%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN037-2 : TPTP v9.0.0. Released v1.0.0.
% 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 05:38:00 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYN037-2 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 12:25:40 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 tff(p_type, type, (
% 0.21/0.40 p: $i > $o)).
% 0.21/0.40 tff(fy_type, type, (
% 0.21/0.40 fy: $i > $i)).
% 0.21/0.40 tff(cv_type, type, (
% 0.21/0.40 cv: $i)).
% 0.21/0.40 tff(m3_type, type, (
% 0.21/0.40 m3: $o)).
% 0.21/0.40 tff(m1_type, type, (
% 0.21/0.40 m1: $o)).
% 0.21/0.40 tff(q_type, type, (
% 0.21/0.40 q: $i > $o)).
% 0.21/0.40 tff(cw_type, type, (
% 0.21/0.40 cw: $i)).
% 0.21/0.40 tff(fy3_type, type, (
% 0.21/0.40 fy3: $i > $i)).
% 0.21/0.40 tff(cx_type, type, (
% 0.21/0.40 cx: $i)).
% 0.21/0.40 tff(cvv_type, type, (
% 0.21/0.40 cvv: $i)).
% 0.21/0.40 tff(m2_type, type, (
% 0.21/0.40 m2: $o)).
% 0.21/0.40 tff(cu_type, type, (
% 0.21/0.40 cu: $i)).
% 0.21/0.40 tff(cuu_type, type, (
% 0.21/0.40 cuu: $i)).
% 0.21/0.40 tff(fz2_type, type, (
% 0.21/0.40 fz2: $i > $i)).
% 0.21/0.40 tff(fz5_type, type, (
% 0.21/0.40 fz5: $i > $i)).
% 0.21/0.40 tff(1,assumption,(~p(fy3(cx))), introduced(assumption)).
% 0.21/0.40 tff(2,assumption,(~p(cvv)), introduced(assumption)).
% 0.21/0.40 tff(3,assumption,(~m1), introduced(assumption)).
% 0.21/0.40 tff(4,assumption,(m2), introduced(assumption)).
% 0.21/0.40 tff(5,assumption,(p(fy3(cvv))), introduced(assumption)).
% 0.21/0.40 tff(6,plain,
% 0.21/0.40 (^[Vv1: $i, V1: $i] : refl(((~p(V1)) | (~m2) | p(Vv1)) <=> ((~p(V1)) | (~m2) | p(Vv1)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(7,plain,
% 0.21/0.40 (![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1)) <=> ![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 (![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1)) <=> ![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(9,plain,
% 0.21/0.40 (^[Vv1: $i, V1: $i] : rewrite((((~m2) | (~p(V1))) | p(Vv1)) <=> ((~p(V1)) | (~m2) | p(Vv1)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(10,plain,
% 0.21/0.40 (![Vv1: $i, V1: $i] : (((~m2) | (~p(V1))) | p(Vv1)) <=> ![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.21/0.40 tff(11,axiom,(![Vv1: $i, V1: $i] : (((~m2) | (~p(V1))) | p(Vv1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_18')).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 (![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.40 tff(13,plain,
% 0.21/0.40 (![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.21/0.40 tff(14,plain,(
% 0.21/0.40 ![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))),
% 0.21/0.40 inference(skolemize,[status(sab)],[13])).
% 0.21/0.40 tff(15,plain,
% 0.21/0.40 (![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.21/0.40 tff(16,plain,
% 0.21/0.40 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~m2) | p(cvv) | (~p(fy3(cvv))))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | p(cvv) | (~p(fy3(cvv))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(17,plain,
% 0.21/0.40 (((~p(fy3(cvv))) | (~m2) | p(cvv)) <=> ((~m2) | p(cvv) | (~p(fy3(cvv))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(18,plain,
% 0.21/0.40 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(fy3(cvv))) | (~m2) | p(cvv))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~m2) | p(cvv) | (~p(fy3(cvv)))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[17])).
% 0.21/0.40 tff(19,plain,
% 0.21/0.40 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(fy3(cvv))) | (~m2) | p(cvv))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | p(cvv) | (~p(fy3(cvv))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[18, 16])).
% 0.21/0.40 tff(20,plain,
% 0.21/0.40 ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(fy3(cvv))) | (~m2) | p(cvv))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(21,plain,
% 0.21/0.40 ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | p(cvv) | (~p(fy3(cvv)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.21/0.40 tff(22,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[21, 15, 4, 2, 5])).
% 0.21/0.40 tff(23,plain,((~p(fy3(cvv))) | (~m2) | p(cvv)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(24,plain,
% 0.21/0.40 (~p(fy3(cvv))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[23, 2, 4])).
% 0.21/0.40 tff(25,plain,
% 0.21/0.40 (^[X2: $i] : refl((m1 | m3 | p(X2) | p(fy3(X2))) <=> (m1 | m3 | p(X2) | p(fy3(X2))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(26,plain,
% 0.21/0.40 (![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2))) <=> ![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 (![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2))) <=> ![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (^[X2: $i] : trans(monotonicity(rewrite(((m1 | m3) | p(X2)) <=> (m1 | m3 | p(X2))), ((((m1 | m3) | p(X2)) | p(fy3(X2))) <=> ((m1 | m3 | p(X2)) | p(fy3(X2))))), rewrite(((m1 | m3 | p(X2)) | p(fy3(X2))) <=> (m1 | m3 | p(X2) | p(fy3(X2)))), ((((m1 | m3) | p(X2)) | p(fy3(X2))) <=> (m1 | m3 | p(X2) | p(fy3(X2)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (![X2: $i] : (((m1 | m3) | p(X2)) | p(fy3(X2))) <=> ![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.41 tff(30,axiom,(![X2: $i] : (((m1 | m3) | p(X2)) | p(fy3(X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_16')).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.21/0.41 tff(33,plain,(
% 0.21/0.41 ![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[32])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (((~![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))) | (m1 | m3 | p(cvv) | p(fy3(cvv)))) <=> ((~![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))) | m1 | m3 | p(cvv) | p(fy3(cvv)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 ((~![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))) | (m1 | m3 | p(cvv) | p(fy3(cvv)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 ((~![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))) | m1 | m3 | p(cvv) | p(fy3(cvv))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (m1 | m3 | p(cvv) | p(fy3(cvv))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[37, 34])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (m3),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[38, 3, 2, 24])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 ((m1 | q(cu)) <=> (m1 | q(cu))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(41,axiom,(m1 | q(cu)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_22')).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (m1 | q(cu)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (q(cu)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[42, 3])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (^[Z: $i] : refl(((~m3) | (~m2) | q(cw) | (~q(Z))) <=> ((~m3) | (~m2) | q(cw) | (~q(Z))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z))) <=> ![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z))) <=> ![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (^[Z: $i] : trans(monotonicity(rewrite((((~m2) | (~m3)) | (~q(Z))) <=> ((~m3) | (~m2) | (~q(Z)))), (((((~m2) | (~m3)) | (~q(Z))) | q(cw)) <=> (((~m3) | (~m2) | (~q(Z))) | q(cw)))), rewrite((((~m3) | (~m2) | (~q(Z))) | q(cw)) <=> ((~m3) | (~m2) | q(cw) | (~q(Z)))), (((((~m2) | (~m3)) | (~q(Z))) | q(cw)) <=> ((~m3) | (~m2) | q(cw) | (~q(Z)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (![Z: $i] : ((((~m2) | (~m3)) | (~q(Z))) | q(cw)) <=> ![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.41 tff(49,axiom,(![Z: $i] : ((((~m2) | (~m3)) | (~q(Z))) | q(cw))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_6')).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.21/0.41 tff(52,plain,(
% 0.21/0.41 ![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[51])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (((~![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))) | ((~m3) | (~m2) | q(cw) | (~q(cu)))) <=> ((~![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))) | (~m3) | (~m2) | q(cw) | (~q(cu)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 ((~![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))) | ((~m3) | (~m2) | q(cw) | (~q(cu)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 ((~![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))) | (~m3) | (~m2) | q(cw) | (~q(cu))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 (q(cw)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[56, 53, 4, 43, 39])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 ((m1 | (~q(cuu))) <=> (m1 | (~q(cuu)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (((~q(cuu)) | m1) <=> (m1 | (~q(cuu)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(60,axiom,((~q(cuu)) | m1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_20')).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 (m1 | (~q(cuu))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (m1 | (~q(cuu))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[61, 58])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (~q(cuu)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[62, 3])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 (^[Z1: $i] : refl(((~m3) | (~m2) | (~q(cw)) | q(Z1)) <=> ((~m3) | (~m2) | (~q(cw)) | q(Z1)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 (![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1)) <=> ![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[64])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 (![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1)) <=> ![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 (^[Z1: $i] : trans(monotonicity(rewrite((((~m2) | (~m3)) | (~q(cw))) <=> ((~m3) | (~m2) | (~q(cw)))), (((((~m2) | (~m3)) | (~q(cw))) | q(Z1)) <=> (((~m3) | (~m2) | (~q(cw))) | q(Z1)))), rewrite((((~m3) | (~m2) | (~q(cw))) | q(Z1)) <=> ((~m3) | (~m2) | (~q(cw)) | q(Z1))), (((((~m2) | (~m3)) | (~q(cw))) | q(Z1)) <=> ((~m3) | (~m2) | (~q(cw)) | q(Z1))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 (![Z1: $i] : ((((~m2) | (~m3)) | (~q(cw))) | q(Z1)) <=> ![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[67])).
