%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN009-3 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:37:57 AM UTC 2025
% Result : Unsatisfiable 0.10s 0.36s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN009-3 : TPTP v9.0.0. Released v2.5.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n014.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Jun 20 12:26:24 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.10/0.36 % SZS status Unsatisfiable
% 0.10/0.36 % SZS output start Proof
% 0.10/0.36 tff(q_type, type, (
% 0.10/0.36 q: ( $i * $i * $i ) > $o)).
% 0.10/0.36 tff(c_type, type, (
% 0.10/0.36 c: $i)).
% 0.10/0.36 tff(t_type, type, (
% 0.10/0.36 t: ( $i * $i * $i ) > $o)).
% 0.10/0.36 tff(v_type, type, (
% 0.10/0.36 v: ( $i * $i * $i ) > $o)).
% 0.10/0.36 tff(u_type, type, (
% 0.10/0.36 u: ( $i * $i * $i ) > $o)).
% 0.10/0.36 tff(p_type, type, (
% 0.10/0.36 p: ( $i * $i * $i ) > $o)).
% 0.10/0.36 tff(r_type, type, (
% 0.10/0.36 r: ( $i * $i * $i ) > $o)).
% 0.10/0.36 tff(s_type, type, (
% 0.10/0.36 s: $i > $o)).
% 0.10/0.36 tff(1,assumption,(v(c, c, c)), introduced(assumption)).
% 0.10/0.36 tff(2,plain,
% 0.10/0.36 (^[Z: $i, Y: $i, X: $i] : refl((~v(X, Y, Z)) <=> (~v(X, Y, Z)))),
% 0.10/0.36 inference(bind,[status(th)],[])).
% 0.10/0.36 tff(3,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : (~v(X, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : (~v(X, Y, Z))),
% 0.10/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.10/0.36 tff(4,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : (~v(X, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : (~v(X, Y, Z))),
% 0.10/0.36 inference(rewrite,[status(thm)],[])).
% 0.10/0.36 tff(5,axiom,(![Z: $i, Y: $i, X: $i] : (~v(X, Y, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_7')).
% 0.10/0.36 tff(6,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : (~v(X, Y, Z))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.10/0.36 tff(7,plain,(
% 0.10/0.36 ![Z: $i, Y: $i, X: $i] : (~v(X, Y, Z))),
% 0.10/0.36 inference(skolemize,[status(sab)],[6])).
% 0.10/0.36 tff(8,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : (~v(X, Y, Z))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.10/0.36 tff(9,plain,
% 0.10/0.36 ((~![Z: $i, Y: $i, X: $i] : (~v(X, Y, Z))) | (~v(c, c, c))),
% 0.10/0.36 inference(quant_inst,[status(thm)],[])).
% 0.10/0.36 tff(10,plain,
% 0.10/0.36 ($false),
% 0.10/0.36 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.10/0.36 tff(11,plain,(~v(c, c, c)), inference(lemma,lemma(discharge,[]))).
% 0.10/0.36 tff(12,plain,
% 0.10/0.36 (^[Z: $i, Y: $i, X: $i] : refl((t(X, Y, Z) | v(X, Y, Z) | (~u(X, Y, Z))) <=> (t(X, Y, Z) | v(X, Y, Z) | (~u(X, Y, Z))))),
% 0.10/0.36 inference(bind,[status(th)],[])).
% 0.10/0.36 tff(13,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : (t(X, Y, Z) | v(X, Y, Z) | (~u(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (t(X, Y, Z) | v(X, Y, Z) | (~u(X, Y, Z)))),
% 0.10/0.36 inference(quant_intro,[status(thm)],[12])).
% 0.10/0.36 tff(14,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : (t(X, Y, Z) | v(X, Y, Z) | (~u(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (t(X, Y, Z) | v(X, Y, Z) | (~u(X, Y, Z)))),
% 0.10/0.36 inference(rewrite,[status(thm)],[])).
% 0.10/0.36 tff(15,plain,
% 0.10/0.36 (^[Z: $i, Y: $i, X: $i] : rewrite((((~u(X, Y, Z)) | t(X, Y, Z)) | v(X, Y, Z)) <=> (t(X, Y, Z) | v(X, Y, Z) | (~u(X, Y, Z))))),
% 0.10/0.36 inference(bind,[status(th)],[])).
% 0.10/0.36 tff(16,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : (((~u(X, Y, Z)) | t(X, Y, Z)) | v(X, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : (t(X, Y, Z) | v(X, Y, Z) | (~u(X, Y, Z)))),
% 0.10/0.36 inference(quant_intro,[status(thm)],[15])).
