%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO216+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:05:59 AM UTC 2025
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO216+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 14:41:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(convergent_lines_type, type, (
% 0.19/0.37 convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.37 tff(tptp_fun_L_0_type, type, (
% 0.19/0.37 tptp_fun_L_0: $i)).
% 0.19/0.37 tff(unorthogonal_lines_type, type, (
% 0.19/0.37 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.19/0.37 tff(orthogonal_lines_type, type, (
% 0.19/0.37 orthogonal_lines: ( $i * $i ) > $o)).
% 0.19/0.37 tff(1,plain,
% 0.19/0.37 (^[X: $i, Y: $i] : refl((~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y))) <=> (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(4,plain,
% 0.19/0.37 (^[X: $i, Y: $i] : trans(rewrite((orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y))) <=> (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))), rewrite((~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y))) <=> (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))), ((orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y))) <=> (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.37 tff(6,axiom,(![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','a5')).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.37 tff(9,plain,(
% 0.19/0.37 ![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[8])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 ((~![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))) | (~(unorthogonal_lines(L!0, L!0) <=> orthogonal_lines(L!0, L!0)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (~(unorthogonal_lines(L!0, L!0) <=> orthogonal_lines(L!0, L!0))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 ((~![L: $i] : (~orthogonal_lines(L, L))) <=> (~![L: $i] : (~orthogonal_lines(L, L)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(14,axiom,(~![L: $i] : (~orthogonal_lines(L, L))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (~![L: $i] : (~orthogonal_lines(L, L))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 (~![L: $i] : (~orthogonal_lines(L, L))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[15, 13])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 (~![L: $i] : (~orthogonal_lines(L, L))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (~![L: $i] : (~orthogonal_lines(L, L))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.37 tff(19,plain,(
% 0.19/0.37 orthogonal_lines(L!0, L!0)),
% 0.19/0.37 inference(skolemize,[status(sab)],[18])).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 ((unorthogonal_lines(L!0, L!0) <=> orthogonal_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)) | (~orthogonal_lines(L!0, L!0))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 ((unorthogonal_lines(L!0, L!0) <=> orthogonal_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (~unorthogonal_lines(L!0, L!0)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[21, 12])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 (^[L: $i, M: $i, N: $i] : refl((unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 (^[L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) <=> (~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))))), rewrite((~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))))), rewrite(((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 (^[L: $i, M: $i, N: $i] : rewrite((((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.37 tff(30,axiom,(![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax','couo1')).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.19/0.37 tff(33,plain,(
% 0.19/0.37 ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.19/0.37 inference(skolemize,[status(sab)],[32])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[34, 24])).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(L!0, L!0) | (~convergent_lines(L!0, L!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(L!0, L!0) | (~convergent_lines(L!0, L!0)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 ((unorthogonal_lines(L!0, L!0) | unorthogonal_lines(L!0, L!0) | (~convergent_lines(L!0, L!0))) <=> (unorthogonal_lines(L!0, L!0) | (~convergent_lines(L!0, L!0)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(L!0, L!0) | unorthogonal_lines(L!0, L!0) | (~convergent_lines(L!0, L!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(L!0, L!0) | (~convergent_lines(L!0, L!0))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[37])).
% 0.19/0.37 tff(39,plain,
% 0.19/0.37 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(L!0, L!0) | unorthogonal_lines(L!0, L!0) | (~convergent_lines(L!0, L!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(L!0, L!0) | (~convergent_lines(L!0, L!0)))),
% 0.19/0.37 inference(transitivity,[status(thm)],[38, 36])).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(L!0, L!0) | unorthogonal_lines(L!0, L!0) | (~convergent_lines(L!0, L!0)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(L!0, L!0) | (~convergent_lines(L!0, L!0))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.37 tff(42,plain,
% 0.19/0.37 (~convergent_lines(L!0, L!0)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[41, 35, 22])).
% 0.19/0.37 tff(43,plain,
% 0.19/0.37 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(44,plain,
% 0.19/0.37 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.37 tff(45,plain,
% 0.19/0.37 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(46,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','occu1')).
% 0.19/0.37 tff(47,plain,
% 0.19/0.37 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.37 tff(48,plain,(
% 0.19/0.37 ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.37 inference(skolemize,[status(sab)],[47])).
% 0.19/0.37 tff(49,plain,
% 0.19/0.37 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.19/0.37 tff(50,plain,
% 0.19/0.37 (((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(L!0, L!0) | unorthogonal_lines(L!0, L!0))) <=> ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(L!0, L!0) | unorthogonal_lines(L!0, L!0))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(51,plain,
% 0.19/0.37 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(L!0, L!0) | unorthogonal_lines(L!0, L!0))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(52,plain,
% 0.19/0.37 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(L!0, L!0) | unorthogonal_lines(L!0, L!0)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.37 tff(53,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[52, 49, 22, 42])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------