%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN381+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:38:56 AM UTC 2025
% Result : Theorem 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN381+1 : TPTP v9.0.0. Released v2.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:34:57 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(big_q_type, type, (
% 0.11/0.36 big_q: ( $i * $i ) > $o)).
% 0.11/0.36 tff(tptp_fun_Z_1_type, type, (
% 0.11/0.36 tptp_fun_Z_1: $i)).
% 0.11/0.36 tff(tptp_fun_U_0_type, type, (
% 0.11/0.36 tptp_fun_U_0: $i > $i)).
% 0.11/0.36 tff(big_p_type, type, (
% 0.11/0.36 big_p: $i > $o)).
% 0.11/0.36 tff(1,assumption,(big_q(Z!1, tptp_fun_U_0(Z!1))), introduced(assumption)).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 ((~![Z: $i] : big_p(Z)) <=> (~![Z: $i] : big_p(Z))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 ((~(((![X: $i] : (?[Y: $i] : big_q(X, Y) => big_p(X)) & ![V: $i] : ?[U: $i] : big_q(U, V)) & ![W: $i, Z: $i] : (big_q(W, Z) => (big_q(Z, W) | big_q(Z, Z)))) => ![Z: $i] : big_p(Z))) <=> (~((~(![X: $i] : (big_p(X) | (~?[Y: $i] : big_q(X, Y))) & ![V: $i] : ?[U: $i] : big_q(U, V) & ![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z))))) | ![Z: $i] : big_p(Z)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(4,axiom,(~(((![X: $i] : (?[Y: $i] : big_q(X, Y) => big_p(X)) & ![V: $i] : ?[U: $i] : big_q(U, V)) & ![W: $i, Z: $i] : (big_q(W, Z) => (big_q(Z, W) | big_q(Z, Z)))) => ![Z: $i] : big_p(Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','x2133')).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 (~((~(![X: $i] : (big_p(X) | (~?[Y: $i] : big_q(X, Y))) & ![V: $i] : ?[U: $i] : big_q(U, V) & ![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z))))) | ![Z: $i] : big_p(Z))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (~![Z: $i] : big_p(Z)),
% 0.11/0.36 inference(or_elim,[status(thm)],[5])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (~![Z: $i] : big_p(Z)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (~![Z: $i] : big_p(Z)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (~![Z: $i] : big_p(Z)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.11/0.36 tff(10,plain,(
% 0.11/0.36 ~big_p(Z!1)),
% 0.11/0.36 inference(skolemize,[status(sab)],[9])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (^[X: $i] : refl((big_p(X) | ![Y: $i] : (~big_q(X, Y))) <=> (big_p(X) | ![Y: $i] : (~big_q(X, Y))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y))) <=> ![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[11])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (^[X: $i] : rewrite((big_p(X) | ![Y: $i] : (~big_q(X, Y))) <=> (big_p(X) | ![Y: $i] : (~big_q(X, Y))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y))) <=> ![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y))) <=> ![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y)))),
% 0.11/0.36 inference(transitivity,[status(thm)],[14, 12])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 (![X: $i] : (big_p(X) | (~?[Y: $i] : big_q(X, Y))) <=> ![X: $i] : (big_p(X) | (~?[Y: $i] : big_q(X, Y)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 (![X: $i] : (big_p(X) | (~?[Y: $i] : big_q(X, Y))) & ![V: $i] : ?[U: $i] : big_q(U, V) & ![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))),
% 0.11/0.36 inference(or_elim,[status(thm)],[5])).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 (![X: $i] : (big_p(X) | (~?[Y: $i] : big_q(X, Y)))),
% 0.11/0.36 inference(and_elim,[status(thm)],[17])).
% 0.11/0.36 tff(19,plain,
% 0.11/0.36 (![X: $i] : (big_p(X) | (~?[Y: $i] : big_q(X, Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[18, 16])).
% 0.11/0.36 tff(20,plain,(
% 0.11/0.36 ![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[19])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 (![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 (((~![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y)))) | (big_p(Z!1) | ![Y: $i] : (~big_q(Z!1, Y)))) <=> ((~![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y)))) | big_p(Z!1) | ![Y: $i] : (~big_q(Z!1, Y)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 ((~![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y)))) | (big_p(Z!1) | ![Y: $i] : (~big_q(Z!1, Y)))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(24,plain,
% 0.11/0.36 ((~![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y)))) | big_p(Z!1) | ![Y: $i] : (~big_q(Z!1, Y))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 (![Y: $i] : (~big_q(Z!1, Y))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[24, 21, 10])).
% 0.11/0.36 tff(26,plain,
% 0.11/0.36 ((~![Y: $i] : (~big_q(Z!1, Y))) | (~big_q(Z!1, tptp_fun_U_0(Z!1)))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(27,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[26, 25, 1])).
