%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWX222-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n025.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 : Tue May 5 07:08:18 PM UTC 2026
% Result : Unsatisfiable 70.95s 71.17s
% Output : Proof 71.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX222-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.14/0.33 % Computer : n025.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 12:35:15 EDT 2026
% 0.14/0.33 % CPUTime :
% 70.95/71.17 % SZS status Unsatisfiable
% 70.95/71.17 % SZS output start Proof
% 70.95/71.17 tff(nf_type, type, (
% 70.95/71.17 nf: $i > $i)).
% 70.95/71.17 tff(lam_type, type, (
% 70.95/71.17 lam: $i > $i)).
% 70.95/71.17 tff(var_type, type, (
% 70.95/71.17 var: $i > $i)).
% 70.95/71.17 tff(zero_type, type, (
% 70.95/71.17 zero: $i)).
% 70.95/71.17 tff(btrue_type, type, (
% 70.95/71.17 btrue: $i)).
% 70.95/71.17 tff(eq4_type, type, (
% 70.95/71.17 eq4: ( $i * $i ) > $i)).
% 70.95/71.17 tff(bfalse_type, type, (
% 70.95/71.17 bfalse: $i)).
% 70.95/71.17 tff(sat_synth_nf_k_type, type, (
% 70.95/71.17 sat_synth_nf_k: $i > $i)).
% 70.95/71.17 tff(notb_type, type, (
% 70.95/71.17 notb: $i > $i)).
% 70.95/71.17 tff(andb_type, type, (
% 70.95/71.17 andb: ( $i * $i ) > $i)).
% 70.95/71.17 tff(tc_type, type, (
% 70.95/71.17 tc: ( $i * $i * $i ) > $i)).
% 70.95/71.17 tff(arr_type, type, (
% 70.95/71.17 arr: ( $i * $i ) > $i)).
% 70.95/71.17 tff(b_type, type, (
% 70.95/71.17 b: $i)).
% 70.95/71.17 tff(a_type, type, (
% 70.95/71.17 a: $i)).
% 70.95/71.17 tff(nil_type, type, (
% 70.95/71.17 nil: $i)).
% 70.95/71.17 tff(eq_type, type, (
% 70.95/71.17 eq: ( $i * $i ) > $i)).
% 70.95/71.17 tff(aux_type, type, (
% 70.95/71.17 aux: ( $i * $i * $i * $i ) > $i)).
% 70.95/71.17 tff(just_type, type, (
% 70.95/71.17 just: $i > $i)).
% 70.95/71.17 tff(cons_type, type, (
% 70.95/71.17 cons: ( $i * $i ) > $i)).
% 70.95/71.17 tff(index_type, type, (
% 70.95/71.17 index: ( $i * $i ) > $i)).
% 70.95/71.17 tff(1,plain,
% 70.95/71.17 (^[X: $i] : refl((eq4(X, X) = btrue) <=> (eq4(X, X) = btrue))),
% 70.95/71.17 inference(bind,[status(th)],[])).
% 70.95/71.17 tff(2,plain,
% 70.95/71.17 (![X: $i] : (eq4(X, X) = btrue) <=> ![X: $i] : (eq4(X, X) = btrue)),
% 70.95/71.17 inference(quant_intro,[status(thm)],[1])).
% 70.95/71.17 tff(3,plain,
% 70.95/71.17 (![X: $i] : (eq4(X, X) = btrue) <=> ![X: $i] : (eq4(X, X) = btrue)),
% 70.95/71.17 inference(rewrite,[status(thm)],[])).
% 70.95/71.17 tff(4,axiom,(![X: $i] : (eq4(X, X) = btrue)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_054')).
% 70.95/71.17 tff(5,plain,
% 70.95/71.17 (![X: $i] : (eq4(X, X) = btrue)),
% 70.95/71.17 inference(modus_ponens,[status(thm)],[4, 3])).
% 70.95/71.17 tff(6,plain,(
% 70.95/71.17 ![X: $i] : (eq4(X, X) = btrue)),
% 70.95/71.17 inference(skolemize,[status(sab)],[5])).
% 70.95/71.17 tff(7,plain,
% 70.95/71.17 (![X: $i] : (eq4(X, X) = btrue)),
% 70.95/71.17 inference(modus_ponens,[status(thm)],[6, 2])).
% 70.95/71.17 tff(8,plain,
% 70.95/71.17 ((~![X: $i] : (eq4(X, X) = btrue)) | (eq4(bfalse, bfalse) = btrue)),
% 70.95/71.17 inference(quant_inst,[status(thm)],[])).
