%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN285-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:38:40 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN285-1 : TPTP v9.0.0. Released v1.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:31:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.45 % SZS status Unsatisfiable
% 0.19/0.45 % SZS output start Proof
% 0.19/0.45 tff(q1_type, type, (
% 0.19/0.45 q1: ( $i * $i * $i ) > $o)).
% 0.19/0.45 tff(e_type, type, (
% 0.19/0.45 e: $i)).
% 0.19/0.45 tff(d_type, type, (
% 0.19/0.45 d: $i)).
% 0.19/0.45 tff(m1_type, type, (
% 0.19/0.45 m1: ( $i * $i * $i ) > $o)).
% 0.19/0.45 tff(r0_type, type, (
% 0.19/0.45 r0: $i > $o)).
% 0.19/0.45 tff(k1_type, type, (
% 0.19/0.45 k1: $i > $o)).
% 0.19/0.45 tff(a_type, type, (
% 0.19/0.45 a: $i)).
% 0.19/0.45 tff(n0_type, type, (
% 0.19/0.45 n0: ( $i * $i ) > $o)).
% 0.19/0.45 tff(b_type, type, (
% 0.19/0.45 b: $i)).
% 0.19/0.45 tff(q0_type, type, (
% 0.19/0.45 q0: ( $i * $i ) > $o)).
% 0.19/0.45 tff(l0_type, type, (
% 0.19/0.45 l0: $i > $o)).
% 0.19/0.45 tff(k0_type, type, (
% 0.19/0.45 k0: $i > $o)).
% 0.19/0.45 tff(1,plain,
% 0.19/0.45 (^[I: $i, J: $i, H: $i] : refl(((~r0(J)) | (~m1(H, I, I)) | q1(H, H, I)) <=> ((~r0(J)) | (~m1(H, I, I)) | q1(H, H, I)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(2,plain,
% 0.19/0.45 (![I: $i, J: $i, H: $i] : ((~r0(J)) | (~m1(H, I, I)) | q1(H, H, I)) <=> ![I: $i, J: $i, H: $i] : ((~r0(J)) | (~m1(H, I, I)) | q1(H, H, I))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.45 tff(3,plain,
% 0.19/0.45 (![I: $i, J: $i, H: $i] : ((~r0(J)) | (~m1(H, I, I)) | q1(H, H, I)) <=> ![I: $i, J: $i, H: $i] : ((~r0(J)) | (~m1(H, I, I)) | q1(H, H, I))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(4,plain,
% 0.19/0.45 (^[I: $i, J: $i, H: $i] : trans(monotonicity(rewrite((q1(H, H, I) | (~r0(J))) <=> ((~r0(J)) | q1(H, H, I))), (((q1(H, H, I) | (~r0(J))) | (~m1(H, I, I))) <=> (((~r0(J)) | q1(H, H, I)) | (~m1(H, I, I))))), rewrite((((~r0(J)) | q1(H, H, I)) | (~m1(H, I, I))) <=> ((~r0(J)) | (~m1(H, I, I)) | q1(H, H, I))), (((q1(H, H, I) | (~r0(J))) | (~m1(H, I, I))) <=> ((~r0(J)) | (~m1(H, I, I)) | q1(H, H, I))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(5,plain,
% 0.19/0.45 (![I: $i, J: $i, H: $i] : ((q1(H, H, I) | (~r0(J))) | (~m1(H, I, I))) <=> ![I: $i, J: $i, H: $i] : ((~r0(J)) | (~m1(H, I, I)) | q1(H, H, I))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.45 tff(6,axiom,(![I: $i, J: $i, H: $i] : ((q1(H, H, I) | (~r0(J))) | (~m1(H, I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_113')).
% 0.19/0.45 tff(7,plain,
% 0.19/0.45 (![I: $i, J: $i, H: $i] : ((~r0(J)) | (~m1(H, I, I)) | q1(H, H, I))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.45 tff(8,plain,
% 0.19/0.45 (![I: $i, J: $i, H: $i] : ((~r0(J)) | (~m1(H, I, I)) | q1(H, H, I))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.45 tff(9,plain,(
% 0.19/0.45 ![I: $i, J: $i, H: $i] : ((~r0(J)) | (~m1(H, I, I)) | q1(H, H, I))),
% 0.19/0.45 inference(skolemize,[status(sab)],[8])).
