%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP777+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 215.18s 215.38s
% Output : Proof 215.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP777+1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 17:08:01 EDT 2025
% 0.12/0.33 % CPUTime :
% 215.18/215.38 % SZS status Theorem
% 215.18/215.38 % SZS output start Proof
% 215.18/215.38 tff(bigC_type, type, (
% 215.18/215.38 bigC: ( $i * $i * $i ) > $i)).
% 215.18/215.38 tff(tptp_fun_X0_0_type, type, (
% 215.18/215.38 tptp_fun_X0_0: $i)).
% 215.18/215.38 tff(c_type, type, (
% 215.18/215.38 c: $i)).
% 215.18/215.38 tff(b_type, type, (
% 215.18/215.38 b: $i)).
% 215.18/215.38 tff(a_type, type, (
% 215.18/215.38 a: $i)).
% 215.18/215.38 tff(product_type, type, (
% 215.18/215.38 product: ( $i * $i ) > $i)).
% 215.18/215.38 tff(quotient_type, type, (
% 215.18/215.38 quotient: ( $i * $i ) > $i)).
% 215.18/215.38 tff(difference_type, type, (
% 215.18/215.38 difference: ( $i * $i ) > $i)).
% 215.18/215.38 tff(1,plain,
% 215.18/215.38 (^[C: $i, B: $i, A: $i] : refl((bigC(A, B, C) = product(product(A, B), product(C, A))) <=> (bigC(A, B, C) = product(product(A, B), product(C, A))))),
% 215.18/215.38 inference(bind,[status(th)],[])).
% 215.18/215.38 tff(2,plain,
% 215.18/215.38 (![C: $i, B: $i, A: $i] : (bigC(A, B, C) = product(product(A, B), product(C, A))) <=> ![C: $i, B: $i, A: $i] : (bigC(A, B, C) = product(product(A, B), product(C, A)))),
% 215.18/215.38 inference(quant_intro,[status(thm)],[1])).
% 215.18/215.38 tff(3,plain,
% 215.18/215.38 (![C: $i, B: $i, A: $i] : (bigC(A, B, C) = product(product(A, B), product(C, A))) <=> ![C: $i, B: $i, A: $i] : (bigC(A, B, C) = product(product(A, B), product(C, A)))),
% 215.18/215.38 inference(rewrite,[status(thm)],[])).
% 215.18/215.38 tff(4,axiom,(![C: $i, B: $i, A: $i] : (bigC(A, B, C) = product(product(A, B), product(C, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos08')).
% 215.18/215.38 tff(5,plain,
% 215.18/215.38 (![C: $i, B: $i, A: $i] : (bigC(A, B, C) = product(product(A, B), product(C, A)))),
% 215.18/215.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 215.18/215.38 tff(6,plain,(
% 215.18/215.38 ![C: $i, B: $i, A: $i] : (bigC(A, B, C) = product(product(A, B), product(C, A)))),
% 215.18/215.38 inference(skolemize,[status(sab)],[5])).
% 215.18/215.38 tff(7,plain,
% 215.18/215.38 (![C: $i, B: $i, A: $i] : (bigC(A, B, C) = product(product(A, B), product(C, A)))),
% 215.18/215.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 215.18/215.38 tff(8,plain,
% 215.18/215.38 ((~![C: $i, B: $i, A: $i] : (bigC(A, B, C) = product(product(A, B), product(C, A)))) | (bigC(c, c, X0!0) = product(product(c, c), product(X0!0, c)))),
% 215.18/215.38 inference(quant_inst,[status(thm)],[])).
% 215.18/215.38 tff(9,plain,
% 215.18/215.38 (bigC(c, c, X0!0) = product(product(c, c), product(X0!0, c))),
% 215.18/215.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 215.18/215.38 tff(10,plain,
% 215.18/215.38 (product(product(c, c), product(X0!0, c)) = bigC(c, c, X0!0)),
% 215.18/215.38 inference(symmetry,[status(thm)],[9])).
% 215.18/215.38 tff(11,plain,
% 215.18/215.38 (^[B: $i, A: $i] : refl((quotient(product(A, B), B) = A) <=> (quotient(product(A, B), B) = A))),
% 215.18/215.38 inference(bind,[status(th)],[])).
% 215.18/215.38 tff(12,plain,
% 215.18/215.38 (![B: $i, A: $i] : (quotient(product(A, B), B) = A) <=> ![B: $i, A: $i] : (quotient(product(A, B), B) = A)),
% 215.18/215.38 inference(quant_intro,[status(thm)],[11])).
% 215.18/215.38 tff(13,plain,
% 215.18/215.38 (![B: $i, A: $i] : (quotient(product(A, B), B) = A) <=> ![B: $i, A: $i] : (quotient(product(A, B), B) = A)),
% 215.18/215.38 inference(rewrite,[status(thm)],[])).
% 215.18/215.38 tff(14,axiom,(![B: $i, A: $i] : (quotient(product(A, B), B) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos03')).
% 215.18/215.38 tff(15,plain,
% 215.18/215.38 (![B: $i, A: $i] : (quotient(product(A, B), B) = A)),
% 215.18/215.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 215.18/215.38 tff(16,plain,(
% 215.18/215.38 ![B: $i, A: $i] : (quotient(product(A, B), B) = A)),
% 215.18/215.38 inference(skolemize,[status(sab)],[15])).
% 215.18/215.38 tff(17,plain,
% 215.18/215.38 (![B: $i, A: $i] : (quotient(product(A, B), B) = A)),
% 215.18/215.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 215.18/215.38 tff(18,plain,
% 215.18/215.38 ((~![B: $i, A: $i] : (quotient(product(A, B), B) = A)) | (quotient(product(product(product(c, c), product(X0!0, c)), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))) = product(product(c, c), product(X0!0, c)))),
% 215.18/215.38 inference(quant_inst,[status(thm)],[])).
% 215.18/215.38 tff(19,plain,
% 215.18/215.38 (quotient(product(product(product(c, c), product(X0!0, c)), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))) = product(product(c, c), product(X0!0, c))),
% 215.18/215.38 inference(unit_resolution,[status(thm)],[18, 17])).
% 215.18/215.38 tff(20,plain,
% 215.18/215.38 (^[B: $i, A: $i] : refl((difference(A, product(A, B)) = B) <=> (difference(A, product(A, B)) = B))),
% 215.18/215.38 inference(bind,[status(th)],[])).
% 215.18/215.38 tff(21,plain,
% 215.18/215.38 (![B: $i, A: $i] : (difference(A, product(A, B)) = B) <=> ![B: $i, A: $i] : (difference(A, product(A, B)) = B)),
% 215.18/215.38 inference(quant_intro,[status(thm)],[20])).
% 215.18/215.38 tff(22,plain,
% 215.18/215.38 (![B: $i, A: $i] : (difference(A, product(A, B)) = B) <=> ![B: $i, A: $i] : (difference(A, product(A, B)) = B)),
% 215.18/215.38 inference(rewrite,[status(thm)],[])).
% 215.18/215.38 tff(23,axiom,(![B: $i, A: $i] : (difference(A, product(A, B)) = B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos01')).
% 215.18/215.38 tff(24,plain,
% 215.18/215.38 (![B: $i, A: $i] : (difference(A, product(A, B)) = B)),
% 215.18/215.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 215.18/215.38 tff(25,plain,(
% 215.18/215.38 ![B: $i, A: $i] : (difference(A, product(A, B)) = B)),
% 215.18/215.38 inference(skolemize,[status(sab)],[24])).
% 215.18/215.38 tff(26,plain,
% 215.18/215.38 (![B: $i, A: $i] : (difference(A, product(A, B)) = B)),
% 215.18/215.38 inference(modus_ponens,[status(thm)],[25, 21])).
% 215.18/215.38 tff(27,plain,
% 215.18/215.38 ((~![B: $i, A: $i] : (difference(A, product(A, B)) = B)) | (difference(product(a, c), product(product(a, c), product(product(c, product(c, c)), product(c, product(b, b))))) = product(product(c, product(c, c)), product(c, product(b, b))))),
% 215.18/215.38 inference(quant_inst,[status(thm)],[])).
% 215.18/215.38 tff(28,plain,
% 215.18/215.38 (difference(product(a, c), product(product(a, c), product(product(c, product(c, c)), product(c, product(b, b))))) = product(product(c, product(c, c)), product(c, product(b, b)))),
% 215.18/215.38 inference(unit_resolution,[status(thm)],[27, 26])).
% 215.18/215.38 tff(29,plain,
% 215.18/215.38 (^[A: $i] : refl((product(A, A) = A) <=> (product(A, A) = A))),
% 215.18/215.38 inference(bind,[status(th)],[])).
% 215.18/215.38 tff(30,plain,
% 215.18/215.38 (![A: $i] : (product(A, A) = A) <=> ![A: $i] : (product(A, A) = A)),
% 215.18/215.38 inference(quant_intro,[status(thm)],[29])).
% 215.18/215.38 tff(31,plain,
% 215.18/215.38 (![A: $i] : (product(A, A) = A) <=> ![A: $i] : (product(A, A) = A)),
% 215.18/215.38 inference(rewrite,[status(thm)],[])).
% 215.18/215.38 tff(32,axiom,(![A: $i] : (product(A, A) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos06')).
% 215.18/215.38 tff(33,plain,
% 215.18/215.38 (![A: $i] : (product(A, A) = A)),
% 215.18/215.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 215.18/215.38 tff(34,plain,(
% 215.18/215.38 ![A: $i] : (product(A, A) = A)),
% 215.18/215.38 inference(skolemize,[status(sab)],[33])).
% 215.18/215.38 tff(35,plain,
% 215.18/215.38 (![A: $i] : (product(A, A) = A)),
% 215.18/215.38 inference(modus_ponens,[status(thm)],[34, 30])).
% 215.18/215.38 tff(36,plain,
% 215.18/215.38 ((~![A: $i] : (product(A, A) = A)) | (product(c, c) = c)),
% 215.18/215.38 inference(quant_inst,[status(thm)],[])).
% 215.18/215.38 tff(37,plain,
% 215.18/215.38 (product(c, c) = c),
% 215.18/215.38 inference(unit_resolution,[status(thm)],[36, 35])).
% 215.18/215.38 tff(38,plain,
% 215.18/215.38 (product(product(c, c), product(product(c, c), product(b, b))) = product(c, product(product(c, c), product(b, b)))),
% 215.18/215.38 inference(monotonicity,[status(thm)],[37])).
% 215.18/215.38 tff(39,plain,
% 215.18/215.38 (^[D: $i, C: $i, B: $i, A: $i] : refl((product(product(A, B), product(C, D)) = product(product(A, C), product(B, D))) <=> (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D))))),
% 215.18/215.38 inference(bind,[status(th)],[])).
% 215.18/215.38 tff(40,plain,
% 215.18/215.38 (![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D))) <=> ![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))),
% 215.18/215.38 inference(quant_intro,[status(thm)],[39])).
% 215.18/215.38 tff(41,plain,
% 215.18/215.38 (![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D))) <=> ![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))),
% 215.18/215.38 inference(rewrite,[status(thm)],[])).
% 215.18/215.38 tff(42,axiom,(![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos05')).
% 215.18/215.38 tff(43,plain,
% 215.18/215.38 (![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))),
% 215.18/215.38 inference(modus_ponens,[status(thm)],[42, 41])).
% 215.18/215.38 tff(44,plain,(
% 215.18/215.38 ![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))),
% 215.18/215.38 inference(skolemize,[status(sab)],[43])).
% 215.18/215.38 tff(45,plain,
% 215.18/215.38 (![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))),
% 215.18/215.38 inference(modus_ponens,[status(thm)],[44, 40])).
% 215.18/215.38 tff(46,plain,
% 215.18/215.38 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(c, c), product(product(c, c), product(b, b))) = product(product(c, product(c, c)), product(c, product(b, b))))),
% 215.18/215.38 inference(quant_inst,[status(thm)],[])).
% 215.18/215.38 tff(47,plain,
% 215.18/215.38 (product(product(c, c), product(product(c, c), product(b, b))) = product(product(c, product(c, c)), product(c, product(b, b)))),
% 215.18/215.38 inference(unit_resolution,[status(thm)],[46, 45])).
% 215.18/215.38 tff(48,plain,
% 215.18/215.38 (product(product(c, product(c, c)), product(c, product(b, b))) = product(product(c, c), product(product(c, c), product(b, b)))),
% 215.18/215.38 inference(symmetry,[status(thm)],[47])).
% 215.18/215.38 tff(49,plain,
% 215.18/215.38 (product(product(c, product(c, c)), product(c, product(b, b))) = product(c, product(product(c, c), product(b, b)))),
% 215.18/215.38 inference(transitivity,[status(thm)],[48, 38])).
% 215.18/215.38 tff(50,plain,
% 215.18/215.38 ((~![A: $i] : (product(A, A) = A)) | (product(product(a, c), product(a, c)) = product(a, c))),
% 215.18/215.38 inference(quant_inst,[status(thm)],[])).
% 215.18/215.38 tff(51,plain,
% 215.18/215.38 (product(product(a, c), product(a, c)) = product(a, c)),
% 215.18/215.38 inference(unit_resolution,[status(thm)],[50, 35])).
% 215.18/215.38 tff(52,plain,
% 215.18/215.38 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(a, c), product(a, c)) = product(product(a, a), product(c, c)))),
% 215.18/215.38 inference(quant_inst,[status(thm)],[])).
% 215.18/215.38 tff(53,plain,
% 215.18/215.38 (product(product(a, c), product(a, c)) = product(product(a, a), product(c, c))),
% 215.18/215.38 inference(unit_resolution,[status(thm)],[52, 45])).
% 215.18/215.38 tff(54,plain,
% 215.18/215.38 (product(product(a, a), product(c, c)) = product(product(a, c), product(a, c))),
% 215.18/215.38 inference(symmetry,[status(thm)],[53])).
% 215.18/215.38 tff(55,plain,
% 215.18/215.38 (product(product(a, a), product(c, c)) = product(a, c)),
% 215.18/215.38 inference(transitivity,[status(thm)],[54, 51])).
% 215.18/215.38 tff(56,plain,
% 215.18/215.38 (product(product(a, c), product(product(a, a), product(c, c))) = product(product(a, c), product(a, c))),
% 215.18/215.38 inference(monotonicity,[status(thm)],[55])).
% 215.18/215.38 tff(57,plain,
% 215.18/215.38 (product(product(a, c), product(a, c)) = product(product(a, c), product(product(a, a), product(c, c)))),
% 215.18/215.38 inference(symmetry,[status(thm)],[56])).
% 215.18/215.38 tff(58,plain,
% 215.18/215.38 (product(a, c) = product(product(a, c), product(a, c))),
% 215.18/215.38 inference(symmetry,[status(thm)],[51])).
% 215.18/215.38 tff(59,plain,
% 215.18/215.38 (product(a, c) = product(product(a, c), product(product(a, a), product(c, c)))),
% 215.18/215.38 inference(transitivity,[status(thm)],[58, 57])).
% 215.18/215.38 tff(60,plain,
% 215.18/215.38 (product(product(a, c), product(product(c, product(c, c)), product(c, product(b, b)))) = product(product(product(a, c), product(product(a, a), product(c, c))), product(c, product(product(c, c), product(b, b))))),
% 215.18/215.38 inference(monotonicity,[status(thm)],[59, 49])).
% 215.18/215.38 tff(61,plain,
% 215.18/215.38 (product(product(product(a, c), product(product(a, a), product(c, c))), product(c, product(product(c, c), product(b, b)))) = product(product(a, c), product(product(c, product(c, c)), product(c, product(b, b))))),
% 215.18/215.38 inference(symmetry,[status(thm)],[60])).
% 215.18/215.38 tff(62,plain,
% 215.18/215.38 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, c), c), product(product(product(a, a), product(c, c)), product(product(c, c), product(b, b)))) = product(product(product(a, c), product(product(a, a), product(c, c))), product(c, product(product(c, c), product(b, b)))))),
% 215.18/215.38 inference(quant_inst,[status(thm)],[])).
% 215.18/215.38 tff(63,plain,
% 215.18/215.38 (product(product(product(a, c), c), product(product(product(a, a), product(c, c)), product(product(c, c), product(b, b)))) = product(product(product(a, c), product(product(a, a), product(c, c))), product(c, product(product(c, c), product(b, b))))),
% 215.18/215.38 inference(unit_resolution,[status(thm)],[62, 45])).
% 215.18/215.38 tff(64,plain,
% 215.18/215.38 ((product(product(a, c), product(c, b)) = product(a, b)) <=> (product(product(a, c), product(c, b)) = product(a, b))),
% 215.18/215.38 inference(rewrite,[status(thm)],[])).
% 215.18/215.38 tff(65,axiom,(product(product(a, c), product(c, b)) = product(a, b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos09')).
% 215.18/215.38 tff(66,plain,
% 215.18/215.38 (product(product(a, c), product(c, b)) = product(a, b)),
% 215.18/215.38 inference(modus_ponens,[status(thm)],[65, 64])).
% 215.18/215.38 tff(67,plain,
% 215.18/215.38 (product(a, b) = product(product(a, c), product(c, b))),
% 215.18/215.38 inference(symmetry,[status(thm)],[66])).
% 215.18/215.38 tff(68,plain,
% 215.18/215.38 (product(product(a, b), product(a, b)) = product(product(product(a, c), product(c, b)), product(product(a, c), product(c, b)))),
% 215.18/215.38 inference(monotonicity,[status(thm)],[67, 67])).
% 215.18/215.38 tff(69,plain,
% 215.18/215.38 (product(product(product(a, c), product(c, b)), product(product(a, c), product(c, b))) = product(product(a, b), product(a, b))),
% 215.18/215.38 inference(symmetry,[status(thm)],[68])).
% 215.18/215.38 tff(70,plain,
% 215.18/215.38 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, c), product(c, b)), product(product(a, c), product(c, b))) = product(product(product(a, c), product(a, c)), product(product(c, b), product(c, b))))),
% 215.18/215.38 inference(quant_inst,[status(thm)],[])).
% 215.18/215.38 tff(71,plain,
% 215.18/215.38 (product(product(product(a, c), product(c, b)), product(product(a, c), product(c, b))) = product(product(product(a, c), product(a, c)), product(product(c, b), product(c, b)))),
% 215.18/215.38 inference(unit_resolution,[status(thm)],[70, 45])).
% 215.18/215.38 tff(72,plain,
% 215.18/215.38 (product(product(product(a, c), product(a, c)), product(product(c, b), product(c, b))) = product(product(product(a, c), product(c, b)), product(product(a, c), product(c, b)))),
% 215.18/215.38 inference(symmetry,[status(thm)],[71])).
% 215.18/215.38 tff(73,plain,
% 215.18/215.38 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(c, b), product(c, b)) = product(product(c, c), product(b, b)))),
% 215.18/215.38 inference(quant_inst,[status(thm)],[])).
