
% 156.91/98.62 ((~((~((~between_c(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23)) | (~((Q!23 = Q!23) | (~part_of(tptp_fun_Cpp_12(Q!23, P!24, Q!23, tptp_fun_C_16(O!25, Q!23, P!24, Q!23)), tptp_fun_C_16(O!25, Q!23, P!24, Q!23))) | (~end_point(Q!23, tptp_fun_Cpp_12(Q!23, P!24, Q!23, tptp_fun_C_16(O!25, Q!23, P!24, Q!23)))) | (~end_point(Q!23, tptp_fun_Cpp_12(Q!23, P!24, Q!23, tptp_fun_C_16(O!25, Q!23, P!24, Q!23)))) | (~inner_point(P!24, tptp_fun_Cpp_12(Q!23, P!24, Q!23, tptp_fun_C_16(O!25, Q!23, P!24, Q!23)))))))) | (~((Q!23 = Q!23) | between_c(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23) | ![Cpp: $i] : ((~end_point(Q!23, Cpp)) | (~part_of(Cpp, tptp_fun_C_16(O!25, Q!23, P!24, Q!23))) | (~end_point(Q!23, Cpp)) | (~inner_point(P!24, Cpp))))))) <=> (~between_c(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23))),
% 156.91/98.62 inference(rewrite,[status(thm)],[])).
% 156.91/98.62 tff(90,plain,
% 156.91/98.62 (((~![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(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23)) | (~((Q!23 = Q!23) | (~part_of(tptp_fun_Cpp_12(Q!23, P!24, Q!23, tptp_fun_C_16(O!25, Q!23, P!24, Q!23)), tptp_fun_C_16(O!25, Q!23, P!24, Q!23))) | (~end_point(Q!23, tptp_fun_Cpp_12(Q!23, P!24, Q!23, tptp_fun_C_16(O!25, Q!23, P!24, Q!23)))) | (~end_point(Q!23, tptp_fun_Cpp_12(Q!23, P!24, Q!23, tptp_fun_C_16(O!25, Q!23, P!24, Q!23)))) | (~inner_point(P!24, tptp_fun_Cpp_12(Q!23, P!24, Q!23, tptp_fun_C_16(O!25, Q!23, P!24, Q!23)))))))) | (~((Q!23 = Q!23) | between_c(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23) | ![Cpp: $i] : ((~end_point(Q!23, Cpp)) | (~part_of(Cpp, tptp_fun_C_16(O!25, Q!23, P!24, Q!23))) | (~end_point(Q!23, Cpp)) | (~inner_point(P!24, 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(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23)))),
% 156.91/98.62 inference(monotonicity,[status(thm)],[89])).
% 156.91/98.62 tff(91,plain,
% 156.91/98.62 (((~![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(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23)) | (~((Q!23 = Q!23) | (~part_of(tptp_fun_Cpp_12(Q!23, P!24, Q!23, tptp_fun_C_16(O!25, Q!23, P!24, Q!23)), tptp_fun_C_16(O!25, Q!23, P!24, Q!23))) | (~end_point(Q!23, tptp_fun_Cpp_12(Q!23, P!24, Q!23, tptp_fun_C_16(O!25, Q!23, P!24, Q!23)))) | (~end_point(Q!23, tptp_fun_Cpp_12(Q!23, P!24, Q!23, tptp_fun_C_16(O!25, Q!23, P!24, Q!23)))) | (~inner_point(P!24, tptp_fun_Cpp_12(Q!23, P!24, Q!23, tptp_fun_C_16(O!25, Q!23, P!24, Q!23)))))))) | (~((Q!23 = Q!23) | between_c(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23) | ![Cpp: $i] : ((~end_point(Q!23, Cpp)) | (~part_of(Cpp, tptp_fun_C_16(O!25, Q!23, P!24, Q!23))) | (~end_point(Q!23, Cpp)) | (~inner_point(P!24, 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(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23)))),
% 156.91/98.62 inference(transitivity,[status(thm)],[90, 88])).
% 156.91/98.62 tff(92,plain,
% 156.91/98.62 ((~![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(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23)) | (~((Q!23 = Q!23) | (~part_of(tptp_fun_Cpp_12(Q!23, P!24, Q!23, tptp_fun_C_16(O!25, Q!23, P!24, Q!23)), tptp_fun_C_16(O!25, Q!23, P!24, Q!23))) | (~end_point(Q!23, tptp_fun_Cpp_12(Q!23, P!24, Q!23, tptp_fun_C_16(O!25, Q!23, P!24, Q!23)))) | (~end_point(Q!23, tptp_fun_Cpp_12(Q!23, P!24, Q!23, tptp_fun_C_16(O!25, Q!23, P!24, Q!23)))) | (~inner_point(P!24, tptp_fun_Cpp_12(Q!23, P!24, Q!23, tptp_fun_C_16(O!25, Q!23, P!24, Q!23)))))))) | (~((Q!23 = Q!23) | between_c(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23) | ![Cpp: $i] : ((~end_point(Q!23, Cpp)) | (~part_of(Cpp, tptp_fun_C_16(O!25, Q!23, P!24, Q!23))) | (~end_point(Q!23, Cpp)) | (~inner_point(P!24, Cpp)))))))),
% 156.91/98.63 inference(quant_inst,[status(thm)],[])).
% 156.91/98.63 tff(93,plain,
% 156.91/98.63 ((~![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: $i] : ((~end_point(R, Cpp)) | (~part_of(Cpp, C)) | (~end_point(P, Cpp)) | (~inner_point(Q, Cpp)))))))) | (~between_c(tptp_fun_C_16(O!25, Q!23, P!24, Q!23), Q!23, P!24, Q!23))),
% 156.91/98.63 inference(modus_ponens,[status(thm)],[92, 91])).
% 156.91/98.63 tff(94,plain,
% 156.91/98.63 ($false),
% 156.91/98.63 inference(unit_resolution,[status(thm)],[93, 87, 68])).
% 156.91/98.63 % SZS output end Proof
%------------------------------------------------------------------------------