% 0.10/0.36 tff(17,axiom,(![Z: $i, Y: $i, X: $i] : (((~u(X, Y, Z)) | t(X, Y, Z)) | v(X, Y, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_10')).
% 0.10/0.36 tff(18,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : (t(X, Y, Z) | v(X, Y, Z) | (~u(X, Y, Z)))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.10/0.36 tff(19,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : (t(X, Y, Z) | v(X, Y, Z) | (~u(X, Y, Z)))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.10/0.36 tff(20,plain,(
% 0.10/0.36 ![Z: $i, Y: $i, X: $i] : (t(X, Y, Z) | v(X, Y, Z) | (~u(X, Y, Z)))),
% 0.10/0.36 inference(skolemize,[status(sab)],[19])).
% 0.10/0.36 tff(21,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : (t(X, Y, Z) | v(X, Y, Z) | (~u(X, Y, Z)))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.10/0.36 tff(22,plain,
% 0.10/0.36 (u(c, c, c) <=> u(c, c, c)),
% 0.10/0.36 inference(rewrite,[status(thm)],[])).
% 0.10/0.36 tff(23,axiom,(u(c, c, c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_8')).
% 0.10/0.36 tff(24,plain,
% 0.10/0.36 (u(c, c, c)),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.10/0.36 tff(25,plain,
% 0.10/0.36 (((~![Z: $i, Y: $i, X: $i] : (t(X, Y, Z) | v(X, Y, Z) | (~u(X, Y, Z)))) | (t(c, c, c) | v(c, c, c) | (~u(c, c, c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (t(X, Y, Z) | v(X, Y, Z) | (~u(X, Y, Z)))) | t(c, c, c) | v(c, c, c) | (~u(c, c, c)))),
% 0.10/0.36 inference(rewrite,[status(thm)],[])).
% 0.10/0.36 tff(26,plain,
% 0.10/0.36 ((~![Z: $i, Y: $i, X: $i] : (t(X, Y, Z) | v(X, Y, Z) | (~u(X, Y, Z)))) | (t(c, c, c) | v(c, c, c) | (~u(c, c, c)))),
% 0.10/0.36 inference(quant_inst,[status(thm)],[])).
% 0.10/0.36 tff(27,plain,
% 0.10/0.36 ((~![Z: $i, Y: $i, X: $i] : (t(X, Y, Z) | v(X, Y, Z) | (~u(X, Y, Z)))) | t(c, c, c) | v(c, c, c) | (~u(c, c, c))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.10/0.36 tff(28,plain,
% 0.10/0.36 (t(c, c, c) | v(c, c, c)),
% 0.10/0.36 inference(unit_resolution,[status(thm)],[27, 24, 21])).
% 0.10/0.36 tff(29,plain,
% 0.10/0.36 (t(c, c, c)),
% 0.10/0.36 inference(unit_resolution,[status(thm)],[28, 11])).
% 0.10/0.36 tff(30,plain,
% 0.10/0.36 (^[Z: $i, Y: $i, X: $i] : refl(((~q(X, Y, Z)) | (~t(X, Y, Z))) <=> ((~q(X, Y, Z)) | (~t(X, Y, Z))))),
% 0.10/0.36 inference(bind,[status(th)],[])).
% 0.10/0.36 tff(31,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : ((~q(X, Y, Z)) | (~t(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~q(X, Y, Z)) | (~t(X, Y, Z)))),
% 0.10/0.36 inference(quant_intro,[status(thm)],[30])).
% 0.10/0.36 tff(32,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : ((~q(X, Y, Z)) | (~t(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~q(X, Y, Z)) | (~t(X, Y, Z)))),
% 0.10/0.36 inference(rewrite,[status(thm)],[])).
% 0.10/0.36 tff(33,axiom,(![Z: $i, Y: $i, X: $i] : ((~q(X, Y, Z)) | (~t(X, Y, Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_2')).
% 0.10/0.36 tff(34,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : ((~q(X, Y, Z)) | (~t(X, Y, Z)))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.10/0.36 tff(35,plain,(
% 0.10/0.36 ![Z: $i, Y: $i, X: $i] : ((~q(X, Y, Z)) | (~t(X, Y, Z)))),
% 0.10/0.36 inference(skolemize,[status(sab)],[34])).