% 0.21/0.41 tff(69,axiom,(![Z1: $i] : ((((~m2) | (~m3)) | (~q(cw))) | q(Z1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_5')).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 (![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 (![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.21/0.41 tff(72,plain,(
% 0.21/0.41 ![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))),
% 0.21/0.41 inference(skolemize,[status(sab)],[71])).
% 0.21/0.41 tff(73,plain,
% 0.21/0.41 (![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.21/0.41 tff(74,plain,
% 0.21/0.41 (((~![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))) | ((~m3) | (~m2) | (~q(cw)) | q(cuu))) <=> ((~![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))) | (~m3) | (~m2) | (~q(cw)) | q(cuu))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(75,plain,
% 0.21/0.41 ((~![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))) | ((~m3) | (~m2) | (~q(cw)) | q(cuu))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 ((~![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))) | (~m3) | (~m2) | (~q(cw)) | q(cuu)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.21/0.41 tff(77,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[76, 73, 4, 63, 39, 57])).
% 0.21/0.41 tff(78,plain,(m1 | (~m2) | p(cvv)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(79,plain,
% 0.21/0.41 (~m2),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[78, 2, 3])).
% 0.21/0.41 tff(80,assumption,(~m2), introduced(assumption)).
% 0.21/0.41 tff(81,plain,
% 0.21/0.41 ((m2 | p(cv)) <=> (m2 | p(cv))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(82,axiom,(m2 | p(cv)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_21')).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 (m2 | p(cv)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.41 tff(84,plain,
% 0.21/0.41 (p(cv)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[83, 80])).
% 0.21/0.41 tff(85,assumption,(m3), introduced(assumption)).
% 0.21/0.41 tff(86,plain,
% 0.21/0.41 (^[Y1: $i] : refl((m1 | (~m3) | (~p(cx)) | p(Y1)) <=> (m1 | (~m3) | (~p(cx)) | p(Y1)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 (![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1)) <=> ![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[86])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 (![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1)) <=> ![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 (^[Y1: $i] : trans(monotonicity(rewrite((((~m3) | (~p(cx))) | m1) <=> (m1 | (~m3) | (~p(cx)))), (((((~m3) | (~p(cx))) | m1) | p(Y1)) <=> ((m1 | (~m3) | (~p(cx))) | p(Y1)))), rewrite(((m1 | (~m3) | (~p(cx))) | p(Y1)) <=> (m1 | (~m3) | (~p(cx)) | p(Y1))), (((((~m3) | (~p(cx))) | m1) | p(Y1)) <=> (m1 | (~m3) | (~p(cx)) | p(Y1))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(90,plain,
% 0.21/0.41 (![Y1: $i] : ((((~m3) | (~p(cx))) | m1) | p(Y1)) <=> ![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[89])).
% 0.21/0.41 tff(91,axiom,(![Y1: $i] : ((((~m3) | (~p(cx))) | m1) | p(Y1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_9')).
% 0.21/0.41 tff(92,plain,
% 0.21/0.41 (![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.41 tff(93,plain,
% 0.21/0.41 (![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.21/0.41 tff(94,plain,(
% 0.21/0.41 ![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))),
% 0.21/0.41 inference(skolemize,[status(sab)],[93])).
% 0.21/0.41 tff(95,plain,
% 0.21/0.41 (![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.21/0.41 tff(96,plain,
% 0.21/0.41 (((~![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))) | (m1 | (~m3) | (~p(cx)) | p(cvv))) <=> ((~![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))) | m1 | (~m3) | (~p(cx)) | p(cvv))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(97,plain,
% 0.21/0.41 ((~![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))) | (m1 | (~m3) | (~p(cx)) | p(cvv))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(98,plain,
% 0.21/0.41 ((~![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))) | m1 | (~m3) | (~p(cx)) | p(cvv)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.21/0.41 tff(99,plain,
% 0.21/0.41 (m1 | (~m3) | (~p(cx))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[98, 95, 2])).
% 0.21/0.41 tff(100,plain,
% 0.21/0.41 (~p(cx)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[99, 85, 3])).
% 0.21/0.41 tff(101,assumption,(p(cv)), introduced(assumption)).
% 0.21/0.41 tff(102,plain,
% 0.21/0.41 (^[Y2: $i] : refl((m1 | (~m3) | p(cx) | (~p(Y2))) <=> (m1 | (~m3) | p(cx) | (~p(Y2))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(103,plain,
% 0.21/0.41 (![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2))) <=> ![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[102])).
% 0.21/0.41 tff(104,plain,
% 0.21/0.41 (![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2))) <=> ![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(105,plain,
% 0.21/0.41 (^[Y2: $i] : trans(monotonicity(rewrite((((~m3) | (~p(Y2))) | m1) <=> (m1 | (~m3) | (~p(Y2)))), (((((~m3) | (~p(Y2))) | m1) | p(cx)) <=> ((m1 | (~m3) | (~p(Y2))) | p(cx)))), rewrite(((m1 | (~m3) | (~p(Y2))) | p(cx)) <=> (m1 | (~m3) | p(cx) | (~p(Y2)))), (((((~m3) | (~p(Y2))) | m1) | p(cx)) <=> (m1 | (~m3) | p(cx) | (~p(Y2)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(106,plain,
% 0.21/0.41 (![Y2: $i] : ((((~m3) | (~p(Y2))) | m1) | p(cx)) <=> ![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[105])).
% 0.21/0.41 tff(107,axiom,(![Y2: $i] : ((((~m3) | (~p(Y2))) | m1) | p(cx))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_10')).
