%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN366+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:38:54 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 : SYN366+1 : TPTP v9.0.0. Released v2.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.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 12:33:50 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(big_r_type, type, (
% 0.11/0.36 big_r: ( $i * $i ) > $o)).
% 0.11/0.36 tff(tptp_fun_Y_0_type, type, (
% 0.11/0.36 tptp_fun_Y_0: $i)).
% 0.11/0.36 tff(tptp_fun_X_1_type, type, (
% 0.11/0.36 tptp_fun_X_1: $i)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 (^[U: $i, V: $i] : refl((big_r(U, U) <=> big_r(U, V)) <=> (big_r(U, U) <=> big_r(U, V)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 (![U: $i, V: $i] : (big_r(U, U) <=> big_r(U, V)) <=> ![U: $i, V: $i] : (big_r(U, U) <=> big_r(U, V))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (![U: $i, V: $i] : (big_r(U, U) <=> big_r(U, V)) <=> ![U: $i, V: $i] : (big_r(U, U) <=> big_r(U, V))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 ((~((![U: $i, V: $i] : (big_r(U, U) <=> big_r(U, V)) & ![W: $i, Z: $i] : (big_r(W, W) <=> big_r(Z, W))) => (?[X: $i] : big_r(X, X) => ![Y: $i] : big_r(Y, Y)))) <=> (~(![Y: $i] : big_r(Y, Y) | (~?[X: $i] : big_r(X, X)) | (~(![U: $i, V: $i] : (big_r(U, U) <=> big_r(U, V)) & ![W: $i, Z: $i] : (big_r(W, W) <=> big_r(Z, W))))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(5,axiom,(~((![U: $i, V: $i] : (big_r(U, U) <=> big_r(U, V)) & ![W: $i, Z: $i] : (big_r(W, W) <=> big_r(Z, W))) => (?[X: $i] : big_r(X, X) => ![Y: $i] : big_r(Y, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x2117')).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (~(![Y: $i] : big_r(Y, Y) | (~?[X: $i] : big_r(X, X)) | (~(![U: $i, V: $i] : (big_r(U, U) <=> big_r(U, V)) & ![W: $i, Z: $i] : (big_r(W, W) <=> big_r(Z, W)))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (![U: $i, V: $i] : (big_r(U, U) <=> big_r(U, V)) & ![W: $i, Z: $i] : (big_r(W, W) <=> big_r(Z, W))),
% 0.11/0.36 inference(or_elim,[status(thm)],[6])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (![U: $i, V: $i] : (big_r(U, U) <=> big_r(U, V))),
% 0.11/0.36 inference(and_elim,[status(thm)],[7])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (![U: $i, V: $i] : (big_r(U, U) <=> big_r(U, V))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.11/0.36 tff(10,plain,(
% 0.11/0.36 ![U: $i, V: $i] : (big_r(U, U) <=> big_r(U, V))),
% 0.11/0.36 inference(skolemize,[status(sab)],[9])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (![U: $i, V: $i] : (big_r(U, U) <=> big_r(U, V))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 ((~![U: $i, V: $i] : (big_r(U, U) <=> big_r(U, V))) | (big_r(X!1, X!1) <=> big_r(X!1, Y!0))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (big_r(X!1, X!1) <=> big_r(X!1, Y!0)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (?[X: $i] : big_r(X, X) <=> ?[X: $i] : big_r(X, X)),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (?[X: $i] : big_r(X, X)),
% 0.11/0.36 inference(or_elim,[status(thm)],[6])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 (?[X: $i] : big_r(X, X)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.11/0.36 tff(17,plain,(
% 0.11/0.36 big_r(X!1, X!1)),
% 0.11/0.36 inference(skolemize,[status(sab)],[16])).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 ((~(big_r(X!1, X!1) <=> big_r(X!1, Y!0))) | (~big_r(X!1, X!1)) | big_r(X!1, Y!0)),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(19,plain,
% 0.11/0.36 ((~(big_r(X!1, X!1) <=> big_r(X!1, Y!0))) | big_r(X!1, Y!0)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 (big_r(X!1, Y!0)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 ((~![Y: $i] : big_r(Y, Y)) <=> (~![Y: $i] : big_r(Y, Y))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 (~![Y: $i] : big_r(Y, Y)),
% 0.11/0.36 inference(or_elim,[status(thm)],[6])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (~![Y: $i] : big_r(Y, Y)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.11/0.36 tff(24,plain,
% 0.11/0.36 (~![Y: $i] : big_r(Y, Y)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[23, 21])).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 (~![Y: $i] : big_r(Y, Y)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.11/0.36 tff(26,plain,(
% 0.11/0.36 ~big_r(Y!0, Y!0)),
% 0.11/0.36 inference(skolemize,[status(sab)],[25])).
% 0.11/0.36 tff(27,plain,
% 0.11/0.36 ((~(big_r(Y!0, Y!0) <=> big_r(X!1, Y!0))) | big_r(Y!0, Y!0) | (~big_r(X!1, Y!0))),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(28,plain,
% 0.11/0.36 (~(big_r(Y!0, Y!0) <=> big_r(X!1, Y!0))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[27, 26, 20])).
% 0.11/0.36 tff(29,plain,
% 0.11/0.36 (^[W: $i, Z: $i] : refl((big_r(W, W) <=> big_r(Z, W)) <=> (big_r(W, W) <=> big_r(Z, W)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(30,plain,
% 0.11/0.36 (![W: $i, Z: $i] : (big_r(W, W) <=> big_r(Z, W)) <=> ![W: $i, Z: $i] : (big_r(W, W) <=> big_r(Z, W))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[29])).
% 0.11/0.36 tff(31,plain,
% 0.11/0.36 (![W: $i, Z: $i] : (big_r(W, W) <=> big_r(Z, W)) <=> ![W: $i, Z: $i] : (big_r(W, W) <=> big_r(Z, W))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(32,plain,
% 0.11/0.36 (![W: $i, Z: $i] : (big_r(W, W) <=> big_r(Z, W))),
% 0.11/0.36 inference(and_elim,[status(thm)],[7])).
% 0.11/0.36 tff(33,plain,
% 0.11/0.36 (![W: $i, Z: $i] : (big_r(W, W) <=> big_r(Z, W))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.11/0.36 tff(34,plain,(
% 0.11/0.36 ![W: $i, Z: $i] : (big_r(W, W) <=> big_r(Z, W))),
% 0.11/0.36 inference(skolemize,[status(sab)],[33])).
% 0.11/0.36 tff(35,plain,
% 0.11/0.36 (![W: $i, Z: $i] : (big_r(W, W) <=> big_r(Z, W))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.11/0.36 tff(36,plain,
% 0.11/0.36 ((~![W: $i, Z: $i] : (big_r(W, W) <=> big_r(Z, W))) | (big_r(Y!0, Y!0) <=> big_r(X!1, Y!0))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(37,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[36, 35, 28])).
% 0.11/0.36 % SZS output end Proof
% 0.11/0.36 % E exiting
%------------------------------------------------------------------------------