% 0.10/0.36 tff(36,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : ((~q(X, Y, Z)) | (~t(X, Y, Z)))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.10/0.36 tff(37,plain,
% 0.10/0.36 (((~![Z: $i, Y: $i, X: $i] : ((~q(X, Y, Z)) | (~t(X, Y, Z)))) | ((~q(c, c, c)) | (~t(c, c, c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~q(X, Y, Z)) | (~t(X, Y, Z)))) | (~q(c, c, c)) | (~t(c, c, c)))),
% 0.10/0.36 inference(rewrite,[status(thm)],[])).
% 0.10/0.36 tff(38,plain,
% 0.10/0.36 ((~![Z: $i, Y: $i, X: $i] : ((~q(X, Y, Z)) | (~t(X, Y, Z)))) | ((~q(c, c, c)) | (~t(c, c, c)))),
% 0.10/0.36 inference(quant_inst,[status(thm)],[])).
% 0.10/0.36 tff(39,plain,
% 0.10/0.36 ((~![Z: $i, Y: $i, X: $i] : ((~q(X, Y, Z)) | (~t(X, Y, Z)))) | (~q(c, c, c)) | (~t(c, c, c))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.10/0.36 tff(40,plain,
% 0.10/0.36 (~q(c, c, c)),
% 0.10/0.36 inference(unit_resolution,[status(thm)],[39, 36, 29])).
% 0.10/0.36 tff(41,plain,
% 0.10/0.36 (^[Z: $i, Y: $i, X: $i] : refl(((~p(X, Y, Z)) | (~t(X, Y, Z))) <=> ((~p(X, Y, Z)) | (~t(X, Y, Z))))),
% 0.10/0.36 inference(bind,[status(th)],[])).
% 0.10/0.36 tff(42,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : ((~p(X, Y, Z)) | (~t(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~p(X, Y, Z)) | (~t(X, Y, Z)))),
% 0.10/0.36 inference(quant_intro,[status(thm)],[41])).
% 0.10/0.36 tff(43,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : ((~p(X, Y, Z)) | (~t(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~p(X, Y, Z)) | (~t(X, Y, Z)))),
% 0.10/0.36 inference(rewrite,[status(thm)],[])).
% 0.10/0.36 tff(44,axiom,(![Z: $i, Y: $i, X: $i] : ((~p(X, Y, Z)) | (~t(X, Y, Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1')).
% 0.10/0.36 tff(45,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : ((~p(X, Y, Z)) | (~t(X, Y, Z)))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.10/0.36 tff(46,plain,(
% 0.10/0.36 ![Z: $i, Y: $i, X: $i] : ((~p(X, Y, Z)) | (~t(X, Y, Z)))),
% 0.10/0.36 inference(skolemize,[status(sab)],[45])).
% 0.10/0.36 tff(47,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : ((~p(X, Y, Z)) | (~t(X, Y, Z)))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.10/0.36 tff(48,plain,
% 0.10/0.36 (((~![Z: $i, Y: $i, X: $i] : ((~p(X, Y, Z)) | (~t(X, Y, Z)))) | ((~p(c, c, c)) | (~t(c, c, c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~p(X, Y, Z)) | (~t(X, Y, Z)))) | (~p(c, c, c)) | (~t(c, c, c)))),
% 0.10/0.36 inference(rewrite,[status(thm)],[])).
% 0.10/0.36 tff(49,plain,
% 0.10/0.36 ((~![Z: $i, Y: $i, X: $i] : ((~p(X, Y, Z)) | (~t(X, Y, Z)))) | ((~p(c, c, c)) | (~t(c, c, c)))),
% 0.10/0.36 inference(quant_inst,[status(thm)],[])).
% 0.10/0.36 tff(50,plain,
% 0.10/0.36 ((~![Z: $i, Y: $i, X: $i] : ((~p(X, Y, Z)) | (~t(X, Y, Z)))) | (~p(c, c, c)) | (~t(c, c, c))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.10/0.36 tff(51,plain,
% 0.10/0.36 (~p(c, c, c)),
% 0.10/0.36 inference(unit_resolution,[status(thm)],[50, 47, 29])).
% 0.10/0.36 tff(52,plain,
% 0.10/0.36 (^[Z: $i, Y: $i, X: $i] : refl(((~r(X, Y, Z)) | (~t(X, Y, Z))) <=> ((~r(X, Y, Z)) | (~t(X, Y, Z))))),
% 0.10/0.36 inference(bind,[status(th)],[])).
% 0.10/0.36 tff(53,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : ((~r(X, Y, Z)) | (~t(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~r(X, Y, Z)) | (~t(X, Y, Z)))),
% 0.10/0.36 inference(quant_intro,[status(thm)],[52])).