% 215.18/215.38 tff(74,plain,
% 215.18/215.38 (product(product(c, b), product(c, b)) = product(product(c, c), product(b, b))),
% 215.18/215.38 inference(unit_resolution,[status(thm)],[73, 45])).
% 215.18/215.38 tff(75,plain,
% 215.18/215.38 (product(product(c, c), product(b, b)) = product(product(c, b), product(c, b))),
% 215.18/215.38 inference(symmetry,[status(thm)],[74])).
% 215.18/215.38 tff(76,plain,
% 215.18/215.38 (product(product(product(a, a), product(c, c)), product(product(c, c), product(b, b))) = product(product(product(a, c), product(a, c)), product(product(c, b), product(c, b)))),
% 215.18/215.38 inference(monotonicity,[status(thm)],[54, 75])).
% 215.18/215.38 tff(77,plain,
% 215.18/215.38 (product(product(product(a, a), product(c, c)), product(product(c, c), product(b, b))) = product(product(a, b), product(a, b))),
% 215.18/215.38 inference(transitivity,[status(thm)],[76, 72, 69])).
% 215.18/215.38 tff(78,plain,
% 215.18/215.38 (product(product(product(a, c), c), product(product(product(a, a), product(c, c)), product(product(c, c), product(b, b)))) = product(product(product(a, c), c), product(product(a, b), product(a, b)))),
% 215.18/215.38 inference(monotonicity,[status(thm)],[77])).
% 215.18/215.38 tff(79,plain,
% 215.18/215.38 (product(product(product(a, c), c), product(product(a, b), product(a, b))) = product(product(product(a, c), c), product(product(product(a, a), product(c, c)), product(product(c, c), product(b, b))))),
% 215.18/215.38 inference(symmetry,[status(thm)],[78])).
% 215.18/215.38 tff(80,plain,
% 215.18/215.38 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(a, b), product(a, b)) = product(product(a, a), product(b, b)))),
% 215.18/215.38 inference(quant_inst,[status(thm)],[])).
% 215.18/215.38 tff(81,plain,
% 215.18/215.38 (product(product(a, b), product(a, b)) = product(product(a, a), product(b, b))),
% 215.18/215.38 inference(unit_resolution,[status(thm)],[80, 45])).
% 215.18/215.38 tff(82,plain,
% 215.18/215.38 (product(product(product(a, c), c), product(product(a, b), product(a, b))) = product(product(product(a, c), c), product(product(a, a), product(b, b)))),
% 215.18/215.38 inference(monotonicity,[status(thm)],[81])).
% 215.18/215.38 tff(83,plain,
% 215.18/215.38 (product(product(product(a, c), c), product(product(a, a), product(b, b))) = product(product(product(a, c), c), product(product(a, b), product(a, b)))),
% 215.18/215.38 inference(symmetry,[status(thm)],[82])).
% 215.18/215.38 tff(84,plain,
% 215.18/215.38 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, c), c), product(product(a, a), product(b, b))) = product(product(product(a, c), product(a, a)), product(c, product(b, b))))),
% 215.18/215.38 inference(quant_inst,[status(thm)],[])).
% 215.18/215.38 tff(85,plain,
% 215.18/215.38 (product(product(product(a, c), c), product(product(a, a), product(b, b))) = product(product(product(a, c), product(a, a)), product(c, product(b, b)))),
% 215.18/215.38 inference(unit_resolution,[status(thm)],[84, 45])).
% 215.18/215.38 tff(86,plain,
% 215.18/215.38 (product(product(product(a, c), product(a, a)), product(c, product(b, b))) = product(product(product(a, c), c), product(product(a, a), product(b, b)))),
% 215.18/215.38 inference(symmetry,[status(thm)],[85])).
% 215.18/215.38 tff(87,plain,
% 215.18/215.38 (c = product(c, c)),
% 215.18/215.38 inference(symmetry,[status(thm)],[37])).
% 215.18/215.38 tff(88,plain,
% 215.18/215.38 (product(c, product(b, b)) = product(product(c, c), product(b, b))),
% 215.18/215.38 inference(monotonicity,[status(thm)],[87])).
% 215.18/215.38 tff(89,plain,
% 215.18/215.38 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(a, c), product(a, a)) = product(product(a, a), product(c, a)))),
% 215.18/215.38 inference(quant_inst,[status(thm)],[])).
% 215.18/215.38 tff(90,plain,
% 215.18/215.38 (product(product(a, c), product(a, a)) = product(product(a, a), product(c, a))),
% 215.18/215.38 inference(unit_resolution,[status(thm)],[89, 45])).
% 215.18/215.38 tff(91,plain,
% 215.18/215.38 (product(product(product(a, c), product(a, a)), product(c, product(b, b))) = product(product(product(a, a), product(c, a)), product(product(c, c), product(b, b)))),
% 215.18/215.38 inference(monotonicity,[status(thm)],[90, 88])).
% 215.18/215.38 tff(92,plain,
% 215.18/215.38 (product(product(product(a, a), product(c, a)), product(product(c, c), product(b, b))) = product(product(product(a, c), product(a, a)), product(c, product(b, b)))),
% 215.18/215.38 inference(symmetry,[status(thm)],[91])).
% 215.18/215.38 tff(93,plain,
% 215.18/215.38 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, a), product(c, c)), product(product(c, a), product(b, b))) = product(product(product(a, a), product(c, a)), product(product(c, c), product(b, b))))),
% 215.18/215.38 inference(quant_inst,[status(thm)],[])).
% 215.18/215.38 tff(94,plain,
% 215.18/215.38 (product(product(product(a, a), product(c, c)), product(product(c, a), product(b, b))) = product(product(product(a, a), product(c, a)), product(product(c, c), product(b, b)))),
% 215.18/215.38 inference(unit_resolution,[status(thm)],[93, 45])).
% 215.18/215.38 tff(95,plain,
% 215.18/215.38 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(c, b), product(a, b)) = product(product(c, a), product(b, b)))),
% 215.18/215.38 inference(quant_inst,[status(thm)],[])).
% 215.18/215.38 tff(96,plain,
% 215.18/215.38 (product(product(c, b), product(a, b)) = product(product(c, a), product(b, b))),
% 215.18/215.38 inference(unit_resolution,[status(thm)],[95, 45])).
% 215.18/215.38 tff(97,plain,
% 215.18/215.38 (product(product(c, a), product(b, b)) = product(product(c, b), product(a, b))),
% 215.18/215.38 inference(symmetry,[status(thm)],[96])).
% 215.18/215.38 tff(98,plain,
% 215.18/215.38 (product(product(product(a, a), product(c, c)), product(product(c, a), product(b, b))) = product(product(product(a, a), product(c, c)), product(product(c, b), product(a, b)))),
% 215.18/215.38 inference(monotonicity,[status(thm)],[97])).
% 215.18/215.38 tff(99,plain,
% 215.18/215.38 (product(product(product(a, a), product(c, c)), product(product(c, b), product(a, b))) = product(product(product(a, a), product(c, c)), product(product(c, a), product(b, b)))),
% 215.18/215.38 inference(symmetry,[status(thm)],[98])).
% 215.18/215.38 tff(100,plain,
% 215.18/215.38 (product(product(product(a, a), product(c, c)), product(product(c, b), product(a, b))) = product(product(product(a, c), product(a, c)), product(product(c, b), product(a, b)))),
% 215.18/215.38 inference(monotonicity,[status(thm)],[54])).
% 215.18/215.38 tff(101,plain,
% 215.18/215.38 (product(product(product(a, c), product(a, c)), product(product(c, b), product(a, b))) = product(product(product(a, a), product(c, c)), product(product(c, b), product(a, b)))),
% 215.18/215.38 inference(symmetry,[status(thm)],[100])).
% 215.18/215.38 tff(102,plain,
% 215.18/215.38 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, c), product(a, c)), product(product(c, b), product(a, b))) = product(product(product(a, c), product(c, b)), product(product(a, c), product(a, b))))),
% 215.18/215.38 inference(quant_inst,[status(thm)],[])).
% 215.18/215.38 tff(103,plain,
% 215.18/215.38 (product(product(product(a, c), product(a, c)), product(product(c, b), product(a, b))) = product(product(product(a, c), product(c, b)), product(product(a, c), product(a, b)))),
% 215.18/215.38 inference(unit_resolution,[status(thm)],[102, 45])).
% 215.18/215.38 tff(104,plain,
% 215.18/215.38 (product(product(product(a, c), product(c, b)), product(product(a, c), product(a, b))) = product(product(product(a, c), product(a, c)), product(product(c, b), product(a, b)))),
% 215.18/215.38 inference(symmetry,[status(thm)],[103])).
% 215.18/215.38 tff(105,plain,
% 215.18/215.38 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(a, c), product(product(a, c), product(c, b))) = product(product(a, product(a, c)), product(c, product(c, b))))),
% 215.18/215.38 inference(quant_inst,[status(thm)],[])).
% 215.18/215.38 tff(106,plain,
% 215.18/215.38 (product(product(a, c), product(product(a, c), product(c, b))) = product(product(a, product(a, c)), product(c, product(c, b)))),
% 215.18/215.38 inference(unit_resolution,[status(thm)],[105, 45])).
% 215.18/215.38 tff(107,plain,
% 215.18/215.38 (product(product(a, c), product(a, b)) = product(product(a, c), product(product(a, c), product(c, b)))),
% 215.18/215.38 inference(monotonicity,[status(thm)],[67])).
% 215.18/215.38 tff(108,plain,
% 215.18/215.38 (product(product(a, c), product(a, b)) = product(product(a, product(a, c)), product(c, product(c, b)))),
% 215.18/215.38 inference(transitivity,[status(thm)],[107, 106])).
% 215.18/215.38 tff(109,plain,
% 215.18/215.38 ((~![A: $i] : (product(A, A) = A)) | (product(product(a, b), product(a, b)) = product(a, b))),
% 215.18/215.38 inference(quant_inst,[status(thm)],[])).
% 215.18/215.38 tff(110,plain,
% 215.18/215.38 (product(product(a, b), product(a, b)) = product(a, b)),
% 215.18/215.38 inference(unit_resolution,[status(thm)],[109, 35])).
% 215.18/215.38 tff(111,plain,
% 215.18/215.38 (product(a, b) = product(product(a, b), product(a, b))),
% 215.18/215.38 inference(symmetry,[status(thm)],[110])).
% 215.18/215.38 tff(112,plain,
% 215.18/215.38 (product(product(a, c), product(c, b)) = product(product(a, b), product(a, b))),
% 215.18/215.38 inference(transitivity,[status(thm)],[66, 111])).
% 215.18/215.38 tff(113,plain,
% 215.18/215.38 (product(product(product(a, c), product(c, b)), product(product(a, c), product(a, b))) = product(product(product(a, b), product(a, b)), product(product(a, product(a, c)), product(c, product(c, b))))),
% 215.18/215.38 inference(monotonicity,[status(thm)],[112, 108])).
% 215.18/215.38 tff(114,plain,
% 215.18/215.38 (product(product(product(a, b), product(a, b)), product(product(a, product(a, c)), product(c, product(c, b)))) = product(product(product(a, c), product(c, b)), product(product(a, c), product(a, b)))),
% 215.18/215.38 inference(symmetry,[status(thm)],[113])).
% 215.18/215.38 tff(115,plain,
% 215.18/215.38 (product(product(product(product(a, a), product(c, c)), product(product(c, c), product(b, b))), product(product(a, product(a, c)), product(c, product(c, b)))) = product(product(product(a, b), product(a, b)), product(product(a, product(a, c)), product(c, product(c, b))))),
% 215.18/215.38 inference(monotonicity,[status(thm)],[77])).
% 215.18/215.38 tff(116,plain,
% 215.18/215.38 (product(product(product(product(a, a), product(c, c)), product(product(c, c), product(b, b))), product(product(a, c), product(a, b))) = product(product(product(product(a, a), product(c, c)), product(product(c, c), product(b, b))), product(product(a, product(a, c)), product(c, product(c, b))))),
% 215.18/215.38 inference(monotonicity,[status(thm)],[108])).
% 215.18/215.38 tff(117,plain,
% 215.18/215.38 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(product(a, a), product(c, c)), product(product(c, c), product(b, b))), product(product(a, c), product(a, b))) = product(product(product(product(a, a), product(c, c)), product(a, c)), product(product(product(c, c), product(b, b)), product(a, b))))),
% 215.18/215.38 inference(quant_inst,[status(thm)],[])).
% 215.18/215.38 tff(118,plain,
% 215.18/215.38 (product(product(product(product(a, a), product(c, c)), product(product(c, c), product(b, b))), product(product(a, c), product(a, b))) = product(product(product(product(a, a), product(c, c)), product(a, c)), product(product(product(c, c), product(b, b)), product(a, b)))),
% 215.18/215.39 inference(unit_resolution,[status(thm)],[117, 45])).
% 215.18/215.39 tff(119,plain,
% 215.18/215.39 (product(product(product(product(a, a), product(c, c)), product(a, c)), product(product(product(c, c), product(b, b)), product(a, b))) = product(product(product(product(a, a), product(c, c)), product(product(c, c), product(b, b))), product(product(a, c), product(a, b)))),
% 215.18/215.39 inference(symmetry,[status(thm)],[118])).
% 215.18/215.39 tff(120,plain,
% 215.18/215.39 ((~![A: $i] : (product(A, A) = A)) | (product(product(c, b), product(c, b)) = product(c, b))),
% 215.18/215.39 inference(quant_inst,[status(thm)],[])).
% 215.18/215.39 tff(121,plain,
% 215.18/215.39 (product(product(c, b), product(c, b)) = product(c, b)),
% 215.18/215.39 inference(unit_resolution,[status(thm)],[120, 35])).
% 215.18/215.39 tff(122,plain,
% 215.18/215.39 (product(product(c, c), product(b, b)) = product(c, b)),
% 215.18/215.39 inference(transitivity,[status(thm)],[75, 121])).
% 215.18/215.39 tff(123,plain,
% 215.18/215.39 (product(product(product(c, c), product(b, b)), product(a, b)) = product(product(c, b), product(product(a, c), product(c, b)))),
% 215.18/215.39 inference(monotonicity,[status(thm)],[122, 67])).
% 215.18/215.39 tff(124,plain,
% 215.18/215.39 (product(product(c, b), product(product(a, c), product(c, b))) = product(product(product(c, c), product(b, b)), product(a, b))),
% 215.18/215.39 inference(symmetry,[status(thm)],[123])).
% 215.18/215.39 tff(125,plain,
% 215.18/215.39 (product(product(c, b), product(product(a, c), product(c, b))) = product(product(c, b), product(product(a, b), product(a, b)))),
% 215.18/215.39 inference(monotonicity,[status(thm)],[112])).
% 215.18/215.39 tff(126,plain,
% 215.18/215.39 (product(product(c, b), product(product(a, b), product(a, b))) = product(product(c, b), product(product(a, c), product(c, b)))),
% 215.18/215.39 inference(symmetry,[status(thm)],[125])).
% 215.18/215.39 tff(127,plain,
% 215.18/215.39 (product(c, b) = product(product(c, b), product(c, b))),
% 215.18/215.39 inference(symmetry,[status(thm)],[121])).
% 215.18/215.39 tff(128,plain,
% 215.18/215.39 (product(c, b) = product(product(c, c), product(b, b))),
% 215.18/215.39 inference(transitivity,[status(thm)],[127, 74])).
% 215.18/215.39 tff(129,plain,
% 215.18/215.39 (product(product(c, b), product(product(a, b), product(a, b))) = product(product(product(c, c), product(b, b)), product(product(a, b), product(a, b)))),
% 215.18/215.39 inference(monotonicity,[status(thm)],[128])).
% 215.18/215.39 tff(130,plain,
% 215.18/215.39 (product(product(product(c, c), product(b, b)), product(product(a, b), product(a, b))) = product(product(c, b), product(product(a, b), product(a, b)))),
% 215.18/215.39 inference(symmetry,[status(thm)],[129])).
% 215.18/215.39 tff(131,plain,
% 215.18/215.39 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(c, c), product(b, b)), product(product(a, b), product(a, b))) = product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))))),
% 215.18/215.39 inference(quant_inst,[status(thm)],[])).
% 215.18/215.39 tff(132,plain,
% 215.18/215.39 (product(product(product(c, c), product(b, b)), product(product(a, b), product(a, b))) = product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))),
% 215.18/215.39 inference(unit_resolution,[status(thm)],[131, 45])).
% 215.18/215.39 tff(133,plain,
% 215.18/215.39 (product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))) = product(product(product(c, c), product(b, b)), product(product(a, b), product(a, b)))),
% 215.18/215.39 inference(symmetry,[status(thm)],[132])).
% 215.18/215.39 tff(134,plain,
% 215.18/215.39 (product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))) = product(product(product(c, c), product(b, b)), product(a, b))),
% 215.18/215.39 inference(transitivity,[status(thm)],[133, 130, 126, 124])).
% 215.18/215.39 tff(135,plain,
% 215.18/215.39 (product(product(product(a, a), product(c, c)), product(a, c)) = product(product(a, c), product(a, c))),
% 215.18/215.39 inference(monotonicity,[status(thm)],[55])).
% 215.18/215.39 tff(136,plain,
% 215.18/215.39 (product(product(a, c), product(a, c)) = product(product(product(a, a), product(c, c)), product(a, c))),
% 215.18/215.39 inference(symmetry,[status(thm)],[135])).
% 215.18/215.39 tff(137,plain,
% 215.18/215.39 (product(a, c) = product(product(product(a, a), product(c, c)), product(a, c))),
% 215.18/215.39 inference(transitivity,[status(thm)],[58, 136])).
% 215.18/215.39 tff(138,plain,
% 215.18/215.39 (product(product(a, c), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))) = product(product(product(product(a, a), product(c, c)), product(a, c)), product(product(product(c, c), product(b, b)), product(a, b)))),
% 215.18/215.39 inference(monotonicity,[status(thm)],[137, 134])).
% 215.18/215.39 tff(139,plain,
% 215.18/215.39 (product(product(a, c), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))) = product(product(a, c), product(product(c, product(c, c)), product(c, product(b, b))))),
% 215.18/215.39 inference(transitivity,[status(thm)],[138, 119, 116, 115, 114, 104, 101, 99, 94, 92, 86, 83, 79, 63, 61])).
% 215.18/215.39 tff(140,plain,
% 215.18/215.39 (difference(product(a, c), product(product(a, c), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))))) = difference(product(a, c), product(product(a, c), product(product(c, product(c, c)), product(c, product(b, b)))))),
% 215.18/215.39 inference(monotonicity,[status(thm)],[139])).