% 70.95/71.17 tff(9,plain,
% 70.95/71.17 (eq4(bfalse, bfalse) = btrue),
% 70.95/71.17 inference(unit_resolution,[status(thm)],[8, 7])).
% 70.95/71.17 tff(10,plain,
% 70.95/71.17 ((notb(btrue) = bfalse) <=> (notb(btrue) = bfalse)),
% 70.95/71.17 inference(rewrite,[status(thm)],[])).
% 70.95/71.17 tff(11,axiom,(notb(btrue) = bfalse), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_002')).
% 70.95/71.17 tff(12,plain,
% 70.95/71.17 (notb(btrue) = bfalse),
% 70.95/71.17 inference(modus_ponens,[status(thm)],[11, 10])).
% 70.95/71.17 tff(13,plain,
% 70.95/71.17 (^[X: $i] : refl((eq(X, X) = btrue) <=> (eq(X, X) = btrue))),
% 70.95/71.17 inference(bind,[status(th)],[])).
% 70.95/71.17 tff(14,plain,
% 70.95/71.17 (![X: $i] : (eq(X, X) = btrue) <=> ![X: $i] : (eq(X, X) = btrue)),
% 70.95/71.17 inference(quant_intro,[status(thm)],[13])).
% 70.95/71.17 tff(15,plain,
% 70.95/71.17 (![X: $i] : (eq(X, X) = btrue) <=> ![X: $i] : (eq(X, X) = btrue)),
% 70.95/71.17 inference(rewrite,[status(thm)],[])).
% 70.95/71.17 tff(16,axiom,(![X: $i] : (eq(X, X) = btrue)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_051')).
% 70.95/71.17 tff(17,plain,
% 70.95/71.17 (![X: $i] : (eq(X, X) = btrue)),
% 70.95/71.17 inference(modus_ponens,[status(thm)],[16, 15])).
% 70.95/71.17 tff(18,plain,(
% 70.95/71.17 ![X: $i] : (eq(X, X) = btrue)),
% 70.95/71.17 inference(skolemize,[status(sab)],[17])).
% 70.95/71.17 tff(19,plain,
% 70.95/71.17 (![X: $i] : (eq(X, X) = btrue)),
% 70.95/71.17 inference(modus_ponens,[status(thm)],[18, 14])).
% 70.95/71.17 tff(20,plain,
% 70.95/71.17 ((~![X: $i] : (eq(X, X) = btrue)) | (eq(b, b) = btrue)),
% 70.95/71.17 inference(quant_inst,[status(thm)],[])).
% 70.95/71.17 tff(21,plain,
% 70.95/71.17 (eq(b, b) = btrue),
% 70.95/71.17 inference(unit_resolution,[status(thm)],[20, 19])).
% 70.95/71.17 tff(22,plain,
% 70.95/71.17 (^[Z: $i, Tx3: $i, X3: $i, X: $i] : refl((aux(X, Z, X3, just(Tx3)) = eq(Tx3, Z)) <=> (aux(X, Z, X3, just(Tx3)) = eq(Tx3, Z)))),
% 70.95/71.17 inference(bind,[status(th)],[])).
% 70.95/71.17 tff(23,plain,
% 70.95/71.17 (![Z: $i, Tx3: $i, X3: $i, X: $i] : (aux(X, Z, X3, just(Tx3)) = eq(Tx3, Z)) <=> ![Z: $i, Tx3: $i, X3: $i, X: $i] : (aux(X, Z, X3, just(Tx3)) = eq(Tx3, Z))),
% 70.95/71.17 inference(quant_intro,[status(thm)],[22])).
% 70.95/71.17 tff(24,plain,
% 70.95/71.17 (![Z: $i, Tx3: $i, X3: $i, X: $i] : (aux(X, Z, X3, just(Tx3)) = eq(Tx3, Z)) <=> ![Z: $i, Tx3: $i, X3: $i, X: $i] : (aux(X, Z, X3, just(Tx3)) = eq(Tx3, Z))),
% 70.95/71.17 inference(rewrite,[status(thm)],[])).
% 70.95/71.17 tff(25,axiom,(![Z: $i, Tx3: $i, X3: $i, X: $i] : (aux(X, Z, X3, just(Tx3)) = eq(Tx3, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_001')).
% 70.95/71.17 tff(26,plain,
% 70.95/71.17 (![Z: $i, Tx3: $i, X3: $i, X: $i] : (aux(X, Z, X3, just(Tx3)) = eq(Tx3, Z))),
% 70.95/71.17 inference(modus_ponens,[status(thm)],[25, 24])).