% 0.19/0.45 tff(10,plain,
% 0.19/0.45 (![I: $i, J: $i, H: $i] : ((~r0(J)) | (~m1(H, I, I)) | q1(H, H, I))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.45 tff(11,plain,
% 0.19/0.45 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(12,plain,
% 0.19/0.45 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.45 tff(13,plain,
% 0.19/0.45 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(14,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.19/0.45 tff(15,plain,
% 0.19/0.45 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.45 tff(16,plain,(
% 0.19/0.45 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[15])).
% 0.19/0.45 tff(17,plain,
% 0.19/0.45 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.45 tff(18,plain,
% 0.19/0.45 (n0(b, a) <=> n0(b, a)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(19,axiom,(n0(b, a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_37')).
% 0.19/0.45 tff(20,plain,
% 0.19/0.45 (n0(b, a)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.45 tff(21,plain,
% 0.19/0.45 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(a) | (~n0(b, a)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(a) | (~n0(b, a)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(22,plain,
% 0.19/0.45 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(a) | (~n0(b, a)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(23,plain,
% 0.19/0.45 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(a) | (~n0(b, a))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.46 tff(24,plain,
% 0.19/0.46 (k1(a)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[23, 20, 17])).
% 0.19/0.46 tff(25,plain,
% 0.19/0.46 (n0(d, e) <=> n0(d, e)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(26,axiom,(n0(d, e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_3')).
% 0.19/0.46 tff(27,plain,
% 0.19/0.46 (n0(d, e)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.46 tff(28,plain,
% 0.19/0.46 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(e) | (~n0(d, e)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(e) | (~n0(d, e)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(29,plain,
% 0.19/0.46 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(e) | (~n0(d, e)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(30,plain,
% 0.19/0.46 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(e) | (~n0(d, e))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.46 tff(31,plain,
% 0.19/0.46 (k1(e)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[30, 27, 17])).
% 0.19/0.46 tff(32,assumption,(~m1(d, e, e)), introduced(assumption)).
% 0.19/0.46 tff(33,plain,
% 0.19/0.46 (^[B: $i, A: $i] : refl(((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B)) <=> ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(34,plain,
% 0.19/0.46 (![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B)) <=> ![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.46 tff(35,plain,
% 0.19/0.46 (![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B)) <=> ![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(36,plain,
% 0.19/0.46 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1(A, B, B) | (~k1(a))) <=> ((~k1(a)) | m1(A, B, B))), (((m1(A, B, B) | (~k1(a))) | (~k1(B))) <=> (((~k1(a)) | m1(A, B, B)) | (~k1(B))))), rewrite((((~k1(a)) | m1(A, B, B)) | (~k1(B))) <=> ((~k1(a)) | (~k1(B)) | m1(A, B, B))), (((m1(A, B, B) | (~k1(a))) | (~k1(B))) <=> ((~k1(a)) | (~k1(B)) | m1(A, B, B)))), ((((m1(A, B, B) | (~k1(a))) | (~k1(B))) | (~q0(A, A))) <=> (((~k1(a)) | (~k1(B)) | m1(A, B, B)) | (~q0(A, A))))), rewrite((((~k1(a)) | (~k1(B)) | m1(A, B, B)) | (~q0(A, A))) <=> ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))), ((((m1(A, B, B) | (~k1(a))) | (~k1(B))) | (~q0(A, A))) <=> ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(37,plain,
% 0.19/0.46 (![B: $i, A: $i] : (((m1(A, B, B) | (~k1(a))) | (~k1(B))) | (~q0(A, A))) <=> ![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.46 tff(38,axiom,(![B: $i, A: $i] : (((m1(A, B, B) | (~k1(a))) | (~k1(B))) | (~q0(A, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_034')).
% 0.19/0.46 tff(39,plain,
% 0.19/0.46 (![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.46 tff(40,plain,
% 0.19/0.46 (![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.19/0.46 tff(41,plain,(
% 0.19/0.46 ![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))),
% 0.19/0.46 inference(skolemize,[status(sab)],[40])).
% 0.19/0.46 tff(42,plain,
% 0.19/0.46 (![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.19/0.46 tff(43,plain,
% 0.19/0.46 (q0(d, d) <=> q0(d, d)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(44,axiom,(q0(d, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_25')).
