TSTP Solution File: GEO219+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO219+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 20:35:48 EDT 2022
% Result : Theorem 0.14s 0.33s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : GEO219+1 : TPTP v8.1.0. Released v3.3.0.
% 0.02/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.08/0.28 % Computer : n029.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Wed Aug 31 07:10:57 EDT 2022
% 0.08/0.29 % CPUTime :
% 0.08/0.29 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.08/0.29 Usage: tptp [options] [-file:]file
% 0.08/0.29 -h, -? prints this message.
% 0.08/0.29 -smt2 print SMT-LIB2 benchmark.
% 0.08/0.29 -m, -model generate model.
% 0.08/0.29 -p, -proof generate proof.
% 0.08/0.29 -c, -core generate unsat core of named formulas.
% 0.08/0.29 -st, -statistics display statistics.
% 0.08/0.29 -t:timeout set timeout (in second).
% 0.08/0.29 -smt2status display status in smt2 format instead of SZS.
% 0.08/0.29 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.08/0.29 -<param>:<value> configuration parameter and value.
% 0.08/0.29 -o:<output-file> file to place output in.
% 0.14/0.33 % SZS status Theorem
% 0.14/0.33 % SZS output start Proof
% 0.14/0.33 tff(convergent_lines_type, type, (
% 0.14/0.33 convergent_lines: ( $i * $i ) > $o)).
% 0.14/0.33 tff(tptp_fun_N_0_type, type, (
% 0.14/0.33 tptp_fun_N_0: $i)).
% 0.14/0.33 tff(tptp_fun_M_1_type, type, (
% 0.14/0.33 tptp_fun_M_1: $i)).
% 0.14/0.33 tff(unorthogonal_lines_type, type, (
% 0.14/0.33 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.14/0.33 tff(tptp_fun_L_2_type, type, (
% 0.14/0.33 tptp_fun_L_2: $i)).
% 0.14/0.33 tff(1,plain,
% 0.14/0.33 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~convergent_lines(L, N)))))) <=> (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~convergent_lines(L, N))))))),
% 0.14/0.33 inference(rewrite,[status(thm)],[])).
% 0.14/0.33 tff(2,plain,
% 0.14/0.33 ((~![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~convergent_lines(L, N))) => (~unorthogonal_lines(M, N)))) <=> (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~convergent_lines(L, N))))))),
% 0.14/0.33 inference(rewrite,[status(thm)],[])).
% 0.14/0.33 tff(3,axiom,(~![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~convergent_lines(L, N))) => (~unorthogonal_lines(M, N)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.14/0.33 tff(4,plain,
% 0.14/0.33 (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.14/0.33 tff(5,plain,
% 0.14/0.33 (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.14/0.33 tff(6,plain,
% 0.14/0.33 (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.14/0.33 tff(7,plain,
% 0.14/0.33 (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.14/0.33 tff(8,plain,
% 0.14/0.33 (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.14/0.33 tff(9,plain,
% 0.14/0.33 (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.14/0.33 tff(10,plain,
% 0.14/0.33 (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.14/0.33 tff(11,plain,(
% 0.14/0.33 ~((~unorthogonal_lines(M!1, N!0)) | (~((~unorthogonal_lines(L!2, M!1)) & (~convergent_lines(L!2, N!0)))))),
% 0.14/0.33 inference(skolemize,[status(sab)],[10])).
% 0.14/0.33 tff(12,plain,
% 0.14/0.33 ((~unorthogonal_lines(L!2, M!1)) & (~convergent_lines(L!2, N!0))),
% 0.14/0.33 inference(or_elim,[status(thm)],[11])).
% 0.14/0.33 tff(13,plain,
% 0.14/0.33 (~convergent_lines(L!2, N!0)),
% 0.14/0.33 inference(and_elim,[status(thm)],[12])).
% 0.14/0.33 tff(14,plain,
% 0.14/0.33 (((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))) | convergent_lines(L!2, N!0)),
% 0.14/0.33 inference(tautology,[status(thm)],[])).