% 0.21/0.41 tff(108,plain,
% 0.21/0.41 (![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.21/0.41 tff(109,plain,
% 0.21/0.41 (![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.21/0.41 tff(110,plain,(
% 0.21/0.41 ![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[109])).
% 0.21/0.41 tff(111,plain,
% 0.21/0.41 (![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.21/0.41 tff(112,plain,
% 0.21/0.41 (((~![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))) | (m1 | (~m3) | p(cx) | (~p(cv)))) <=> ((~![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))) | m1 | (~m3) | p(cx) | (~p(cv)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 ((~![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))) | (m1 | (~m3) | p(cx) | (~p(cv)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 ((~![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))) | m1 | (~m3) | p(cx) | (~p(cv))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 (m1 | (~m3) | p(cx)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[114, 111, 101])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[115, 100, 85, 3])).
% 0.21/0.42 tff(117,plain,((~m3) | m1 | (~p(cv)) | p(cvv)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 (~m3),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[117, 3, 84, 2])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 (^[Z3: $i] : refl((m3 | m2 | q(cw) | (~q(Z3))) <=> (m3 | m2 | q(cw) | (~q(Z3))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 (![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3))) <=> ![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[119])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 (![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3))) <=> ![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 (^[Z3: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~q(Z3)) | m2) <=> (m2 | (~q(Z3)))), ((((~q(Z3)) | m2) | m3) <=> ((m2 | (~q(Z3))) | m3))), rewrite(((m2 | (~q(Z3))) | m3) <=> (m3 | m2 | (~q(Z3)))), ((((~q(Z3)) | m2) | m3) <=> (m3 | m2 | (~q(Z3))))), (((((~q(Z3)) | m2) | m3) | q(cw)) <=> ((m3 | m2 | (~q(Z3))) | q(cw)))), rewrite(((m3 | m2 | (~q(Z3))) | q(cw)) <=> (m3 | m2 | q(cw) | (~q(Z3)))), (((((~q(Z3)) | m2) | m3) | q(cw)) <=> (m3 | m2 | q(cw) | (~q(Z3)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 (![Z3: $i] : ((((~q(Z3)) | m2) | m3) | q(cw)) <=> ![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[122])).
% 0.21/0.42 tff(124,axiom,(![Z3: $i] : ((((~q(Z3)) | m2) | m3) | q(cw))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_15')).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 (![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.21/0.42 tff(126,plain,
% 0.21/0.42 (![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.21/0.42 tff(127,plain,(
% 0.21/0.42 ![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[126])).
% 0.21/0.42 tff(128,plain,
% 0.21/0.42 (![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.21/0.42 tff(129,plain,
% 0.21/0.42 (((~![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))) | (m3 | m2 | q(cw) | (~q(cu)))) <=> ((~![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))) | m3 | m2 | q(cw) | (~q(cu)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(130,plain,
% 0.21/0.42 ((~![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))) | (m3 | m2 | q(cw) | (~q(cu)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(131,plain,
% 0.21/0.42 ((~![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))) | m3 | m2 | q(cw) | (~q(cu))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.42 tff(132,plain,
% 0.21/0.42 (m3 | q(cw)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[131, 128, 80, 43])).
% 0.21/0.42 tff(133,plain,
% 0.21/0.42 (q(cw)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[132, 118])).
% 0.21/0.42 tff(134,plain,
% 0.21/0.42 (^[Z4: $i] : refl((m3 | m2 | (~q(cw)) | q(Z4)) <=> (m3 | m2 | (~q(cw)) | q(Z4)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(135,plain,
% 0.21/0.42 (![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4)) <=> ![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[134])).
% 0.21/0.42 tff(136,plain,
% 0.21/0.42 (![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4)) <=> ![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(137,plain,
% 0.21/0.42 (^[Z4: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~q(cw)) | m2) <=> (m2 | (~q(cw)))), ((((~q(cw)) | m2) | m3) <=> ((m2 | (~q(cw))) | m3))), rewrite(((m2 | (~q(cw))) | m3) <=> (m3 | m2 | (~q(cw)))), ((((~q(cw)) | m2) | m3) <=> (m3 | m2 | (~q(cw))))), (((((~q(cw)) | m2) | m3) | q(Z4)) <=> ((m3 | m2 | (~q(cw))) | q(Z4)))), rewrite(((m3 | m2 | (~q(cw))) | q(Z4)) <=> (m3 | m2 | (~q(cw)) | q(Z4))), (((((~q(cw)) | m2) | m3) | q(Z4)) <=> (m3 | m2 | (~q(cw)) | q(Z4))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(138,plain,
% 0.21/0.42 (![Z4: $i] : ((((~q(cw)) | m2) | m3) | q(Z4)) <=> ![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[137])).
% 0.21/0.42 tff(139,axiom,(![Z4: $i] : ((((~q(cw)) | m2) | m3) | q(Z4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_14')).
% 0.21/0.42 tff(140,plain,
% 0.21/0.42 (![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.21/0.42 tff(141,plain,
% 0.21/0.42 (![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.21/0.42 tff(142,plain,(
% 0.21/0.42 ![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))),
% 0.21/0.42 inference(skolemize,[status(sab)],[141])).
% 0.21/0.42 tff(143,plain,
% 0.21/0.42 (![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[142, 135])).
% 0.21/0.42 tff(144,plain,
% 0.21/0.42 (((~![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))) | (m3 | m2 | (~q(cw)) | q(cuu))) <=> ((~![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))) | m3 | m2 | (~q(cw)) | q(cuu))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(145,plain,
% 0.21/0.42 ((~![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))) | (m3 | m2 | (~q(cw)) | q(cuu))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(146,plain,
% 0.21/0.42 ((~![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))) | m3 | m2 | (~q(cw)) | q(cuu)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.21/0.42 tff(147,plain,
% 0.21/0.42 (m3 | (~q(cw))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[146, 143, 80, 63])).
% 0.21/0.42 tff(148,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[147, 133, 118])).
% 0.21/0.42 tff(149,plain,(m1 | m2 | p(cvv)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(150,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[149, 79, 2, 3])).
% 0.21/0.42 tff(151,plain,(p(cvv) | m1), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(152,plain,
% 0.21/0.42 (m1),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[151, 2])).
% 0.21/0.42 tff(153,assumption,(m1), introduced(assumption)).
% 0.21/0.42 tff(154,assumption,(~m3), introduced(assumption)).
% 0.21/0.42 tff(155,plain,
% 0.21/0.42 (^[Y5: $i] : refl(((~m1) | m3 | p(cx) | (~p(Y5))) <=> ((~m1) | m3 | p(cx) | (~p(Y5))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(156,plain,
% 0.21/0.42 (![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5))) <=> ![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[155])).
% 0.21/0.42 tff(157,plain,
% 0.21/0.42 (![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5))) <=> ![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(158,plain,
% 0.21/0.42 (^[Y5: $i] : trans(monotonicity(rewrite((((~m1) | (~p(Y5))) | m3) <=> ((~m1) | m3 | (~p(Y5)))), (((((~m1) | (~p(Y5))) | m3) | p(cx)) <=> (((~m1) | m3 | (~p(Y5))) | p(cx)))), rewrite((((~m1) | m3 | (~p(Y5))) | p(cx)) <=> ((~m1) | m3 | p(cx) | (~p(Y5)))), (((((~m1) | (~p(Y5))) | m3) | p(cx)) <=> ((~m1) | m3 | p(cx) | (~p(Y5)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(159,plain,
% 0.21/0.42 (![Y5: $i] : ((((~m1) | (~p(Y5))) | m3) | p(cx)) <=> ![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[158])).