% 70.95/71.17 tff(27,plain,(
% 70.95/71.17 ![Z: $i, Tx3: $i, X3: $i, X: $i] : (aux(X, Z, X3, just(Tx3)) = eq(Tx3, Z))),
% 70.95/71.17 inference(skolemize,[status(sab)],[26])).
% 70.95/71.17 tff(28,plain,
% 70.95/71.17 (![Z: $i, Tx3: $i, X3: $i, X: $i] : (aux(X, Z, X3, just(Tx3)) = eq(Tx3, Z))),
% 70.95/71.17 inference(modus_ponens,[status(thm)],[27, 23])).
% 70.95/71.17 tff(29,plain,
% 70.95/71.17 ((~![Z: $i, Tx3: $i, X3: $i, X: $i] : (aux(X, Z, X3, just(Tx3)) = eq(Tx3, Z))) | (aux(cons(b, cons(a, nil)), b, zero, just(b)) = eq(b, b))),
% 70.95/71.17 inference(quant_inst,[status(thm)],[])).
% 70.95/71.17 tff(30,plain,
% 70.95/71.17 (aux(cons(b, cons(a, nil)), b, zero, just(b)) = eq(b, b)),
% 70.95/71.17 inference(unit_resolution,[status(thm)],[29, 28])).
% 70.95/71.17 tff(31,plain,
% 70.95/71.17 (^[Xs: $i, Z: $i] : refl((index(cons(Z, Xs), zero) = just(Z)) <=> (index(cons(Z, Xs), zero) = just(Z)))),
% 70.95/71.17 inference(bind,[status(th)],[])).
% 70.95/71.17 tff(32,plain,
% 70.95/71.17 (![Xs: $i, Z: $i] : (index(cons(Z, Xs), zero) = just(Z)) <=> ![Xs: $i, Z: $i] : (index(cons(Z, Xs), zero) = just(Z))),
% 70.95/71.17 inference(quant_intro,[status(thm)],[31])).
% 70.95/71.17 tff(33,plain,
% 70.95/71.17 (![Xs: $i, Z: $i] : (index(cons(Z, Xs), zero) = just(Z)) <=> ![Xs: $i, Z: $i] : (index(cons(Z, Xs), zero) = just(Z))),
% 70.95/71.17 inference(rewrite,[status(thm)],[])).
% 70.95/71.17 tff(34,axiom,(![Xs: $i, Z: $i] : (index(cons(Z, Xs), zero) = just(Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_005')).
% 70.95/71.17 tff(35,plain,
% 70.95/71.17 (![Xs: $i, Z: $i] : (index(cons(Z, Xs), zero) = just(Z))),
% 70.95/71.17 inference(modus_ponens,[status(thm)],[34, 33])).
% 70.95/71.17 tff(36,plain,(
% 70.95/71.17 ![Xs: $i, Z: $i] : (index(cons(Z, Xs), zero) = just(Z))),
% 70.95/71.17 inference(skolemize,[status(sab)],[35])).
% 70.95/71.17 tff(37,plain,
% 70.95/71.17 (![Xs: $i, Z: $i] : (index(cons(Z, Xs), zero) = just(Z))),
% 70.95/71.17 inference(modus_ponens,[status(thm)],[36, 32])).
% 70.95/71.17 tff(38,plain,
% 70.95/71.17 ((~![Xs: $i, Z: $i] : (index(cons(Z, Xs), zero) = just(Z))) | (index(cons(b, cons(a, nil)), zero) = just(b))),
% 70.95/71.17 inference(quant_inst,[status(thm)],[])).
% 70.95/71.17 tff(39,plain,
% 70.95/71.17 (index(cons(b, cons(a, nil)), zero) = just(b)),
% 70.95/71.17 inference(unit_resolution,[status(thm)],[38, 37])).
% 70.95/71.17 tff(40,plain,
% 70.95/71.17 (aux(cons(b, cons(a, nil)), b, zero, index(cons(b, cons(a, nil)), zero)) = aux(cons(b, cons(a, nil)), b, zero, just(b))),
% 70.95/71.17 inference(monotonicity,[status(thm)],[39])).
% 70.95/71.17 tff(41,plain,
% 70.95/71.17 (^[Z: $i, X3: $i, X: $i] : refl((tc(X, var(X3), Z) = aux(X, Z, X3, index(X, X3))) <=> (tc(X, var(X3), Z) = aux(X, Z, X3, index(X, X3))))),
% 70.95/71.17 inference(bind,[status(th)],[])).