% 215.18/215.39 tff(141,plain,
% 215.18/215.39 ((~![B: $i, A: $i] : (difference(A, product(A, B)) = B)) | (difference(product(a, c), product(product(a, c), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))))) = product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))))),
% 215.18/215.39 inference(quant_inst,[status(thm)],[])).
% 215.18/215.39 tff(142,plain,
% 215.18/215.39 (difference(product(a, c), product(product(a, c), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))))) = product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))),
% 215.18/215.39 inference(unit_resolution,[status(thm)],[141, 26])).
% 215.18/215.39 tff(143,plain,
% 215.18/215.39 (product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))) = difference(product(a, c), product(product(a, c), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))))),
% 215.18/215.39 inference(symmetry,[status(thm)],[142])).
% 215.18/215.39 tff(144,plain,
% 215.18/215.39 (product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))) = product(product(c, product(c, c)), product(c, product(b, b)))),
% 215.18/215.39 inference(transitivity,[status(thm)],[143, 140, 28])).
% 215.18/215.39 tff(145,plain,
% 215.18/215.39 (product(c, product(product(c, c), product(b, b))) = product(c, product(c, b))),
% 215.18/215.39 inference(monotonicity,[status(thm)],[122])).
% 215.18/215.39 tff(146,plain,
% 215.18/215.39 (product(product(c, product(c, c)), product(c, product(b, b))) = product(c, product(c, b))),
% 215.18/215.39 inference(transitivity,[status(thm)],[48, 38, 145])).
% 215.18/215.39 tff(147,plain,
% 215.18/215.39 (product(product(a, b), product(X0!0, a)) = product(product(product(a, b), product(a, b)), product(X0!0, a))),
% 215.18/215.39 inference(monotonicity,[status(thm)],[111])).
% 215.18/215.39 tff(148,plain,
% 215.18/215.39 (product(product(product(a, b), product(a, b)), product(X0!0, a)) = product(product(a, b), product(X0!0, a))),
% 215.18/215.39 inference(symmetry,[status(thm)],[147])).
% 215.18/215.39 tff(149,plain,
% 215.18/215.39 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, b), product(a, b)), product(X0!0, a)) = product(product(product(a, b), X0!0), product(product(a, b), a)))),
% 215.18/215.39 inference(quant_inst,[status(thm)],[])).
% 215.18/215.39 tff(150,plain,
% 215.18/215.39 (product(product(product(a, b), product(a, b)), product(X0!0, a)) = product(product(product(a, b), X0!0), product(product(a, b), a))),
% 215.18/215.39 inference(unit_resolution,[status(thm)],[149, 45])).
% 215.18/215.39 tff(151,plain,
% 215.18/215.39 (product(product(product(a, b), X0!0), product(product(a, b), a)) = product(product(product(a, b), product(a, b)), product(X0!0, a))),
% 215.18/215.39 inference(symmetry,[status(thm)],[150])).
% 215.18/215.39 tff(152,plain,
% 215.18/215.39 (product(product(product(a, b), X0!0), product(product(a, b), a)) = product(product(a, b), product(X0!0, a))),
% 215.18/215.39 inference(transitivity,[status(thm)],[151, 148])).
% 215.18/215.39 tff(153,plain,
% 215.18/215.39 (product(product(product(product(a, b), X0!0), product(product(a, b), a)), product(product(c, product(c, c)), product(c, product(b, b)))) = product(product(product(a, b), product(X0!0, a)), product(c, product(c, b)))),
% 215.18/215.39 inference(monotonicity,[status(thm)],[152, 146])).
% 215.18/215.39 tff(154,plain,
% 215.18/215.39 (product(product(product(a, b), product(X0!0, a)), product(c, product(c, b))) = product(product(product(product(a, b), X0!0), product(product(a, b), a)), product(product(c, product(c, c)), product(c, product(b, b))))),
% 215.18/215.39 inference(symmetry,[status(thm)],[153])).
% 215.18/215.39 tff(155,plain,
% 215.18/215.39 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, b), product(X0!0, a)), product(c, product(c, b))) = product(product(product(a, b), c), product(product(X0!0, a), product(c, b))))),
% 215.18/215.39 inference(quant_inst,[status(thm)],[])).
% 215.18/215.39 tff(156,plain,
% 215.18/215.39 (product(product(product(a, b), product(X0!0, a)), product(c, product(c, b))) = product(product(product(a, b), c), product(product(X0!0, a), product(c, b)))),
% 215.18/215.39 inference(unit_resolution,[status(thm)],[155, 45])).
% 215.18/215.39 tff(157,plain,
% 215.18/215.39 (product(product(product(a, b), c), product(product(X0!0, a), product(c, b))) = product(product(product(a, b), product(X0!0, a)), product(c, product(c, b)))),
% 215.18/215.39 inference(symmetry,[status(thm)],[156])).
% 215.18/215.39 tff(158,plain,
% 215.18/215.39 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(a, b), product(c, c)) = product(product(a, c), product(b, c)))),
% 215.18/215.39 inference(quant_inst,[status(thm)],[])).
% 215.18/215.39 tff(159,plain,
% 215.18/215.39 (product(product(a, b), product(c, c)) = product(product(a, c), product(b, c))),
% 215.18/215.39 inference(unit_resolution,[status(thm)],[158, 45])).
% 215.18/215.39 tff(160,plain,
% 215.18/215.39 (product(product(a, b), product(c, c)) = product(product(a, b), c)),
% 215.18/215.39 inference(monotonicity,[status(thm)],[37])).
% 215.18/215.39 tff(161,plain,
% 215.18/215.39 (product(product(a, b), c) = product(product(a, b), product(c, c))),
% 215.18/215.39 inference(symmetry,[status(thm)],[160])).
% 215.18/215.39 tff(162,plain,
% 215.18/215.39 (product(product(a, b), c) = product(product(a, c), product(b, c))),
% 215.18/215.39 inference(transitivity,[status(thm)],[161, 159])).
% 215.18/215.39 tff(163,plain,
% 215.18/215.39 (product(product(product(a, b), c), product(product(X0!0, a), product(c, b))) = product(product(product(a, c), product(b, c)), product(product(X0!0, a), product(c, b)))),
% 215.18/215.39 inference(monotonicity,[status(thm)],[162])).
% 215.18/215.39 tff(164,plain,
% 215.18/215.39 (product(product(product(a, c), product(b, c)), product(product(X0!0, a), product(c, b))) = product(product(product(a, b), c), product(product(X0!0, a), product(c, b)))),
% 215.18/215.39 inference(symmetry,[status(thm)],[163])).
% 215.18/215.39 tff(165,plain,
% 215.18/215.39 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, c), product(b, c)), product(product(X0!0, a), product(c, b))) = product(product(product(a, c), product(X0!0, a)), product(product(b, c), product(c, b))))),
% 215.18/215.39 inference(quant_inst,[status(thm)],[])).
% 215.18/215.39 tff(166,plain,
% 215.18/215.39 (product(product(product(a, c), product(b, c)), product(product(X0!0, a), product(c, b))) = product(product(product(a, c), product(X0!0, a)), product(product(b, c), product(c, b)))),
% 215.18/215.39 inference(unit_resolution,[status(thm)],[165, 45])).
% 215.18/215.39 tff(167,plain,
% 215.18/215.39 (product(product(product(a, c), product(X0!0, a)), product(product(b, c), product(c, b))) = product(product(product(a, c), product(b, c)), product(product(X0!0, a), product(c, b)))),
% 215.18/215.39 inference(symmetry,[status(thm)],[166])).
% 215.18/215.39 tff(168,plain,
% 215.18/215.39 ((~![A: $i] : (product(A, A) = A)) | (product(a, a) = a)),
% 215.18/215.39 inference(quant_inst,[status(thm)],[])).
% 215.18/215.39 tff(169,plain,
% 215.18/215.39 (product(a, a) = a),
% 215.18/215.39 inference(unit_resolution,[status(thm)],[168, 35])).
% 215.18/215.39 tff(170,plain,
% 215.18/215.39 (a = product(a, a)),
% 215.18/215.39 inference(symmetry,[status(thm)],[169])).
% 215.18/215.39 tff(171,plain,
% 215.18/215.39 (product(product(a, c), a) = product(product(a, c), product(a, a))),
% 215.18/215.39 inference(monotonicity,[status(thm)],[170])).
% 215.18/215.39 tff(172,plain,
% 215.18/215.39 (product(product(a, c), product(a, a)) = product(product(a, c), a)),
% 215.18/215.39 inference(symmetry,[status(thm)],[171])).
% 215.18/215.39 tff(173,plain,
% 215.18/215.39 (product(a, c) = product(product(a, a), product(c, c))),
% 215.18/215.39 inference(transitivity,[status(thm)],[58, 53])).
% 215.18/215.39 tff(174,plain,
% 215.18/215.39 (product(product(a, c), product(a, a)) = product(product(product(a, a), product(c, c)), product(a, a))),
% 215.18/215.39 inference(monotonicity,[status(thm)],[173])).
% 215.18/215.39 tff(175,plain,
% 215.18/215.39 (product(product(product(a, a), product(c, c)), product(a, a)) = product(product(a, c), product(a, a))),
% 215.18/215.39 inference(symmetry,[status(thm)],[174])).
% 215.18/215.39 tff(176,plain,
% 215.18/215.39 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, a), product(c, c)), product(a, a)) = product(product(product(a, a), a), product(product(c, c), a)))),
% 215.18/215.39 inference(quant_inst,[status(thm)],[])).
% 215.18/215.39 tff(177,plain,
% 215.18/215.39 (product(product(product(a, a), product(c, c)), product(a, a)) = product(product(product(a, a), a), product(product(c, c), a))),
% 215.18/215.39 inference(unit_resolution,[status(thm)],[176, 45])).
% 215.18/215.39 tff(178,plain,
% 215.18/215.39 (product(product(product(a, a), a), product(product(c, c), a)) = product(product(product(a, a), product(c, c)), product(a, a))),
% 215.18/215.39 inference(symmetry,[status(thm)],[177])).
% 215.18/215.39 tff(179,plain,
% 215.18/215.39 (product(product(product(a, a), a), product(product(c, c), a)) = product(product(a, c), a)),
% 215.18/215.39 inference(transitivity,[status(thm)],[178, 175, 172])).
% 215.18/215.39 tff(180,plain,
% 215.18/215.39 (product(product(product(a, c), X0!0), product(product(product(a, a), a), product(product(c, c), a))) = product(product(product(a, c), X0!0), product(product(a, c), a))),
% 215.18/215.39 inference(monotonicity,[status(thm)],[179])).
% 215.18/215.39 tff(181,plain,
% 215.18/215.39 (product(product(product(a, c), X0!0), product(product(a, c), a)) = product(product(product(a, c), X0!0), product(product(product(a, a), a), product(product(c, c), a)))),
% 215.18/215.39 inference(symmetry,[status(thm)],[180])).
% 215.18/215.39 tff(182,plain,
% 215.18/215.39 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, c), product(a, c)), product(X0!0, a)) = product(product(product(a, c), X0!0), product(product(a, c), a)))),
% 215.18/215.39 inference(quant_inst,[status(thm)],[])).
% 215.18/215.39 tff(183,plain,
% 215.18/215.39 (product(product(product(a, c), product(a, c)), product(X0!0, a)) = product(product(product(a, c), X0!0), product(product(a, c), a))),
% 215.18/215.39 inference(unit_resolution,[status(thm)],[182, 45])).
% 215.18/215.39 tff(184,plain,
% 215.18/215.39 (product(product(product(a, c), product(a, c)), product(X0!0, a)) = product(product(product(a, a), product(c, c)), product(X0!0, a))),
% 215.18/215.39 inference(monotonicity,[status(thm)],[53])).
% 215.18/215.39 tff(185,plain,
% 215.18/215.39 (product(product(product(a, a), product(c, c)), product(X0!0, a)) = product(product(product(a, c), product(a, c)), product(X0!0, a))),
% 215.18/215.39 inference(symmetry,[status(thm)],[184])).
% 215.18/215.39 tff(186,plain,
% 215.18/215.39 (product(product(product(a, a), product(c, c)), product(X0!0, a)) = product(product(a, c), product(X0!0, a))),
% 215.18/215.39 inference(monotonicity,[status(thm)],[55])).
% 215.18/215.39 tff(187,plain,
% 215.18/215.39 (product(product(a, c), product(X0!0, a)) = product(product(product(a, a), product(c, c)), product(X0!0, a))),
% 215.18/215.39 inference(symmetry,[status(thm)],[186])).
% 215.18/215.39 tff(188,plain,
% 215.18/215.39 (product(product(a, c), product(X0!0, a)) = product(product(product(a, c), X0!0), product(product(product(a, a), a), product(product(c, c), a)))),
% 215.18/215.39 inference(transitivity,[status(thm)],[187, 185, 183, 181])).
% 215.18/215.39 tff(189,plain,
% 215.18/215.39 (product(product(product(a, c), product(X0!0, a)), product(product(b, c), product(c, b))) = product(product(product(product(a, c), X0!0), product(product(product(a, a), a), product(product(c, c), a))), product(product(b, c), product(c, b)))),
% 215.18/215.39 inference(monotonicity,[status(thm)],[188])).
% 215.18/215.39 tff(190,plain,
% 215.18/215.39 (product(product(product(product(a, c), X0!0), product(product(product(a, a), a), product(product(c, c), a))), product(product(b, c), product(c, b))) = product(product(product(a, c), product(X0!0, a)), product(product(b, c), product(c, b)))),
% 215.18/215.39 inference(symmetry,[status(thm)],[189])).
% 215.18/215.39 tff(191,plain,
% 215.18/215.39 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(product(a, c), X0!0), product(b, c)), product(product(product(product(a, a), a), product(product(c, c), a)), product(c, b))) = product(product(product(product(a, c), X0!0), product(product(product(a, a), a), product(product(c, c), a))), product(product(b, c), product(c, b))))),
% 215.18/215.39 inference(quant_inst,[status(thm)],[])).
% 215.18/215.39 tff(192,plain,
% 215.18/215.39 (product(product(product(product(a, c), X0!0), product(b, c)), product(product(product(product(a, a), a), product(product(c, c), a)), product(c, b))) = product(product(product(product(a, c), X0!0), product(product(product(a, a), a), product(product(c, c), a))), product(product(b, c), product(c, b)))),
% 215.18/215.39 inference(unit_resolution,[status(thm)],[191, 45])).
% 215.18/215.39 tff(193,plain,
% 215.18/215.39 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(product(a, c), a), product(product(c, b), c)), product(product(a, product(a, c)), product(b, product(c, b)))) = product(product(product(product(a, c), a), product(a, product(a, c))), product(product(product(c, b), c), product(b, product(c, b)))))),
% 215.18/215.39 inference(quant_inst,[status(thm)],[])).
% 215.18/215.39 tff(194,plain,
% 215.18/215.39 (product(product(product(product(a, c), a), product(product(c, b), c)), product(product(a, product(a, c)), product(b, product(c, b)))) = product(product(product(product(a, c), a), product(a, product(a, c))), product(product(product(c, b), c), product(b, product(c, b))))),
% 215.18/215.39 inference(unit_resolution,[status(thm)],[193, 45])).
% 215.18/215.39 tff(195,plain,
% 215.18/215.39 (product(product(a, b), product(product(a, c), product(c, b))) = product(product(product(a, c), product(c, b)), product(product(a, c), product(c, b)))),
% 215.18/215.39 inference(monotonicity,[status(thm)],[67])).
% 215.18/215.39 tff(196,plain,
% 215.18/215.39 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(a, b), product(product(a, c), product(c, b))) = product(product(a, product(a, c)), product(b, product(c, b))))),
% 215.18/215.39 inference(quant_inst,[status(thm)],[])).
% 215.18/215.39 tff(197,plain,
% 215.18/215.39 (product(product(a, b), product(product(a, c), product(c, b))) = product(product(a, product(a, c)), product(b, product(c, b)))),
% 215.18/215.39 inference(unit_resolution,[status(thm)],[196, 45])).
% 215.18/215.39 tff(198,plain,
% 215.18/215.39 (product(product(a, product(a, c)), product(b, product(c, b))) = product(product(a, b), product(product(a, c), product(c, b)))),
% 215.18/215.39 inference(symmetry,[status(thm)],[197])).
% 215.18/215.39 tff(199,plain,
% 215.18/215.39 (product(product(a, product(a, c)), product(b, product(c, b))) = product(product(a, b), product(a, b))),
% 215.18/215.39 inference(transitivity,[status(thm)],[198, 195, 69])).
% 215.18/215.39 tff(200,plain,
% 215.18/215.39 (product(product(a, b), product(a, c)) = product(product(product(a, c), product(c, b)), product(a, c))),
% 215.18/215.39 inference(monotonicity,[status(thm)],[67])).
% 215.18/215.39 tff(201,plain,
% 215.18/215.39 (product(product(product(a, c), product(c, b)), product(a, c)) = product(product(a, b), product(a, c))),
% 215.18/215.39 inference(symmetry,[status(thm)],[200])).
% 215.18/215.39 tff(202,plain,
% 215.18/215.39 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, c), product(c, b)), product(a, c)) = product(product(product(a, c), a), product(product(c, b), c)))),
% 215.18/215.39 inference(quant_inst,[status(thm)],[])).
% 215.18/215.39 tff(203,plain,
% 215.18/215.39 (product(product(product(a, c), product(c, b)), product(a, c)) = product(product(product(a, c), a), product(product(c, b), c))),
% 215.18/215.39 inference(unit_resolution,[status(thm)],[202, 45])).
% 215.18/215.39 tff(204,plain,
% 215.18/215.39 (product(product(product(a, c), a), product(product(c, b), c)) = product(product(product(a, c), product(c, b)), product(a, c))),
% 215.18/215.39 inference(symmetry,[status(thm)],[203])).
% 215.18/215.39 tff(205,plain,
% 215.18/215.39 (product(product(product(a, c), a), product(product(c, b), c)) = product(product(a, b), product(a, c))),
% 215.18/215.39 inference(transitivity,[status(thm)],[204, 201])).
% 215.18/215.39 tff(206,plain,
% 215.18/215.39 (product(product(product(product(a, c), a), product(product(c, b), c)), product(product(a, product(a, c)), product(b, product(c, b)))) = product(product(product(a, b), product(a, c)), product(product(a, b), product(a, b)))),
% 215.18/215.39 inference(monotonicity,[status(thm)],[205, 199])).
% 215.18/215.39 tff(207,plain,
% 215.18/215.39 (product(product(product(a, b), product(a, c)), product(product(a, b), product(a, b))) = product(product(product(product(a, c), a), product(product(c, b), c)), product(product(a, product(a, c)), product(b, product(c, b))))),
% 215.18/215.39 inference(symmetry,[status(thm)],[206])).
% 215.18/215.39 tff(208,plain,
% 215.18/215.39 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, b), product(a, b)), product(product(a, c), product(a, b))) = product(product(product(a, b), product(a, c)), product(product(a, b), product(a, b))))),
% 215.18/215.40 inference(quant_inst,[status(thm)],[])).