% 0.21/0.42 tff(160,axiom,(![Y5: $i] : ((((~m1) | (~p(Y5))) | m3) | p(cx))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_4')).
% 0.21/0.42 tff(161,plain,
% 0.21/0.42 (![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.21/0.42 tff(162,plain,
% 0.21/0.42 (![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.21/0.42 tff(163,plain,(
% 0.21/0.42 ![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[162])).
% 0.21/0.42 tff(164,plain,
% 0.21/0.42 (![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[163, 156])).
% 0.21/0.42 tff(165,plain,
% 0.21/0.42 (((~![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))) | ((~m1) | m3 | p(cx) | (~p(cv)))) <=> ((~![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))) | (~m1) | m3 | p(cx) | (~p(cv)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(166,plain,
% 0.21/0.42 ((~![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))) | ((~m1) | m3 | p(cx) | (~p(cv)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(167,plain,
% 0.21/0.42 ((~![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))) | (~m1) | m3 | p(cx) | (~p(cv))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.21/0.42 tff(168,plain,
% 0.21/0.42 ((~m1) | m3 | p(cx)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[167, 164, 101])).
% 0.21/0.42 tff(169,plain,
% 0.21/0.42 (p(cx)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[168, 154, 153])).
% 0.21/0.42 tff(170,plain,
% 0.21/0.42 (^[Y4: $i] : refl(((~m1) | m3 | (~p(cx)) | p(Y4)) <=> ((~m1) | m3 | (~p(cx)) | p(Y4)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(171,plain,
% 0.21/0.42 (![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4)) <=> ![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[170])).
% 0.21/0.42 tff(172,plain,
% 0.21/0.42 (![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4)) <=> ![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(173,plain,
% 0.21/0.42 (^[Y4: $i] : trans(monotonicity(rewrite((((~m1) | (~p(cx))) | m3) <=> ((~m1) | m3 | (~p(cx)))), (((((~m1) | (~p(cx))) | m3) | p(Y4)) <=> (((~m1) | m3 | (~p(cx))) | p(Y4)))), rewrite((((~m1) | m3 | (~p(cx))) | p(Y4)) <=> ((~m1) | m3 | (~p(cx)) | p(Y4))), (((((~m1) | (~p(cx))) | m3) | p(Y4)) <=> ((~m1) | m3 | (~p(cx)) | p(Y4))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(174,plain,
% 0.21/0.42 (![Y4: $i] : ((((~m1) | (~p(cx))) | m3) | p(Y4)) <=> ![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[173])).
% 0.21/0.42 tff(175,axiom,(![Y4: $i] : ((((~m1) | (~p(cx))) | m3) | p(Y4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_3')).
% 0.21/0.42 tff(176,plain,
% 0.21/0.42 (![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.21/0.42 tff(177,plain,
% 0.21/0.42 (![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[176, 172])).
% 0.21/0.42 tff(178,plain,(
% 0.21/0.42 ![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))),
% 0.21/0.42 inference(skolemize,[status(sab)],[177])).
% 0.21/0.42 tff(179,plain,
% 0.21/0.42 (![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[178, 171])).
% 0.21/0.42 tff(180,plain,
% 0.21/0.42 (((~![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))) | ((~m1) | m3 | (~p(cx)) | p(cvv))) <=> ((~![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))) | (~m1) | m3 | (~p(cx)) | p(cvv))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(181,plain,
% 0.21/0.42 ((~![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))) | ((~m1) | m3 | (~p(cx)) | p(cvv))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(182,plain,
% 0.21/0.42 ((~![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))) | (~m1) | m3 | (~p(cx)) | p(cvv)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.21/0.42 tff(183,plain,
% 0.21/0.42 ((~m1) | m3 | (~p(cx))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[182, 179, 2])).
% 0.21/0.42 tff(184,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[183, 169, 154, 153])).
% 0.21/0.42 tff(185,plain,(m3 | (~m1) | p(cvv) | (~p(cv))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(186,plain,
% 0.21/0.42 (m3),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[185, 84, 2, 152])).
% 0.21/0.42 tff(187,assumption,(~q(cvv)), introduced(assumption)).
% 0.21/0.42 tff(188,plain,
% 0.21/0.42 (^[W1: $i] : refl(((~m3) | m2 | q(W1) | q(fz2(W1))) <=> ((~m3) | m2 | q(W1) | q(fz2(W1))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(189,plain,
% 0.21/0.42 (![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1))) <=> ![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[188])).
% 0.21/0.42 tff(190,plain,
% 0.21/0.42 (![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1))) <=> ![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(191,plain,
% 0.21/0.42 (^[W1: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~m3) | m2) <=> ((~m3) | m2)), ((((~m3) | m2) | q(W1)) <=> (((~m3) | m2) | q(W1)))), rewrite((((~m3) | m2) | q(W1)) <=> ((~m3) | m2 | q(W1))), ((((~m3) | m2) | q(W1)) <=> ((~m3) | m2 | q(W1)))), (((((~m3) | m2) | q(W1)) | q(fz2(W1))) <=> (((~m3) | m2 | q(W1)) | q(fz2(W1))))), rewrite((((~m3) | m2 | q(W1)) | q(fz2(W1))) <=> ((~m3) | m2 | q(W1) | q(fz2(W1)))), (((((~m3) | m2) | q(W1)) | q(fz2(W1))) <=> ((~m3) | m2 | q(W1) | q(fz2(W1)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(192,plain,
% 0.21/0.42 (![W1: $i] : ((((~m3) | m2) | q(W1)) | q(fz2(W1))) <=> ![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[191])).
% 0.21/0.42 tff(193,axiom,(![W1: $i] : ((((~m3) | m2) | q(W1)) | q(fz2(W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_12')).
% 0.21/0.43 tff(194,plain,
% 0.21/0.43 (![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.21/0.43 tff(195,plain,
% 0.21/0.43 (![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[194, 190])).
% 0.21/0.43 tff(196,plain,(
% 0.21/0.43 ![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[195])).
% 0.21/0.43 tff(197,plain,
% 0.21/0.43 (![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[196, 189])).
% 0.21/0.43 tff(198,plain,
% 0.21/0.43 (((~![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))) | ((~m3) | m2 | q(cvv) | q(fz2(cvv)))) <=> ((~![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))) | (~m3) | m2 | q(cvv) | q(fz2(cvv)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(199,plain,
% 0.21/0.43 ((~![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))) | ((~m3) | m2 | q(cvv) | q(fz2(cvv)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(200,plain,
% 0.21/0.43 ((~![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))) | (~m3) | m2 | q(cvv) | q(fz2(cvv))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.21/0.43 tff(201,plain,
% 0.21/0.43 ((~m3) | m2 | q(cvv) | q(fz2(cvv))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[200, 197])).
% 0.21/0.43 tff(202,plain,
% 0.21/0.43 (q(fz2(cvv))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[201, 187, 80, 85])).
% 0.21/0.43 tff(203,plain,
% 0.21/0.43 (^[Uu1: $i, U1: $i] : refl(((~m1) | (~q(U1)) | q(Uu1)) <=> ((~m1) | (~q(U1)) | q(Uu1)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(204,plain,
% 0.21/0.43 (![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1)) <=> ![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[203])).
% 0.21/0.43 tff(205,plain,
% 0.21/0.43 (![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1)) <=> ![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(206,plain,
% 0.21/0.43 (^[Uu1: $i, U1: $i] : rewrite((((~m1) | (~q(U1))) | q(Uu1)) <=> ((~m1) | (~q(U1)) | q(Uu1)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(207,plain,
% 0.21/0.43 (![Uu1: $i, U1: $i] : (((~m1) | (~q(U1))) | q(Uu1)) <=> ![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[206])).