% 0.19/0.46 tff(45,plain,
% 0.19/0.46 (q0(d, d)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.46 tff(46,plain,
% 0.19/0.46 (((~![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))) | ((~k1(a)) | (~q0(d, d)) | m1(d, e, e) | (~k1(e)))) <=> ((~![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))) | (~k1(a)) | (~q0(d, d)) | m1(d, e, e) | (~k1(e)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(47,plain,
% 0.19/0.46 (((~k1(a)) | (~q0(d, d)) | (~k1(e)) | m1(d, e, e)) <=> ((~k1(a)) | (~q0(d, d)) | m1(d, e, e) | (~k1(e)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(48,plain,
% 0.19/0.46 (((~![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))) | ((~k1(a)) | (~q0(d, d)) | (~k1(e)) | m1(d, e, e))) <=> ((~![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))) | ((~k1(a)) | (~q0(d, d)) | m1(d, e, e) | (~k1(e))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[47])).
% 0.19/0.46 tff(49,plain,
% 0.19/0.46 (((~![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))) | ((~k1(a)) | (~q0(d, d)) | (~k1(e)) | m1(d, e, e))) <=> ((~![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))) | (~k1(a)) | (~q0(d, d)) | m1(d, e, e) | (~k1(e)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[48, 46])).
% 0.19/0.46 tff(50,plain,
% 0.19/0.46 ((~![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))) | ((~k1(a)) | (~q0(d, d)) | (~k1(e)) | m1(d, e, e))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(51,plain,
% 0.19/0.46 ((~![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))) | (~k1(a)) | (~q0(d, d)) | m1(d, e, e) | (~k1(e))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.46 tff(52,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[51, 45, 42, 32, 31, 24])).
% 0.19/0.46 tff(53,plain,(m1(d, e, e)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(54,plain,
% 0.19/0.46 (r0(b) <=> r0(b)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(55,axiom,(r0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_9')).
% 0.19/0.46 tff(56,plain,
% 0.19/0.46 (r0(b)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.46 tff(57,plain,
% 0.19/0.46 (((~![I: $i, J: $i, H: $i] : ((~r0(J)) | (~m1(H, I, I)) | q1(H, H, I))) | ((~r0(b)) | (~m1(d, e, e)) | q1(d, d, e))) <=> ((~![I: $i, J: $i, H: $i] : ((~r0(J)) | (~m1(H, I, I)) | q1(H, H, I))) | (~r0(b)) | (~m1(d, e, e)) | q1(d, d, e))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(58,plain,
% 0.19/0.46 ((~![I: $i, J: $i, H: $i] : ((~r0(J)) | (~m1(H, I, I)) | q1(H, H, I))) | ((~r0(b)) | (~m1(d, e, e)) | q1(d, d, e))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(59,plain,
% 0.19/0.46 ((~![I: $i, J: $i, H: $i] : ((~r0(J)) | (~m1(H, I, I)) | q1(H, H, I))) | (~r0(b)) | (~m1(d, e, e)) | q1(d, d, e)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.46 tff(60,plain,
% 0.19/0.46 (q1(d, d, e)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[59, 56, 53, 10])).
% 0.19/0.46 tff(61,plain,
% 0.19/0.46 ((~q1(a, d, d)) <=> (~q1(a, d, d))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(62,axiom,(~q1(a, d, d)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.19/0.46 tff(63,plain,
% 0.19/0.46 (~q1(a, d, d)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.46 tff(64,plain,
% 0.19/0.46 (^[E: $i, F: $i, G: $i] : refl(((~k0(G)) | (~l0(E)) | (~q1(F, F, G)) | q1(E, F, F)) <=> ((~k0(G)) | (~l0(E)) | (~q1(F, F, G)) | q1(E, F, F)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(65,plain,
% 0.19/0.46 (![E: $i, F: $i, G: $i] : ((~k0(G)) | (~l0(E)) | (~q1(F, F, G)) | q1(E, F, F)) <=> ![E: $i, F: $i, G: $i] : ((~k0(G)) | (~l0(E)) | (~q1(F, F, G)) | q1(E, F, F))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.46 tff(66,plain,