% 0.14/0.33 tff(15,plain,
% 0.14/0.33 ((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.14/0.33 tff(16,plain,
% 0.14/0.33 (~unorthogonal_lines(L!2, M!1)),
% 0.14/0.33 inference(and_elim,[status(thm)],[12])).
% 0.14/0.33 tff(17,plain,
% 0.14/0.33 (((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))) | unorthogonal_lines(L!2, M!1)),
% 0.14/0.33 inference(tautology,[status(thm)],[])).
% 0.14/0.33 tff(18,plain,
% 0.14/0.33 ((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.14/0.33 tff(19,plain,
% 0.14/0.33 (unorthogonal_lines(M!1, N!0)),
% 0.14/0.33 inference(or_elim,[status(thm)],[11])).
% 0.14/0.33 tff(20,plain,
% 0.14/0.33 (^[L: $i, M: $i, N: $i] : refl(((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.14/0.33 inference(bind,[status(th)],[])).
% 0.14/0.33 tff(21,plain,
% 0.14/0.33 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.14/0.33 inference(quant_intro,[status(thm)],[20])).
% 0.14/0.33 tff(22,plain,
% 0.14/0.33 (^[L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) <=> (~((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))), ((~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> (~(~((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))))), rewrite((~(~((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))) <=> ((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))), ((~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> ((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))), (((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | ((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))))), rewrite(((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | ((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))), (((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))))),
% 0.14/0.33 inference(bind,[status(th)],[])).
% 0.14/0.33 tff(23,plain,
% 0.14/0.33 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.14/0.33 inference(quant_intro,[status(thm)],[22])).
% 0.14/0.33 tff(24,plain,
% 0.14/0.33 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.14/0.33 inference(rewrite,[status(thm)],[])).
% 0.14/0.33 tff(25,plain,
% 0.14/0.33 (^[L: $i, M: $i, N: $i] : rewrite(((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) => ((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))))),
% 0.14/0.33 inference(bind,[status(th)],[])).
% 0.14/0.33 tff(26,plain,
% 0.14/0.33 (![L: $i, M: $i, N: $i] : ((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) => ((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.14/0.33 inference(quant_intro,[status(thm)],[25])).
% 0.14/0.33 tff(27,axiom,(![L: $i, M: $i, N: $i] : ((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) => ((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax','cotno1')).
% 0.14/0.33 tff(28,plain,
% 0.14/0.33 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.14/0.33 tff(29,plain,
% 0.14/0.33 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.14/0.33 tff(30,plain,(
% 0.14/0.33 ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.14/0.33 inference(skolemize,[status(sab)],[29])).
% 0.14/0.33 tff(31,plain,
% 0.14/0.33 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.14/0.33 tff(32,plain,
% 0.14/0.33 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.14/0.33 tff(33,plain,
% 0.14/0.33 (((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))),
% 0.14/0.33 inference(rewrite,[status(thm)],[])).
% 0.14/0.33 tff(34,plain,
% 0.14/0.33 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))),
% 0.14/0.33 inference(quant_inst,[status(thm)],[])).
% 0.14/0.33 tff(35,plain,
% 0.14/0.33 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.14/0.33 tff(36,plain,
% 0.14/0.33 (~convergent_lines(M!1, N!0)),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[35, 32, 19, 18, 15])).
% 0.14/0.33 tff(37,plain,
% 0.14/0.33 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.14/0.33 inference(bind,[status(th)],[])).
% 0.14/0.33 tff(38,plain,
% 0.14/0.33 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.14/0.33 inference(quant_intro,[status(thm)],[37])).
% 0.14/0.33 tff(39,plain,
% 0.14/0.33 (^[L: $i, M: $i] : trans(monotonicity(rewrite(((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M))) <=> (~(convergent_lines(L, M) | unorthogonal_lines(L, M)))), ((~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M)))) <=> (~(~(convergent_lines(L, M) | unorthogonal_lines(L, M)))))), rewrite((~(~(convergent_lines(L, M) | unorthogonal_lines(L, M)))) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M))), ((~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M)))) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M))))),
% 0.14/0.33 inference(bind,[status(th)],[])).