% 0.21/0.43 tff(208,axiom,(![Uu1: $i, U1: $i] : (((~m1) | (~q(U1))) | q(Uu1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_17')).
% 0.21/0.43 tff(209,plain,
% 0.21/0.43 (![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.21/0.43 tff(210,plain,
% 0.21/0.43 (![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[209, 205])).
% 0.21/0.43 tff(211,plain,(
% 0.21/0.43 ![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))),
% 0.21/0.43 inference(skolemize,[status(sab)],[210])).
% 0.21/0.43 tff(212,plain,
% 0.21/0.43 (![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[211, 204])).
% 0.21/0.43 tff(213,plain,
% 0.21/0.43 (((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | q(cvv) | (~q(fz2(cvv))))) <=> ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | (~m1) | q(cvv) | (~q(fz2(cvv))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(214,plain,
% 0.21/0.43 (((~m1) | (~q(fz2(cvv))) | q(cvv)) <=> ((~m1) | q(cvv) | (~q(fz2(cvv))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(215,plain,
% 0.21/0.43 (((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | (~q(fz2(cvv))) | q(cvv))) <=> ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | q(cvv) | (~q(fz2(cvv)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[214])).
% 0.21/0.43 tff(216,plain,
% 0.21/0.43 (((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | (~q(fz2(cvv))) | q(cvv))) <=> ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | (~m1) | q(cvv) | (~q(fz2(cvv))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[215, 213])).
% 0.21/0.43 tff(217,plain,
% 0.21/0.43 ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | (~q(fz2(cvv))) | q(cvv))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(218,plain,
% 0.21/0.43 ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | (~m1) | q(cvv) | (~q(fz2(cvv)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.21/0.43 tff(219,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[218, 212, 153, 187, 202])).
% 0.21/0.43 tff(220,plain,(q(cvv) | (~m1) | m2 | (~m3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(221,plain,
% 0.21/0.43 (q(cvv)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[220, 186, 152, 80])).
% 0.21/0.43 tff(222,plain,
% 0.21/0.43 (^[W1: $i] : refl(((~m3) | m2 | (~q(W1)) | (~q(fz2(W1)))) <=> ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(223,plain,
% 0.21/0.43 (![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1)))) <=> ![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[222])).
% 0.21/0.43 tff(224,plain,
% 0.21/0.43 (![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1)))) <=> ![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(225,plain,
% 0.21/0.43 (^[W1: $i] : trans(monotonicity(rewrite((((~m3) | (~q(W1))) | (~q(fz2(W1)))) <=> ((~m3) | (~q(W1)) | (~q(fz2(W1))))), (((((~m3) | (~q(W1))) | (~q(fz2(W1)))) | m2) <=> (((~m3) | (~q(W1)) | (~q(fz2(W1)))) | m2))), rewrite((((~m3) | (~q(W1)) | (~q(fz2(W1)))) | m2) <=> ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))), (((((~m3) | (~q(W1))) | (~q(fz2(W1)))) | m2) <=> ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(226,plain,
% 0.21/0.43 (![W1: $i] : ((((~m3) | (~q(W1))) | (~q(fz2(W1)))) | m2) <=> ![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[225])).
% 0.21/0.43 tff(227,axiom,(![W1: $i] : ((((~m3) | (~q(W1))) | (~q(fz2(W1)))) | m2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_11')).
% 0.21/0.43 tff(228,plain,
% 0.21/0.43 (![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.21/0.43 tff(229,plain,
% 0.21/0.43 (![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[228, 224])).
% 0.21/0.43 tff(230,plain,(
% 0.21/0.43 ![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[229])).
% 0.21/0.43 tff(231,plain,
% 0.21/0.43 (![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[230, 223])).
% 0.21/0.43 tff(232,plain,
% 0.21/0.43 (((~![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))) | ((~m3) | m2 | (~q(fz2(cvv))) | (~q(cvv)))) <=> ((~![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))) | (~m3) | m2 | (~q(fz2(cvv))) | (~q(cvv)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(233,plain,
% 0.21/0.43 (((~m3) | m2 | (~q(cvv)) | (~q(fz2(cvv)))) <=> ((~m3) | m2 | (~q(fz2(cvv))) | (~q(cvv)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(234,plain,
% 0.21/0.43 (((~![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))) | ((~m3) | m2 | (~q(cvv)) | (~q(fz2(cvv))))) <=> ((~![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))) | ((~m3) | m2 | (~q(fz2(cvv))) | (~q(cvv))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[233])).
% 0.21/0.43 tff(235,plain,
% 0.21/0.43 (((~![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))) | ((~m3) | m2 | (~q(cvv)) | (~q(fz2(cvv))))) <=> ((~![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))) | (~m3) | m2 | (~q(fz2(cvv))) | (~q(cvv)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[234, 232])).
% 0.21/0.43 tff(236,plain,
% 0.21/0.43 ((~![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))) | ((~m3) | m2 | (~q(cvv)) | (~q(fz2(cvv))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(237,plain,
% 0.21/0.43 ((~![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))) | (~m3) | m2 | (~q(fz2(cvv))) | (~q(cvv))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.21/0.43 tff(238,plain,
% 0.21/0.43 ((~m3) | m2 | (~q(fz2(cvv))) | (~q(cvv))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[237, 231])).
% 0.21/0.43 tff(239,plain,
% 0.21/0.43 (~q(fz2(cvv))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[238, 221, 80, 186])).
% 0.21/0.43 tff(240,plain,
% 0.21/0.43 (((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | (~q(cvv)) | q(fz2(cvv)))) <=> ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | (~m1) | (~q(cvv)) | q(fz2(cvv)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(241,plain,
% 0.21/0.43 ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | (~q(cvv)) | q(fz2(cvv)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(242,plain,
% 0.21/0.43 ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | (~m1) | (~q(cvv)) | q(fz2(cvv))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.21/0.43 tff(243,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[242, 212, 152, 221, 239])).
% 0.21/0.43 tff(244,plain,(m2 | p(cvv)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(245,plain,
% 0.21/0.43 (m2),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[244, 2])).
% 0.21/0.43 tff(246,assumption,(~q(cu)), introduced(assumption)).
% 0.21/0.43 tff(247,plain,
% 0.21/0.43 (^[W2: $i] : refl((m3 | (~m2) | q(W2) | q(fz5(W2))) <=> (m3 | (~m2) | q(W2) | q(fz5(W2))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(248,plain,
% 0.21/0.43 (![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2))) <=> ![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[247])).
% 0.21/0.43 tff(249,plain,
% 0.21/0.43 (![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2))) <=> ![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(250,plain,
% 0.21/0.43 (^[W2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~m2) | m3) <=> (m3 | (~m2))), ((((~m2) | m3) | q(W2)) <=> ((m3 | (~m2)) | q(W2)))), rewrite(((m3 | (~m2)) | q(W2)) <=> (m3 | (~m2) | q(W2))), ((((~m2) | m3) | q(W2)) <=> (m3 | (~m2) | q(W2)))), (((((~m2) | m3) | q(W2)) | q(fz5(W2))) <=> ((m3 | (~m2) | q(W2)) | q(fz5(W2))))), rewrite(((m3 | (~m2) | q(W2)) | q(fz5(W2))) <=> (m3 | (~m2) | q(W2) | q(fz5(W2)))), (((((~m2) | m3) | q(W2)) | q(fz5(W2))) <=> (m3 | (~m2) | q(W2) | q(fz5(W2)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(251,plain,
% 0.21/0.43 (![W2: $i] : ((((~m2) | m3) | q(W2)) | q(fz5(W2))) <=> ![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[250])).
