%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP776+1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:08:39 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP776+1 : TPTP v9.0.0. Released v4.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 17:07:46 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(opp_type, type, (
% 0.12/0.38 opp: $i > $i)).
% 0.12/0.38 tff(f_type, type, (
% 0.12/0.38 f: $i > $i)).
% 0.12/0.38 tff(tptp_fun_X0_0_type, type, (
% 0.12/0.38 tptp_fun_X0_0: $i)).
% 0.12/0.38 tff(inv_type, type, (
% 0.12/0.38 inv: $i > $i)).
% 0.12/0.38 tff(sum_type, type, (
% 0.12/0.38 sum: ( $i * $i ) > $i)).
% 0.12/0.38 tff(eg_type, type, (
% 0.12/0.38 eg: $i)).
% 0.12/0.38 tff(h_type, type, (
% 0.12/0.38 h: $i > $o)).
% 0.12/0.38 tff(product_type, type, (
% 0.12/0.38 product: ( $i * $i ) > $i)).
% 0.12/0.38 tff(eh_type, type, (
% 0.12/0.38 eh: $i)).
% 0.12/0.38 tff(g_type, type, (
% 0.12/0.38 g: $i > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (h(eg) <=> h(eg)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,axiom,(h(eg)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos11')).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (h(eg)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (^[B: $i, A: $i] : refl((h(opp(B)) | (~h(A))) <=> (h(opp(B)) | (~h(A))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![B: $i, A: $i] : (h(opp(B)) | (~h(A))) <=> ![B: $i, A: $i] : (h(opp(B)) | (~h(A)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (![B: $i, A: $i] : (h(opp(B)) | (~h(A))) <=> ![B: $i, A: $i] : (h(opp(B)) | (~h(A)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (^[B: $i, A: $i] : rewrite((h(A) => h(opp(B))) <=> (h(opp(B)) | (~h(A))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![B: $i, A: $i] : (h(A) => h(opp(B))) <=> ![B: $i, A: $i] : (h(opp(B)) | (~h(A)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[7])).
% 0.12/0.38 tff(9,axiom,(![B: $i, A: $i] : (h(A) => h(opp(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos10')).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (![B: $i, A: $i] : (h(opp(B)) | (~h(A)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (![B: $i, A: $i] : (h(opp(B)) | (~h(A)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.12/0.38 tff(12,plain,(
% 0.12/0.38 ![B: $i, A: $i] : (h(opp(B)) | (~h(A)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[11])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![B: $i, A: $i] : (h(opp(B)) | (~h(A)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (((~![B: $i, A: $i] : (h(opp(B)) | (~h(A)))) | ((~h(eg)) | h(opp(f(X0!0))))) <=> ((~![B: $i, A: $i] : (h(opp(B)) | (~h(A)))) | (~h(eg)) | h(opp(f(X0!0))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 ((h(opp(f(X0!0))) | (~h(eg))) <=> ((~h(eg)) | h(opp(f(X0!0))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (((~![B: $i, A: $i] : (h(opp(B)) | (~h(A)))) | (h(opp(f(X0!0))) | (~h(eg)))) <=> ((~![B: $i, A: $i] : (h(opp(B)) | (~h(A)))) | ((~h(eg)) | h(opp(f(X0!0)))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[15])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (((~![B: $i, A: $i] : (h(opp(B)) | (~h(A)))) | (h(opp(f(X0!0))) | (~h(eg)))) <=> ((~![B: $i, A: $i] : (h(opp(B)) | (~h(A)))) | (~h(eg)) | h(opp(f(X0!0))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[16, 14])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 ((~![B: $i, A: $i] : (h(opp(B)) | (~h(A)))) | (h(opp(f(X0!0))) | (~h(eg)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 ((~![B: $i, A: $i] : (h(opp(B)) | (~h(A)))) | (~h(eg)) | h(opp(f(X0!0)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (h(opp(f(X0!0)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[19, 13, 3])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (^[A: $i] : refl(((~h(A)) | (sum(A, eg) = A)) <=> ((~h(A)) | (sum(A, eg) = A)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![A: $i] : ((~h(A)) | (sum(A, eg) = A)) <=> ![A: $i] : ((~h(A)) | (sum(A, eg) = A))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (![A: $i] : ((~h(A)) | (sum(A, eg) = A)) <=> ![A: $i] : ((~h(A)) | (sum(A, eg) = A))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (^[A: $i] : rewrite((h(A) => (sum(A, eg) = A)) <=> ((~h(A)) | (sum(A, eg) = A)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![A: $i] : (h(A) => (sum(A, eg) = A)) <=> ![A: $i] : ((~h(A)) | (sum(A, eg) = A))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.38 tff(26,axiom,(![A: $i] : (h(A) => (sum(A, eg) = A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos14')).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![A: $i] : ((~h(A)) | (sum(A, eg) = A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (![A: $i] : ((~h(A)) | (sum(A, eg) = A))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.12/0.39 tff(29,plain,(
% 0.12/0.39 ![A: $i] : ((~h(A)) | (sum(A, eg) = A))),
% 0.12/0.39 inference(skolemize,[status(sab)],[28])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (![A: $i] : ((~h(A)) | (sum(A, eg) = A))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (((~![A: $i] : ((~h(A)) | (sum(A, eg) = A))) | ((~h(opp(f(X0!0)))) | (sum(opp(f(X0!0)), eg) = opp(f(X0!0))))) <=> ((~![A: $i] : ((~h(A)) | (sum(A, eg) = A))) | (~h(opp(f(X0!0)))) | (sum(opp(f(X0!0)), eg) = opp(f(X0!0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 ((~![A: $i] : ((~h(A)) | (sum(A, eg) = A))) | ((~h(opp(f(X0!0)))) | (sum(opp(f(X0!0)), eg) = opp(f(X0!0))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 ((~![A: $i] : ((~h(A)) | (sum(A, eg) = A))) | (~h(opp(f(X0!0)))) | (sum(opp(f(X0!0)), eg) = opp(f(X0!0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (sum(opp(f(X0!0)), eg) = opp(f(X0!0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[33, 30, 20])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (^[B: $i, A: $i] : refl((f(product(A, B)) = sum(f(A), f(B))) <=> (f(product(A, B)) = sum(f(A), f(B))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (![B: $i, A: $i] : (f(product(A, B)) = sum(f(A), f(B))) <=> ![B: $i, A: $i] : (f(product(A, B)) = sum(f(A), f(B)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (![B: $i, A: $i] : (f(product(A, B)) = sum(f(A), f(B))) <=> ![B: $i, A: $i] : (f(product(A, B)) = sum(f(A), f(B)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(38,axiom,(![B: $i, A: $i] : (f(product(A, B)) = sum(f(A), f(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos18')).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (![B: $i, A: $i] : (f(product(A, B)) = sum(f(A), f(B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.12/0.39 tff(40,plain,(