% 0.14/0.33 tff(40,plain,
% 0.14/0.33 (![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M)))) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.14/0.33 inference(quant_intro,[status(thm)],[39])).
% 0.14/0.33 tff(41,plain,
% 0.14/0.33 (![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M)))) <=> ![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M))))),
% 0.14/0.33 inference(rewrite,[status(thm)],[])).
% 0.14/0.33 tff(42,axiom,(![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax','coipo1')).
% 0.14/0.33 tff(43,plain,
% 0.14/0.33 (![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M))))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.14/0.33 tff(44,plain,(
% 0.14/0.33 ![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M))))),
% 0.14/0.33 inference(skolemize,[status(sab)],[43])).
% 0.14/0.33 tff(45,plain,
% 0.14/0.33 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.14/0.33 tff(46,plain,
% 0.14/0.33 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.14/0.33 tff(47,plain,
% 0.14/0.33 (((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(L!2, M!1) | unorthogonal_lines(L!2, M!1))) <=> ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(L!2, M!1) | unorthogonal_lines(L!2, M!1))),
% 0.14/0.33 inference(rewrite,[status(thm)],[])).
% 0.14/0.33 tff(48,plain,
% 0.14/0.33 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(L!2, M!1) | unorthogonal_lines(L!2, M!1))),
% 0.14/0.33 inference(quant_inst,[status(thm)],[])).
% 0.14/0.33 tff(49,plain,
% 0.14/0.33 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(L!2, M!1) | unorthogonal_lines(L!2, M!1)),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.14/0.33 tff(50,plain,
% 0.14/0.33 (convergent_lines(L!2, M!1)),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[49, 46, 16])).
% 0.14/0.33 tff(51,plain,
% 0.14/0.33 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.14/0.33 inference(bind,[status(th)],[])).
% 0.14/0.33 tff(52,plain,
% 0.14/0.33 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.14/0.33 inference(quant_intro,[status(thm)],[51])).
% 0.14/0.33 tff(53,plain,
% 0.14/0.33 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(54,plain,
% 0.14/0.34 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((convergent_lines(X, Z) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.14/0.34 inference(bind,[status(th)],[])).
% 0.14/0.34 tff(55,plain,
% 0.14/0.34 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.14/0.34 inference(quant_intro,[status(thm)],[54])).
% 0.14/0.34 tff(56,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ax6')).
% 0.14/0.34 tff(57,plain,
% 0.14/0.34 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.14/0.34 tff(58,plain,
% 0.14/0.34 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.14/0.34 tff(59,plain,(
% 0.14/0.34 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.14/0.34 inference(skolemize,[status(sab)],[58])).
% 0.14/0.34 tff(60,plain,
% 0.14/0.34 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.14/0.34 tff(61,plain,
% 0.14/0.34 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(L!2, M!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(L!2, M!1)))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(62,plain,
% 0.14/0.34 ((convergent_lines(M!1, N!0) | convergent_lines(L!2, N!0) | (~convergent_lines(L!2, M!1))) <=> (convergent_lines(L!2, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(L!2, M!1)))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(63,plain,
% 0.14/0.34 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, N!0) | convergent_lines(L!2, N!0) | (~convergent_lines(L!2, M!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(L!2, M!1))))),
% 0.14/0.34 inference(monotonicity,[status(thm)],[62])).
% 0.14/0.34 tff(64,plain,
% 0.14/0.34 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, N!0) | convergent_lines(L!2, N!0) | (~convergent_lines(L!2, M!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(L!2, M!1)))),
% 0.14/0.34 inference(transitivity,[status(thm)],[63, 61])).
% 0.14/0.34 tff(65,plain,
% 0.14/0.34 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, N!0) | convergent_lines(L!2, N!0) | (~convergent_lines(L!2, M!1)))),
% 0.14/0.34 inference(quant_inst,[status(thm)],[])).
% 0.14/0.34 tff(66,plain,
% 0.14/0.34 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(L!2, M!1))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.14/0.34 tff(67,plain,
% 0.14/0.34 ($false),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[66, 60, 13, 50, 36])).
% 0.14/0.34 % SZS output end Proof
%------------------------------------------------------------------------------