TSTP Solution File: FLD047-4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : FLD047-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 14:55:54 EDT 2022
% Result : Unsatisfiable 253.08s 158.87s
% Output : Proof 253.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : FLD047-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n025.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 : Wed Aug 31 03:06:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 253.08/158.87 % SZS status Unsatisfiable
% 253.08/158.87 % SZS output start Proof
% 253.08/158.87 tff(sum_type, type, (
% 253.08/158.87 sum: ( $i * $i * $i ) > $o)).
% 253.08/158.87 tff(t_type, type, (
% 253.08/158.87 t: $i)).
% 253.08/158.87 tff(a_type, type, (
% 253.08/158.87 a: $i)).
% 253.08/158.87 tff(additive_inverse_type, type, (
% 253.08/158.87 additive_inverse: $i > $i)).
% 253.08/158.87 tff(additive_identity_type, type, (
% 253.08/158.87 additive_identity: $i)).
% 253.08/158.87 tff(defined_type, type, (
% 253.08/158.87 defined: $i > $o)).
% 253.08/158.87 tff(product_type, type, (
% 253.08/158.87 product: ( $i * $i * $i ) > $o)).
% 253.08/158.87 tff(multiplicative_identity_type, type, (
% 253.08/158.87 multiplicative_identity: $i)).
% 253.08/158.87 tff(multiplicative_inverse_type, type, (
% 253.08/158.87 multiplicative_inverse: $i > $i)).
% 253.08/158.87 tff(s_type, type, (
% 253.08/158.87 s: $i)).
% 253.08/158.87 tff(u_type, type, (
% 253.08/158.87 u: $i)).
% 253.08/158.87 tff(c_type, type, (
% 253.08/158.87 c: $i)).
% 253.08/158.87 tff(b_type, type, (
% 253.08/158.87 b: $i)).
% 253.08/158.87 tff(1,plain,
% 253.08/158.87 (defined(t) <=> defined(t)),
% 253.08/158.87 inference(rewrite,[status(thm)],[])).
% 253.08/158.87 tff(2,axiom,(defined(t)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t_is_defined')).
% 253.08/158.87 tff(3,plain,
% 253.08/158.87 (defined(t)),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[2, 1])).
% 253.08/158.87 tff(4,plain,
% 253.08/158.87 (^[X: $i] : refl(((~defined(X)) | sum(additive_identity, X, X)) <=> ((~defined(X)) | sum(additive_identity, X, X)))),
% 253.08/158.87 inference(bind,[status(th)],[])).
% 253.08/158.87 tff(5,plain,
% 253.08/158.87 (![X: $i] : ((~defined(X)) | sum(additive_identity, X, X)) <=> ![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))),
% 253.08/158.87 inference(quant_intro,[status(thm)],[4])).
% 253.08/158.87 tff(6,plain,
% 253.08/158.87 (![X: $i] : ((~defined(X)) | sum(additive_identity, X, X)) <=> ![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))),
% 253.08/158.87 inference(rewrite,[status(thm)],[])).
% 253.08/158.87 tff(7,plain,
% 253.08/158.87 (^[X: $i] : rewrite((sum(additive_identity, X, X) | (~defined(X))) <=> ((~defined(X)) | sum(additive_identity, X, X)))),
% 253.08/158.87 inference(bind,[status(th)],[])).
% 253.08/158.87 tff(8,plain,
% 253.08/158.87 (![X: $i] : (sum(additive_identity, X, X) | (~defined(X))) <=> ![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))),
% 253.08/158.87 inference(quant_intro,[status(thm)],[7])).
% 253.08/158.87 tff(9,axiom,(![X: $i] : (sum(additive_identity, X, X) | (~defined(X)))), file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax','existence_of_identity_addition')).
% 253.08/158.87 tff(10,plain,
% 253.08/158.87 (![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[9, 8])).
% 253.08/158.87 tff(11,plain,
% 253.08/158.87 (![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[10, 6])).
% 253.08/158.87 tff(12,plain,(
% 253.08/158.87 ![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))),
% 253.08/158.87 inference(skolemize,[status(sab)],[11])).
% 253.08/158.87 tff(13,plain,
% 253.08/158.87 (![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[12, 5])).
% 253.08/158.87 tff(14,plain,
% 253.08/158.87 (((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))) | ((~defined(t)) | sum(additive_identity, t, t))) <=> ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))) | (~defined(t)) | sum(additive_identity, t, t))),
% 253.08/158.87 inference(rewrite,[status(thm)],[])).