% 0.12/0.39 ![B: $i, A: $i] : (f(product(A, B)) = sum(f(A), f(B)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[39])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (![B: $i, A: $i] : (f(product(A, B)) = sum(f(A), f(B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 ((~![B: $i, A: $i] : (f(product(A, B)) = sum(f(A), f(B)))) | (f(product(X0!0, inv(X0!0))) = sum(f(X0!0), f(inv(X0!0))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (f(product(X0!0, inv(X0!0))) = sum(f(X0!0), f(inv(X0!0)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (^[A: $i] : refl((h(f(A)) | (~g(A))) <=> (h(f(A)) | (~g(A))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 (![A: $i] : (h(f(A)) | (~g(A))) <=> ![A: $i] : (h(f(A)) | (~g(A)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[44])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (![A: $i] : (h(f(A)) | (~g(A))) <=> ![A: $i] : (h(f(A)) | (~g(A)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (^[A: $i] : rewrite((g(A) => h(f(A))) <=> (h(f(A)) | (~g(A))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (![A: $i] : (g(A) => h(f(A))) <=> ![A: $i] : (h(f(A)) | (~g(A)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.39 tff(49,axiom,(![A: $i] : (g(A) => h(f(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos17')).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (![A: $i] : (h(f(A)) | (~g(A)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (![A: $i] : (h(f(A)) | (~g(A)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.20/0.39 tff(52,plain,(
% 0.20/0.39 ![A: $i] : (h(f(A)) | (~g(A)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[51])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (![A: $i] : (h(f(A)) | (~g(A)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (g(eh) <=> g(eh)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(55,axiom,(g(eh)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos03')).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (g(eh)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (((~![A: $i] : (h(f(A)) | (~g(A)))) | (h(f(eh)) | (~g(eh)))) <=> ((~![A: $i] : (h(f(A)) | (~g(A)))) | h(f(eh)) | (~g(eh)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 ((~![A: $i] : (h(f(A)) | (~g(A)))) | (h(f(eh)) | (~g(eh)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 ((~![A: $i] : (h(f(A)) | (~g(A)))) | h(f(eh)) | (~g(eh))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (h(f(eh))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[59, 56, 53])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (^[A: $i] : refl(((~h(A)) | (sum(opp(A), A) = eg)) <=> ((~h(A)) | (sum(opp(A), A) = eg)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 (![A: $i] : ((~h(A)) | (sum(opp(A), A) = eg)) <=> ![A: $i] : ((~h(A)) | (sum(opp(A), A) = eg))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (![A: $i] : ((~h(A)) | (sum(opp(A), A) = eg)) <=> ![A: $i] : ((~h(A)) | (sum(opp(A), A) = eg))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (^[A: $i] : rewrite((h(A) => (sum(opp(A), A) = eg)) <=> ((~h(A)) | (sum(opp(A), A) = eg)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (![A: $i] : (h(A) => (sum(opp(A), A) = eg)) <=> ![A: $i] : ((~h(A)) | (sum(opp(A), A) = eg))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.39 tff(66,axiom,(![A: $i] : (h(A) => (sum(opp(A), A) = eg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos16')).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 (![A: $i] : ((~h(A)) | (sum(opp(A), A) = eg))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 (![A: $i] : ((~h(A)) | (sum(opp(A), A) = eg))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.20/0.39 tff(69,plain,(
% 0.20/0.39 ![A: $i] : ((~h(A)) | (sum(opp(A), A) = eg))),
% 0.20/0.39 inference(skolemize,[status(sab)],[68])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 (![A: $i] : ((~h(A)) | (sum(opp(A), A) = eg))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 (((~![A: $i] : ((~h(A)) | (sum(opp(A), A) = eg))) | ((~h(f(eh))) | (sum(opp(f(eh)), f(eh)) = eg))) <=> ((~![A: $i] : ((~h(A)) | (sum(opp(A), A) = eg))) | (~h(f(eh))) | (sum(opp(f(eh)), f(eh)) = eg))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 ((~![A: $i] : ((~h(A)) | (sum(opp(A), A) = eg))) | ((~h(f(eh))) | (sum(opp(f(eh)), f(eh)) = eg))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 ((~![A: $i] : ((~h(A)) | (sum(opp(A), A) = eg))) | (~h(f(eh))) | (sum(opp(f(eh)), f(eh)) = eg)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.39 tff(74,plain,
% 0.20/0.39 (sum(opp(f(eh)), f(eh)) = eg),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[73, 70, 60])).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 (^[A: $i] : refl(((~g(A)) | (product(eh, A) = A)) <=> ((~g(A)) | (product(eh, A) = A)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(76,plain,
% 0.20/0.39 (![A: $i] : ((~g(A)) | (product(eh, A) = A)) <=> ![A: $i] : ((~g(A)) | (product(eh, A) = A))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 (![A: $i] : ((~g(A)) | (product(eh, A) = A)) <=> ![A: $i] : ((~g(A)) | (product(eh, A) = A))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(78,plain,
% 0.20/0.39 (^[A: $i] : rewrite((g(A) => (product(eh, A) = A)) <=> ((~g(A)) | (product(eh, A) = A)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(79,plain,
% 0.20/0.39 (![A: $i] : (g(A) => (product(eh, A) = A)) <=> ![A: $i] : ((~g(A)) | (product(eh, A) = A))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.39 tff(80,axiom,(![A: $i] : (g(A) => (product(eh, A) = A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos05')).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 (![A: $i] : ((~g(A)) | (product(eh, A) = A))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.39 tff(82,plain,
% 0.20/0.39 (![A: $i] : ((~g(A)) | (product(eh, A) = A))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.20/0.39 tff(83,plain,(
% 0.20/0.39 ![A: $i] : ((~g(A)) | (product(eh, A) = A))),
% 0.20/0.39 inference(skolemize,[status(sab)],[82])).