% 70.95/71.17 tff(42,plain,
% 70.95/71.17 (![Z: $i, X3: $i, X: $i] : (tc(X, var(X3), Z) = aux(X, Z, X3, index(X, X3))) <=> ![Z: $i, X3: $i, X: $i] : (tc(X, var(X3), Z) = aux(X, Z, X3, index(X, X3)))),
% 70.95/71.17 inference(quant_intro,[status(thm)],[41])).
% 70.95/71.17 tff(43,plain,
% 70.95/71.17 (![Z: $i, X3: $i, X: $i] : (tc(X, var(X3), Z) = aux(X, Z, X3, index(X, X3))) <=> ![Z: $i, X3: $i, X: $i] : (tc(X, var(X3), Z) = aux(X, Z, X3, index(X, X3)))),
% 70.95/71.17 inference(rewrite,[status(thm)],[])).
% 70.95/71.17 tff(44,axiom,(![Z: $i, X3: $i, X: $i] : (tc(X, var(X3), Z) = aux(X, Z, X3, index(X, X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_019')).
% 70.95/71.17 tff(45,plain,
% 70.95/71.17 (![Z: $i, X3: $i, X: $i] : (tc(X, var(X3), Z) = aux(X, Z, X3, index(X, X3)))),
% 70.95/71.17 inference(modus_ponens,[status(thm)],[44, 43])).
% 70.95/71.17 tff(46,plain,(
% 70.95/71.17 ![Z: $i, X3: $i, X: $i] : (tc(X, var(X3), Z) = aux(X, Z, X3, index(X, X3)))),
% 70.95/71.17 inference(skolemize,[status(sab)],[45])).
% 70.95/71.17 tff(47,plain,
% 70.95/71.17 (![Z: $i, X3: $i, X: $i] : (tc(X, var(X3), Z) = aux(X, Z, X3, index(X, X3)))),
% 70.95/71.17 inference(modus_ponens,[status(thm)],[46, 42])).
% 70.95/71.17 tff(48,plain,
% 70.95/71.17 ((~![Z: $i, X3: $i, X: $i] : (tc(X, var(X3), Z) = aux(X, Z, X3, index(X, X3)))) | (tc(cons(b, cons(a, nil)), var(zero), b) = aux(cons(b, cons(a, nil)), b, zero, index(cons(b, cons(a, nil)), zero)))),
% 70.95/71.17 inference(quant_inst,[status(thm)],[])).
% 70.95/71.17 tff(49,plain,
% 70.95/71.17 (tc(cons(b, cons(a, nil)), var(zero), b) = aux(cons(b, cons(a, nil)), b, zero, index(cons(b, cons(a, nil)), zero))),
% 70.95/71.17 inference(unit_resolution,[status(thm)],[48, 47])).
% 70.95/71.17 tff(50,plain,
% 70.95/71.17 (^[E: $i, Tx2: $i, T1: $i, X: $i] : refl((tc(X, lam(E), arr(Tx2, T1)) = tc(cons(Tx2, X), E, T1)) <=> (tc(X, lam(E), arr(Tx2, T1)) = tc(cons(Tx2, X), E, T1)))),
% 70.95/71.18 inference(bind,[status(th)],[])).
% 70.95/71.18 tff(51,plain,
% 70.95/71.18 (![E: $i, Tx2: $i, T1: $i, X: $i] : (tc(X, lam(E), arr(Tx2, T1)) = tc(cons(Tx2, X), E, T1)) <=> ![E: $i, Tx2: $i, T1: $i, X: $i] : (tc(X, lam(E), arr(Tx2, T1)) = tc(cons(Tx2, X), E, T1))),
% 70.95/71.18 inference(quant_intro,[status(thm)],[50])).
% 70.95/71.18 tff(52,plain,
% 70.95/71.18 (![E: $i, Tx2: $i, T1: $i, X: $i] : (tc(X, lam(E), arr(Tx2, T1)) = tc(cons(Tx2, X), E, T1)) <=> ![E: $i, Tx2: $i, T1: $i, X: $i] : (tc(X, lam(E), arr(Tx2, T1)) = tc(cons(Tx2, X), E, T1))),
% 70.95/71.18 inference(rewrite,[status(thm)],[])).
% 70.95/71.18 tff(53,axiom,(![E: $i, Tx2: $i, T1: $i, X: $i] : (tc(X, lam(E), arr(Tx2, T1)) = tc(cons(Tx2, X), E, T1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_015')).