% 253.08/158.87 tff(15,plain,
% 253.08/158.87 ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))) | ((~defined(t)) | sum(additive_identity, t, t))),
% 253.08/158.87 inference(quant_inst,[status(thm)],[])).
% 253.08/158.87 tff(16,plain,
% 253.08/158.87 ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))) | (~defined(t)) | sum(additive_identity, t, t)),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[15, 14])).
% 253.08/158.87 tff(17,plain,
% 253.08/158.87 (sum(additive_identity, t, t)),
% 253.08/158.87 inference(unit_resolution,[status(thm)],[16, 13, 3])).
% 253.08/158.87 tff(18,plain,
% 253.08/158.87 (defined(c) <=> defined(c)),
% 253.08/158.87 inference(rewrite,[status(thm)],[])).
% 253.08/158.87 tff(19,axiom,(defined(c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_is_defined')).
% 253.08/158.87 tff(20,plain,
% 253.08/158.87 (defined(c)),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[19, 18])).
% 253.08/158.87 tff(21,plain,
% 253.08/158.87 (^[X: $i] : refl(((~defined(X)) | product(multiplicative_identity, X, X)) <=> ((~defined(X)) | product(multiplicative_identity, X, X)))),
% 253.08/158.87 inference(bind,[status(th)],[])).
% 253.08/158.87 tff(22,plain,
% 253.08/158.87 (![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X)) <=> ![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))),
% 253.08/158.87 inference(quant_intro,[status(thm)],[21])).
% 253.08/158.87 tff(23,plain,
% 253.08/158.87 (![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X)) <=> ![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))),
% 253.08/158.87 inference(rewrite,[status(thm)],[])).
% 253.08/158.87 tff(24,plain,
% 253.08/158.87 (^[X: $i] : rewrite((product(multiplicative_identity, X, X) | (~defined(X))) <=> ((~defined(X)) | product(multiplicative_identity, X, X)))),
% 253.08/158.87 inference(bind,[status(th)],[])).
% 253.08/158.87 tff(25,plain,
% 253.08/158.87 (![X: $i] : (product(multiplicative_identity, X, X) | (~defined(X))) <=> ![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))),
% 253.08/158.87 inference(quant_intro,[status(thm)],[24])).
% 253.08/158.87 tff(26,axiom,(![X: $i] : (product(multiplicative_identity, X, X) | (~defined(X)))), file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax','existence_of_identity_multiplication')).
% 253.08/158.87 tff(27,plain,
% 253.08/158.87 (![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[26, 25])).
% 253.08/158.87 tff(28,plain,
% 253.08/158.87 (![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[27, 23])).
% 253.08/158.87 tff(29,plain,(
% 253.08/158.87 ![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))),
% 253.08/158.87 inference(skolemize,[status(sab)],[28])).
% 253.08/158.87 tff(30,plain,
% 253.08/158.87 (![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[29, 22])).
% 253.08/158.87 tff(31,plain,
% 253.08/158.87 (((~![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))) | ((~defined(c)) | product(multiplicative_identity, c, c))) <=> ((~![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))) | (~defined(c)) | product(multiplicative_identity, c, c))),
% 253.08/158.87 inference(rewrite,[status(thm)],[])).
% 253.08/158.87 tff(32,plain,
% 253.08/158.87 ((~![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))) | ((~defined(c)) | product(multiplicative_identity, c, c))),
% 253.08/158.87 inference(quant_inst,[status(thm)],[])).
% 253.08/158.87 tff(33,plain,
% 253.08/158.87 ((~![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))) | (~defined(c)) | product(multiplicative_identity, c, c)),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[32, 31])).
% 253.08/158.87 tff(34,plain,
% 253.08/158.87 (product(multiplicative_identity, c, c)),
% 253.08/158.87 inference(unit_resolution,[status(thm)],[33, 30, 20])).
% 253.08/158.87 tff(35,plain,
% 253.08/158.87 ((~sum(additive_identity, b, additive_identity)) <=> (~sum(additive_identity, b, additive_identity))),
% 253.08/158.87 inference(rewrite,[status(thm)],[])).
% 253.08/158.87 tff(36,axiom,(~sum(additive_identity, b, additive_identity)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_sum_7')).
% 253.08/158.87 tff(37,plain,
% 253.08/158.87 (~sum(additive_identity, b, additive_identity)),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[36, 35])).