% 0.20/0.39 tff(84,plain,
% 0.20/0.39 (![A: $i] : ((~g(A)) | (product(eh, A) = A))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.20/0.39 tff(85,plain,
% 0.20/0.39 (((~![A: $i] : ((~g(A)) | (product(eh, A) = A))) | ((~g(eh)) | (product(eh, eh) = eh))) <=> ((~![A: $i] : ((~g(A)) | (product(eh, A) = A))) | (~g(eh)) | (product(eh, eh) = eh))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(86,plain,
% 0.20/0.39 ((~![A: $i] : ((~g(A)) | (product(eh, A) = A))) | ((~g(eh)) | (product(eh, eh) = eh))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(87,plain,
% 0.20/0.39 ((~![A: $i] : ((~g(A)) | (product(eh, A) = A))) | (~g(eh)) | (product(eh, eh) = eh)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.39 tff(88,plain,
% 0.20/0.39 (product(eh, eh) = eh),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[87, 56, 84])).
% 0.20/0.39 tff(89,plain,
% 0.20/0.39 (f(product(eh, eh)) = f(eh)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[88])).
% 0.20/0.39 tff(90,plain,
% 0.20/0.39 ((~![B: $i, A: $i] : (f(product(A, B)) = sum(f(A), f(B)))) | (f(product(eh, eh)) = sum(f(eh), f(eh)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(91,plain,
% 0.20/0.39 (f(product(eh, eh)) = sum(f(eh), f(eh))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[90, 41])).
% 0.20/0.39 tff(92,plain,
% 0.20/0.39 (sum(f(eh), f(eh)) = f(product(eh, eh))),
% 0.20/0.39 inference(symmetry,[status(thm)],[91])).
% 0.20/0.39 tff(93,plain,
% 0.20/0.39 (sum(f(eh), f(eh)) = f(eh)),
% 0.20/0.39 inference(transitivity,[status(thm)],[92, 89])).
% 0.20/0.39 tff(94,plain,
% 0.20/0.39 (sum(opp(f(eh)), sum(f(eh), f(eh))) = sum(opp(f(eh)), f(eh))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[93])).
% 0.20/0.39 tff(95,plain,
% 0.20/0.39 (((~![B: $i, A: $i] : (h(opp(B)) | (~h(A)))) | ((~h(eg)) | h(opp(f(eh))))) <=> ((~![B: $i, A: $i] : (h(opp(B)) | (~h(A)))) | (~h(eg)) | h(opp(f(eh))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(96,plain,
% 0.20/0.39 ((h(opp(f(eh))) | (~h(eg))) <=> ((~h(eg)) | h(opp(f(eh))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(97,plain,
% 0.20/0.39 (((~![B: $i, A: $i] : (h(opp(B)) | (~h(A)))) | (h(opp(f(eh))) | (~h(eg)))) <=> ((~![B: $i, A: $i] : (h(opp(B)) | (~h(A)))) | ((~h(eg)) | h(opp(f(eh)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[96])).
% 0.20/0.39 tff(98,plain,
% 0.20/0.39 (((~![B: $i, A: $i] : (h(opp(B)) | (~h(A)))) | (h(opp(f(eh))) | (~h(eg)))) <=> ((~![B: $i, A: $i] : (h(opp(B)) | (~h(A)))) | (~h(eg)) | h(opp(f(eh))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[97, 95])).
% 0.20/0.39 tff(99,plain,
% 0.20/0.39 ((~![B: $i, A: $i] : (h(opp(B)) | (~h(A)))) | (h(opp(f(eh))) | (~h(eg)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(100,plain,
% 0.20/0.39 ((~![B: $i, A: $i] : (h(opp(B)) | (~h(A)))) | (~h(eg)) | h(opp(f(eh)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.39 tff(101,plain,
% 0.20/0.39 (h(opp(f(eh)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[100, 13, 3])).
% 0.20/0.39 tff(102,plain,
% 0.20/0.39 (^[C: $i, B: $i, A: $i] : refl(((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C))) <=> ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(103,plain,
% 0.20/0.39 (![C: $i, B: $i, A: $i] : ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C))) <=> ![C: $i, B: $i, A: $i] : ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[102])).