% 215.18/215.40 tff(209,plain,
% 215.18/215.40 (product(product(product(a, b), product(a, b)), product(product(a, c), product(a, b))) = product(product(product(a, b), product(a, c)), product(product(a, b), product(a, b)))),
% 215.18/215.40 inference(unit_resolution,[status(thm)],[208, 45])).
% 215.18/215.40 tff(210,plain,
% 215.18/215.40 (product(product(product(a, b), product(a, b)), product(product(a, c), product(a, b))) = product(product(product(a, b), product(a, b)), product(product(a, product(a, c)), product(c, product(c, b))))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[108])).
% 215.18/215.40 tff(211,plain,
% 215.18/215.40 (product(product(product(a, b), product(a, b)), product(product(a, product(a, c)), product(c, product(c, b)))) = product(product(product(a, b), product(a, b)), product(product(a, c), product(a, b)))),
% 215.18/215.40 inference(symmetry,[status(thm)],[210])).
% 215.18/215.40 tff(212,plain,
% 215.18/215.40 (product(product(product(a, a), product(c, a)), product(product(c, c), product(b, b))) = product(product(product(a, a), product(c, c)), product(product(c, a), product(b, b)))),
% 215.18/215.40 inference(symmetry,[status(thm)],[94])).
% 215.18/215.40 tff(213,plain,
% 215.18/215.40 (product(product(product(a, a), a), product(product(c, c), a)) = product(product(a, a), product(c, a))),
% 215.18/215.40 inference(transitivity,[status(thm)],[178, 175, 90])).
% 215.18/215.40 tff(214,plain,
% 215.18/215.40 (product(product(product(product(a, a), a), product(product(c, c), a)), product(c, b)) = product(product(product(a, a), product(c, a)), product(product(c, c), product(b, b)))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[213, 128])).
% 215.18/215.40 tff(215,plain,
% 215.18/215.40 (product(product(product(product(a, a), a), product(product(c, c), a)), product(c, b)) = product(product(product(product(a, c), a), product(a, product(a, c))), product(product(product(c, b), c), product(b, product(c, b))))),
% 215.18/215.40 inference(transitivity,[status(thm)],[214, 212, 98, 100, 103, 113, 211, 209, 207, 194])).
% 215.18/215.40 tff(216,plain,
% 215.18/215.40 (product(product(product(product(a, c), X0!0), product(b, c)), product(product(product(product(a, a), a), product(product(c, c), a)), product(c, b))) = product(product(product(product(a, c), X0!0), product(b, c)), product(product(product(product(a, c), a), product(a, product(a, c))), product(product(product(c, b), c), product(b, product(c, b)))))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[215])).
% 215.18/215.40 tff(217,plain,
% 215.18/215.40 (product(product(product(product(a, c), X0!0), product(b, c)), product(product(product(product(a, c), a), product(a, product(a, c))), product(product(product(c, b), c), product(b, product(c, b))))) = product(product(product(product(a, c), X0!0), product(b, c)), product(product(product(product(a, a), a), product(product(c, c), a)), product(c, b)))),
% 215.18/215.40 inference(symmetry,[status(thm)],[216])).
% 215.18/215.40 tff(218,plain,
% 215.18/215.40 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(a, c), product(a, b)) = product(product(a, a), product(c, b)))),
% 215.18/215.40 inference(quant_inst,[status(thm)],[])).
% 215.18/215.40 tff(219,plain,
% 215.18/215.40 (product(product(a, c), product(a, b)) = product(product(a, a), product(c, b))),
% 215.18/215.40 inference(unit_resolution,[status(thm)],[218, 45])).
% 215.18/215.40 tff(220,plain,
% 215.18/215.40 (product(product(a, a), product(c, b)) = product(product(a, c), product(a, b))),
% 215.18/215.40 inference(symmetry,[status(thm)],[219])).
% 215.18/215.40 tff(221,plain,
% 215.18/215.40 (product(product(a, a), product(c, b)) = product(product(a, product(a, c)), product(c, product(c, b)))),
% 215.18/215.40 inference(transitivity,[status(thm)],[220, 107, 106])).
% 215.18/215.40 tff(222,plain,
% 215.18/215.40 (product(product(a, a), product(b, b)) = product(product(a, b), product(a, b))),
% 215.18/215.40 inference(symmetry,[status(thm)],[81])).
% 215.18/215.40 tff(223,plain,
% 215.18/215.40 (product(product(product(a, a), product(b, b)), product(product(a, a), product(c, b))) = product(product(product(a, b), product(a, b)), product(product(a, product(a, c)), product(c, product(c, b))))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[222, 221])).
% 215.18/215.40 tff(224,plain,
% 215.18/215.40 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, a), product(b, b)), product(product(a, a), product(c, b))) = product(product(product(a, a), product(a, a)), product(product(b, b), product(c, b))))),
% 215.18/215.40 inference(quant_inst,[status(thm)],[])).
% 215.18/215.40 tff(225,plain,
% 215.18/215.40 (product(product(product(a, a), product(b, b)), product(product(a, a), product(c, b))) = product(product(product(a, a), product(a, a)), product(product(b, b), product(c, b)))),
% 215.18/215.40 inference(unit_resolution,[status(thm)],[224, 45])).
% 215.18/215.40 tff(226,plain,
% 215.18/215.40 (product(product(product(a, a), product(a, a)), product(product(b, b), product(c, b))) = product(product(product(a, a), product(b, b)), product(product(a, a), product(c, b)))),
% 215.18/215.40 inference(symmetry,[status(thm)],[225])).
% 215.18/215.40 tff(227,plain,
% 215.18/215.40 (product(product(b, b), product(c, b)) = product(product(b, b), product(product(c, c), product(b, b)))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[128])).
% 215.18/215.40 tff(228,plain,
% 215.18/215.40 (product(product(b, b), product(product(c, c), product(b, b))) = product(product(b, b), product(c, b))),
% 215.18/215.40 inference(symmetry,[status(thm)],[227])).
% 215.18/215.40 tff(229,plain,
% 215.18/215.40 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(b, b), product(product(c, c), product(b, b))) = product(product(b, product(c, c)), product(b, product(b, b))))),
% 215.18/215.40 inference(quant_inst,[status(thm)],[])).
% 215.18/215.40 tff(230,plain,
% 215.18/215.40 (product(product(b, b), product(product(c, c), product(b, b))) = product(product(b, product(c, c)), product(b, product(b, b)))),
% 215.18/215.40 inference(unit_resolution,[status(thm)],[229, 45])).
% 215.18/215.40 tff(231,plain,
% 215.18/215.40 (product(product(b, product(c, c)), product(b, product(b, b))) = product(product(b, b), product(product(c, c), product(b, b)))),
% 215.18/215.40 inference(symmetry,[status(thm)],[230])).
% 215.18/215.40 tff(232,plain,
% 215.18/215.40 (product(product(b, product(c, c)), product(b, product(b, b))) = product(product(b, b), product(c, b))),
% 215.18/215.40 inference(transitivity,[status(thm)],[231, 228])).
% 215.18/215.40 tff(233,plain,
% 215.18/215.40 (product(product(a, a), product(a, a)) = product(a, a)),
% 215.18/215.40 inference(monotonicity,[status(thm)],[169, 169])).
% 215.18/215.40 tff(234,plain,
% 215.18/215.40 (product(a, a) = product(product(a, a), product(a, a))),
% 215.18/215.40 inference(symmetry,[status(thm)],[233])).
% 215.18/215.40 tff(235,plain,
% 215.18/215.40 (a = product(product(a, a), product(a, a))),
% 215.18/215.40 inference(transitivity,[status(thm)],[170, 234])).
% 215.18/215.40 tff(236,plain,
% 215.18/215.40 (product(a, product(product(b, product(c, c)), product(b, product(b, b)))) = product(product(product(a, a), product(a, a)), product(product(b, b), product(c, b)))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[235, 232])).
% 215.18/215.40 tff(237,plain,
% 215.18/215.40 (product(a, product(product(b, product(c, c)), product(b, product(b, b)))) = product(product(product(product(a, c), a), product(a, product(a, c))), product(product(product(c, b), c), product(b, product(c, b))))),
% 215.18/215.40 inference(transitivity,[status(thm)],[236, 226, 223, 211, 209, 207, 194])).
% 215.18/215.40 tff(238,plain,
% 215.18/215.40 (product(product(product(product(a, c), X0!0), product(b, c)), product(a, product(product(b, product(c, c)), product(b, product(b, b))))) = product(product(product(product(a, c), X0!0), product(b, c)), product(product(product(product(a, c), a), product(a, product(a, c))), product(product(product(c, b), c), product(b, product(c, b)))))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[237])).
% 215.18/215.40 tff(239,plain,
% 215.18/215.40 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(product(a, c), X0!0), a), product(product(b, c), product(product(b, product(c, c)), product(b, product(b, b))))) = product(product(product(product(a, c), X0!0), product(b, c)), product(a, product(product(b, product(c, c)), product(b, product(b, b))))))),
% 215.18/215.40 inference(quant_inst,[status(thm)],[])).
% 215.18/215.40 tff(240,plain,
% 215.18/215.40 (product(product(product(product(a, c), X0!0), a), product(product(b, c), product(product(b, product(c, c)), product(b, product(b, b))))) = product(product(product(product(a, c), X0!0), product(b, c)), product(a, product(product(b, product(c, c)), product(b, product(b, b)))))),
% 215.18/215.40 inference(unit_resolution,[status(thm)],[239, 45])).
% 215.18/215.40 tff(241,plain,
% 215.18/215.40 ((~![A: $i] : (product(A, A) = A)) | (product(b, b) = b)),
% 215.18/215.40 inference(quant_inst,[status(thm)],[])).
% 215.18/215.40 tff(242,plain,
% 215.18/215.40 (product(b, b) = b),
% 215.18/215.40 inference(unit_resolution,[status(thm)],[241, 35])).
% 215.18/215.40 tff(243,plain,
% 215.18/215.40 (b = product(b, b)),
% 215.18/215.40 inference(symmetry,[status(thm)],[242])).
% 215.18/215.40 tff(244,plain,
% 215.18/215.40 (product(b, product(c, b)) = product(product(b, b), product(c, b))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[243])).
% 215.18/215.40 tff(245,plain,
% 215.18/215.40 (product(product(b, b), product(c, b)) = product(b, product(c, b))),
% 215.18/215.40 inference(symmetry,[status(thm)],[244])).
% 215.18/215.40 tff(246,plain,
% 215.18/215.40 (product(product(b, product(c, c)), product(b, product(b, b))) = product(b, product(c, b))),
% 215.18/215.40 inference(transitivity,[status(thm)],[231, 228, 245])).
% 215.18/215.40 tff(247,plain,
% 215.18/215.40 (product(product(b, c), product(product(b, product(c, c)), product(b, product(b, b)))) = product(product(b, c), product(b, product(c, b)))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[246])).
% 215.18/215.40 tff(248,plain,
% 215.18/215.40 (product(product(b, c), product(b, product(c, b))) = product(product(b, c), product(product(b, product(c, c)), product(b, product(b, b))))),
% 215.18/215.40 inference(symmetry,[status(thm)],[247])).
% 215.18/215.40 tff(249,plain,
% 215.18/215.40 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(b, b), product(c, product(c, b))) = product(product(b, c), product(b, product(c, b))))),
% 215.18/215.40 inference(quant_inst,[status(thm)],[])).
% 215.18/215.40 tff(250,plain,
% 215.18/215.40 (product(product(b, b), product(c, product(c, b))) = product(product(b, c), product(b, product(c, b)))),
% 215.18/215.40 inference(unit_resolution,[status(thm)],[249, 45])).
% 215.18/215.40 tff(251,plain,
% 215.18/215.40 (product(product(b, b), product(c, product(c, b))) = product(b, product(c, product(c, b)))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[242])).
% 215.18/215.40 tff(252,plain,
% 215.18/215.40 (product(b, product(c, product(c, b))) = product(product(b, b), product(c, product(c, b)))),
% 215.18/215.40 inference(symmetry,[status(thm)],[251])).
% 215.18/215.40 tff(253,plain,
% 215.18/215.40 (product(b, product(product(c, product(c, c)), product(c, product(b, b)))) = product(b, product(c, product(c, b)))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[146])).
% 215.18/215.40 tff(254,plain,
% 215.18/215.40 (product(b, product(product(c, product(c, c)), product(c, product(b, b)))) = product(product(b, c), product(product(b, product(c, c)), product(b, product(b, b))))),
% 215.18/215.40 inference(transitivity,[status(thm)],[253, 252, 250, 248])).
% 215.18/215.40 tff(255,plain,
% 215.18/215.40 (product(product(product(product(a, c), X0!0), a), product(b, product(product(c, product(c, c)), product(c, product(b, b))))) = product(product(product(product(a, c), X0!0), a), product(product(b, c), product(product(b, product(c, c)), product(b, product(b, b)))))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[254])).
% 215.18/215.40 tff(256,plain,
% 215.18/215.40 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(product(a, c), X0!0), a), product(b, product(product(c, product(c, c)), product(c, product(b, b))))) = product(product(product(product(a, c), X0!0), b), product(a, product(product(c, product(c, c)), product(c, product(b, b))))))),
% 215.18/215.40 inference(quant_inst,[status(thm)],[])).
% 215.18/215.40 tff(257,plain,
% 215.18/215.40 (product(product(product(product(a, c), X0!0), a), product(b, product(product(c, product(c, c)), product(c, product(b, b))))) = product(product(product(product(a, c), X0!0), b), product(a, product(product(c, product(c, c)), product(c, product(b, b)))))),
% 215.18/215.40 inference(unit_resolution,[status(thm)],[256, 45])).
% 215.18/215.40 tff(258,plain,
% 215.18/215.40 (product(product(product(product(a, c), X0!0), b), product(a, product(product(c, product(c, c)), product(c, product(b, b))))) = product(product(product(product(a, c), X0!0), a), product(b, product(product(c, product(c, c)), product(c, product(b, b)))))),
% 215.18/215.40 inference(symmetry,[status(thm)],[257])).
% 215.18/215.40 tff(259,plain,
% 215.18/215.40 (product(a, product(product(c, product(c, c)), product(c, product(b, b)))) = product(a, product(c, product(c, b)))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[146])).
% 215.18/215.40 tff(260,plain,
% 215.18/215.40 (product(a, product(c, product(c, b))) = product(a, product(product(c, product(c, c)), product(c, product(b, b))))),
% 215.18/215.40 inference(symmetry,[status(thm)],[259])).
% 215.18/215.40 tff(261,plain,
% 215.18/215.40 (product(a, product(c, product(c, b))) = product(product(a, a), product(c, product(c, b)))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[170])).
% 215.18/215.40 tff(262,plain,
% 215.18/215.40 (product(product(a, a), product(c, product(c, b))) = product(a, product(c, product(c, b)))),
% 215.18/215.40 inference(symmetry,[status(thm)],[261])).
% 215.18/215.40 tff(263,plain,
% 215.18/215.40 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(a, a), product(c, product(c, b))) = product(product(a, c), product(a, product(c, b))))),
% 215.18/215.40 inference(quant_inst,[status(thm)],[])).
% 215.18/215.40 tff(264,plain,
% 215.18/215.40 (product(product(a, a), product(c, product(c, b))) = product(product(a, c), product(a, product(c, b)))),
% 215.18/215.40 inference(unit_resolution,[status(thm)],[263, 45])).
% 215.18/215.40 tff(265,plain,
% 215.18/215.40 (product(product(a, c), product(a, product(c, b))) = product(product(a, a), product(c, product(c, b)))),
% 215.18/215.40 inference(symmetry,[status(thm)],[264])).
% 215.18/215.40 tff(266,plain,
% 215.18/215.40 (product(a, product(c, b)) = product(product(a, a), product(c, b))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[170])).
% 215.18/215.40 tff(267,plain,
% 215.18/215.40 (product(a, product(c, b)) = product(product(a, product(a, c)), product(c, product(c, b)))),
% 215.18/215.40 inference(transitivity,[status(thm)],[266, 220, 107, 106])).
% 215.18/215.40 tff(268,plain,
% 215.18/215.40 (product(product(a, c), product(a, product(c, b))) = product(product(a, c), product(product(a, product(a, c)), product(c, product(c, b))))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[267])).
% 215.18/215.40 tff(269,plain,
% 215.18/215.40 (product(product(a, c), product(product(a, product(a, c)), product(c, product(c, b)))) = product(product(a, c), product(a, product(c, b)))),
% 215.18/215.40 inference(symmetry,[status(thm)],[268])).
% 215.18/215.40 tff(270,plain,
% 215.18/215.40 (product(product(a, c), product(product(a, c), product(c, b))) = product(product(a, c), product(product(a, b), product(a, b)))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[112])).
% 215.18/215.40 tff(271,plain,
% 215.18/215.40 (product(product(a, c), product(product(a, b), product(a, b))) = product(product(a, c), product(product(a, c), product(c, b)))),
% 215.18/215.40 inference(symmetry,[status(thm)],[270])).
% 215.18/215.40 tff(272,plain,
% 215.18/215.40 (product(product(a, c), product(product(a, b), product(a, b))) = product(product(product(a, a), product(c, c)), product(product(a, b), product(a, b)))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[173])).
% 215.18/215.40 tff(273,plain,
% 215.18/215.40 (product(product(product(a, a), product(c, c)), product(product(a, b), product(a, b))) = product(product(a, c), product(product(a, b), product(a, b)))),
% 215.18/215.40 inference(symmetry,[status(thm)],[272])).
% 215.18/215.40 tff(274,plain,
% 215.18/215.40 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, a), product(c, c)), product(product(a, b), product(a, b))) = product(product(product(a, a), product(a, b)), product(product(c, c), product(a, b))))),
% 215.18/215.40 inference(quant_inst,[status(thm)],[])).
% 215.18/215.40 tff(275,plain,
% 215.18/215.40 (product(product(product(a, a), product(c, c)), product(product(a, b), product(a, b))) = product(product(product(a, a), product(a, b)), product(product(c, c), product(a, b)))),
% 215.18/215.40 inference(unit_resolution,[status(thm)],[274, 45])).
% 215.18/215.40 tff(276,plain,
% 215.18/215.40 (product(product(product(a, a), product(a, b)), product(product(c, c), product(a, b))) = product(product(product(a, a), product(c, c)), product(product(a, b), product(a, b)))),
% 215.18/215.40 inference(symmetry,[status(thm)],[275])).
% 215.18/215.40 tff(277,plain,
% 215.18/215.40 (product(product(product(a, a), product(a, b)), product(product(c, c), product(a, b))) = product(product(a, product(a, c)), product(c, product(c, b)))),
% 215.18/215.40 inference(transitivity,[status(thm)],[276, 273, 271, 106])).