% 0.10/0.36 tff(54,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : ((~r(X, Y, Z)) | (~t(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~r(X, Y, Z)) | (~t(X, Y, Z)))),
% 0.10/0.36 inference(rewrite,[status(thm)],[])).
% 0.10/0.36 tff(55,axiom,(![Z: $i, Y: $i, X: $i] : ((~r(X, Y, Z)) | (~t(X, Y, Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_3')).
% 0.10/0.36 tff(56,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : ((~r(X, Y, Z)) | (~t(X, Y, Z)))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.10/0.36 tff(57,plain,(
% 0.10/0.36 ![Z: $i, Y: $i, X: $i] : ((~r(X, Y, Z)) | (~t(X, Y, Z)))),
% 0.10/0.36 inference(skolemize,[status(sab)],[56])).
% 0.10/0.36 tff(58,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : ((~r(X, Y, Z)) | (~t(X, Y, Z)))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.10/0.36 tff(59,plain,
% 0.10/0.36 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y, Z)) | (~t(X, Y, Z)))) | ((~r(c, c, c)) | (~t(c, c, c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y, Z)) | (~t(X, Y, Z)))) | (~r(c, c, c)) | (~t(c, c, c)))),
% 0.10/0.36 inference(rewrite,[status(thm)],[])).
% 0.10/0.36 tff(60,plain,
% 0.10/0.36 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y, Z)) | (~t(X, Y, Z)))) | ((~r(c, c, c)) | (~t(c, c, c)))),
% 0.10/0.36 inference(quant_inst,[status(thm)],[])).
% 0.10/0.36 tff(61,plain,
% 0.10/0.36 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y, Z)) | (~t(X, Y, Z)))) | (~r(c, c, c)) | (~t(c, c, c))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.10/0.36 tff(62,plain,
% 0.10/0.36 (~r(c, c, c)),
% 0.10/0.36 inference(unit_resolution,[status(thm)],[61, 58, 29])).
% 0.10/0.36 tff(63,plain,
% 0.10/0.36 (^[Z: $i, Y: $i, X: $i] : refl((p(X, Y, Z) | q(X, Y, Z) | r(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))) <=> (p(X, Y, Z) | q(X, Y, Z) | r(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))))),
% 0.10/0.36 inference(bind,[status(th)],[])).
% 0.10/0.36 tff(64,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : (p(X, Y, Z) | q(X, Y, Z) | r(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))) <=> ![Z: $i, Y: $i, X: $i] : (p(X, Y, Z) | q(X, Y, Z) | r(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))),
% 0.10/0.36 inference(quant_intro,[status(thm)],[63])).
% 0.10/0.36 tff(65,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : (p(X, Y, Z) | q(X, Y, Z) | r(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))) <=> ![Z: $i, Y: $i, X: $i] : (p(X, Y, Z) | q(X, Y, Z) | r(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))),
% 0.10/0.36 inference(rewrite,[status(thm)],[])).
% 0.10/0.36 tff(66,plain,
% 0.10/0.36 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~s(X)) | (~s(Y))) | (~s(Z))) <=> ((~s(Z)) | (~s(Y)) | (~s(X)))), (((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) <=> (((~s(Z)) | (~s(Y)) | (~s(X))) | p(X, Y, Z)))), rewrite((((~s(Z)) | (~s(Y)) | (~s(X))) | p(X, Y, Z)) <=> (p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))), (((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) <=> (p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))))), ((((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) | q(X, Y, Z)) <=> ((p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))) | q(X, Y, Z)))), rewrite(((p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))) | q(X, Y, Z)) <=> (p(X, Y, Z) | q(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))), ((((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) | q(X, Y, Z)) <=> (p(X, Y, Z) | q(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))))), (((((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) | q(X, Y, Z)) | r(X, Y, Z)) <=> ((p(X, Y, Z) | q(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))) | r(X, Y, Z)))), rewrite(((p(X, Y, Z) | q(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))) | r(X, Y, Z)) <=> (p(X, Y, Z) | q(X, Y, Z) | r(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))), (((((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) | q(X, Y, Z)) | r(X, Y, Z)) <=> (p(X, Y, Z) | q(X, Y, Z) | r(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))))),
% 0.10/0.36 inference(bind,[status(th)],[])).
% 0.10/0.36 tff(67,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : ((((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) | q(X, Y, Z)) | r(X, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : (p(X, Y, Z) | q(X, Y, Z) | r(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))),
% 0.10/0.36 inference(quant_intro,[status(thm)],[66])).