% 0.20/0.39 tff(104,plain,
% 0.20/0.39 (^[C: $i, B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((h(A) & h(B) & h(C)) <=> (~((~h(A)) | (~h(B)) | (~h(C))))), ((~(h(A) & h(B) & h(C))) <=> (~(~((~h(A)) | (~h(B)) | (~h(C))))))), rewrite((~(~((~h(A)) | (~h(B)) | (~h(C))))) <=> ((~h(A)) | (~h(B)) | (~h(C)))), ((~(h(A) & h(B) & h(C))) <=> ((~h(A)) | (~h(B)) | (~h(C))))), (((~(h(A) & h(B) & h(C))) | (sum(sum(A, B), C) = sum(A, sum(B, C)))) <=> (((~h(A)) | (~h(B)) | (~h(C))) | (sum(sum(A, B), C) = sum(A, sum(B, C)))))), rewrite((((~h(A)) | (~h(B)) | (~h(C))) | (sum(sum(A, B), C) = sum(A, sum(B, C)))) <=> ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))), (((~(h(A) & h(B) & h(C))) | (sum(sum(A, B), C) = sum(A, sum(B, C)))) <=> ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(105,plain,
% 0.20/0.39 (![C: $i, B: $i, A: $i] : ((~(h(A) & h(B) & h(C))) | (sum(sum(A, B), C) = sum(A, sum(B, C)))) <=> ![C: $i, B: $i, A: $i] : ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.39 tff(106,plain,
% 0.20/0.39 (![C: $i, B: $i, A: $i] : ((~(h(A) & h(B) & h(C))) | (sum(sum(A, B), C) = sum(A, sum(B, C)))) <=> ![C: $i, B: $i, A: $i] : ((~(h(A) & h(B) & h(C))) | (sum(sum(A, B), C) = sum(A, sum(B, C))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(107,plain,
% 0.20/0.39 (^[C: $i, B: $i, A: $i] : trans(monotonicity(rewrite(((h(A) & h(B)) & h(C)) <=> (h(A) & h(B) & h(C))), ((((h(A) & h(B)) & h(C)) => (sum(sum(A, B), C) = sum(A, sum(B, C)))) <=> ((h(A) & h(B) & h(C)) => (sum(sum(A, B), C) = sum(A, sum(B, C)))))), rewrite(((h(A) & h(B) & h(C)) => (sum(sum(A, B), C) = sum(A, sum(B, C)))) <=> ((~(h(A) & h(B) & h(C))) | (sum(sum(A, B), C) = sum(A, sum(B, C))))), ((((h(A) & h(B)) & h(C)) => (sum(sum(A, B), C) = sum(A, sum(B, C)))) <=> ((~(h(A) & h(B) & h(C))) | (sum(sum(A, B), C) = sum(A, sum(B, C))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(108,plain,
% 0.20/0.40 (![C: $i, B: $i, A: $i] : (((h(A) & h(B)) & h(C)) => (sum(sum(A, B), C) = sum(A, sum(B, C)))) <=> ![C: $i, B: $i, A: $i] : ((~(h(A) & h(B) & h(C))) | (sum(sum(A, B), C) = sum(A, sum(B, C))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.40 tff(109,axiom,(![C: $i, B: $i, A: $i] : (((h(A) & h(B)) & h(C)) => (sum(sum(A, B), C) = sum(A, sum(B, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos12')).
% 0.20/0.40 tff(110,plain,
% 0.20/0.40 (![C: $i, B: $i, A: $i] : ((~(h(A) & h(B) & h(C))) | (sum(sum(A, B), C) = sum(A, sum(B, C))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.40 tff(111,plain,
% 0.20/0.40 (![C: $i, B: $i, A: $i] : ((~(h(A) & h(B) & h(C))) | (sum(sum(A, B), C) = sum(A, sum(B, C))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.20/0.40 tff(112,plain,(
% 0.20/0.40 ![C: $i, B: $i, A: $i] : ((~(h(A) & h(B) & h(C))) | (sum(sum(A, B), C) = sum(A, sum(B, C))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[111])).
% 0.20/0.40 tff(113,plain,
% 0.20/0.40 (![C: $i, B: $i, A: $i] : ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.20/0.40 tff(114,plain,
% 0.20/0.40 (![C: $i, B: $i, A: $i] : ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[113, 103])).
% 0.20/0.40 tff(115,plain,
% 0.20/0.40 (((~![C: $i, B: $i, A: $i] : ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))) | ((~h(f(eh))) | (sum(sum(opp(f(eh)), f(eh)), f(eh)) = sum(opp(f(eh)), sum(f(eh), f(eh)))) | (~h(opp(f(eh)))))) <=> ((~![C: $i, B: $i, A: $i] : ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))) | (~h(f(eh))) | (sum(sum(opp(f(eh)), f(eh)), f(eh)) = sum(opp(f(eh)), sum(f(eh), f(eh)))) | (~h(opp(f(eh)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(116,plain,
% 0.20/0.40 (((sum(sum(opp(f(eh)), f(eh)), f(eh)) = sum(opp(f(eh)), sum(f(eh), f(eh)))) | (~h(opp(f(eh)))) | (~h(f(eh))) | (~h(f(eh)))) <=> ((~h(f(eh))) | (sum(sum(opp(f(eh)), f(eh)), f(eh)) = sum(opp(f(eh)), sum(f(eh), f(eh)))) | (~h(opp(f(eh)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(117,plain,
% 0.20/0.40 (((~![C: $i, B: $i, A: $i] : ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))) | ((sum(sum(opp(f(eh)), f(eh)), f(eh)) = sum(opp(f(eh)), sum(f(eh), f(eh)))) | (~h(opp(f(eh)))) | (~h(f(eh))) | (~h(f(eh))))) <=> ((~![C: $i, B: $i, A: $i] : ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))) | ((~h(f(eh))) | (sum(sum(opp(f(eh)), f(eh)), f(eh)) = sum(opp(f(eh)), sum(f(eh), f(eh)))) | (~h(opp(f(eh))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[116])).
% 0.20/0.40 tff(118,plain,
% 0.20/0.40 (((~![C: $i, B: $i, A: $i] : ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))) | ((sum(sum(opp(f(eh)), f(eh)), f(eh)) = sum(opp(f(eh)), sum(f(eh), f(eh)))) | (~h(opp(f(eh)))) | (~h(f(eh))) | (~h(f(eh))))) <=> ((~![C: $i, B: $i, A: $i] : ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))) | (~h(f(eh))) | (sum(sum(opp(f(eh)), f(eh)), f(eh)) = sum(opp(f(eh)), sum(f(eh), f(eh)))) | (~h(opp(f(eh)))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[117, 115])).
% 0.20/0.40 tff(119,plain,
% 0.20/0.40 ((~![C: $i, B: $i, A: $i] : ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))) | ((sum(sum(opp(f(eh)), f(eh)), f(eh)) = sum(opp(f(eh)), sum(f(eh), f(eh)))) | (~h(opp(f(eh)))) | (~h(f(eh))) | (~h(f(eh))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(120,plain,
% 0.20/0.40 ((~![C: $i, B: $i, A: $i] : ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))) | (~h(f(eh))) | (sum(sum(opp(f(eh)), f(eh)), f(eh)) = sum(opp(f(eh)), sum(f(eh), f(eh)))) | (~h(opp(f(eh))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.40 tff(121,plain,
% 0.20/0.40 ((sum(sum(opp(f(eh)), f(eh)), f(eh)) = sum(opp(f(eh)), sum(f(eh), f(eh)))) | (~h(opp(f(eh))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[120, 114, 60])).