% 70.95/71.18 tff(54,plain,
% 70.95/71.18 (![E: $i, Tx2: $i, T1: $i, X: $i] : (tc(X, lam(E), arr(Tx2, T1)) = tc(cons(Tx2, X), E, T1))),
% 70.95/71.18 inference(modus_ponens,[status(thm)],[53, 52])).
% 70.95/71.18 tff(55,plain,(
% 70.95/71.18 ![E: $i, Tx2: $i, T1: $i, X: $i] : (tc(X, lam(E), arr(Tx2, T1)) = tc(cons(Tx2, X), E, T1))),
% 70.95/71.18 inference(skolemize,[status(sab)],[54])).
% 70.95/71.18 tff(56,plain,
% 70.95/71.18 (![E: $i, Tx2: $i, T1: $i, X: $i] : (tc(X, lam(E), arr(Tx2, T1)) = tc(cons(Tx2, X), E, T1))),
% 70.95/71.18 inference(modus_ponens,[status(thm)],[55, 51])).
% 70.95/71.18 tff(57,plain,
% 70.95/71.18 ((~![E: $i, Tx2: $i, T1: $i, X: $i] : (tc(X, lam(E), arr(Tx2, T1)) = tc(cons(Tx2, X), E, T1))) | (tc(cons(a, nil), lam(var(zero)), arr(b, b)) = tc(cons(b, cons(a, nil)), var(zero), b))),
% 70.95/71.18 inference(quant_inst,[status(thm)],[])).
% 70.95/71.18 tff(58,plain,
% 70.95/71.18 (tc(cons(a, nil), lam(var(zero)), arr(b, b)) = tc(cons(b, cons(a, nil)), var(zero), b)),
% 70.95/71.18 inference(unit_resolution,[status(thm)],[57, 56])).
% 70.95/71.18 tff(59,plain,
% 70.95/71.18 ((~![E: $i, Tx2: $i, T1: $i, X: $i] : (tc(X, lam(E), arr(Tx2, T1)) = tc(cons(Tx2, X), E, T1))) | (tc(nil, lam(lam(var(zero))), arr(a, arr(b, b))) = tc(cons(a, nil), lam(var(zero)), arr(b, b)))),
% 70.95/71.18 inference(quant_inst,[status(thm)],[])).
% 70.95/71.18 tff(60,plain,
% 70.95/71.18 (tc(nil, lam(lam(var(zero))), arr(a, arr(b, b))) = tc(cons(a, nil), lam(var(zero)), arr(b, b))),
% 70.95/71.18 inference(unit_resolution,[status(thm)],[59, 56])).
% 70.95/71.18 tff(61,plain,
% 70.95/71.18 (^[Q: $i] : refl((andb(btrue, Q) = Q) <=> (andb(btrue, Q) = Q))),
% 70.95/71.18 inference(bind,[status(th)],[])).
% 70.95/71.18 tff(62,plain,
% 70.95/71.18 (![Q: $i] : (andb(btrue, Q) = Q) <=> ![Q: $i] : (andb(btrue, Q) = Q)),
% 70.95/71.18 inference(quant_intro,[status(thm)],[61])).
% 70.95/71.18 tff(63,plain,
% 70.95/71.18 (![Q: $i] : (andb(btrue, Q) = Q) <=> ![Q: $i] : (andb(btrue, Q) = Q)),
% 70.95/71.18 inference(rewrite,[status(thm)],[])).
% 70.95/71.18 tff(64,axiom,(![Q: $i] : (andb(btrue, Q) = Q)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_007')).
% 70.95/71.18 tff(65,plain,
% 70.95/71.18 (![Q: $i] : (andb(btrue, Q) = Q)),
% 70.95/71.18 inference(modus_ponens,[status(thm)],[64, 63])).
% 70.95/71.18 tff(66,plain,(
% 70.95/71.18 ![Q: $i] : (andb(btrue, Q) = Q)),
% 70.95/71.18 inference(skolemize,[status(sab)],[65])).
% 70.95/71.18 tff(67,plain,
% 70.95/71.18 (![Q: $i] : (andb(btrue, Q) = Q)),
% 70.95/71.18 inference(modus_ponens,[status(thm)],[66, 62])).
% 70.95/71.18 tff(68,plain,
% 70.95/71.18 ((~![Q: $i] : (andb(btrue, Q) = Q)) | (andb(btrue, tc(nil, lam(lam(var(zero))), arr(a, arr(b, b)))) = tc(nil, lam(lam(var(zero))), arr(a, arr(b, b))))),
% 70.95/71.18 inference(quant_inst,[status(thm)],[])).