% 215.18/215.40 tff(278,plain,
% 215.18/215.40 (product(product(a, c), product(product(product(a, a), product(a, b)), product(product(c, c), product(a, b)))) = product(product(a, c), product(product(a, product(a, c)), product(c, product(c, b))))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[277])).
% 215.18/215.40 tff(279,plain,
% 215.18/215.40 (product(product(a, c), product(product(product(a, a), product(a, b)), product(product(c, c), product(a, b)))) = product(a, product(product(c, product(c, c)), product(c, product(b, b))))),
% 215.18/215.40 inference(transitivity,[status(thm)],[278, 269, 265, 262, 260])).
% 215.18/215.40 tff(280,plain,
% 215.18/215.40 (product(product(product(product(a, c), X0!0), b), product(product(a, c), product(product(product(a, a), product(a, b)), product(product(c, c), product(a, b))))) = product(product(product(product(a, c), X0!0), b), product(a, product(product(c, product(c, c)), product(c, product(b, b)))))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[279])).
% 215.18/215.40 tff(281,plain,
% 215.18/215.40 (product(product(a, c), product(product(a, product(a, c)), product(c, product(c, b)))) = product(product(a, c), product(product(product(a, a), product(a, b)), product(product(c, c), product(a, b))))),
% 215.18/215.40 inference(symmetry,[status(thm)],[278])).
% 215.18/215.40 tff(282,plain,
% 215.18/215.40 (product(product(a, c), product(product(a, c), product(c, b))) = product(product(a, c), product(a, b))),
% 215.18/215.40 inference(symmetry,[status(thm)],[107])).
% 215.18/215.40 tff(283,plain,
% 215.18/215.40 (product(product(a, product(a, c)), product(c, product(c, b))) = product(product(a, c), product(product(a, c), product(c, b)))),
% 215.18/215.40 inference(symmetry,[status(thm)],[106])).
% 215.18/215.40 tff(284,plain,
% 215.18/215.40 (product(product(a, product(a, c)), product(c, product(c, b))) = product(product(a, c), product(a, b))),
% 215.18/215.40 inference(transitivity,[status(thm)],[283, 282])).
% 215.18/215.40 tff(285,plain,
% 215.18/215.40 (product(product(a, c), product(product(a, product(a, c)), product(c, product(c, b)))) = product(product(product(a, a), product(c, c)), product(product(a, c), product(a, b)))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[173, 284])).
% 215.18/215.40 tff(286,plain,
% 215.18/215.40 (product(product(product(a, a), product(c, c)), product(product(a, c), product(a, b))) = product(product(a, c), product(product(a, product(a, c)), product(c, product(c, b))))),
% 215.18/215.40 inference(symmetry,[status(thm)],[285])).
% 215.18/215.40 tff(287,plain,
% 215.18/215.40 (product(product(product(a, c), product(a, c)), product(product(a, a), product(c, b))) = product(product(product(a, a), product(c, c)), product(product(a, c), product(a, b)))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[53, 220])).
% 215.18/215.40 tff(288,plain,
% 215.18/215.40 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, c), product(a, c)), product(product(a, a), product(c, b))) = product(product(product(a, c), product(a, a)), product(product(a, c), product(c, b))))),
% 215.18/215.40 inference(quant_inst,[status(thm)],[])).
% 215.18/215.40 tff(289,plain,
% 215.18/215.40 (product(product(product(a, c), product(a, c)), product(product(a, a), product(c, b))) = product(product(product(a, c), product(a, a)), product(product(a, c), product(c, b)))),
% 215.18/215.40 inference(unit_resolution,[status(thm)],[288, 45])).
% 215.18/215.40 tff(290,plain,
% 215.18/215.40 (product(product(product(a, c), product(a, a)), product(product(a, c), product(c, b))) = product(product(product(a, c), product(a, c)), product(product(a, a), product(c, b)))),
% 215.18/215.40 inference(symmetry,[status(thm)],[289])).
% 215.18/215.40 tff(291,plain,
% 215.18/215.40 (product(product(product(a, c), product(a, c)), product(product(c, b), product(c, b))) = product(product(a, c), product(c, b))),
% 215.18/215.40 inference(transitivity,[status(thm)],[72, 69, 110, 67])).
% 215.18/215.40 tff(292,plain,
% 215.18/215.40 (product(product(product(a, a), a), product(product(c, c), a)) = product(product(a, c), product(a, a))),
% 215.18/215.40 inference(transitivity,[status(thm)],[178, 175])).
% 215.18/215.40 tff(293,plain,
% 215.18/215.40 (product(product(product(product(a, a), a), product(product(c, c), a)), product(product(product(a, c), product(a, c)), product(product(c, b), product(c, b)))) = product(product(product(a, c), product(a, a)), product(product(a, c), product(c, b)))),
% 215.18/215.40 inference(monotonicity,[status(thm)],[292, 291])).
% 215.18/215.40 tff(294,plain,
% 215.18/215.40 (product(product(product(product(a, a), a), product(product(c, c), a)), product(product(product(a, c), product(a, c)), product(product(c, b), product(c, b)))) = product(product(a, c), product(product(product(a, a), product(a, b)), product(product(c, c), product(a, b))))),
% 215.18/215.40 inference(transitivity,[status(thm)],[293, 290, 287, 286, 281])).
% 215.18/215.41 tff(295,plain,
% 215.18/215.41 (product(product(product(product(a, c), X0!0), b), product(product(product(product(a, a), a), product(product(c, c), a)), product(product(product(a, c), product(a, c)), product(product(c, b), product(c, b))))) = product(product(product(product(a, c), X0!0), b), product(product(a, c), product(product(product(a, a), product(a, b)), product(product(c, c), product(a, b)))))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[294])).
% 215.18/215.41 tff(296,plain,
% 215.18/215.41 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(product(a, c), X0!0), product(product(product(a, a), a), product(product(c, c), a))), product(b, product(product(product(a, c), product(a, c)), product(product(c, b), product(c, b))))) = product(product(product(product(a, c), X0!0), b), product(product(product(product(a, a), a), product(product(c, c), a)), product(product(product(a, c), product(a, c)), product(product(c, b), product(c, b))))))),
% 215.18/215.41 inference(quant_inst,[status(thm)],[])).
% 215.18/215.41 tff(297,plain,
% 215.18/215.41 (product(product(product(product(a, c), X0!0), product(product(product(a, a), a), product(product(c, c), a))), product(b, product(product(product(a, c), product(a, c)), product(product(c, b), product(c, b))))) = product(product(product(product(a, c), X0!0), b), product(product(product(product(a, a), a), product(product(c, c), a)), product(product(product(a, c), product(a, c)), product(product(c, b), product(c, b)))))),
% 215.18/215.41 inference(unit_resolution,[status(thm)],[296, 45])).
% 215.18/215.41 tff(298,plain,
% 215.18/215.41 (product(product(product(a, c), product(X0!0, a)), product(b, product(product(product(a, c), product(a, c)), product(product(c, b), product(c, b))))) = product(product(product(product(a, c), X0!0), product(product(product(a, a), a), product(product(c, c), a))), product(b, product(product(product(a, c), product(a, c)), product(product(c, b), product(c, b)))))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[188])).
% 215.18/215.41 tff(299,plain,
% 215.18/215.41 (product(product(product(a, c), product(a, c)), product(product(c, b), product(c, b))) = product(product(a, b), product(a, b))),
% 215.18/215.41 inference(transitivity,[status(thm)],[72, 69])).
% 215.18/215.41 tff(300,plain,
% 215.18/215.41 (product(b, product(product(product(a, c), product(a, c)), product(product(c, b), product(c, b)))) = product(product(b, b), product(product(a, b), product(a, b)))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[243, 299])).
% 215.18/215.41 tff(301,plain,
% 215.18/215.41 (product(product(b, b), product(product(a, b), product(a, b))) = product(b, product(product(product(a, c), product(a, c)), product(product(c, b), product(c, b))))),
% 215.18/215.41 inference(symmetry,[status(thm)],[300])).
% 215.18/215.41 tff(302,plain,
% 215.18/215.41 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(b, b), product(product(a, b), product(a, b))) = product(product(b, product(a, b)), product(b, product(a, b))))),
% 215.18/215.41 inference(quant_inst,[status(thm)],[])).
% 215.18/215.41 tff(303,plain,
% 215.18/215.41 (product(product(b, b), product(product(a, b), product(a, b))) = product(product(b, product(a, b)), product(b, product(a, b)))),
% 215.18/215.41 inference(unit_resolution,[status(thm)],[302, 45])).
% 215.18/215.41 tff(304,plain,
% 215.18/215.41 (product(product(b, product(a, b)), product(b, product(a, b))) = product(product(b, b), product(product(a, b), product(a, b)))),
% 215.18/215.41 inference(symmetry,[status(thm)],[303])).
% 215.18/215.41 tff(305,plain,
% 215.18/215.41 (product(product(b, product(a, b)), product(b, product(a, b))) = product(b, product(product(product(a, c), product(a, c)), product(product(c, b), product(c, b))))),
% 215.18/215.41 inference(transitivity,[status(thm)],[304, 301])).
% 215.18/215.41 tff(306,plain,
% 215.18/215.41 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, a), product(c, c)), product(X0!0, a)) = product(product(product(a, a), X0!0), product(product(c, c), a)))),
% 215.18/215.41 inference(quant_inst,[status(thm)],[])).
% 215.18/215.41 tff(307,plain,
% 215.18/215.41 (product(product(product(a, a), product(c, c)), product(X0!0, a)) = product(product(product(a, a), X0!0), product(product(c, c), a))),
% 215.18/215.41 inference(unit_resolution,[status(thm)],[306, 45])).
% 215.18/215.41 tff(308,plain,
% 215.18/215.41 (product(product(product(a, a), X0!0), product(product(c, c), a)) = product(product(product(a, a), product(c, c)), product(X0!0, a))),
% 215.18/215.41 inference(symmetry,[status(thm)],[307])).
% 215.18/215.41 tff(309,plain,
% 215.18/215.41 (product(product(product(a, a), X0!0), product(product(c, c), a)) = product(product(a, c), product(X0!0, a))),
% 215.18/215.41 inference(transitivity,[status(thm)],[308, 186])).
% 215.18/215.41 tff(310,plain,
% 215.18/215.41 (product(product(product(product(a, a), X0!0), product(product(c, c), a)), product(product(b, product(a, b)), product(b, product(a, b)))) = product(product(product(a, c), product(X0!0, a)), product(b, product(product(product(a, c), product(a, c)), product(product(c, b), product(c, b)))))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[309, 305])).
% 215.18/215.41 tff(311,plain,
% 215.18/215.41 (product(product(b, b), product(product(a, b), product(a, b))) = product(b, product(a, b))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[242, 110])).
% 215.18/215.41 tff(312,plain,
% 215.18/215.41 (product(product(b, product(a, b)), product(b, product(a, b))) = product(b, product(a, b))),
% 215.18/215.41 inference(transitivity,[status(thm)],[304, 311])).
% 215.18/215.41 tff(313,plain,
% 215.18/215.41 (product(product(product(b, product(a, b)), product(b, product(a, b))), product(product(b, product(a, b)), product(b, product(a, b)))) = product(product(b, product(a, b)), product(b, product(a, b)))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[312, 312])).
% 215.18/215.41 tff(314,plain,
% 215.18/215.41 (product(product(a, c), product(X0!0, a)) = product(product(product(a, a), X0!0), product(product(c, c), a))),
% 215.18/215.41 inference(transitivity,[status(thm)],[187, 307])).
% 215.18/215.41 tff(315,plain,
% 215.18/215.41 (product(product(product(a, c), product(X0!0, a)), product(product(product(b, product(a, b)), product(b, product(a, b))), product(product(b, product(a, b)), product(b, product(a, b))))) = product(product(product(product(a, a), X0!0), product(product(c, c), a)), product(product(b, product(a, b)), product(b, product(a, b))))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[314, 313])).
% 215.18/215.41 tff(316,plain,
% 215.18/215.41 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, c), product(X0!0, a)), product(product(product(b, product(a, b)), product(b, product(a, b))), product(product(b, product(a, b)), product(b, product(a, b))))) = product(product(product(a, c), product(product(b, product(a, b)), product(b, product(a, b)))), product(product(X0!0, a), product(product(b, product(a, b)), product(b, product(a, b))))))),
% 215.18/215.41 inference(quant_inst,[status(thm)],[])).
% 215.18/215.41 tff(317,plain,
% 215.18/215.41 (product(product(product(a, c), product(X0!0, a)), product(product(product(b, product(a, b)), product(b, product(a, b))), product(product(b, product(a, b)), product(b, product(a, b))))) = product(product(product(a, c), product(product(b, product(a, b)), product(b, product(a, b)))), product(product(X0!0, a), product(product(b, product(a, b)), product(b, product(a, b)))))),
% 215.18/215.41 inference(unit_resolution,[status(thm)],[316, 45])).
% 215.18/215.41 tff(318,plain,
% 215.18/215.41 (product(product(product(a, c), product(product(b, product(a, b)), product(b, product(a, b)))), product(product(X0!0, a), product(product(b, product(a, b)), product(b, product(a, b))))) = product(product(product(a, c), product(X0!0, a)), product(product(product(b, product(a, b)), product(b, product(a, b))), product(product(b, product(a, b)), product(b, product(a, b)))))),
% 215.18/215.41 inference(symmetry,[status(thm)],[317])).
% 215.18/215.41 tff(319,plain,
% 215.18/215.41 (product(b, product(a, b)) = product(product(b, b), product(a, b))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[243])).
% 215.18/215.41 tff(320,plain,
% 215.18/215.41 (product(product(b, product(a, b)), product(b, product(a, b))) = product(product(b, b), product(a, b))),
% 215.18/215.41 inference(transitivity,[status(thm)],[304, 311, 319])).
% 215.18/215.41 tff(321,plain,
% 215.18/215.41 (product(product(a, c), product(product(b, product(a, b)), product(b, product(a, b)))) = product(product(product(a, c), product(a, c)), product(product(b, b), product(a, b)))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[58, 320])).
% 215.18/215.41 tff(322,plain,
% 215.18/215.41 (product(product(product(a, c), product(a, c)), product(product(b, b), product(a, b))) = product(product(a, c), product(product(b, product(a, b)), product(b, product(a, b))))),
% 215.18/215.41 inference(symmetry,[status(thm)],[321])).
% 215.18/215.41 tff(323,plain,
% 215.18/215.41 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, c), product(b, b)), product(product(a, c), product(a, b))) = product(product(product(a, c), product(a, c)), product(product(b, b), product(a, b))))),
% 215.18/215.41 inference(quant_inst,[status(thm)],[])).
% 215.18/215.41 tff(324,plain,
% 215.18/215.41 (product(product(product(a, c), product(b, b)), product(product(a, c), product(a, b))) = product(product(product(a, c), product(a, c)), product(product(b, b), product(a, b)))),
% 215.18/215.41 inference(unit_resolution,[status(thm)],[323, 45])).
% 215.18/215.41 tff(325,plain,
% 215.18/215.41 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(a, b), product(c, b)) = product(product(a, c), product(b, b)))),
% 215.18/215.41 inference(quant_inst,[status(thm)],[])).
% 215.18/215.41 tff(326,plain,
% 215.18/215.41 (product(product(a, b), product(c, b)) = product(product(a, c), product(b, b))),
% 215.18/215.41 inference(unit_resolution,[status(thm)],[325, 45])).
% 215.18/215.41 tff(327,plain,
% 215.18/215.41 (product(product(a, c), product(b, b)) = product(product(a, b), product(c, b))),
% 215.18/215.41 inference(symmetry,[status(thm)],[326])).
% 215.18/215.41 tff(328,plain,
% 215.18/215.41 (product(product(product(a, c), product(b, b)), product(product(a, c), product(a, b))) = product(product(product(a, b), product(c, b)), product(product(a, product(a, c)), product(c, product(c, b))))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[327, 108])).
% 215.18/215.41 tff(329,plain,
% 215.18/215.41 (product(product(product(a, b), product(c, b)), product(product(a, product(a, c)), product(c, product(c, b)))) = product(product(product(a, c), product(b, b)), product(product(a, c), product(a, b)))),
% 215.18/215.41 inference(symmetry,[status(thm)],[328])).
% 215.18/215.41 tff(330,plain,
% 215.18/215.41 (product(product(a, b), product(c, b)) = product(product(product(a, c), product(c, b)), product(c, b))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[67])).
% 215.18/215.41 tff(331,plain,
% 215.18/215.41 (product(product(product(a, c), product(c, b)), product(c, b)) = product(product(a, b), product(c, b))),
% 215.18/215.41 inference(symmetry,[status(thm)],[330])).
% 215.18/215.41 tff(332,plain,
% 215.18/215.41 (product(product(product(a, c), product(c, b)), product(c, b)) = product(product(product(a, b), product(a, b)), product(c, b))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[112])).
% 215.18/215.41 tff(333,plain,
% 215.18/215.41 (product(product(product(a, b), product(a, b)), product(c, b)) = product(product(product(a, c), product(c, b)), product(c, b))),
% 215.18/215.41 inference(symmetry,[status(thm)],[332])).
% 215.18/215.41 tff(334,plain,
% 215.18/215.41 (product(product(product(a, b), product(a, b)), product(c, b)) = product(product(product(a, b), product(a, b)), product(product(c, c), product(b, b)))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[128])).
% 215.18/215.41 tff(335,plain,
% 215.18/215.41 (product(product(product(a, b), product(a, b)), product(product(c, c), product(b, b))) = product(product(product(a, b), product(a, b)), product(c, b))),
% 215.18/215.41 inference(symmetry,[status(thm)],[334])).
% 215.18/215.41 tff(336,plain,
% 215.18/215.41 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, b), product(a, b)), product(product(c, c), product(b, b))) = product(product(product(a, b), product(c, c)), product(product(a, b), product(b, b))))),
% 215.18/215.41 inference(quant_inst,[status(thm)],[])).
% 215.18/215.41 tff(337,plain,
% 215.18/215.41 (product(product(product(a, b), product(a, b)), product(product(c, c), product(b, b))) = product(product(product(a, b), product(c, c)), product(product(a, b), product(b, b)))),
% 215.18/215.41 inference(unit_resolution,[status(thm)],[336, 45])).
% 215.18/215.41 tff(338,plain,
% 215.18/215.41 (product(product(product(a, b), product(c, c)), product(product(a, b), product(b, b))) = product(product(product(a, b), product(a, b)), product(product(c, c), product(b, b)))),
% 215.18/215.41 inference(symmetry,[status(thm)],[337])).
% 215.18/215.41 tff(339,plain,
% 215.18/215.41 (product(product(product(a, b), product(c, c)), product(product(a, b), product(b, b))) = product(product(a, b), product(c, b))),
% 215.18/215.41 inference(transitivity,[status(thm)],[338, 335, 333, 331])).