% 0.19/0.46 (![E: $i, F: $i, G: $i] : ((~k0(G)) | (~l0(E)) | (~q1(F, F, G)) | q1(E, F, F)) <=> ![E: $i, F: $i, G: $i] : ((~k0(G)) | (~l0(E)) | (~q1(F, F, G)) | q1(E, F, F))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(67,plain,
% 0.19/0.46 (^[E: $i, F: $i, G: $i] : trans(monotonicity(trans(monotonicity(rewrite((q1(E, F, F) | (~k0(G))) <=> ((~k0(G)) | q1(E, F, F))), (((q1(E, F, F) | (~k0(G))) | (~l0(E))) <=> (((~k0(G)) | q1(E, F, F)) | (~l0(E))))), rewrite((((~k0(G)) | q1(E, F, F)) | (~l0(E))) <=> ((~k0(G)) | (~l0(E)) | q1(E, F, F))), (((q1(E, F, F) | (~k0(G))) | (~l0(E))) <=> ((~k0(G)) | (~l0(E)) | q1(E, F, F)))), ((((q1(E, F, F) | (~k0(G))) | (~l0(E))) | (~q1(F, F, G))) <=> (((~k0(G)) | (~l0(E)) | q1(E, F, F)) | (~q1(F, F, G))))), rewrite((((~k0(G)) | (~l0(E)) | q1(E, F, F)) | (~q1(F, F, G))) <=> ((~k0(G)) | (~l0(E)) | (~q1(F, F, G)) | q1(E, F, F))), ((((q1(E, F, F) | (~k0(G))) | (~l0(E))) | (~q1(F, F, G))) <=> ((~k0(G)) | (~l0(E)) | (~q1(F, F, G)) | q1(E, F, F))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(68,plain,
% 0.19/0.46 (![E: $i, F: $i, G: $i] : (((q1(E, F, F) | (~k0(G))) | (~l0(E))) | (~q1(F, F, G))) <=> ![E: $i, F: $i, G: $i] : ((~k0(G)) | (~l0(E)) | (~q1(F, F, G)) | q1(E, F, F))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[67])).
% 0.19/0.47 tff(69,axiom,(![E: $i, F: $i, G: $i] : (((q1(E, F, F) | (~k0(G))) | (~l0(E))) | (~q1(F, F, G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_099')).
% 0.19/0.47 tff(70,plain,
% 0.19/0.47 (![E: $i, F: $i, G: $i] : ((~k0(G)) | (~l0(E)) | (~q1(F, F, G)) | q1(E, F, F))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.47 tff(71,plain,
% 0.19/0.47 (![E: $i, F: $i, G: $i] : ((~k0(G)) | (~l0(E)) | (~q1(F, F, G)) | q1(E, F, F))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.19/0.47 tff(72,plain,(
% 0.19/0.47 ![E: $i, F: $i, G: $i] : ((~k0(G)) | (~l0(E)) | (~q1(F, F, G)) | q1(E, F, F))),
% 0.19/0.47 inference(skolemize,[status(sab)],[71])).
% 0.19/0.47 tff(73,plain,
% 0.19/0.47 (![E: $i, F: $i, G: $i] : ((~k0(G)) | (~l0(E)) | (~q1(F, F, G)) | q1(E, F, F))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.19/0.47 tff(74,plain,
% 0.19/0.47 (k0(e) <=> k0(e)),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(75,axiom,(k0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 0.19/0.47 tff(76,plain,
% 0.19/0.47 (k0(e)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.47 tff(77,plain,
% 0.19/0.47 (l0(a) <=> l0(a)),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(78,axiom,(l0(a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.19/0.47 tff(79,plain,
% 0.19/0.47 (l0(a)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.47 tff(80,plain,
% 0.19/0.47 (((~![E: $i, F: $i, G: $i] : ((~k0(G)) | (~l0(E)) | (~q1(F, F, G)) | q1(E, F, F))) | ((~k0(e)) | (~l0(a)) | (~q1(d, d, e)) | q1(a, d, d))) <=> ((~![E: $i, F: $i, G: $i] : ((~k0(G)) | (~l0(E)) | (~q1(F, F, G)) | q1(E, F, F))) | (~k0(e)) | (~l0(a)) | (~q1(d, d, e)) | q1(a, d, d))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(81,plain,
% 0.19/0.47 ((~![E: $i, F: $i, G: $i] : ((~k0(G)) | (~l0(E)) | (~q1(F, F, G)) | q1(E, F, F))) | ((~k0(e)) | (~l0(a)) | (~q1(d, d, e)) | q1(a, d, d))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(82,plain,
% 0.19/0.47 ((~![E: $i, F: $i, G: $i] : ((~k0(G)) | (~l0(E)) | (~q1(F, F, G)) | q1(E, F, F))) | (~k0(e)) | (~l0(a)) | (~q1(d, d, e)) | q1(a, d, d)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.47 tff(83,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[82, 79, 76, 73, 63, 60])).
% 0.19/0.47 % SZS output end Proof
% 0.19/0.47 % E exiting
%------------------------------------------------------------------------------