% 70.95/71.18 tff(69,plain,
% 70.95/71.18 (andb(btrue, tc(nil, lam(lam(var(zero))), arr(a, arr(b, b)))) = tc(nil, lam(lam(var(zero))), arr(a, arr(b, b)))),
% 70.95/71.18 inference(unit_resolution,[status(thm)],[68, 67])).
% 70.95/71.18 tff(70,plain,
% 70.95/71.18 (^[X4: $i] : refl((nf(var(X4)) = btrue) <=> (nf(var(X4)) = btrue))),
% 70.95/71.18 inference(bind,[status(th)],[])).
% 70.95/71.18 tff(71,plain,
% 70.95/71.18 (![X4: $i] : (nf(var(X4)) = btrue) <=> ![X4: $i] : (nf(var(X4)) = btrue)),
% 70.95/71.18 inference(quant_intro,[status(thm)],[70])).
% 70.95/71.18 tff(72,plain,
% 70.95/71.18 (![X4: $i] : (nf(var(X4)) = btrue) <=> ![X4: $i] : (nf(var(X4)) = btrue)),
% 70.95/71.18 inference(rewrite,[status(thm)],[])).
% 70.95/71.18 tff(73,axiom,(![X4: $i] : (nf(var(X4)) = btrue)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_013')).
% 70.95/71.18 tff(74,plain,
% 70.95/71.18 (![X4: $i] : (nf(var(X4)) = btrue)),
% 70.95/71.18 inference(modus_ponens,[status(thm)],[73, 72])).
% 70.95/71.18 tff(75,plain,(
% 70.95/71.18 ![X4: $i] : (nf(var(X4)) = btrue)),
% 70.95/71.18 inference(skolemize,[status(sab)],[74])).
% 70.95/71.18 tff(76,plain,
% 70.95/71.18 (![X4: $i] : (nf(var(X4)) = btrue)),
% 70.95/71.18 inference(modus_ponens,[status(thm)],[75, 71])).
% 70.95/71.18 tff(77,plain,
% 70.95/71.18 ((~![X4: $i] : (nf(var(X4)) = btrue)) | (nf(var(zero)) = btrue)),
% 70.95/71.18 inference(quant_inst,[status(thm)],[])).
% 70.95/71.18 tff(78,plain,
% 70.95/71.18 (nf(var(zero)) = btrue),
% 70.95/71.18 inference(unit_resolution,[status(thm)],[77, 76])).
% 70.95/71.18 tff(79,plain,
% 70.95/71.18 (^[E: $i] : refl((nf(lam(E)) = nf(E)) <=> (nf(lam(E)) = nf(E)))),
% 70.95/71.18 inference(bind,[status(th)],[])).
% 70.95/71.18 tff(80,plain,
% 70.95/71.18 (![E: $i] : (nf(lam(E)) = nf(E)) <=> ![E: $i] : (nf(lam(E)) = nf(E))),
% 70.95/71.18 inference(quant_intro,[status(thm)],[79])).
% 70.95/71.18 tff(81,plain,
% 70.95/71.18 (![E: $i] : (nf(lam(E)) = nf(E)) <=> ![E: $i] : (nf(lam(E)) = nf(E))),
% 70.95/71.18 inference(rewrite,[status(thm)],[])).
% 70.95/71.18 tff(82,axiom,(![E: $i] : (nf(lam(E)) = nf(E))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_012')).
% 70.95/71.18 tff(83,plain,
% 70.95/71.18 (![E: $i] : (nf(lam(E)) = nf(E))),
% 70.95/71.18 inference(modus_ponens,[status(thm)],[82, 81])).
% 70.95/71.18 tff(84,plain,(
% 70.95/71.18 ![E: $i] : (nf(lam(E)) = nf(E))),
% 70.95/71.18 inference(skolemize,[status(sab)],[83])).
% 70.95/71.18 tff(85,plain,
% 70.95/71.18 (![E: $i] : (nf(lam(E)) = nf(E))),
% 70.95/71.18 inference(modus_ponens,[status(thm)],[84, 80])).
% 70.95/71.18 tff(86,plain,
% 70.95/71.18 ((~![E: $i] : (nf(lam(E)) = nf(E))) | (nf(lam(var(zero))) = nf(var(zero)))),
% 70.95/71.18 inference(quant_inst,[status(thm)],[])).
% 70.95/71.18 tff(87,plain,
% 70.95/71.18 (nf(lam(var(zero))) = nf(var(zero))),
% 70.95/71.18 inference(unit_resolution,[status(thm)],[86, 85])).
