%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN369+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:38:55 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN369+1 : TPTP v9.0.0. Released v2.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:31:25 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(big_p_type, type, (
% 0.12/0.38 big_p: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_Y_0_type, type, (
% 0.12/0.38 tptp_fun_Y_0: $i > $i)).
% 0.12/0.38 tff(elem_1_type, type, (
% 0.12/0.38 elem_1: $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 ((~?[X: $i] : ![Y: $i] : big_p(X, Y)) <=> (~?[X: $i] : ![Y: $i] : big_p(X, Y))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 ((~(![U: $i, V: $i, W: $i] : (big_p(U, V) | big_p(V, W)) => ?[X: $i] : ![Y: $i] : big_p(X, Y))) <=> (~((~![U: $i, V: $i, W: $i] : (big_p(V, W) | big_p(U, V))) | ?[X: $i] : ![Y: $i] : big_p(X, Y)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(3,axiom,(~(![U: $i, V: $i, W: $i] : (big_p(U, V) | big_p(V, W)) => ?[X: $i] : ![Y: $i] : big_p(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','x2120')).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (~((~![U: $i, V: $i, W: $i] : (big_p(V, W) | big_p(U, V))) | ?[X: $i] : ![Y: $i] : big_p(X, Y))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (~?[X: $i] : ![Y: $i] : big_p(X, Y)),
% 0.12/0.38 inference(or_elim,[status(thm)],[4])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (~?[X: $i] : ![Y: $i] : big_p(X, Y)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (~?[X: $i] : ![Y: $i] : big_p(X, Y)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (~?[X: $i] : ![Y: $i] : big_p(X, Y)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (^[X: $i] : sk($oeq((~![Y: $i] : big_p(X, Y)), (~big_p(X, tptp_fun_Y_0(X)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(10,plain,(
% 0.12/0.38 ![X: $i] : (~big_p(X, tptp_fun_Y_0(X)))),
% 0.12/0.38 inference(nnf-neg,[status(sab)],[8, 9])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 ((~![X: $i] : (~big_p(X, tptp_fun_Y_0(X)))) | (~big_p(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (~big_p(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 ((~![X: $i] : (~big_p(X, tptp_fun_Y_0(X)))) | (~big_p(elem!1, tptp_fun_Y_0(elem!1)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (~big_p(elem!1, tptp_fun_Y_0(elem!1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[13, 10])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (^[U: $i, V: $i, W: $i] : refl((big_p(V, W) | big_p(U, V)) <=> (big_p(V, W) | big_p(U, V)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![U: $i, V: $i, W: $i] : (big_p(V, W) | big_p(U, V)) <=> ![U: $i, V: $i, W: $i] : (big_p(V, W) | big_p(U, V))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![U: $i, V: $i, W: $i] : (big_p(V, W) | big_p(U, V)) <=> ![U: $i, V: $i, W: $i] : (big_p(V, W) | big_p(U, V))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (![U: $i, V: $i, W: $i] : (big_p(V, W) | big_p(U, V))),
% 0.12/0.38 inference(or_elim,[status(thm)],[4])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![U: $i, V: $i, W: $i] : (big_p(V, W) | big_p(U, V))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.38 tff(20,plain,(
% 0.12/0.38 ![U: $i, V: $i, W: $i] : (big_p(V, W) | big_p(U, V))),
% 0.12/0.38 inference(skolemize,[status(sab)],[19])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (![U: $i, V: $i, W: $i] : (big_p(V, W) | big_p(U, V))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (((~![U: $i, V: $i, W: $i] : (big_p(V, W) | big_p(U, V))) | (big_p(elem!1, tptp_fun_Y_0(elem!1)) | big_p(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))) <=> ((~![U: $i, V: $i, W: $i] : (big_p(V, W) | big_p(U, V))) | big_p(elem!1, tptp_fun_Y_0(elem!1)) | big_p(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 ((big_p(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))) | big_p(elem!1, tptp_fun_Y_0(elem!1))) <=> (big_p(elem!1, tptp_fun_Y_0(elem!1)) | big_p(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (((~![U: $i, V: $i, W: $i] : (big_p(V, W) | big_p(U, V))) | (big_p(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))) | big_p(elem!1, tptp_fun_Y_0(elem!1)))) <=> ((~![U: $i, V: $i, W: $i] : (big_p(V, W) | big_p(U, V))) | (big_p(elem!1, tptp_fun_Y_0(elem!1)) | big_p(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[23])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (((~![U: $i, V: $i, W: $i] : (big_p(V, W) | big_p(U, V))) | (big_p(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))) | big_p(elem!1, tptp_fun_Y_0(elem!1)))) <=> ((~![U: $i, V: $i, W: $i] : (big_p(V, W) | big_p(U, V))) | big_p(elem!1, tptp_fun_Y_0(elem!1)) | big_p(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[24, 22])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 ((~![U: $i, V: $i, W: $i] : (big_p(V, W) | big_p(U, V))) | (big_p(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))) | big_p(elem!1, tptp_fun_Y_0(elem!1)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 ((~![U: $i, V: $i, W: $i] : (big_p(V, W) | big_p(U, V))) | big_p(elem!1, tptp_fun_Y_0(elem!1)) | big_p(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[27, 21, 14, 12])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------