% 0.20/0.40 tff(122,plain,
% 0.20/0.40 (sum(sum(opp(f(eh)), f(eh)), f(eh)) = sum(opp(f(eh)), sum(f(eh), f(eh)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[121, 101])).
% 0.20/0.40 tff(123,plain,
% 0.20/0.40 (eg = sum(opp(f(eh)), f(eh))),
% 0.20/0.40 inference(symmetry,[status(thm)],[74])).
% 0.20/0.40 tff(124,plain,
% 0.20/0.40 (sum(eg, f(eh)) = sum(sum(opp(f(eh)), f(eh)), f(eh))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[123])).
% 0.20/0.40 tff(125,plain,
% 0.20/0.40 (^[A: $i] : refl(((~h(A)) | (sum(eg, A) = A)) <=> ((~h(A)) | (sum(eg, A) = A)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(126,plain,
% 0.20/0.40 (![A: $i] : ((~h(A)) | (sum(eg, A) = A)) <=> ![A: $i] : ((~h(A)) | (sum(eg, A) = A))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[125])).
% 0.20/0.40 tff(127,plain,
% 0.20/0.40 (![A: $i] : ((~h(A)) | (sum(eg, A) = A)) <=> ![A: $i] : ((~h(A)) | (sum(eg, A) = A))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(128,plain,
% 0.20/0.40 (^[A: $i] : rewrite((h(A) => (sum(eg, A) = A)) <=> ((~h(A)) | (sum(eg, A) = A)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(129,plain,
% 0.20/0.40 (![A: $i] : (h(A) => (sum(eg, A) = A)) <=> ![A: $i] : ((~h(A)) | (sum(eg, A) = A))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[128])).
% 0.20/0.40 tff(130,axiom,(![A: $i] : (h(A) => (sum(eg, A) = A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos13')).
% 0.20/0.40 tff(131,plain,
% 0.20/0.40 (![A: $i] : ((~h(A)) | (sum(eg, A) = A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.40 tff(132,plain,
% 0.20/0.40 (![A: $i] : ((~h(A)) | (sum(eg, A) = A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.20/0.40 tff(133,plain,(
% 0.20/0.40 ![A: $i] : ((~h(A)) | (sum(eg, A) = A))),
% 0.20/0.40 inference(skolemize,[status(sab)],[132])).
% 0.20/0.40 tff(134,plain,
% 0.20/0.40 (![A: $i] : ((~h(A)) | (sum(eg, A) = A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.20/0.40 tff(135,plain,
% 0.20/0.40 (((~![A: $i] : ((~h(A)) | (sum(eg, A) = A))) | ((~h(f(eh))) | (sum(eg, f(eh)) = f(eh)))) <=> ((~![A: $i] : ((~h(A)) | (sum(eg, A) = A))) | (~h(f(eh))) | (sum(eg, f(eh)) = f(eh)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(136,plain,
% 0.20/0.40 ((~![A: $i] : ((~h(A)) | (sum(eg, A) = A))) | ((~h(f(eh))) | (sum(eg, f(eh)) = f(eh)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(137,plain,
% 0.20/0.40 ((~![A: $i] : ((~h(A)) | (sum(eg, A) = A))) | (~h(f(eh))) | (sum(eg, f(eh)) = f(eh))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.40 tff(138,plain,
% 0.20/0.40 (sum(eg, f(eh)) = f(eh)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[137, 134, 60])).
% 0.20/0.40 tff(139,plain,
% 0.20/0.40 (f(eh) = sum(eg, f(eh))),
% 0.20/0.40 inference(symmetry,[status(thm)],[138])).
% 0.20/0.40 tff(140,plain,
% 0.20/0.40 (f(eh) = eg),
% 0.20/0.40 inference(transitivity,[status(thm)],[139, 124, 122, 94, 74])).
% 0.20/0.40 tff(141,plain,
% 0.20/0.40 ((~(~((~(f(eh) = eg)) | (~((~g(X0!0)) | (f(inv(X0!0)) = opp(f(X0!0)))))))) <=> ((~(f(eh) = eg)) | (~((~g(X0!0)) | (f(inv(X0!0)) = opp(f(X0!0))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(142,plain,
% 0.20/0.40 (((f(eh) = eg) & ((~g(X0!0)) | (f(inv(X0!0)) = opp(f(X0!0))))) <=> (~((~(f(eh) = eg)) | (~((~g(X0!0)) | (f(inv(X0!0)) = opp(f(X0!0)))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(143,plain,
% 0.20/0.40 ((~((f(eh) = eg) & ((~g(X0!0)) | (f(inv(X0!0)) = opp(f(X0!0)))))) <=> (~(~((~(f(eh) = eg)) | (~((~g(X0!0)) | (f(inv(X0!0)) = opp(f(X0!0))))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[142])).
% 0.20/0.40 tff(144,plain,
% 0.20/0.40 ((~((f(eh) = eg) & ((~g(X0!0)) | (f(inv(X0!0)) = opp(f(X0!0)))))) <=> ((~(f(eh) = eg)) | (~((~g(X0!0)) | (f(inv(X0!0)) = opp(f(X0!0))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[143, 141])).
% 0.20/0.40 tff(145,plain,
% 0.20/0.40 ((~![X0: $i] : ((f(eh) = eg) & ((~g(X0)) | (f(inv(X0)) = opp(f(X0)))))) <=> (~![X0: $i] : ((f(eh) = eg) & ((~g(X0)) | (f(inv(X0)) = opp(f(X0))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(146,axiom,(~![X0: $i] : ((f(eh) = eg) & ((~g(X0)) | (f(inv(X0)) = opp(f(X0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.20/0.40 tff(147,plain,
% 0.20/0.40 (~![X0: $i] : ((f(eh) = eg) & ((~g(X0)) | (f(inv(X0)) = opp(f(X0)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.20/0.40 tff(148,plain,
% 0.20/0.40 (~![X0: $i] : ((f(eh) = eg) & ((~g(X0)) | (f(inv(X0)) = opp(f(X0)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[147, 145])).