% 215.18/215.41 tff(340,plain,
% 215.18/215.41 (product(product(product(product(a, b), product(c, c)), product(product(a, b), product(b, b))), product(product(product(a, a), product(a, b)), product(product(c, c), product(a, b)))) = product(product(product(a, b), product(c, b)), product(product(a, product(a, c)), product(c, product(c, b))))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[339, 277])).
% 215.18/215.41 tff(341,plain,
% 215.18/215.41 (product(product(product(product(a, b), product(c, c)), product(product(a, b), product(b, b))), product(product(product(a, a), product(a, b)), product(product(c, c), product(a, b)))) = product(product(a, c), product(product(b, product(a, b)), product(b, product(a, b))))),
% 215.18/215.41 inference(transitivity,[status(thm)],[340, 329, 324, 322])).
% 215.18/215.41 tff(342,plain,
% 215.18/215.41 (product(product(product(product(product(a, b), product(c, c)), product(product(a, b), product(b, b))), product(product(product(a, a), product(a, b)), product(product(c, c), product(a, b)))), product(product(X0!0, a), product(product(b, product(a, b)), product(b, product(a, b))))) = product(product(product(a, c), product(product(b, product(a, b)), product(b, product(a, b)))), product(product(X0!0, a), product(product(b, product(a, b)), product(b, product(a, b)))))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[341])).
% 215.18/215.41 tff(343,plain,
% 215.18/215.41 (product(product(product(a, b), product(c, b)), product(product(a, product(a, c)), product(c, product(c, b)))) = product(product(product(product(a, b), product(c, c)), product(product(a, b), product(b, b))), product(product(product(a, a), product(a, b)), product(product(c, c), product(a, b))))),
% 215.18/215.41 inference(symmetry,[status(thm)],[340])).
% 215.18/215.41 tff(344,plain,
% 215.18/215.41 (product(product(product(a, c), product(b, b)), product(product(a, a), product(c, b))) = product(product(product(a, b), product(c, b)), product(product(a, product(a, c)), product(c, product(c, b))))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[327, 221])).
% 215.18/215.41 tff(345,plain,
% 215.18/215.41 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, c), product(b, b)), product(product(a, a), product(c, b))) = product(product(product(a, c), product(a, a)), product(product(b, b), product(c, b))))),
% 215.18/215.41 inference(quant_inst,[status(thm)],[])).
% 215.18/215.41 tff(346,plain,
% 215.18/215.41 (product(product(product(a, c), product(b, b)), product(product(a, a), product(c, b))) = product(product(product(a, c), product(a, a)), product(product(b, b), product(c, b)))),
% 215.18/215.41 inference(unit_resolution,[status(thm)],[345, 45])).
% 215.18/215.41 tff(347,plain,
% 215.18/215.41 (product(product(product(a, c), product(a, a)), product(product(b, b), product(c, b))) = product(product(product(a, c), product(b, b)), product(product(a, a), product(c, b)))),
% 215.18/215.41 inference(symmetry,[status(thm)],[346])).
% 215.18/215.41 tff(348,plain,
% 215.18/215.41 (product(product(product(product(a, a), a), product(product(c, c), a)), product(product(b, product(c, c)), product(b, product(b, b)))) = product(product(product(a, c), product(a, a)), product(product(b, b), product(c, b)))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[292, 232])).
% 215.18/215.41 tff(349,plain,
% 215.18/215.41 (product(product(product(product(a, a), a), product(product(c, c), a)), product(product(b, product(c, c)), product(b, product(b, b)))) = product(product(product(product(a, b), product(c, c)), product(product(a, b), product(b, b))), product(product(product(a, a), product(a, b)), product(product(c, c), product(a, b))))),
% 215.18/215.41 inference(transitivity,[status(thm)],[348, 347, 344, 343])).
% 215.18/215.41 tff(350,plain,
% 215.18/215.41 (product(product(product(product(product(a, a), a), product(product(c, c), a)), product(product(b, product(c, c)), product(b, product(b, b)))), product(product(X0!0, a), product(product(b, product(a, b)), product(b, product(a, b))))) = product(product(product(product(product(a, b), product(c, c)), product(product(a, b), product(b, b))), product(product(product(a, a), product(a, b)), product(product(c, c), product(a, b)))), product(product(X0!0, a), product(product(b, product(a, b)), product(b, product(a, b)))))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[349])).
% 215.18/215.41 tff(351,plain,
% 215.18/215.41 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(product(product(a, a), a), product(product(c, c), a)), product(X0!0, a)), product(product(product(b, product(c, c)), product(b, product(b, b))), product(product(b, product(a, b)), product(b, product(a, b))))) = product(product(product(product(product(a, a), a), product(product(c, c), a)), product(product(b, product(c, c)), product(b, product(b, b)))), product(product(X0!0, a), product(product(b, product(a, b)), product(b, product(a, b))))))),
% 215.18/215.41 inference(quant_inst,[status(thm)],[])).
% 215.18/215.41 tff(352,plain,
% 215.18/215.41 (product(product(product(product(product(a, a), a), product(product(c, c), a)), product(X0!0, a)), product(product(product(b, product(c, c)), product(b, product(b, b))), product(product(b, product(a, b)), product(b, product(a, b))))) = product(product(product(product(product(a, a), a), product(product(c, c), a)), product(product(b, product(c, c)), product(b, product(b, b)))), product(product(X0!0, a), product(product(b, product(a, b)), product(b, product(a, b)))))),
% 215.18/215.41 inference(unit_resolution,[status(thm)],[351, 45])).
% 215.18/215.41 tff(353,plain,
% 215.18/215.41 (product(product(product(b, product(c, c)), product(b, product(b, b))), product(product(b, product(a, b)), product(b, product(a, b)))) = product(product(b, product(c, b)), product(b, product(a, b)))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[246, 312])).
% 215.18/215.41 tff(354,plain,
% 215.18/215.41 (product(product(b, product(c, b)), product(b, product(a, b))) = product(product(product(b, product(c, c)), product(b, product(b, b))), product(product(b, product(a, b)), product(b, product(a, b))))),
% 215.18/215.41 inference(symmetry,[status(thm)],[353])).
% 215.18/215.41 tff(355,plain,
% 215.18/215.41 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(b, b), product(product(c, b), product(a, b))) = product(product(b, product(c, b)), product(b, product(a, b))))),
% 215.18/215.41 inference(quant_inst,[status(thm)],[])).
% 215.18/215.41 tff(356,plain,
% 215.18/215.41 (product(product(b, b), product(product(c, b), product(a, b))) = product(product(b, product(c, b)), product(b, product(a, b)))),
% 215.18/215.41 inference(unit_resolution,[status(thm)],[355, 45])).
% 215.18/215.41 tff(357,plain,
% 215.18/215.41 (product(product(c, b), product(a, b)) = product(product(c, b), product(product(a, c), product(c, b)))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[67])).
% 215.18/215.41 tff(358,plain,
% 215.18/215.41 (product(product(c, b), product(product(a, c), product(c, b))) = product(product(c, b), product(a, b))),
% 215.18/215.41 inference(symmetry,[status(thm)],[357])).
% 215.18/215.41 tff(359,plain,
% 215.18/215.41 (product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))) = product(product(c, b), product(a, b))),
% 215.18/215.41 inference(transitivity,[status(thm)],[133, 130, 126, 358])).
% 215.18/215.41 tff(360,plain,
% 215.18/215.41 (product(b, product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))) = product(product(b, b), product(product(c, b), product(a, b)))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[243, 359])).
% 215.18/215.41 tff(361,plain,
% 215.18/215.41 (product(b, product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))) = product(product(product(b, product(c, c)), product(b, product(b, b))), product(product(b, product(a, b)), product(b, product(a, b))))),
% 215.18/215.41 inference(transitivity,[status(thm)],[360, 356, 354])).
% 215.18/215.41 tff(362,plain,
% 215.18/215.41 (product(product(product(product(product(a, a), a), product(product(c, c), a)), product(X0!0, a)), product(b, product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))))) = product(product(product(product(product(a, a), a), product(product(c, c), a)), product(X0!0, a)), product(product(product(b, product(c, c)), product(b, product(b, b))), product(product(b, product(a, b)), product(b, product(a, b)))))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[361])).
% 215.18/215.41 tff(363,plain,
% 215.18/215.41 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(product(product(a, a), a), product(product(c, c), a)), b), product(product(X0!0, a), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))))) = product(product(product(product(product(a, a), a), product(product(c, c), a)), product(X0!0, a)), product(b, product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))))))),
% 215.18/215.41 inference(quant_inst,[status(thm)],[])).
% 215.18/215.41 tff(364,plain,
% 215.18/215.41 (product(product(product(product(product(a, a), a), product(product(c, c), a)), b), product(product(X0!0, a), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))))) = product(product(product(product(product(a, a), a), product(product(c, c), a)), product(X0!0, a)), product(b, product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))))),
% 215.18/215.41 inference(unit_resolution,[status(thm)],[363, 45])).
% 215.18/215.41 tff(365,plain,
% 215.18/215.41 (product(product(product(product(a, a), a), product(product(c, c), a)), b) = product(product(product(a, c), a), b)),
% 215.18/215.41 inference(monotonicity,[status(thm)],[179])).
% 215.18/215.41 tff(366,plain,
% 215.18/215.41 (product(product(product(a, c), a), b) = product(product(product(product(a, a), a), product(product(c, c), a)), b)),
% 215.18/215.41 inference(symmetry,[status(thm)],[365])).
% 215.18/215.41 tff(367,plain,
% 215.18/215.41 (product(product(product(a, c), a), b) = product(product(product(a, c), a), product(b, b))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[243])).
% 215.18/215.41 tff(368,plain,
% 215.18/215.41 (product(product(product(a, c), a), product(b, b)) = product(product(product(a, c), a), b)),
% 215.18/215.41 inference(symmetry,[status(thm)],[367])).
% 215.18/215.41 tff(369,plain,
% 215.18/215.41 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, c), a), product(b, b)) = product(product(product(a, c), b), product(a, b)))),
% 215.18/215.41 inference(quant_inst,[status(thm)],[])).
% 215.18/215.41 tff(370,plain,
% 215.18/215.41 (product(product(product(a, c), a), product(b, b)) = product(product(product(a, c), b), product(a, b))),
% 215.18/215.41 inference(unit_resolution,[status(thm)],[369, 45])).
% 215.18/215.41 tff(371,plain,
% 215.18/215.41 (product(product(product(a, c), b), product(a, b)) = product(product(product(a, c), a), product(b, b))),
% 215.18/215.41 inference(symmetry,[status(thm)],[370])).
% 215.18/215.41 tff(372,plain,
% 215.18/215.41 (product(product(product(a, c), b), product(a, b)) = product(product(product(a, c), b), product(product(a, c), product(c, b)))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[67])).
% 215.18/215.41 tff(373,plain,
% 215.18/215.41 (product(product(product(a, c), b), product(product(a, c), product(c, b))) = product(product(product(a, c), b), product(a, b))),
% 215.18/215.41 inference(symmetry,[status(thm)],[372])).
% 215.18/215.41 tff(374,plain,
% 215.18/215.41 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, c), product(a, c)), product(b, product(c, b))) = product(product(product(a, c), b), product(product(a, c), product(c, b))))),
% 215.18/215.41 inference(quant_inst,[status(thm)],[])).
% 215.18/215.41 tff(375,plain,
% 215.18/215.41 (product(product(product(a, c), product(a, c)), product(b, product(c, b))) = product(product(product(a, c), b), product(product(a, c), product(c, b)))),
% 215.18/215.41 inference(unit_resolution,[status(thm)],[374, 45])).
% 215.18/215.41 tff(376,plain,
% 215.18/215.41 (product(product(product(a, c), product(a, c)), product(b, product(c, b))) = product(product(product(a, a), product(c, c)), product(b, product(c, b)))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[53])).
% 215.18/215.41 tff(377,plain,
% 215.18/215.41 (product(product(product(a, a), product(c, c)), product(b, product(c, b))) = product(product(product(a, c), product(a, c)), product(b, product(c, b)))),
% 215.18/215.41 inference(symmetry,[status(thm)],[376])).
% 215.18/215.41 tff(378,plain,
% 215.18/215.41 (product(product(product(a, a), product(c, c)), product(b, product(c, b))) = product(product(a, c), product(b, product(c, b)))),
% 215.18/215.41 inference(monotonicity,[status(thm)],[55])).
% 215.18/215.41 tff(379,plain,
% 215.18/215.41 (product(product(a, c), product(b, product(c, b))) = product(product(product(a, a), product(c, c)), product(b, product(c, b)))),
% 215.18/215.41 inference(symmetry,[status(thm)],[378])).
% 215.18/215.41 tff(380,plain,
% 215.18/215.41 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(a, b), product(c, product(c, b))) = product(product(a, c), product(b, product(c, b))))),
% 215.18/215.42 inference(quant_inst,[status(thm)],[])).
% 215.18/215.42 tff(381,plain,
% 215.18/215.42 (product(product(a, b), product(c, product(c, b))) = product(product(a, c), product(b, product(c, b)))),
% 215.18/215.42 inference(unit_resolution,[status(thm)],[380, 45])).
% 215.18/215.42 tff(382,plain,
% 215.18/215.42 (product(product(a, b), product(c, product(c, b))) = product(product(product(a, b), product(a, b)), product(c, product(c, b)))),
% 215.18/215.42 inference(monotonicity,[status(thm)],[111])).
% 215.18/215.42 tff(383,plain,
% 215.18/215.42 (product(product(product(a, b), product(a, b)), product(c, product(c, b))) = product(product(a, b), product(c, product(c, b)))),
% 215.18/215.42 inference(symmetry,[status(thm)],[382])).
% 215.18/215.42 tff(384,plain,
% 215.18/215.42 (product(product(product(a, b), product(a, b)), product(c, product(c, b))) = product(product(product(a, a), product(b, b)), product(c, product(c, b)))),
% 215.18/215.42 inference(monotonicity,[status(thm)],[81])).
% 215.18/215.42 tff(385,plain,
% 215.18/215.42 (product(product(product(a, a), product(b, b)), product(c, product(c, b))) = product(product(product(a, b), product(a, b)), product(c, product(c, b)))),
% 215.18/215.42 inference(symmetry,[status(thm)],[384])).
% 215.18/215.42 tff(386,plain,
% 215.18/215.42 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, a), product(b, b)), product(c, product(c, b))) = product(product(product(a, a), c), product(product(b, b), product(c, b))))),
% 215.18/215.42 inference(quant_inst,[status(thm)],[])).
% 215.18/215.42 tff(387,plain,
% 215.18/215.42 (product(product(product(a, a), product(b, b)), product(c, product(c, b))) = product(product(product(a, a), c), product(product(b, b), product(c, b)))),
% 215.18/215.42 inference(unit_resolution,[status(thm)],[386, 45])).
% 215.18/215.42 tff(388,plain,
% 215.18/215.42 (product(product(product(a, a), c), product(product(b, b), product(c, b))) = product(product(product(a, a), product(b, b)), product(c, product(c, b)))),
% 215.18/215.42 inference(symmetry,[status(thm)],[387])).
% 215.18/215.42 tff(389,plain,
% 215.18/215.42 (product(product(a, a), c) = product(product(a, a), product(c, c))),
% 215.18/215.42 inference(monotonicity,[status(thm)],[87])).
% 215.18/215.42 tff(390,plain,
% 215.18/215.42 (product(product(a, a), c) = product(product(a, c), product(a, c))),
% 215.18/215.42 inference(transitivity,[status(thm)],[389, 54])).
% 215.18/215.42 tff(391,plain,
% 215.18/215.42 (product(product(product(a, a), c), product(product(b, b), product(c, b))) = product(product(product(a, c), product(a, c)), product(product(b, b), product(c, b)))),
% 215.18/215.42 inference(monotonicity,[status(thm)],[390])).
% 215.18/215.42 tff(392,plain,
% 215.18/215.42 (product(product(product(a, c), product(a, c)), product(product(b, b), product(c, b))) = product(product(product(a, a), c), product(product(b, b), product(c, b)))),
% 215.18/215.42 inference(symmetry,[status(thm)],[391])).
% 215.18/215.42 tff(393,plain,
% 215.18/215.42 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, c), product(b, b)), product(product(a, c), product(c, b))) = product(product(product(a, c), product(a, c)), product(product(b, b), product(c, b))))),
% 215.18/215.42 inference(quant_inst,[status(thm)],[])).
% 215.18/215.42 tff(394,plain,
% 215.18/215.42 (product(product(product(a, c), product(b, b)), product(product(a, c), product(c, b))) = product(product(product(a, c), product(a, c)), product(product(b, b), product(c, b)))),
% 215.18/215.42 inference(unit_resolution,[status(thm)],[393, 45])).
% 215.18/215.42 tff(395,plain,
% 215.18/215.42 (product(product(product(a, c), product(b, b)), product(product(a, c), product(c, b))) = product(product(product(a, b), product(c, b)), product(product(a, c), product(c, b)))),
% 215.18/215.42 inference(monotonicity,[status(thm)],[327])).
% 215.18/215.42 tff(396,plain,
% 215.18/215.42 (product(product(product(a, b), product(c, b)), product(product(a, c), product(c, b))) = product(product(product(a, c), product(b, b)), product(product(a, c), product(c, b)))),
% 215.18/215.42 inference(symmetry,[status(thm)],[395])).
% 215.18/215.42 tff(397,plain,
% 215.18/215.42 (product(product(product(a, b), product(c, b)), product(product(a, c), product(c, b))) = product(product(product(a, b), product(c, b)), product(product(a, b), product(a, b)))),
% 215.18/215.42 inference(monotonicity,[status(thm)],[112])).
% 215.18/215.42 tff(398,plain,
% 215.18/215.42 (product(product(product(a, b), product(c, b)), product(product(a, b), product(a, b))) = product(product(product(a, b), product(c, b)), product(product(a, c), product(c, b)))),
% 215.18/215.42 inference(symmetry,[status(thm)],[397])).
% 215.18/215.42 tff(399,plain,
% 215.18/215.42 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, b), product(a, b)), product(product(c, b), product(a, b))) = product(product(product(a, b), product(c, b)), product(product(a, b), product(a, b))))),
% 215.18/215.42 inference(quant_inst,[status(thm)],[])).
% 215.18/215.42 tff(400,plain,
% 215.18/215.42 (product(product(product(a, b), product(a, b)), product(product(c, b), product(a, b))) = product(product(product(a, b), product(c, b)), product(product(a, b), product(a, b)))),
% 215.18/215.42 inference(unit_resolution,[status(thm)],[399, 45])).
% 215.18/215.42 tff(401,plain,
% 215.18/215.42 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(c, b), product(product(a, c), product(c, b))) = product(product(c, product(a, c)), product(b, product(c, b))))),
% 215.18/215.42 inference(quant_inst,[status(thm)],[])).