% 0.21/0.43 tff(252,axiom,(![W2: $i] : ((((~m2) | m3) | q(W2)) | q(fz5(W2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_8')).
% 0.21/0.43 tff(253,plain,
% 0.21/0.43 (![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.21/0.43 tff(254,plain,
% 0.21/0.43 (![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[253, 249])).
% 0.21/0.43 tff(255,plain,(
% 0.21/0.43 ![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[254])).
% 0.21/0.43 tff(256,plain,
% 0.21/0.43 (![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[255, 248])).
% 0.21/0.43 tff(257,plain,
% 0.21/0.43 (((~![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))) | (m3 | (~m2) | q(cu) | q(fz5(cu)))) <=> ((~![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))) | m3 | (~m2) | q(cu) | q(fz5(cu)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(258,plain,
% 0.21/0.43 ((~![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))) | (m3 | (~m2) | q(cu) | q(fz5(cu)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(259,plain,
% 0.21/0.43 ((~![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))) | m3 | (~m2) | q(cu) | q(fz5(cu))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.21/0.43 tff(260,plain,
% 0.21/0.43 (m3 | (~m2) | q(cu) | q(fz5(cu))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[259, 256])).
% 0.21/0.43 tff(261,plain,
% 0.21/0.43 (q(fz5(cu))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[260, 246, 4, 154])).
% 0.21/0.43 tff(262,plain,
% 0.21/0.43 (((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | q(cu) | (~q(fz5(cu))))) <=> ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | (~m1) | q(cu) | (~q(fz5(cu))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(263,plain,
% 0.21/0.43 (((~m1) | (~q(fz5(cu))) | q(cu)) <=> ((~m1) | q(cu) | (~q(fz5(cu))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(264,plain,
% 0.21/0.43 (((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | (~q(fz5(cu))) | q(cu))) <=> ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | q(cu) | (~q(fz5(cu)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[263])).
% 0.21/0.43 tff(265,plain,
% 0.21/0.43 (((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | (~q(fz5(cu))) | q(cu))) <=> ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | (~m1) | q(cu) | (~q(fz5(cu))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[264, 262])).
% 0.21/0.43 tff(266,plain,
% 0.21/0.43 ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | (~q(fz5(cu))) | q(cu))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(267,plain,
% 0.21/0.43 ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | (~m1) | q(cu) | (~q(fz5(cu)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.21/0.44 tff(268,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[267, 212, 153, 246, 261])).
% 0.21/0.44 tff(269,plain,(q(cu) | (~m1) | (~m2) | m3), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(270,plain,
% 0.21/0.44 (q(cu)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[269, 154, 4, 153])).
% 0.21/0.44 tff(271,plain,
% 0.21/0.44 (^[W2: $i] : refl((m3 | (~m2) | (~q(W2)) | (~q(fz5(W2)))) <=> (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(272,plain,
% 0.21/0.44 (![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2)))) <=> ![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[271])).
% 0.21/0.44 tff(273,plain,
% 0.21/0.44 (![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2)))) <=> ![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(274,plain,
% 0.21/0.44 (^[W2: $i] : trans(monotonicity(rewrite((((~m2) | (~q(W2))) | (~q(fz5(W2)))) <=> ((~m2) | (~q(W2)) | (~q(fz5(W2))))), (((((~m2) | (~q(W2))) | (~q(fz5(W2)))) | m3) <=> (((~m2) | (~q(W2)) | (~q(fz5(W2)))) | m3))), rewrite((((~m2) | (~q(W2)) | (~q(fz5(W2)))) | m3) <=> (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))), (((((~m2) | (~q(W2))) | (~q(fz5(W2)))) | m3) <=> (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(275,plain,
% 0.21/0.44 (![W2: $i] : ((((~m2) | (~q(W2))) | (~q(fz5(W2)))) | m3) <=> ![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[274])).
% 0.21/0.44 tff(276,axiom,(![W2: $i] : ((((~m2) | (~q(W2))) | (~q(fz5(W2)))) | m3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_7')).
% 0.21/0.44 tff(277,plain,
% 0.21/0.44 (![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.21/0.44 tff(278,plain,
% 0.21/0.44 (![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[277, 273])).
% 0.21/0.44 tff(279,plain,(
% 0.21/0.44 ![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[278])).
% 0.21/0.44 tff(280,plain,
% 0.21/0.44 (![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[279, 272])).
% 0.21/0.44 tff(281,plain,
% 0.21/0.44 (((~![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))) | (m3 | (~m2) | (~q(cu)) | (~q(fz5(cu))))) <=> ((~![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))) | m3 | (~m2) | (~q(cu)) | (~q(fz5(cu))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(282,plain,
% 0.21/0.44 ((~![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))) | (m3 | (~m2) | (~q(cu)) | (~q(fz5(cu))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(283,plain,
% 0.21/0.44 ((~![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))) | m3 | (~m2) | (~q(cu)) | (~q(fz5(cu)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.21/0.44 tff(284,plain,
% 0.21/0.44 (m3 | (~m2) | (~q(cu)) | (~q(fz5(cu)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[283, 280])).
% 0.21/0.44 tff(285,plain,
% 0.21/0.44 (~q(fz5(cu))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[284, 270, 154, 4])).
% 0.21/0.44 tff(286,plain,
% 0.21/0.44 (((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | (~q(cu)) | q(fz5(cu)))) <=> ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | (~m1) | (~q(cu)) | q(fz5(cu)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(287,plain,
% 0.21/0.44 ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | (~q(cu)) | q(fz5(cu)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(288,plain,
% 0.21/0.44 ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | (~m1) | (~q(cu)) | q(fz5(cu))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.21/0.44 tff(289,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[288, 212, 153, 270, 285])).
% 0.21/0.44 tff(290,plain,(m3 | (~m1) | (~m2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(291,plain,
% 0.21/0.44 (m3),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[290, 152, 245])).
% 0.21/0.44 tff(292,plain,
% 0.21/0.44 (^[X1: $i] : refl(((~m1) | (~m3) | p(fy(X1)) | p(X1)) <=> ((~m1) | (~m3) | p(fy(X1)) | p(X1)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(293,plain,
% 0.21/0.44 (![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1)) <=> ![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[292])).
% 0.21/0.44 tff(294,plain,
% 0.21/0.44 (![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1)) <=> ![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(295,plain,
% 0.21/0.44 (^[X1: $i] : trans(monotonicity(rewrite((((~m1) | (~m3)) | p(X1)) <=> ((~m1) | (~m3) | p(X1))), (((((~m1) | (~m3)) | p(X1)) | p(fy(X1))) <=> (((~m1) | (~m3) | p(X1)) | p(fy(X1))))), rewrite((((~m1) | (~m3) | p(X1)) | p(fy(X1))) <=> ((~m1) | (~m3) | p(fy(X1)) | p(X1))), (((((~m1) | (~m3)) | p(X1)) | p(fy(X1))) <=> ((~m1) | (~m3) | p(fy(X1)) | p(X1))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(296,plain,
% 0.21/0.44 (![X1: $i] : ((((~m1) | (~m3)) | p(X1)) | p(fy(X1))) <=> ![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[295])).
% 0.21/0.44 tff(297,axiom,(![X1: $i] : ((((~m1) | (~m3)) | p(X1)) | p(fy(X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_2')).