% 0.20/0.40 tff(149,plain,
% 0.20/0.40 (~![X0: $i] : ((f(eh) = eg) & ((~g(X0)) | (f(inv(X0)) = opp(f(X0)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[148, 145])).
% 0.20/0.40 tff(150,plain,
% 0.20/0.40 (~![X0: $i] : ((f(eh) = eg) & ((~g(X0)) | (f(inv(X0)) = opp(f(X0)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.20/0.40 tff(151,plain,(
% 0.20/0.40 ~((f(eh) = eg) & ((~g(X0!0)) | (f(inv(X0!0)) = opp(f(X0!0)))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[150])).
% 0.20/0.40 tff(152,plain,
% 0.20/0.40 ((~(f(eh) = eg)) | (~((~g(X0!0)) | (f(inv(X0!0)) = opp(f(X0!0)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.20/0.40 tff(153,plain,
% 0.20/0.40 (~((~g(X0!0)) | (f(inv(X0!0)) = opp(f(X0!0))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[152, 140])).
% 0.20/0.40 tff(154,plain,
% 0.20/0.40 (((~g(X0!0)) | (f(inv(X0!0)) = opp(f(X0!0)))) | g(X0!0)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(155,plain,
% 0.20/0.40 (g(X0!0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.20/0.40 tff(156,plain,
% 0.20/0.40 (^[A: $i] : refl(((~g(A)) | (product(A, inv(A)) = eh)) <=> ((~g(A)) | (product(A, inv(A)) = eh)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(157,plain,
% 0.20/0.40 (![A: $i] : ((~g(A)) | (product(A, inv(A)) = eh)) <=> ![A: $i] : ((~g(A)) | (product(A, inv(A)) = eh))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[156])).
% 0.20/0.40 tff(158,plain,
% 0.20/0.40 (![A: $i] : ((~g(A)) | (product(A, inv(A)) = eh)) <=> ![A: $i] : ((~g(A)) | (product(A, inv(A)) = eh))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(159,plain,
% 0.20/0.40 (^[A: $i] : rewrite((g(A) => (product(A, inv(A)) = eh)) <=> ((~g(A)) | (product(A, inv(A)) = eh)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(160,plain,
% 0.20/0.40 (![A: $i] : (g(A) => (product(A, inv(A)) = eh)) <=> ![A: $i] : ((~g(A)) | (product(A, inv(A)) = eh))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[159])).
% 0.20/0.40 tff(161,axiom,(![A: $i] : (g(A) => (product(A, inv(A)) = eh))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos07')).
% 0.20/0.40 tff(162,plain,
% 0.20/0.40 (![A: $i] : ((~g(A)) | (product(A, inv(A)) = eh))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.20/0.40 tff(163,plain,
% 0.20/0.40 (![A: $i] : ((~g(A)) | (product(A, inv(A)) = eh))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.20/0.40 tff(164,plain,(
% 0.20/0.40 ![A: $i] : ((~g(A)) | (product(A, inv(A)) = eh))),
% 0.20/0.40 inference(skolemize,[status(sab)],[163])).
% 0.20/0.40 tff(165,plain,
% 0.20/0.40 (![A: $i] : ((~g(A)) | (product(A, inv(A)) = eh))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[164, 157])).
% 0.20/0.40 tff(166,plain,
% 0.20/0.40 (((~![A: $i] : ((~g(A)) | (product(A, inv(A)) = eh))) | ((~g(X0!0)) | (product(X0!0, inv(X0!0)) = eh))) <=> ((~![A: $i] : ((~g(A)) | (product(A, inv(A)) = eh))) | (~g(X0!0)) | (product(X0!0, inv(X0!0)) = eh))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(167,plain,
% 0.20/0.40 ((~![A: $i] : ((~g(A)) | (product(A, inv(A)) = eh))) | ((~g(X0!0)) | (product(X0!0, inv(X0!0)) = eh))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(168,plain,
% 0.20/0.40 ((~![A: $i] : ((~g(A)) | (product(A, inv(A)) = eh))) | (~g(X0!0)) | (product(X0!0, inv(X0!0)) = eh)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.40 tff(169,plain,
% 0.20/0.40 (product(X0!0, inv(X0!0)) = eh),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[168, 165, 155])).
% 0.20/0.40 tff(170,plain,
% 0.20/0.40 (f(product(X0!0, inv(X0!0))) = f(eh)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[169])).
% 0.20/0.40 tff(171,plain,
% 0.20/0.40 (f(eh) = f(product(X0!0, inv(X0!0)))),
% 0.20/0.40 inference(symmetry,[status(thm)],[170])).
% 0.20/0.40 tff(172,plain,
% 0.20/0.40 (sum(sum(opp(f(eh)), f(eh)), f(eh)) = sum(eg, f(eh))),
% 0.20/0.40 inference(symmetry,[status(thm)],[124])).
% 0.20/0.40 tff(173,plain,
% 0.20/0.40 (sum(opp(f(eh)), sum(f(eh), f(eh))) = sum(sum(opp(f(eh)), f(eh)), f(eh))),
% 0.20/0.40 inference(symmetry,[status(thm)],[122])).
% 0.20/0.40 tff(174,plain,
% 0.20/0.40 (sum(opp(f(eh)), f(eh)) = sum(opp(f(eh)), sum(f(eh), f(eh)))),
% 0.20/0.40 inference(symmetry,[status(thm)],[94])).
% 0.20/0.40 tff(175,plain,
% 0.20/0.40 (eg = sum(f(X0!0), f(inv(X0!0)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[123, 174, 173, 172, 138, 171, 43])).
% 0.20/0.40 tff(176,plain,
% 0.20/0.40 (sum(opp(f(X0!0)), eg) = sum(opp(f(X0!0)), sum(f(X0!0), f(inv(X0!0))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[175])).
% 0.20/0.40 tff(177,plain,
% 0.20/0.40 (sum(opp(f(X0!0)), sum(f(X0!0), f(inv(X0!0)))) = sum(opp(f(X0!0)), eg)),
% 0.20/0.40 inference(symmetry,[status(thm)],[176])).