% 70.95/71.18 tff(88,assumption,(nf(lam(lam(var(zero)))) = nf(lam(var(zero)))), introduced(assumption)).
% 70.95/71.18 tff(89,plain,
% 70.95/71.18 (nf(lam(lam(var(zero)))) = btrue),
% 70.95/71.18 inference(transitivity,[status(thm)],[88, 87, 78])).
% 70.95/71.18 tff(90,plain,
% 70.95/71.18 (andb(nf(lam(lam(var(zero)))), tc(nil, lam(lam(var(zero))), arr(a, arr(b, b)))) = andb(btrue, tc(nil, lam(lam(var(zero))), arr(a, arr(b, b))))),
% 70.95/71.18 inference(monotonicity,[status(thm)],[89])).
% 70.95/71.18 tff(91,plain,
% 70.95/71.18 (andb(nf(lam(lam(var(zero)))), tc(nil, lam(lam(var(zero))), arr(a, arr(b, b)))) = btrue),
% 70.95/71.18 inference(transitivity,[status(thm)],[90, 69, 60, 58, 49, 40, 30, 21])).
% 70.95/71.18 tff(92,plain,
% 70.95/71.18 (notb(andb(nf(lam(lam(var(zero)))), tc(nil, lam(lam(var(zero))), arr(a, arr(b, b))))) = notb(btrue)),
% 70.95/71.18 inference(monotonicity,[status(thm)],[91])).
% 70.95/71.18 tff(93,plain,
% 70.95/71.18 (^[X: $i] : refl((sat_synth_nf_k(X) = notb(andb(nf(X), tc(nil, X, arr(a, arr(b, b)))))) <=> (sat_synth_nf_k(X) = notb(andb(nf(X), tc(nil, X, arr(a, arr(b, b)))))))),
% 70.95/71.18 inference(bind,[status(th)],[])).
% 70.95/71.18 tff(94,plain,
% 70.95/71.18 (![X: $i] : (sat_synth_nf_k(X) = notb(andb(nf(X), tc(nil, X, arr(a, arr(b, b)))))) <=> ![X: $i] : (sat_synth_nf_k(X) = notb(andb(nf(X), tc(nil, X, arr(a, arr(b, b))))))),
% 70.95/71.18 inference(quant_intro,[status(thm)],[93])).
% 70.95/71.18 tff(95,plain,
% 70.95/71.18 (![X: $i] : (sat_synth_nf_k(X) = notb(andb(nf(X), tc(nil, X, arr(a, arr(b, b)))))) <=> ![X: $i] : (sat_synth_nf_k(X) = notb(andb(nf(X), tc(nil, X, arr(a, arr(b, b))))))),
% 70.95/71.18 inference(rewrite,[status(thm)],[])).
% 70.95/71.18 tff(96,axiom,(![X: $i] : (sat_synth_nf_k(X) = notb(andb(nf(X), tc(nil, X, arr(a, arr(b, b))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_020')).
% 70.95/71.18 tff(97,plain,
% 70.95/71.18 (![X: $i] : (sat_synth_nf_k(X) = notb(andb(nf(X), tc(nil, X, arr(a, arr(b, b))))))),
% 70.95/71.18 inference(modus_ponens,[status(thm)],[96, 95])).
% 70.95/71.18 tff(98,plain,(
% 70.95/71.18 ![X: $i] : (sat_synth_nf_k(X) = notb(andb(nf(X), tc(nil, X, arr(a, arr(b, b))))))),
% 70.95/71.18 inference(skolemize,[status(sab)],[97])).
% 70.95/71.18 tff(99,plain,
% 70.95/71.18 (![X: $i] : (sat_synth_nf_k(X) = notb(andb(nf(X), tc(nil, X, arr(a, arr(b, b))))))),
% 70.95/71.18 inference(modus_ponens,[status(thm)],[98, 94])).
% 70.95/71.18 tff(100,plain,
% 70.95/71.18 ((~![X: $i] : (sat_synth_nf_k(X) = notb(andb(nf(X), tc(nil, X, arr(a, arr(b, b))))))) | (sat_synth_nf_k(lam(lam(var(zero)))) = notb(andb(nf(lam(lam(var(zero)))), tc(nil, lam(lam(var(zero))), arr(a, arr(b, b))))))),
% 70.95/71.18 inference(quant_inst,[status(thm)],[])).