% 0.21/0.44 tff(298,plain,
% 0.21/0.44 (![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.21/0.44 tff(299,plain,
% 0.21/0.44 (![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[298, 294])).
% 0.21/0.44 tff(300,plain,(
% 0.21/0.44 ![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))),
% 0.21/0.44 inference(skolemize,[status(sab)],[299])).
% 0.21/0.44 tff(301,plain,
% 0.21/0.44 (![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[300, 293])).
% 0.21/0.44 tff(302,plain,
% 0.21/0.44 (((~![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))) | ((~m1) | (~m3) | p(cvv) | p(fy(cvv)))) <=> ((~![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))) | (~m1) | (~m3) | p(cvv) | p(fy(cvv)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(303,plain,
% 0.21/0.44 (((~m1) | (~m3) | p(fy(cvv)) | p(cvv)) <=> ((~m1) | (~m3) | p(cvv) | p(fy(cvv)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(304,plain,
% 0.21/0.44 (((~![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))) | ((~m1) | (~m3) | p(fy(cvv)) | p(cvv))) <=> ((~![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))) | ((~m1) | (~m3) | p(cvv) | p(fy(cvv))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[303])).
% 0.21/0.44 tff(305,plain,
% 0.21/0.44 (((~![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))) | ((~m1) | (~m3) | p(fy(cvv)) | p(cvv))) <=> ((~![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))) | (~m1) | (~m3) | p(cvv) | p(fy(cvv)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[304, 302])).
% 0.21/0.44 tff(306,plain,
% 0.21/0.44 ((~![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))) | ((~m1) | (~m3) | p(fy(cvv)) | p(cvv))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(307,plain,
% 0.21/0.44 ((~![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))) | (~m1) | (~m3) | p(cvv) | p(fy(cvv))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.21/0.44 tff(308,plain,
% 0.21/0.44 ((~m1) | (~m3) | p(cvv) | p(fy(cvv))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[307, 301])).
% 0.21/0.44 tff(309,plain,
% 0.21/0.44 (p(fy(cvv))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[308, 291, 2, 152])).
% 0.21/0.44 tff(310,plain,
% 0.21/0.44 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~m2) | p(cvv) | (~p(fy(cvv))))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | p(cvv) | (~p(fy(cvv))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(311,plain,
% 0.21/0.44 (((~p(fy(cvv))) | (~m2) | p(cvv)) <=> ((~m2) | p(cvv) | (~p(fy(cvv))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(312,plain,
% 0.21/0.44 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(fy(cvv))) | (~m2) | p(cvv))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~m2) | p(cvv) | (~p(fy(cvv)))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[311])).
% 0.21/0.44 tff(313,plain,
% 0.21/0.44 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(fy(cvv))) | (~m2) | p(cvv))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | p(cvv) | (~p(fy(cvv))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[312, 310])).
% 0.21/0.44 tff(314,plain,
% 0.21/0.44 ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(fy(cvv))) | (~m2) | p(cvv))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(315,plain,
% 0.21/0.44 ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | p(cvv) | (~p(fy(cvv)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.21/0.44 tff(316,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[315, 15, 245, 2, 309])).
% 0.21/0.44 tff(317,plain,(p(cvv)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(318,plain,
% 0.21/0.44 ((m2 | (~p(cvv))) <=> (m2 | (~p(cvv)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(319,plain,
% 0.21/0.44 (((~p(cvv)) | m2) <=> (m2 | (~p(cvv)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(320,axiom,((~p(cvv)) | m2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_19')).
% 0.21/0.44 tff(321,plain,
% 0.21/0.44 (m2 | (~p(cvv))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.21/0.44 tff(322,plain,
% 0.21/0.44 (m2 | (~p(cvv))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[321, 318])).
% 0.21/0.44 tff(323,plain,
% 0.21/0.44 (m2),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[322, 317])).
% 0.21/0.44 tff(324,plain,
% 0.21/0.44 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~m2) | (~p(cvv)) | p(fy3(cx)))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | (~p(cvv)) | p(fy3(cx)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(325,plain,
% 0.21/0.44 (((~p(cvv)) | (~m2) | p(fy3(cx))) <=> ((~m2) | (~p(cvv)) | p(fy3(cx)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(326,plain,
% 0.21/0.44 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(cvv)) | (~m2) | p(fy3(cx)))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~m2) | (~p(cvv)) | p(fy3(cx))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[325])).
% 0.21/0.44 tff(327,plain,
% 0.21/0.44 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(cvv)) | (~m2) | p(fy3(cx)))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | (~p(cvv)) | p(fy3(cx)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[326, 324])).
% 0.21/0.44 tff(328,plain,
% 0.21/0.44 ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(cvv)) | (~m2) | p(fy3(cx)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(329,plain,
% 0.21/0.44 ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | (~p(cvv)) | p(fy3(cx))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.21/0.44 tff(330,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[329, 15, 323, 317, 1])).
% 0.21/0.44 tff(331,plain,(p(fy3(cx))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(332,assumption,(~p(cx)), introduced(assumption)).
% 0.21/0.44 tff(333,assumption,(p(cvv)), introduced(assumption)).
% 0.21/0.44 tff(334,plain,
% 0.21/0.44 (m2),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[322, 333])).
% 0.21/0.44 tff(335,plain,
% 0.21/0.44 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (p(cx) | (~m2) | (~p(cvv)))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | p(cx) | (~m2) | (~p(cvv)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(336,plain,
% 0.21/0.44 (((~p(cvv)) | (~m2) | p(cx)) <=> (p(cx) | (~m2) | (~p(cvv)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(337,plain,
% 0.21/0.44 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(cvv)) | (~m2) | p(cx))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (p(cx) | (~m2) | (~p(cvv))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[336])).
% 0.21/0.44 tff(338,plain,
% 0.21/0.44 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(cvv)) | (~m2) | p(cx))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | p(cx) | (~m2) | (~p(cvv)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[337, 335])).
% 0.21/0.44 tff(339,plain,
% 0.21/0.44 ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(cvv)) | (~m2) | p(cx))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(340,plain,
% 0.21/0.44 ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | p(cx) | (~m2) | (~p(cvv))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.21/0.44 tff(341,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[340, 15, 334, 333, 332])).
% 0.21/0.44 tff(342,plain,(p(cx) | (~p(cvv))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(343,plain,
% 0.21/0.44 (p(cx)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[342, 317])).
% 0.21/0.44 tff(344,plain,
% 0.21/0.44 (^[X2: $i] : refl((m1 | m3 | (~p(X2)) | (~p(fy3(X2)))) <=> (m1 | m3 | (~p(X2)) | (~p(fy3(X2)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(345,plain,
% 0.21/0.44 (![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2)))) <=> ![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[344])).
% 0.21/0.44 tff(346,plain,
% 0.21/0.44 (![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2)))) <=> ![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(347,plain,
% 0.21/0.45 (^[X2: $i] : trans(monotonicity(rewrite((((~p(X2)) | (~p(fy3(X2)))) | m1) <=> (m1 | (~p(X2)) | (~p(fy3(X2))))), (((((~p(X2)) | (~p(fy3(X2)))) | m1) | m3) <=> ((m1 | (~p(X2)) | (~p(fy3(X2)))) | m3))), rewrite(((m1 | (~p(X2)) | (~p(fy3(X2)))) | m3) <=> (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))), (((((~p(X2)) | (~p(fy3(X2)))) | m1) | m3) <=> (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(348,plain,
% 0.21/0.45 (![X2: $i] : ((((~p(X2)) | (~p(fy3(X2)))) | m1) | m3) <=> ![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[347])).