% 0.20/0.40 tff(178,plain,
% 0.20/0.40 (^[A: $i] : refl((g(inv(A)) | (~g(A))) <=> (g(inv(A)) | (~g(A))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(179,plain,
% 0.20/0.40 (![A: $i] : (g(inv(A)) | (~g(A))) <=> ![A: $i] : (g(inv(A)) | (~g(A)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[178])).
% 0.20/0.40 tff(180,plain,
% 0.20/0.40 (![A: $i] : (g(inv(A)) | (~g(A))) <=> ![A: $i] : (g(inv(A)) | (~g(A)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(181,plain,
% 0.20/0.40 (^[A: $i] : rewrite((g(A) => g(inv(A))) <=> (g(inv(A)) | (~g(A))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(182,plain,
% 0.20/0.40 (![A: $i] : (g(A) => g(inv(A))) <=> ![A: $i] : (g(inv(A)) | (~g(A)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[181])).
% 0.20/0.40 tff(183,axiom,(![A: $i] : (g(A) => g(inv(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos02')).
% 0.20/0.40 tff(184,plain,
% 0.20/0.40 (![A: $i] : (g(inv(A)) | (~g(A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.20/0.40 tff(185,plain,
% 0.20/0.40 (![A: $i] : (g(inv(A)) | (~g(A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[184, 180])).
% 0.20/0.40 tff(186,plain,(
% 0.20/0.40 ![A: $i] : (g(inv(A)) | (~g(A)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[185])).
% 0.20/0.40 tff(187,plain,
% 0.20/0.40 (![A: $i] : (g(inv(A)) | (~g(A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[186, 179])).
% 0.20/0.40 tff(188,plain,
% 0.20/0.40 (((~![A: $i] : (g(inv(A)) | (~g(A)))) | (g(inv(X0!0)) | (~g(X0!0)))) <=> ((~![A: $i] : (g(inv(A)) | (~g(A)))) | g(inv(X0!0)) | (~g(X0!0)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(189,plain,
% 0.20/0.40 ((~![A: $i] : (g(inv(A)) | (~g(A)))) | (g(inv(X0!0)) | (~g(X0!0)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(190,plain,
% 0.20/0.40 ((~![A: $i] : (g(inv(A)) | (~g(A)))) | g(inv(X0!0)) | (~g(X0!0))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.20/0.40 tff(191,plain,
% 0.20/0.40 (g(inv(X0!0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[190, 187, 155])).
% 0.20/0.40 tff(192,plain,
% 0.20/0.40 (((~![A: $i] : (h(f(A)) | (~g(A)))) | (h(f(inv(X0!0))) | (~g(inv(X0!0))))) <=> ((~![A: $i] : (h(f(A)) | (~g(A)))) | h(f(inv(X0!0))) | (~g(inv(X0!0))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(193,plain,
% 0.20/0.40 ((~![A: $i] : (h(f(A)) | (~g(A)))) | (h(f(inv(X0!0))) | (~g(inv(X0!0))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(194,plain,
% 0.20/0.40 ((~![A: $i] : (h(f(A)) | (~g(A)))) | h(f(inv(X0!0))) | (~g(inv(X0!0)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.20/0.40 tff(195,plain,
% 0.20/0.40 (h(f(inv(X0!0))) | (~g(inv(X0!0)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[194, 53])).
% 0.20/0.40 tff(196,plain,
% 0.20/0.40 (h(f(inv(X0!0)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[195, 191])).
% 0.20/0.40 tff(197,plain,
% 0.20/0.40 (((~![A: $i] : (h(f(A)) | (~g(A)))) | (h(f(X0!0)) | (~g(X0!0)))) <=> ((~![A: $i] : (h(f(A)) | (~g(A)))) | h(f(X0!0)) | (~g(X0!0)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(198,plain,
% 0.20/0.40 ((~![A: $i] : (h(f(A)) | (~g(A)))) | (h(f(X0!0)) | (~g(X0!0)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(199,plain,
% 0.20/0.40 ((~![A: $i] : (h(f(A)) | (~g(A)))) | h(f(X0!0)) | (~g(X0!0))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.20/0.40 tff(200,plain,
% 0.20/0.40 (h(f(X0!0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[199, 53, 155])).
% 0.20/0.40 tff(201,plain,
% 0.20/0.40 (((~![C: $i, B: $i, A: $i] : ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))) | ((~h(f(X0!0))) | (~h(opp(f(X0!0)))) | (~h(f(inv(X0!0)))) | (sum(sum(opp(f(X0!0)), f(X0!0)), f(inv(X0!0))) = sum(opp(f(X0!0)), sum(f(X0!0), f(inv(X0!0))))))) <=> ((~![C: $i, B: $i, A: $i] : ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))) | (~h(f(X0!0))) | (~h(opp(f(X0!0)))) | (~h(f(inv(X0!0)))) | (sum(sum(opp(f(X0!0)), f(X0!0)), f(inv(X0!0))) = sum(opp(f(X0!0)), sum(f(X0!0), f(inv(X0!0))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(202,plain,
% 0.20/0.40 (((sum(sum(opp(f(X0!0)), f(X0!0)), f(inv(X0!0))) = sum(opp(f(X0!0)), sum(f(X0!0), f(inv(X0!0))))) | (~h(opp(f(X0!0)))) | (~h(f(X0!0))) | (~h(f(inv(X0!0))))) <=> ((~h(f(X0!0))) | (~h(opp(f(X0!0)))) | (~h(f(inv(X0!0)))) | (sum(sum(opp(f(X0!0)), f(X0!0)), f(inv(X0!0))) = sum(opp(f(X0!0)), sum(f(X0!0), f(inv(X0!0))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(203,plain,
% 0.20/0.41 (((~![C: $i, B: $i, A: $i] : ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))) | ((sum(sum(opp(f(X0!0)), f(X0!0)), f(inv(X0!0))) = sum(opp(f(X0!0)), sum(f(X0!0), f(inv(X0!0))))) | (~h(opp(f(X0!0)))) | (~h(f(X0!0))) | (~h(f(inv(X0!0)))))) <=> ((~![C: $i, B: $i, A: $i] : ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))) | ((~h(f(X0!0))) | (~h(opp(f(X0!0)))) | (~h(f(inv(X0!0)))) | (sum(sum(opp(f(X0!0)), f(X0!0)), f(inv(X0!0))) = sum(opp(f(X0!0)), sum(f(X0!0), f(inv(X0!0)))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[202])).