% 215.18/215.42 tff(402,plain,
% 215.18/215.42 (product(product(c, b), product(product(a, c), product(c, b))) = product(product(c, product(a, c)), product(b, product(c, b)))),
% 215.18/215.42 inference(unit_resolution,[status(thm)],[401, 45])).
% 215.18/215.42 tff(403,plain,
% 215.18/215.42 (product(product(c, b), product(a, b)) = product(product(c, product(a, c)), product(b, product(c, b)))),
% 215.18/215.42 inference(transitivity,[status(thm)],[357, 402])).
% 215.18/215.42 tff(404,plain,
% 215.18/215.42 (product(product(product(a, b), product(a, b)), product(product(c, b), product(a, b))) = product(product(product(a, b), product(a, b)), product(product(c, product(a, c)), product(b, product(c, b))))),
% 215.18/215.42 inference(monotonicity,[status(thm)],[403])).
% 215.18/215.42 tff(405,plain,
% 215.18/215.42 (product(product(product(a, b), product(a, b)), product(product(c, product(a, c)), product(b, product(c, b)))) = product(product(product(a, b), product(a, b)), product(product(c, b), product(a, b)))),
% 215.18/215.42 inference(symmetry,[status(thm)],[404])).
% 215.18/215.42 tff(406,plain,
% 215.18/215.42 (product(product(product(a, c), product(c, b)), product(a, b)) = product(product(product(a, c), product(c, b)), product(product(a, c), product(c, b)))),
% 215.18/215.42 inference(monotonicity,[status(thm)],[67])).
% 215.18/215.42 tff(407,plain,
% 215.18/215.42 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, c), product(c, b)), product(a, b)) = product(product(product(a, c), a), product(product(c, b), b)))),
% 215.18/215.42 inference(quant_inst,[status(thm)],[])).
% 215.18/215.42 tff(408,plain,
% 215.18/215.42 (product(product(product(a, c), product(c, b)), product(a, b)) = product(product(product(a, c), a), product(product(c, b), b))),
% 215.18/215.42 inference(unit_resolution,[status(thm)],[407, 45])).
% 215.18/215.42 tff(409,plain,
% 215.18/215.42 (product(product(product(a, c), a), product(product(c, b), b)) = product(product(product(a, c), product(c, b)), product(a, b))),
% 215.18/215.42 inference(symmetry,[status(thm)],[408])).
% 215.18/215.42 tff(410,plain,
% 215.18/215.42 (product(product(product(a, c), a), product(product(c, b), b)) = product(product(a, b), product(a, b))),
% 215.18/215.42 inference(transitivity,[status(thm)],[409, 406, 69])).
% 215.18/215.42 tff(411,plain,
% 215.18/215.42 (product(product(product(product(a, c), a), product(product(c, b), b)), product(product(c, product(a, c)), product(b, product(c, b)))) = product(product(product(a, b), product(a, b)), product(product(c, product(a, c)), product(b, product(c, b))))),
% 215.18/215.42 inference(monotonicity,[status(thm)],[410])).
% 215.18/215.42 tff(412,plain,
% 215.18/215.42 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(product(a, c), a), product(product(c, b), b)), product(product(c, product(a, c)), product(b, product(c, b)))) = product(product(product(product(a, c), a), product(c, product(a, c))), product(product(product(c, b), b), product(b, product(c, b)))))),
% 215.18/215.42 inference(quant_inst,[status(thm)],[])).
% 215.18/215.42 tff(413,plain,
% 215.18/215.42 (product(product(product(product(a, c), a), product(product(c, b), b)), product(product(c, product(a, c)), product(b, product(c, b)))) = product(product(product(product(a, c), a), product(c, product(a, c))), product(product(product(c, b), b), product(b, product(c, b))))),
% 215.18/215.42 inference(unit_resolution,[status(thm)],[412, 45])).
% 215.18/215.42 tff(414,plain,
% 215.18/215.42 (product(product(product(product(a, c), a), product(c, product(a, c))), product(product(product(c, b), b), product(b, product(c, b)))) = product(product(product(product(a, c), a), product(product(c, b), b)), product(product(c, product(a, c)), product(b, product(c, b))))),
% 215.18/215.42 inference(symmetry,[status(thm)],[413])).
% 215.18/215.42 tff(415,plain,
% 215.18/215.42 (product(product(product(product(a, c), a), product(c, product(a, c))), product(product(product(c, b), b), product(b, product(c, b)))) = product(product(product(product(a, a), a), product(product(c, c), a)), b)),
% 215.18/215.42 inference(transitivity,[status(thm)],[414, 411, 405, 400, 398, 396, 394, 392, 388, 385, 383, 381, 379, 377, 375, 373, 371, 368, 366])).
% 215.18/215.42 tff(416,plain,
% 215.18/215.42 (product(product(product(product(product(a, c), a), product(c, product(a, c))), product(product(product(c, b), b), product(b, product(c, b)))), product(product(X0!0, a), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))))) = product(product(product(product(product(a, a), a), product(product(c, c), a)), b), product(product(X0!0, a), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))))),
% 215.18/215.42 inference(monotonicity,[status(thm)],[415])).
% 215.18/215.42 tff(417,plain,
% 215.18/215.42 (product(product(product(a, b), product(a, b)), product(product(c, product(a, c)), product(b, product(c, b)))) = product(product(product(product(a, c), a), product(product(c, b), b)), product(product(c, product(a, c)), product(b, product(c, b))))),
% 215.18/215.42 inference(symmetry,[status(thm)],[411])).
% 215.18/215.42 tff(418,plain,
% 215.18/215.42 (product(product(product(a, b), product(c, b)), product(product(a, b), product(a, b))) = product(product(product(a, b), product(a, b)), product(product(c, b), product(a, b)))),
% 215.18/215.42 inference(symmetry,[status(thm)],[400])).
% 215.18/215.42 tff(419,plain,
% 215.18/215.42 (product(product(product(a, c), product(a, c)), product(product(b, b), product(c, b))) = product(product(product(a, c), product(b, b)), product(product(a, c), product(c, b)))),
% 215.18/215.42 inference(symmetry,[status(thm)],[394])).
% 215.18/215.42 tff(420,plain,
% 215.18/215.42 (product(product(product(a, c), product(c, b)), product(c, product(c, b))) = product(product(a, b), product(c, product(c, b)))),
% 215.18/215.42 inference(monotonicity,[status(thm)],[66])).
% 215.18/215.42 tff(421,plain,
% 215.18/215.42 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, c), product(c, b)), product(c, product(c, b))) = product(product(product(a, c), c), product(product(c, b), product(c, b))))),
% 215.18/215.42 inference(quant_inst,[status(thm)],[])).
% 215.18/215.42 tff(422,plain,
% 215.18/215.42 (product(product(product(a, c), product(c, b)), product(c, product(c, b))) = product(product(product(a, c), c), product(product(c, b), product(c, b)))),
% 215.18/215.42 inference(unit_resolution,[status(thm)],[421, 45])).
% 215.18/215.42 tff(423,plain,
% 215.18/215.42 (product(product(product(a, c), c), product(product(c, b), product(c, b))) = product(product(product(a, c), product(c, b)), product(c, product(c, b)))),
% 215.18/215.42 inference(symmetry,[status(thm)],[422])).
% 215.18/215.42 tff(424,plain,
% 215.18/215.42 (product(product(product(a, c), c), product(product(c, c), product(b, b))) = product(product(product(a, c), c), product(product(c, b), product(c, b)))),
% 215.18/215.42 inference(monotonicity,[status(thm)],[75])).
% 215.18/215.42 tff(425,plain,
% 215.18/215.42 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, c), c), product(product(c, c), product(b, b))) = product(product(product(a, c), product(c, c)), product(c, product(b, b))))),
% 215.18/215.42 inference(quant_inst,[status(thm)],[])).
% 215.18/215.42 tff(426,plain,
% 215.18/215.42 (product(product(product(a, c), c), product(product(c, c), product(b, b))) = product(product(product(a, c), product(c, c)), product(c, product(b, b)))),
% 215.18/215.42 inference(unit_resolution,[status(thm)],[425, 45])).
% 215.18/215.42 tff(427,plain,
% 215.18/215.42 (product(product(product(a, c), product(c, c)), product(c, product(b, b))) = product(product(product(a, c), c), product(product(c, c), product(b, b)))),
% 215.18/215.42 inference(symmetry,[status(thm)],[426])).
% 215.18/215.42 tff(428,plain,
% 215.18/215.42 (product(product(c, c), product(b, b)) = product(c, product(b, b))),
% 215.18/215.42 inference(symmetry,[status(thm)],[88])).
% 215.18/215.42 tff(429,plain,
% 215.18/215.42 (product(c, b) = product(c, product(b, b))),
% 215.18/215.42 inference(transitivity,[status(thm)],[127, 74, 428])).
% 215.18/215.42 tff(430,plain,
% 215.18/215.42 (product(product(product(a, a), product(c, c)), product(c, c)) = product(product(a, c), product(c, c))),
% 215.18/215.42 inference(monotonicity,[status(thm)],[55])).
% 215.18/215.42 tff(431,plain,
% 215.18/215.42 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(a, a), product(c, c)), product(c, c)) = product(product(product(a, a), c), product(product(c, c), c)))),
% 215.18/215.42 inference(quant_inst,[status(thm)],[])).
% 215.18/215.42 tff(432,plain,
% 215.18/215.42 (product(product(product(a, a), product(c, c)), product(c, c)) = product(product(product(a, a), c), product(product(c, c), c))),
% 215.18/215.42 inference(unit_resolution,[status(thm)],[431, 45])).
% 215.18/215.42 tff(433,plain,
% 215.18/215.42 (product(product(product(a, a), c), product(product(c, c), c)) = product(product(product(a, a), product(c, c)), product(c, c))),
% 215.18/215.42 inference(symmetry,[status(thm)],[432])).
% 215.18/215.42 tff(434,plain,
% 215.18/215.42 (product(product(product(a, a), c), product(product(c, c), c)) = product(product(a, c), product(c, c))),
% 215.18/215.42 inference(transitivity,[status(thm)],[433, 430])).
% 215.18/215.42 tff(435,plain,
% 215.18/215.42 (product(product(product(product(a, a), c), product(product(c, c), c)), product(c, b)) = product(product(product(a, c), product(c, c)), product(c, product(b, b)))),
% 215.18/215.42 inference(monotonicity,[status(thm)],[434, 429])).
% 215.18/215.42 tff(436,plain,
% 215.18/215.42 (product(product(product(product(a, a), c), product(product(c, c), c)), product(c, b)) = product(product(product(product(a, c), a), product(c, product(a, c))), product(product(product(c, b), b), product(b, product(c, b))))),
% 215.18/215.42 inference(transitivity,[status(thm)],[435, 427, 424, 423, 420, 382, 384, 387, 391, 419, 395, 397, 418, 404, 417, 413])).
% 215.18/215.42 tff(437,plain,
% 215.18/215.42 (product(product(product(product(product(a, a), c), product(product(c, c), c)), product(c, b)), product(product(X0!0, a), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))))) = product(product(product(product(product(a, c), a), product(c, product(a, c))), product(product(product(c, b), b), product(b, product(c, b)))), product(product(X0!0, a), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))))),
% 215.18/215.42 inference(monotonicity,[status(thm)],[436])).
% 215.18/215.42 tff(438,plain,
% 215.18/215.42 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(product(product(a, a), c), product(product(c, c), c)), product(c, b)), product(product(X0!0, a), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))))) = product(product(product(product(product(a, a), c), product(product(c, c), c)), product(X0!0, a)), product(product(c, b), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))))))),
% 215.18/215.42 inference(quant_inst,[status(thm)],[])).
% 215.18/215.42 tff(439,plain,
% 215.18/215.42 (product(product(product(product(product(a, a), c), product(product(c, c), c)), product(c, b)), product(product(X0!0, a), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))))) = product(product(product(product(product(a, a), c), product(product(c, c), c)), product(X0!0, a)), product(product(c, b), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))))),
% 215.18/215.42 inference(unit_resolution,[status(thm)],[438, 45])).
% 215.18/215.42 tff(440,plain,
% 215.18/215.42 (product(product(product(product(product(a, a), c), product(product(c, c), c)), product(X0!0, a)), product(product(c, b), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))))) = product(product(product(product(product(a, a), c), product(product(c, c), c)), product(c, b)), product(product(X0!0, a), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))))),
% 215.18/215.42 inference(symmetry,[status(thm)],[439])).
% 215.18/215.42 tff(441,plain,
% 215.18/215.42 (product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))) = product(product(c, product(a, c)), product(b, product(c, b)))),
% 215.18/215.42 inference(transitivity,[status(thm)],[133, 130, 126, 402])).
% 215.18/215.42 tff(442,plain,
% 215.18/215.42 (product(product(c, b), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))) = product(product(c, b), product(product(c, product(a, c)), product(b, product(c, b))))),
% 215.18/215.42 inference(monotonicity,[status(thm)],[441])).
% 215.18/215.42 tff(443,plain,
% 215.18/215.42 (product(product(c, b), product(product(c, product(a, c)), product(b, product(c, b)))) = product(product(c, b), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))))),
% 215.18/215.42 inference(symmetry,[status(thm)],[442])).
% 215.18/215.42 tff(444,plain,
% 215.18/215.42 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(c, b), product(product(c, product(a, c)), product(b, product(c, b)))) = product(product(c, product(c, product(a, c))), product(b, product(b, product(c, b)))))),
% 215.18/215.42 inference(quant_inst,[status(thm)],[])).
% 215.18/215.42 tff(445,plain,
% 215.18/215.42 (product(product(c, b), product(product(c, product(a, c)), product(b, product(c, b)))) = product(product(c, product(c, product(a, c))), product(b, product(b, product(c, b))))),
% 215.18/215.42 inference(unit_resolution,[status(thm)],[444, 45])).
% 215.18/215.42 tff(446,plain,
% 215.18/215.42 (product(product(c, product(c, product(a, c))), product(b, product(b, product(c, b)))) = product(product(c, b), product(product(c, product(a, c)), product(b, product(c, b))))),
% 215.18/215.42 inference(symmetry,[status(thm)],[445])).
% 215.18/215.42 tff(447,plain,
% 215.18/215.42 (product(product(c, product(c, product(a, c))), product(b, product(b, product(c, b)))) = product(product(c, b), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))))),
% 215.18/215.42 inference(transitivity,[status(thm)],[446, 443])).
% 215.18/215.42 tff(448,plain,
% 215.18/215.42 (product(product(product(product(product(a, a), c), product(product(c, c), c)), product(X0!0, a)), product(product(c, product(c, product(a, c))), product(b, product(b, product(c, b))))) = product(product(product(product(product(a, a), c), product(product(c, c), c)), product(X0!0, a)), product(product(c, b), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))))),
% 215.18/215.42 inference(monotonicity,[status(thm)],[447])).
% 215.18/215.42 tff(449,plain,
% 215.18/215.42 (product(product(c, a), product(b, b)) = product(product(c, product(a, c)), product(b, product(c, b)))),
% 215.18/215.42 inference(transitivity,[status(thm)],[97, 357, 402])).
% 215.18/215.42 tff(450,plain,
% 215.18/215.42 (product(product(c, b), product(product(c, a), product(b, b))) = product(product(c, b), product(product(c, product(a, c)), product(b, product(c, b))))),
% 215.18/215.42 inference(monotonicity,[status(thm)],[449])).
% 215.18/215.42 tff(451,plain,
% 215.18/215.42 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(c, b), product(product(c, a), product(b, b))) = product(product(c, product(c, a)), product(b, product(b, b))))),
% 215.18/215.42 inference(quant_inst,[status(thm)],[])).
% 215.18/215.42 tff(452,plain,
% 215.18/215.42 (product(product(c, b), product(product(c, a), product(b, b))) = product(product(c, product(c, a)), product(b, product(b, b)))),
% 215.18/215.42 inference(unit_resolution,[status(thm)],[451, 45])).
% 215.18/215.42 tff(453,plain,
% 215.18/215.42 (product(product(c, product(c, a)), product(b, product(b, b))) = product(product(c, b), product(product(c, a), product(b, b)))),
% 215.18/215.42 inference(symmetry,[status(thm)],[452])).
% 215.18/215.42 tff(454,plain,
% 215.18/215.42 (product(b, product(b, b)) = product(b, b)),
% 215.18/215.42 inference(monotonicity,[status(thm)],[242])).
% 215.18/215.42 tff(455,plain,
% 215.18/215.42 (product(b, b) = product(b, product(b, b))),
% 215.18/215.42 inference(symmetry,[status(thm)],[454])).
% 215.18/215.42 tff(456,plain,
% 215.18/215.42 (b = product(b, product(b, b))),
% 215.18/215.42 inference(transitivity,[status(thm)],[243, 455])).
% 215.18/215.42 tff(457,plain,
% 215.18/215.42 (product(product(c, product(c, a)), b) = product(product(c, product(c, a)), product(b, product(b, b)))),
% 215.18/215.42 inference(monotonicity,[status(thm)],[456])).
% 215.18/215.42 tff(458,plain,
% 215.18/215.42 (product(product(c, product(c, a)), b) = product(product(c, product(c, product(a, c))), product(b, product(b, product(c, b))))),
% 215.18/215.43 inference(transitivity,[status(thm)],[457, 453, 450, 445])).
% 215.18/215.43 tff(459,plain,
% 215.18/215.43 (product(product(product(product(product(a, a), c), product(product(c, c), c)), product(X0!0, a)), product(product(c, product(c, a)), b)) = product(product(product(product(product(a, a), c), product(product(c, c), c)), product(X0!0, a)), product(product(c, product(c, product(a, c))), product(b, product(b, product(c, b)))))),
% 215.18/215.43 inference(monotonicity,[status(thm)],[458])).
% 215.18/215.43 tff(460,plain,
% 215.18/215.43 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(product(product(a, a), c), product(product(c, c), c)), product(c, product(c, a))), product(product(X0!0, a), b)) = product(product(product(product(product(a, a), c), product(product(c, c), c)), product(X0!0, a)), product(product(c, product(c, a)), b)))),
% 215.18/215.43 inference(quant_inst,[status(thm)],[])).
% 215.18/215.43 tff(461,plain,
% 215.18/215.43 (product(product(product(product(product(a, a), c), product(product(c, c), c)), product(c, product(c, a))), product(product(X0!0, a), b)) = product(product(product(product(product(a, a), c), product(product(c, c), c)), product(X0!0, a)), product(product(c, product(c, a)), b))),
% 215.18/215.43 inference(unit_resolution,[status(thm)],[460, 45])).
% 215.18/215.43 tff(462,plain,
% 215.18/215.43 (product(product(X0!0, a), b) = product(product(X0!0, a), product(b, b))),
% 215.18/215.43 inference(monotonicity,[status(thm)],[243])).
