%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN370+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN370+1 : TPTP v9.0.0. Released v2.0.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 12:32:40 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(big_p_type, type, (
% 0.19/0.39 big_p: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(h_type, type, (
% 0.19/0.39 h: $i > $i)).
% 0.19/0.39 tff(tptp_fun_Y_0_type, type, (
% 0.19/0.39 tptp_fun_Y_0: $i > $i)).
% 0.19/0.39 tff(a_type, type, (
% 0.19/0.39 a: $i)).
% 0.19/0.39 tff(f_type, type, (
% 0.19/0.39 f: $i > $i)).
% 0.19/0.39 tff(elem_1_type, type, (
% 0.19/0.39 elem_1: $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (![V: $i] : ![Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z))) <=> ![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))),
% 0.19/0.39 inference(pull_quant,[status(thm)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 ((~?[V: $i] : ![Y: $i] : ?[Z: $i] : ((~(big_p(a, Y, h(Y)) | big_p(V, Y, f(Y)))) | big_p(V, Y, Z))) <=> (~?[V: $i] : ![Y: $i] : ?[Z: $i] : ((~(big_p(a, Y, h(Y)) | big_p(V, Y, f(Y)))) | big_p(V, Y, Z)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 ((~?[V: $i] : ![Y: $i] : ?[Z: $i] : ((big_p(a, Y, h(Y)) | big_p(V, Y, f(Y))) => big_p(V, Y, Z))) <=> (~?[V: $i] : ![Y: $i] : ?[Z: $i] : ((~(big_p(a, Y, h(Y)) | big_p(V, Y, f(Y)))) | big_p(V, Y, Z)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,axiom,(~?[V: $i] : ![Y: $i] : ?[Z: $i] : ((big_p(a, Y, h(Y)) | big_p(V, Y, f(Y))) => big_p(V, Y, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x2121')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (~?[V: $i] : ![Y: $i] : ?[Z: $i] : ((~(big_p(a, Y, h(Y)) | big_p(V, Y, f(Y)))) | big_p(V, Y, Z))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (~?[V: $i] : ![Y: $i] : ?[Z: $i] : ((~(big_p(a, Y, h(Y)) | big_p(V, Y, f(Y)))) | big_p(V, Y, Z))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (~?[V: $i] : ![Y: $i] : ?[Z: $i] : ((~(big_p(a, Y, h(Y)) | big_p(V, Y, f(Y)))) | big_p(V, Y, Z))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (~?[V: $i] : ![Y: $i] : ?[Z: $i] : ((~(big_p(a, Y, h(Y)) | big_p(V, Y, f(Y)))) | big_p(V, Y, Z))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (^[V: $i] : trans(sk($oeq((~![Y: $i] : ?[Z: $i] : ((~(big_p(a, Y, h(Y)) | big_p(V, Y, f(Y)))) | big_p(V, Y, Z))), (~?[Z: $i] : ((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z))))), nnf_neg(proof_bind(^[Z: $i] : refl($oeq((~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z))), (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))))), $oeq((~?[Z: $i] : ((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z))), ![Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z))))), $oeq((~![Y: $i] : ?[Z: $i] : ((~(big_p(a, Y, h(Y)) | big_p(V, Y, f(Y)))) | big_p(V, Y, Z))), ![Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(10,plain,(
% 0.19/0.39 ![V: $i] : ![Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))),
% 0.19/0.39 inference(nnf-neg,[status(sab)],[8, 9])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[10, 1])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 ((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (~((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a)))) | (~big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (~big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 ((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(elem!1)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (~((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(elem!1))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[16, 11])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(elem!1)))) | (big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 ((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[21, 15])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a)))) | (~big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 ((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 ((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[25, 11, 24])).
% 0.19/0.39 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------