% 0.20/0.41 tff(204,plain,
% 0.20/0.41 (((~![C: $i, B: $i, A: $i] : ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))) | ((sum(sum(opp(f(X0!0)), f(X0!0)), f(inv(X0!0))) = sum(opp(f(X0!0)), sum(f(X0!0), f(inv(X0!0))))) | (~h(opp(f(X0!0)))) | (~h(f(X0!0))) | (~h(f(inv(X0!0)))))) <=> ((~![C: $i, B: $i, A: $i] : ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))) | (~h(f(X0!0))) | (~h(opp(f(X0!0)))) | (~h(f(inv(X0!0)))) | (sum(sum(opp(f(X0!0)), f(X0!0)), f(inv(X0!0))) = sum(opp(f(X0!0)), sum(f(X0!0), f(inv(X0!0))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[203, 201])).
% 0.20/0.41 tff(205,plain,
% 0.20/0.41 ((~![C: $i, B: $i, A: $i] : ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))) | ((sum(sum(opp(f(X0!0)), f(X0!0)), f(inv(X0!0))) = sum(opp(f(X0!0)), sum(f(X0!0), f(inv(X0!0))))) | (~h(opp(f(X0!0)))) | (~h(f(X0!0))) | (~h(f(inv(X0!0)))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(206,plain,
% 0.20/0.41 ((~![C: $i, B: $i, A: $i] : ((sum(sum(A, B), C) = sum(A, sum(B, C))) | (~h(A)) | (~h(B)) | (~h(C)))) | (~h(f(X0!0))) | (~h(opp(f(X0!0)))) | (~h(f(inv(X0!0)))) | (sum(sum(opp(f(X0!0)), f(X0!0)), f(inv(X0!0))) = sum(opp(f(X0!0)), sum(f(X0!0), f(inv(X0!0)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.20/0.41 tff(207,plain,
% 0.20/0.41 (sum(sum(opp(f(X0!0)), f(X0!0)), f(inv(X0!0))) = sum(opp(f(X0!0)), sum(f(X0!0), f(inv(X0!0))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[206, 114, 200, 20, 196])).
% 0.20/0.41 tff(208,plain,
% 0.20/0.41 (((~![A: $i] : ((~h(A)) | (sum(opp(A), A) = eg))) | ((~h(f(X0!0))) | (sum(opp(f(X0!0)), f(X0!0)) = eg))) <=> ((~![A: $i] : ((~h(A)) | (sum(opp(A), A) = eg))) | (~h(f(X0!0))) | (sum(opp(f(X0!0)), f(X0!0)) = eg))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(209,plain,
% 0.20/0.41 ((~![A: $i] : ((~h(A)) | (sum(opp(A), A) = eg))) | ((~h(f(X0!0))) | (sum(opp(f(X0!0)), f(X0!0)) = eg))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(210,plain,
% 0.20/0.41 ((~![A: $i] : ((~h(A)) | (sum(opp(A), A) = eg))) | (~h(f(X0!0))) | (sum(opp(f(X0!0)), f(X0!0)) = eg)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.20/0.41 tff(211,plain,
% 0.20/0.41 ((~h(f(X0!0))) | (sum(opp(f(X0!0)), f(X0!0)) = eg)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[210, 70])).
% 0.20/0.41 tff(212,plain,
% 0.20/0.41 (sum(opp(f(X0!0)), f(X0!0)) = eg),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[211, 200])).
% 0.20/0.41 tff(213,plain,
% 0.20/0.41 (sum(sum(opp(f(X0!0)), f(X0!0)), f(inv(X0!0))) = sum(eg, f(inv(X0!0)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[212])).
% 0.20/0.41 tff(214,plain,
% 0.20/0.41 (sum(eg, f(inv(X0!0))) = sum(sum(opp(f(X0!0)), f(X0!0)), f(inv(X0!0)))),
% 0.20/0.41 inference(symmetry,[status(thm)],[213])).
% 0.20/0.41 tff(215,plain,
% 0.20/0.41 (((~![A: $i] : ((~h(A)) | (sum(eg, A) = A))) | ((~h(f(inv(X0!0)))) | (sum(eg, f(inv(X0!0))) = f(inv(X0!0))))) <=> ((~![A: $i] : ((~h(A)) | (sum(eg, A) = A))) | (~h(f(inv(X0!0)))) | (sum(eg, f(inv(X0!0))) = f(inv(X0!0))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(216,plain,
% 0.20/0.41 ((~![A: $i] : ((~h(A)) | (sum(eg, A) = A))) | ((~h(f(inv(X0!0)))) | (sum(eg, f(inv(X0!0))) = f(inv(X0!0))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(217,plain,
% 0.20/0.41 ((~![A: $i] : ((~h(A)) | (sum(eg, A) = A))) | (~h(f(inv(X0!0)))) | (sum(eg, f(inv(X0!0))) = f(inv(X0!0)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.20/0.41 tff(218,plain,
% 0.20/0.41 (sum(eg, f(inv(X0!0))) = f(inv(X0!0))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[217, 134, 196])).
% 0.20/0.41 tff(219,plain,
% 0.20/0.41 (f(inv(X0!0)) = sum(eg, f(inv(X0!0)))),
% 0.20/0.41 inference(symmetry,[status(thm)],[218])).
% 0.20/0.41 tff(220,plain,
% 0.20/0.41 (f(inv(X0!0)) = opp(f(X0!0))),
% 0.20/0.41 inference(transitivity,[status(thm)],[219, 214, 207, 177, 34])).
% 0.20/0.41 tff(221,plain,
% 0.20/0.41 (((~g(X0!0)) | (f(inv(X0!0)) = opp(f(X0!0)))) | (~(f(inv(X0!0)) = opp(f(X0!0))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(222,plain,
% 0.20/0.41 (~(f(inv(X0!0)) = opp(f(X0!0)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[221, 153])).
% 0.20/0.41 tff(223,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[222, 220])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------