% 215.18/215.43 tff(463,plain,
% 215.18/215.43 (product(product(X0!0, a), product(b, b)) = product(product(X0!0, a), b)),
% 215.18/215.43 inference(symmetry,[status(thm)],[462])).
% 215.18/215.43 tff(464,plain,
% 215.18/215.43 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(X0!0, a), product(b, b)) = product(product(X0!0, b), product(a, b)))),
% 215.18/215.43 inference(quant_inst,[status(thm)],[])).
% 215.18/215.43 tff(465,plain,
% 215.18/215.43 (product(product(X0!0, a), product(b, b)) = product(product(X0!0, b), product(a, b))),
% 215.18/215.43 inference(unit_resolution,[status(thm)],[464, 45])).
% 215.18/215.43 tff(466,plain,
% 215.18/215.43 (product(product(X0!0, b), product(a, b)) = product(product(X0!0, a), product(b, b))),
% 215.18/215.43 inference(symmetry,[status(thm)],[465])).
% 215.18/215.43 tff(467,plain,
% 215.18/215.43 (product(product(X0!0, b), product(a, b)) = product(product(X0!0, a), b)),
% 215.18/215.43 inference(transitivity,[status(thm)],[466, 463])).
% 215.18/215.43 tff(468,plain,
% 215.18/215.43 (product(product(a, c), product(c, c)) = product(product(a, c), c)),
% 215.18/215.43 inference(monotonicity,[status(thm)],[37])).
% 215.18/215.43 tff(469,plain,
% 215.18/215.43 (product(product(product(a, a), c), product(product(c, c), c)) = product(product(a, c), c)),
% 215.18/215.43 inference(transitivity,[status(thm)],[433, 430, 468])).
% 215.18/215.43 tff(470,plain,
% 215.18/215.43 (product(product(product(product(a, a), c), product(product(c, c), c)), product(c, product(c, a))) = product(product(product(a, c), c), product(c, product(c, a)))),
% 215.18/215.43 inference(monotonicity,[status(thm)],[469])).
% 215.18/215.43 tff(471,plain,
% 215.18/215.43 (product(product(product(a, c), c), product(c, product(c, a))) = product(product(product(product(a, a), c), product(product(c, c), c)), product(c, product(c, a)))),
% 215.18/215.43 inference(symmetry,[status(thm)],[470])).
% 215.18/215.43 tff(472,plain,
% 215.18/215.43 (^[B: $i, A: $i] : refl((product(product(product(A, B), B), product(B, product(B, A))) = B) <=> (product(product(product(A, B), B), product(B, product(B, A))) = B))),
% 215.18/215.43 inference(bind,[status(th)],[])).
% 215.18/215.43 tff(473,plain,
% 215.18/215.43 (![B: $i, A: $i] : (product(product(product(A, B), B), product(B, product(B, A))) = B) <=> ![B: $i, A: $i] : (product(product(product(A, B), B), product(B, product(B, A))) = B)),
% 215.18/215.43 inference(quant_intro,[status(thm)],[472])).
% 215.18/215.43 tff(474,plain,
% 215.18/215.43 (![B: $i, A: $i] : (product(product(product(A, B), B), product(B, product(B, A))) = B) <=> ![B: $i, A: $i] : (product(product(product(A, B), B), product(B, product(B, A))) = B)),
% 215.18/215.43 inference(rewrite,[status(thm)],[])).
% 215.18/215.43 tff(475,axiom,(![B: $i, A: $i] : (product(product(product(A, B), B), product(B, product(B, A))) = B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos07')).
% 215.18/215.43 tff(476,plain,
% 215.18/215.43 (![B: $i, A: $i] : (product(product(product(A, B), B), product(B, product(B, A))) = B)),
% 215.18/215.43 inference(modus_ponens,[status(thm)],[475, 474])).
% 215.18/215.43 tff(477,plain,(
% 215.18/215.43 ![B: $i, A: $i] : (product(product(product(A, B), B), product(B, product(B, A))) = B)),
% 215.18/215.43 inference(skolemize,[status(sab)],[476])).
% 215.18/215.43 tff(478,plain,
% 215.18/215.43 (![B: $i, A: $i] : (product(product(product(A, B), B), product(B, product(B, A))) = B)),
% 215.18/215.43 inference(modus_ponens,[status(thm)],[477, 473])).
% 215.18/215.43 tff(479,plain,
% 215.18/215.43 ((~![B: $i, A: $i] : (product(product(product(A, B), B), product(B, product(B, A))) = B)) | (product(product(product(a, c), c), product(c, product(c, a))) = c)),
% 215.18/215.43 inference(quant_inst,[status(thm)],[])).
% 215.18/215.43 tff(480,plain,
% 215.18/215.43 (product(product(product(a, c), c), product(c, product(c, a))) = c),
% 215.18/215.43 inference(unit_resolution,[status(thm)],[479, 478])).
% 215.18/215.43 tff(481,plain,
% 215.18/215.43 (c = product(product(product(a, c), c), product(c, product(c, a)))),
% 215.18/215.43 inference(symmetry,[status(thm)],[480])).
% 215.18/215.43 tff(482,plain,
% 215.18/215.43 (c = product(product(product(product(a, a), c), product(product(c, c), c)), product(c, product(c, a)))),
% 215.18/215.43 inference(transitivity,[status(thm)],[481, 471])).
% 215.18/215.43 tff(483,plain,
% 215.18/215.43 (product(c, product(product(X0!0, b), product(a, b))) = product(product(product(product(product(a, a), c), product(product(c, c), c)), product(c, product(c, a))), product(product(X0!0, a), b))),
% 215.18/215.43 inference(monotonicity,[status(thm)],[482, 467])).
% 215.18/215.43 tff(484,plain,
% 215.18/215.43 (product(product(X0!0, a), b) = product(product(X0!0, b), product(a, b))),
% 215.18/215.43 inference(transitivity,[status(thm)],[462, 465])).
% 215.18/215.43 tff(485,plain,
% 215.18/215.43 (product(product(c, c), product(product(X0!0, a), b)) = product(c, product(product(X0!0, b), product(a, b)))),
% 215.18/215.43 inference(monotonicity,[status(thm)],[37, 484])).
% 215.18/215.43 tff(486,plain,
% 215.18/215.43 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(c, product(X0!0, a)), product(c, b)) = product(product(c, c), product(product(X0!0, a), b)))),
% 215.18/215.43 inference(quant_inst,[status(thm)],[])).
% 215.18/215.43 tff(487,plain,
% 215.18/215.43 (product(product(c, product(X0!0, a)), product(c, b)) = product(product(c, c), product(product(X0!0, a), b))),
% 215.18/215.43 inference(unit_resolution,[status(thm)],[486, 45])).
% 215.18/215.43 tff(488,plain,
% 215.18/215.43 (product(product(c, c), product(X0!0, a)) = product(c, product(X0!0, a))),
% 215.18/215.43 inference(monotonicity,[status(thm)],[37])).
% 215.18/215.43 tff(489,plain,
% 215.18/215.43 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(c, c), product(X0!0, a)) = product(product(c, X0!0), product(c, a)))),
% 215.18/215.43 inference(quant_inst,[status(thm)],[])).
% 215.18/215.43 tff(490,plain,
% 215.18/215.43 (product(product(c, c), product(X0!0, a)) = product(product(c, X0!0), product(c, a))),
% 215.18/215.43 inference(unit_resolution,[status(thm)],[489, 45])).
% 215.18/215.43 tff(491,plain,
% 215.18/215.43 (product(product(c, X0!0), product(c, a)) = product(product(c, c), product(X0!0, a))),
% 215.18/215.43 inference(symmetry,[status(thm)],[490])).
% 215.18/215.43 tff(492,plain,
% 215.18/215.43 (product(product(c, X0!0), product(c, a)) = product(c, product(X0!0, a))),
% 215.18/215.43 inference(transitivity,[status(thm)],[491, 488])).
% 215.18/215.43 tff(493,plain,
% 215.18/215.43 (product(product(product(c, X0!0), product(c, a)), product(c, b)) = product(product(c, product(X0!0, a)), product(c, b))),
% 215.18/215.43 inference(monotonicity,[status(thm)],[492])).
% 215.18/215.43 tff(494,plain,
% 215.18/215.43 (product(c, product(X0!0, a)) = product(product(c, c), product(X0!0, a))),
% 215.18/215.43 inference(symmetry,[status(thm)],[488])).
% 215.18/215.43 tff(495,plain,
% 215.18/215.43 (product(c, product(X0!0, a)) = product(product(c, X0!0), product(c, a))),
% 215.18/215.43 inference(transitivity,[status(thm)],[494, 490])).
% 215.18/215.43 tff(496,plain,
% 215.18/215.43 (product(product(c, product(X0!0, a)), product(product(c, b), product(c, b))) = product(product(product(c, X0!0), product(c, a)), product(c, b))),
% 215.18/215.43 inference(monotonicity,[status(thm)],[495, 121])).
% 215.18/215.43 tff(497,plain,
% 215.18/215.43 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(c, product(X0!0, a)), product(product(c, b), product(c, b))) = product(product(c, product(c, b)), product(product(X0!0, a), product(c, b))))),
% 215.18/215.43 inference(quant_inst,[status(thm)],[])).
% 215.18/215.43 tff(498,plain,
% 215.18/215.43 (product(product(c, product(X0!0, a)), product(product(c, b), product(c, b))) = product(product(c, product(c, b)), product(product(X0!0, a), product(c, b)))),
% 215.18/215.43 inference(unit_resolution,[status(thm)],[497, 45])).
% 215.18/215.43 tff(499,plain,
% 215.18/215.43 (product(product(c, product(c, b)), product(product(X0!0, a), product(c, b))) = product(product(c, product(X0!0, a)), product(product(c, b), product(c, b)))),
% 215.18/215.43 inference(symmetry,[status(thm)],[498])).
% 215.18/215.43 tff(500,plain,
% 215.18/215.43 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(X0!0, a), product(c, b)) = product(product(X0!0, c), product(a, b)))),
% 215.18/215.43 inference(quant_inst,[status(thm)],[])).
% 215.18/215.43 tff(501,plain,
% 215.18/215.43 (product(product(X0!0, a), product(c, b)) = product(product(X0!0, c), product(a, b))),
% 215.18/215.43 inference(unit_resolution,[status(thm)],[500, 45])).
% 215.18/215.43 tff(502,plain,
% 215.18/215.43 (product(product(X0!0, c), product(a, b)) = product(product(X0!0, a), product(c, b))),
% 215.18/215.43 inference(symmetry,[status(thm)],[501])).
% 215.18/215.43 tff(503,plain,
% 215.18/215.43 (product(product(c, c), product(c, b)) = product(c, product(c, b))),
% 215.18/215.43 inference(monotonicity,[status(thm)],[37])).
% 215.18/215.43 tff(504,plain,
% 215.18/215.43 (product(product(product(c, c), product(c, b)), product(product(X0!0, c), product(a, b))) = product(product(c, product(c, b)), product(product(X0!0, a), product(c, b)))),
% 215.18/215.43 inference(monotonicity,[status(thm)],[503, 502])).
% 215.18/215.43 tff(505,plain,
% 215.18/215.43 ((~![D: $i, C: $i, B: $i, A: $i] : (product(product(A, B), product(C, D)) = product(product(A, C), product(B, D)))) | (product(product(product(c, c), product(X0!0, c)), product(product(c, b), product(a, b))) = product(product(product(c, c), product(c, b)), product(product(X0!0, c), product(a, b))))),
% 215.18/215.43 inference(quant_inst,[status(thm)],[])).
% 215.18/215.43 tff(506,plain,
% 215.18/215.43 (product(product(product(c, c), product(X0!0, c)), product(product(c, b), product(a, b))) = product(product(product(c, c), product(c, b)), product(product(X0!0, c), product(a, b)))),
% 215.18/215.43 inference(unit_resolution,[status(thm)],[505, 45])).
% 215.18/215.43 tff(507,plain,
% 215.18/215.43 (product(product(c, product(a, c)), product(b, product(c, b))) = product(product(c, b), product(product(a, c), product(c, b)))),
% 215.18/215.43 inference(symmetry,[status(thm)],[402])).
% 215.18/215.43 tff(508,plain,
% 215.18/215.43 (product(product(c, product(a, c)), product(b, product(c, b))) = product(product(c, b), product(a, b))),
% 215.18/215.43 inference(transitivity,[status(thm)],[507, 358])).
% 215.18/215.43 tff(509,plain,
% 215.18/215.43 (product(product(product(c, c), product(X0!0, c)), product(product(c, product(a, c)), product(b, product(c, b)))) = product(product(product(c, c), product(X0!0, c)), product(product(c, b), product(a, b)))),
% 215.18/215.43 inference(monotonicity,[status(thm)],[508])).
% 215.18/215.43 tff(510,plain,
% 215.18/215.43 (product(product(product(c, c), product(X0!0, c)), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))) = product(product(product(c, c), product(X0!0, c)), product(product(c, product(a, c)), product(b, product(c, b))))),
% 215.18/215.43 inference(monotonicity,[status(thm)],[441])).
% 215.18/215.43 tff(511,plain,
% 215.18/215.43 (product(product(product(c, c), product(X0!0, c)), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))) = product(product(product(product(a, b), X0!0), product(product(a, b), a)), product(product(c, product(c, c)), product(c, product(b, b))))),
% 215.18/215.43 inference(transitivity,[status(thm)],[510, 509, 506, 504, 499, 496, 493, 487, 485, 483, 461, 459, 448, 440, 437, 416, 364, 362, 352, 350, 342, 318, 315, 310, 298, 297, 295, 280, 258, 255, 240, 238, 217, 192, 190, 167, 164, 157, 154])).
% 215.18/215.43 tff(512,plain,
% 215.18/215.43 (quotient(product(product(product(c, c), product(X0!0, c)), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))) = quotient(product(product(product(product(a, b), X0!0), product(product(a, b), a)), product(product(c, product(c, c)), product(c, product(b, b)))), product(product(c, product(c, c)), product(c, product(b, b))))),
% 215.18/215.43 inference(monotonicity,[status(thm)],[511, 144])).
% 215.35/215.59 tff(513,plain,
% 215.35/215.59 (quotient(product(product(product(product(a, b), X0!0), product(product(a, b), a)), product(product(c, product(c, c)), product(c, product(b, b)))), product(product(c, product(c, c)), product(c, product(b, b)))) = quotient(product(product(product(c, c), product(X0!0, c)), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b)))), product(product(product(c, c), product(a, b)), product(product(b, b), product(a, b))))),
% 215.35/215.59 inference(symmetry,[status(thm)],[512])).
% 215.35/215.59 tff(514,plain,
% 215.35/215.59 ((~![B: $i, A: $i] : (quotient(product(A, B), B) = A)) | (quotient(product(product(product(product(a, b), X0!0), product(product(a, b), a)), product(product(c, product(c, c)), product(c, product(b, b)))), product(product(c, product(c, c)), product(c, product(b, b)))) = product(product(product(a, b), X0!0), product(product(a, b), a)))),
% 215.35/215.59 inference(quant_inst,[status(thm)],[])).
% 215.35/215.59 tff(515,plain,
% 215.35/215.59 (quotient(product(product(product(product(a, b), X0!0), product(product(a, b), a)), product(product(c, product(c, c)), product(c, product(b, b)))), product(product(c, product(c, c)), product(c, product(b, b)))) = product(product(product(a, b), X0!0), product(product(a, b), a))),
% 215.35/215.59 inference(unit_resolution,[status(thm)],[514, 17])).
% 215.35/215.59 tff(516,plain,
% 215.35/215.59 (product(product(product(a, b), X0!0), product(product(a, b), a)) = quotient(product(product(product(product(a, b), X0!0), product(product(a, b), a)), product(product(c, product(c, c)), product(c, product(b, b)))), product(product(c, product(c, c)), product(c, product(b, b))))),
% 215.35/215.59 inference(symmetry,[status(thm)],[515])).
% 215.35/215.59 tff(517,plain,
% 215.35/215.59 ((~![C: $i, B: $i, A: $i] : (bigC(A, B, C) = product(product(A, B), product(C, A)))) | (bigC(a, b, X0!0) = product(product(a, b), product(X0!0, a)))),
% 215.35/215.59 inference(quant_inst,[status(thm)],[])).
% 215.35/215.59 tff(518,plain,
% 215.35/215.59 (bigC(a, b, X0!0) = product(product(a, b), product(X0!0, a))),
% 215.35/215.59 inference(unit_resolution,[status(thm)],[517, 7])).
% 215.35/215.59 tff(519,plain,
% 215.35/215.59 (bigC(a, b, X0!0) = bigC(c, c, X0!0)),
% 215.35/215.59 inference(transitivity,[status(thm)],[518, 147, 150, 516, 513, 19, 10])).
% 215.35/215.59 tff(520,plain,
% 215.35/215.59 ((~![X0: $i] : (bigC(a, b, X0) = bigC(c, c, X0))) <=> (~![X0: $i] : (bigC(a, b, X0) = bigC(c, c, X0)))),
% 215.35/215.59 inference(rewrite,[status(thm)],[])).
% 215.35/215.59 tff(521,axiom,(~![X0: $i] : (bigC(a, b, X0) = bigC(c, c, X0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 215.35/215.59 tff(522,plain,
% 215.35/215.59 (~![X0: $i] : (bigC(a, b, X0) = bigC(c, c, X0))),
% 215.35/215.59 inference(modus_ponens,[status(thm)],[521, 520])).
% 215.35/215.59 tff(523,plain,
% 215.35/215.59 (~![X0: $i] : (bigC(a, b, X0) = bigC(c, c, X0))),
% 215.35/215.59 inference(modus_ponens,[status(thm)],[522, 520])).
% 215.35/215.59 tff(524,plain,
% 215.35/215.59 (~![X0: $i] : (bigC(a, b, X0) = bigC(c, c, X0))),
% 215.35/215.59 inference(modus_ponens,[status(thm)],[523, 520])).
% 215.35/215.59 tff(525,plain,
% 215.35/215.59 (~![X0: $i] : (bigC(a, b, X0) = bigC(c, c, X0))),
% 215.35/215.59 inference(modus_ponens,[status(thm)],[524, 520])).
% 215.35/215.59 tff(526,plain,(
% 215.35/215.59 ~(bigC(a, b, X0!0) = bigC(c, c, X0!0))),
% 215.35/215.59 inference(skolemize,[status(sab)],[525])).
% 215.35/215.59 tff(527,plain,
% 215.35/215.59 ($false),
% 215.35/215.59 inference(unit_resolution,[status(thm)],[526, 519])).
% 215.35/215.59 % SZS output end Proof
% 215.44/215.64 % E exiting
%------------------------------------------------------------------------------