% 0.11/0.36 tff(28,plain,(~big_q(Z!1, tptp_fun_U_0(Z!1))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.36 tff(29,plain,
% 0.11/0.36 (![V: $i] : ?[U: $i] : big_q(U, V) <=> ![V: $i] : ?[U: $i] : big_q(U, V)),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(30,plain,
% 0.11/0.36 (![V: $i] : ?[U: $i] : big_q(U, V)),
% 0.11/0.36 inference(and_elim,[status(thm)],[17])).
% 0.11/0.36 tff(31,plain,
% 0.11/0.36 (![V: $i] : ?[U: $i] : big_q(U, V)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.11/0.36 tff(32,plain,(
% 0.11/0.36 ![V: $i] : big_q(tptp_fun_U_0(V), V)),
% 0.11/0.36 inference(skolemize,[status(sab)],[31])).
% 0.11/0.36 tff(33,plain,
% 0.11/0.36 ((~![V: $i] : big_q(tptp_fun_U_0(V), V)) | big_q(tptp_fun_U_0(Z!1), Z!1)),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(34,plain,
% 0.11/0.36 (big_q(tptp_fun_U_0(Z!1), Z!1)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.11/0.36 tff(35,plain,
% 0.11/0.36 (^[W: $i, Z: $i] : refl((big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z))) <=> (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(36,plain,
% 0.11/0.36 (![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z))) <=> ![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[35])).
% 0.11/0.36 tff(37,plain,
% 0.11/0.36 (![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z))) <=> ![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(38,plain,
% 0.11/0.36 (![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))),
% 0.11/0.36 inference(and_elim,[status(thm)],[17])).
% 0.11/0.36 tff(39,plain,
% 0.11/0.36 (![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.11/0.36 tff(40,plain,(
% 0.11/0.36 ![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[39])).
% 0.11/0.36 tff(41,plain,
% 0.11/0.36 (![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.11/0.36 tff(42,plain,
% 0.11/0.36 (((~![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))) | (big_q(Z!1, Z!1) | (~big_q(tptp_fun_U_0(Z!1), Z!1)) | big_q(Z!1, tptp_fun_U_0(Z!1)))) <=> ((~![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))) | big_q(Z!1, Z!1) | (~big_q(tptp_fun_U_0(Z!1), Z!1)) | big_q(Z!1, tptp_fun_U_0(Z!1)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(43,plain,
% 0.11/0.36 ((big_q(Z!1, tptp_fun_U_0(Z!1)) | big_q(Z!1, Z!1) | (~big_q(tptp_fun_U_0(Z!1), Z!1))) <=> (big_q(Z!1, Z!1) | (~big_q(tptp_fun_U_0(Z!1), Z!1)) | big_q(Z!1, tptp_fun_U_0(Z!1)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(44,plain,
% 0.11/0.36 (((~![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))) | (big_q(Z!1, tptp_fun_U_0(Z!1)) | big_q(Z!1, Z!1) | (~big_q(tptp_fun_U_0(Z!1), Z!1)))) <=> ((~![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))) | (big_q(Z!1, Z!1) | (~big_q(tptp_fun_U_0(Z!1), Z!1)) | big_q(Z!1, tptp_fun_U_0(Z!1))))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[43])).
% 0.11/0.36 tff(45,plain,
% 0.11/0.36 (((~![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))) | (big_q(Z!1, tptp_fun_U_0(Z!1)) | big_q(Z!1, Z!1) | (~big_q(tptp_fun_U_0(Z!1), Z!1)))) <=> ((~![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))) | big_q(Z!1, Z!1) | (~big_q(tptp_fun_U_0(Z!1), Z!1)) | big_q(Z!1, tptp_fun_U_0(Z!1)))),
% 0.11/0.36 inference(transitivity,[status(thm)],[44, 42])).
% 0.11/0.36 tff(46,plain,
% 0.11/0.36 ((~![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))) | (big_q(Z!1, tptp_fun_U_0(Z!1)) | big_q(Z!1, Z!1) | (~big_q(tptp_fun_U_0(Z!1), Z!1)))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(47,plain,
% 0.11/0.36 ((~![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))) | big_q(Z!1, Z!1) | (~big_q(tptp_fun_U_0(Z!1), Z!1)) | big_q(Z!1, tptp_fun_U_0(Z!1))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.11/0.36 tff(48,plain,
% 0.11/0.36 (big_q(Z!1, Z!1) | big_q(Z!1, tptp_fun_U_0(Z!1))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[47, 41, 34])).
% 0.11/0.37 tff(49,plain,
% 0.11/0.37 (big_q(Z!1, Z!1)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[48, 28])).
% 0.11/0.37 tff(50,plain,
% 0.11/0.37 ((~![Y: $i] : (~big_q(Z!1, Y))) | (~big_q(Z!1, Z!1))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(51,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[50, 25, 49])).
% 0.11/0.37 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------