% 0.21/0.45 tff(349,axiom,(![X2: $i] : ((((~p(X2)) | (~p(fy3(X2)))) | m1) | m3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_13')).
% 0.21/0.45 tff(350,plain,
% 0.21/0.45 (![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.21/0.45 tff(351,plain,
% 0.21/0.45 (![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[350, 346])).
% 0.21/0.45 tff(352,plain,(
% 0.21/0.45 ![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[351])).
% 0.21/0.45 tff(353,plain,
% 0.21/0.45 (![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[352, 345])).
% 0.21/0.45 tff(354,plain,
% 0.21/0.45 (((~![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))) | (m1 | m3 | (~p(cx)) | (~p(fy3(cx))))) <=> ((~![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))) | m1 | m3 | (~p(cx)) | (~p(fy3(cx))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(355,plain,
% 0.21/0.45 ((~![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))) | (m1 | m3 | (~p(cx)) | (~p(fy3(cx))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(356,plain,
% 0.21/0.45 ((~![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))) | m1 | m3 | (~p(cx)) | (~p(fy3(cx)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.21/0.45 tff(357,plain,
% 0.21/0.45 (m1 | m3 | (~p(cx)) | (~p(fy3(cx)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[356, 353])).
% 0.21/0.45 tff(358,plain,
% 0.21/0.45 (m1 | m3 | (~p(fy3(cx)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[357, 343])).
% 0.21/0.45 tff(359,plain,
% 0.21/0.45 (m3),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[358, 3, 331])).
% 0.21/0.45 tff(360,plain,
% 0.21/0.45 (q(cw)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[56, 53, 323, 43, 359])).
% 0.21/0.45 tff(361,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[76, 73, 323, 63, 359, 360])).
% 0.21/0.45 tff(362,plain,(m1), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(363,plain,
% 0.21/0.45 (m3 | (~m1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[290, 323])).
% 0.21/0.45 tff(364,plain,
% 0.21/0.45 (m3),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[363, 362])).
% 0.21/0.45 tff(365,assumption,(~p(cv)), introduced(assumption)).
% 0.21/0.45 tff(366,plain,
% 0.21/0.45 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~m2) | (~p(cvv)) | p(cv))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | (~p(cvv)) | p(cv))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(367,plain,
% 0.21/0.45 (((~p(cvv)) | (~m2) | p(cv)) <=> ((~m2) | (~p(cvv)) | p(cv))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(368,plain,
% 0.21/0.45 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(cvv)) | (~m2) | p(cv))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~m2) | (~p(cvv)) | p(cv)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[367])).
% 0.21/0.45 tff(369,plain,
% 0.21/0.45 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(cvv)) | (~m2) | p(cv))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | (~p(cvv)) | p(cv))),
% 0.21/0.45 inference(transitivity,[status(thm)],[368, 366])).
% 0.21/0.45 tff(370,plain,
% 0.21/0.45 ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(cvv)) | (~m2) | p(cv))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(371,plain,
% 0.21/0.45 ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | (~p(cvv)) | p(cv)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.21/0.45 tff(372,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[371, 15, 323, 317, 365])).
% 0.21/0.45 tff(373,plain,(p(cv)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(374,plain,
% 0.21/0.45 (^[X1: $i] : refl(((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1))) <=> ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(375,plain,
% 0.21/0.45 (![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1))) <=> ![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[374])).
% 0.21/0.45 tff(376,plain,
% 0.21/0.45 (![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1))) <=> ![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(377,plain,
% 0.21/0.45 (^[X1: $i] : trans(monotonicity(rewrite((((~m1) | (~m3)) | (~p(X1))) <=> ((~m1) | (~m3) | (~p(X1)))), (((((~m1) | (~m3)) | (~p(X1))) | (~p(fy(X1)))) <=> (((~m1) | (~m3) | (~p(X1))) | (~p(fy(X1)))))), rewrite((((~m1) | (~m3) | (~p(X1))) | (~p(fy(X1)))) <=> ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))), (((((~m1) | (~m3)) | (~p(X1))) | (~p(fy(X1)))) <=> ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(378,plain,
% 0.21/0.45 (![X1: $i] : ((((~m1) | (~m3)) | (~p(X1))) | (~p(fy(X1)))) <=> ![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[377])).
% 0.21/0.45 tff(379,axiom,(![X1: $i] : ((((~m1) | (~m3)) | (~p(X1))) | (~p(fy(X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1')).
% 0.21/0.45 tff(380,plain,
% 0.21/0.45 (![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.21/0.45 tff(381,plain,
% 0.21/0.45 (![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[380, 376])).
% 0.21/0.45 tff(382,plain,(
% 0.21/0.45 ![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[381])).
% 0.21/0.45 tff(383,plain,
% 0.21/0.45 (![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[382, 375])).
% 0.21/0.45 tff(384,plain,
% 0.21/0.45 (((~![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))) | ((~m1) | (~m3) | (~p(cv)) | (~p(fy(cv))))) <=> ((~![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))) | (~m1) | (~m3) | (~p(cv)) | (~p(fy(cv))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(385,plain,
% 0.21/0.45 (((~m1) | (~m3) | (~p(fy(cv))) | (~p(cv))) <=> ((~m1) | (~m3) | (~p(cv)) | (~p(fy(cv))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(386,plain,
% 0.21/0.45 (((~![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))) | ((~m1) | (~m3) | (~p(fy(cv))) | (~p(cv)))) <=> ((~![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))) | ((~m1) | (~m3) | (~p(cv)) | (~p(fy(cv)))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[385])).
% 0.21/0.45 tff(387,plain,
% 0.21/0.45 (((~![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))) | ((~m1) | (~m3) | (~p(fy(cv))) | (~p(cv)))) <=> ((~![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))) | (~m1) | (~m3) | (~p(cv)) | (~p(fy(cv))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[386, 384])).
% 0.21/0.45 tff(388,plain,
% 0.21/0.45 ((~![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))) | ((~m1) | (~m3) | (~p(fy(cv))) | (~p(cv)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(389,plain,
% 0.21/0.45 ((~![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))) | (~m1) | (~m3) | (~p(cv)) | (~p(fy(cv)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.21/0.45 tff(390,plain,
% 0.21/0.45 ((~m1) | (~m3) | (~p(cv)) | (~p(fy(cv)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[389, 383])).
% 0.21/0.45 tff(391,plain,
% 0.21/0.45 (~p(fy(cv))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[390, 373, 362, 364])).
% 0.21/0.45 tff(392,plain,
% 0.21/0.45 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~m2) | (~p(cv)) | p(fy(cv)))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | (~p(cv)) | p(fy(cv)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(393,plain,
% 0.21/0.45 (((~p(cv)) | (~m2) | p(fy(cv))) <=> ((~m2) | (~p(cv)) | p(fy(cv)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(394,plain,
% 0.21/0.45 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(cv)) | (~m2) | p(fy(cv)))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~m2) | (~p(cv)) | p(fy(cv))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[393])).
% 0.21/0.45 tff(395,plain,
% 0.21/0.45 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(cv)) | (~m2) | p(fy(cv)))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | (~p(cv)) | p(fy(cv)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[394, 392])).
% 0.21/0.45 tff(396,plain,
% 0.21/0.45 ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(cv)) | (~m2) | p(fy(cv)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(397,plain,
% 0.21/0.45 ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | (~p(cv)) | p(fy(cv))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.21/0.45 tff(398,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[397, 15, 323, 373, 391])).
% 0.21/0.45 % SZS output end Proof
% 0.21/0.45 % E exiting
%------------------------------------------------------------------------------