% 70.95/71.18 tff(101,plain,
% 70.95/71.18 (sat_synth_nf_k(lam(lam(var(zero)))) = notb(andb(nf(lam(lam(var(zero)))), tc(nil, lam(lam(var(zero))), arr(a, arr(b, b)))))),
% 70.95/71.18 inference(unit_resolution,[status(thm)],[100, 99])).
% 70.95/71.18 tff(102,plain,
% 70.95/71.18 (sat_synth_nf_k(lam(lam(var(zero)))) = bfalse),
% 70.95/71.18 inference(transitivity,[status(thm)],[101, 92, 12])).
% 71.03/71.20 tff(103,plain,
% 71.03/71.20 (eq4(sat_synth_nf_k(lam(lam(var(zero)))), bfalse) = eq4(bfalse, bfalse)),
% 71.03/71.20 inference(monotonicity,[status(thm)],[102])).
% 71.03/71.20 tff(104,plain,
% 71.03/71.20 (eq4(sat_synth_nf_k(lam(lam(var(zero)))), bfalse) = btrue),
% 71.03/71.20 inference(transitivity,[status(thm)],[103, 9])).
% 71.03/71.20 tff(105,plain,
% 71.03/71.20 (^[X: $i] : refl((~(eq4(sat_synth_nf_k(X), bfalse) = btrue)) <=> (~(eq4(sat_synth_nf_k(X), bfalse) = btrue)))),
% 71.03/71.20 inference(bind,[status(th)],[])).
% 71.03/71.20 tff(106,plain,
% 71.03/71.20 (![X: $i] : (~(eq4(sat_synth_nf_k(X), bfalse) = btrue)) <=> ![X: $i] : (~(eq4(sat_synth_nf_k(X), bfalse) = btrue))),
% 71.03/71.20 inference(quant_intro,[status(thm)],[105])).
% 71.03/71.20 tff(107,plain,
% 71.03/71.20 (![X: $i] : (~(eq4(sat_synth_nf_k(X), bfalse) = btrue)) <=> ![X: $i] : (~(eq4(sat_synth_nf_k(X), bfalse) = btrue))),
% 71.03/71.20 inference(rewrite,[status(thm)],[])).
% 71.03/71.20 tff(108,axiom,(![X: $i] : (~(eq4(sat_synth_nf_k(X), bfalse) = btrue))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goal')).
% 71.03/71.20 tff(109,plain,
% 71.03/71.20 (![X: $i] : (~(eq4(sat_synth_nf_k(X), bfalse) = btrue))),
% 71.03/71.20 inference(modus_ponens,[status(thm)],[108, 107])).
% 71.03/71.20 tff(110,plain,(
% 71.03/71.20 ![X: $i] : (~(eq4(sat_synth_nf_k(X), bfalse) = btrue))),
% 71.03/71.20 inference(skolemize,[status(sab)],[109])).
% 71.03/71.20 tff(111,plain,
% 71.03/71.20 (![X: $i] : (~(eq4(sat_synth_nf_k(X), bfalse) = btrue))),
% 71.03/71.20 inference(modus_ponens,[status(thm)],[110, 106])).
% 71.03/71.20 tff(112,plain,
% 71.03/71.20 ((~![X: $i] : (~(eq4(sat_synth_nf_k(X), bfalse) = btrue))) | (~(eq4(sat_synth_nf_k(lam(lam(var(zero)))), bfalse) = btrue))),
% 71.03/71.20 inference(quant_inst,[status(thm)],[])).
% 71.03/71.20 tff(113,plain,
% 71.03/71.20 (~(eq4(sat_synth_nf_k(lam(lam(var(zero)))), bfalse) = btrue)),
% 71.03/71.20 inference(unit_resolution,[status(thm)],[112, 111])).
% 71.03/71.20 tff(114,plain,
% 71.03/71.20 ($false),
% 71.03/71.20 inference(unit_resolution,[status(thm)],[113, 104])).
% 71.03/71.20 tff(115,plain,(~(nf(lam(lam(var(zero)))) = nf(lam(var(zero))))), inference(lemma,lemma(discharge,[]))).
% 71.03/71.20 tff(116,plain,
% 71.03/71.20 ((~![E: $i] : (nf(lam(E)) = nf(E))) | (nf(lam(lam(var(zero)))) = nf(lam(var(zero))))),
% 71.03/71.20 inference(quant_inst,[status(thm)],[])).
% 71.03/71.20 tff(117,plain,
% 71.03/71.20 ($false),
% 71.03/71.20 inference(unit_resolution,[status(thm)],[116, 85, 115])).
% 71.03/71.20 % SZS output end Proof
% 71.03/71.20 % E exiting
%------------------------------------------------------------------------------