% 0.10/0.36 tff(68,axiom,(![Z: $i, Y: $i, X: $i] : ((((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) | q(X, Y, Z)) | r(X, Y, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_9')).
% 0.10/0.36 tff(69,plain,
% 0.10/0.36 (![Z: $i, Y: $i, X: $i] : (p(X, Y, Z) | q(X, Y, Z) | r(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))),
% 0.10/0.37 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.10/0.37 tff(70,plain,
% 0.10/0.37 (![Z: $i, Y: $i, X: $i] : (p(X, Y, Z) | q(X, Y, Z) | r(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))),
% 0.10/0.37 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.10/0.37 tff(71,plain,(
% 0.10/0.37 ![Z: $i, Y: $i, X: $i] : (p(X, Y, Z) | q(X, Y, Z) | r(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))),
% 0.10/0.37 inference(skolemize,[status(sab)],[70])).
% 0.10/0.37 tff(72,plain,
% 0.10/0.37 (![Z: $i, Y: $i, X: $i] : (p(X, Y, Z) | q(X, Y, Z) | r(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))),
% 0.10/0.37 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.10/0.37 tff(73,plain,
% 0.10/0.37 (s(c) <=> s(c)),
% 0.10/0.37 inference(rewrite,[status(thm)],[])).
% 0.10/0.37 tff(74,axiom,(s(c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_6')).
% 0.10/0.37 tff(75,plain,
% 0.10/0.37 (s(c)),
% 0.10/0.37 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.10/0.37 tff(76,plain,
% 0.10/0.37 (((~![Z: $i, Y: $i, X: $i] : (p(X, Y, Z) | q(X, Y, Z) | r(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | (r(c, c, c) | p(c, c, c) | q(c, c, c) | (~s(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (p(X, Y, Z) | q(X, Y, Z) | r(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | r(c, c, c) | p(c, c, c) | q(c, c, c) | (~s(c)))),
% 0.10/0.37 inference(rewrite,[status(thm)],[])).
% 0.10/0.37 tff(77,plain,
% 0.10/0.37 ((p(c, c, c) | q(c, c, c) | r(c, c, c) | (~s(c)) | (~s(c)) | (~s(c))) <=> (r(c, c, c) | p(c, c, c) | q(c, c, c) | (~s(c)))),
% 0.10/0.37 inference(rewrite,[status(thm)],[])).
% 0.10/0.37 tff(78,plain,
% 0.10/0.37 (((~![Z: $i, Y: $i, X: $i] : (p(X, Y, Z) | q(X, Y, Z) | r(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | (p(c, c, c) | q(c, c, c) | r(c, c, c) | (~s(c)) | (~s(c)) | (~s(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (p(X, Y, Z) | q(X, Y, Z) | r(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | (r(c, c, c) | p(c, c, c) | q(c, c, c) | (~s(c))))),
% 0.10/0.37 inference(monotonicity,[status(thm)],[77])).
% 0.10/0.37 tff(79,plain,
% 0.10/0.37 (((~![Z: $i, Y: $i, X: $i] : (p(X, Y, Z) | q(X, Y, Z) | r(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | (p(c, c, c) | q(c, c, c) | r(c, c, c) | (~s(c)) | (~s(c)) | (~s(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (p(X, Y, Z) | q(X, Y, Z) | r(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | r(c, c, c) | p(c, c, c) | q(c, c, c) | (~s(c)))),
% 0.10/0.37 inference(transitivity,[status(thm)],[78, 76])).
% 0.10/0.37 tff(80,plain,
% 0.10/0.37 ((~![Z: $i, Y: $i, X: $i] : (p(X, Y, Z) | q(X, Y, Z) | r(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | (p(c, c, c) | q(c, c, c) | r(c, c, c) | (~s(c)) | (~s(c)) | (~s(c)))),
% 0.10/0.37 inference(quant_inst,[status(thm)],[])).
% 0.10/0.37 tff(81,plain,
% 0.10/0.37 ((~![Z: $i, Y: $i, X: $i] : (p(X, Y, Z) | q(X, Y, Z) | r(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | r(c, c, c) | p(c, c, c) | q(c, c, c) | (~s(c))),
% 0.10/0.37 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.10/0.37 tff(82,plain,
% 0.10/0.37 ($false),
% 0.10/0.37 inference(unit_resolution,[status(thm)],[81, 75, 72, 62, 51, 40])).
% 0.10/0.37 % SZS output end Proof
% 0.10/0.37 % E exiting
%------------------------------------------------------------------------------