% 253.08/158.87 tff(38,plain,
% 253.08/158.87 (defined(b) <=> defined(b)),
% 253.08/158.87 inference(rewrite,[status(thm)],[])).
% 253.08/158.87 tff(39,axiom,(defined(b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b_is_defined')).
% 253.08/158.87 tff(40,plain,
% 253.08/158.87 (defined(b)),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[39, 38])).
% 253.08/158.87 tff(41,plain,
% 253.08/158.87 (^[X: $i] : refl(((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity)) <=> ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity)))),
% 253.08/158.87 inference(bind,[status(th)],[])).
% 253.08/158.87 tff(42,plain,
% 253.08/158.87 (![X: $i] : ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity)) <=> ![X: $i] : ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))),
% 253.08/158.87 inference(quant_intro,[status(thm)],[41])).
% 253.08/158.87 tff(43,plain,
% 253.08/158.87 (![X: $i] : ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity)) <=> ![X: $i] : ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))),
% 253.08/158.87 inference(rewrite,[status(thm)],[])).
% 253.08/158.87 tff(44,plain,
% 253.08/158.87 (^[X: $i] : trans(monotonicity(rewrite((product(multiplicative_inverse(X), X, multiplicative_identity) | sum(additive_identity, X, additive_identity)) <=> (sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))), (((product(multiplicative_inverse(X), X, multiplicative_identity) | sum(additive_identity, X, additive_identity)) | (~defined(X))) <=> ((sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity)) | (~defined(X))))), rewrite(((sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity)) | (~defined(X))) <=> ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))), (((product(multiplicative_inverse(X), X, multiplicative_identity) | sum(additive_identity, X, additive_identity)) | (~defined(X))) <=> ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))))),
% 253.08/158.87 inference(bind,[status(th)],[])).
% 253.08/158.87 tff(45,plain,
% 253.08/158.87 (![X: $i] : ((product(multiplicative_inverse(X), X, multiplicative_identity) | sum(additive_identity, X, additive_identity)) | (~defined(X))) <=> ![X: $i] : ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))),
% 253.08/158.87 inference(quant_intro,[status(thm)],[44])).
% 253.08/158.87 tff(46,axiom,(![X: $i] : ((product(multiplicative_inverse(X), X, multiplicative_identity) | sum(additive_identity, X, additive_identity)) | (~defined(X)))), file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax','existence_of_inverse_multiplication')).
% 253.08/158.87 tff(47,plain,
% 253.08/158.87 (![X: $i] : ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[46, 45])).
% 253.08/158.87 tff(48,plain,
% 253.08/158.87 (![X: $i] : ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[47, 43])).
% 253.08/158.87 tff(49,plain,(
% 253.08/158.87 ![X: $i] : ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))),
% 253.08/158.87 inference(skolemize,[status(sab)],[48])).
% 253.08/158.87 tff(50,plain,
% 253.08/158.87 (![X: $i] : ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[49, 42])).
% 253.08/158.87 tff(51,plain,
% 253.08/158.87 (((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))) | ((~defined(b)) | sum(additive_identity, b, additive_identity) | product(multiplicative_inverse(b), b, multiplicative_identity))) <=> ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))) | (~defined(b)) | sum(additive_identity, b, additive_identity) | product(multiplicative_inverse(b), b, multiplicative_identity))),
% 253.08/158.87 inference(rewrite,[status(thm)],[])).
% 253.08/158.87 tff(52,plain,
% 253.08/158.87 ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))) | ((~defined(b)) | sum(additive_identity, b, additive_identity) | product(multiplicative_inverse(b), b, multiplicative_identity))),
% 253.08/158.87 inference(quant_inst,[status(thm)],[])).
% 253.08/158.87 tff(53,plain,
% 253.08/158.87 ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))) | (~defined(b)) | sum(additive_identity, b, additive_identity) | product(multiplicative_inverse(b), b, multiplicative_identity)),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[52, 51])).
% 253.08/158.87 tff(54,plain,
% 253.08/158.87 (product(multiplicative_inverse(b), b, multiplicative_identity)),
% 253.08/158.87 inference(unit_resolution,[status(thm)],[53, 50, 40, 37])).
% 253.08/158.87 tff(55,plain,
% 253.08/158.87 (product(b, c, t) <=> product(b, c, t)),
% 253.08/158.87 inference(rewrite,[status(thm)],[])).
% 253.08/158.87 tff(56,axiom,(product(b, c, t)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_11')).
% 253.08/158.87 tff(57,plain,
% 253.08/158.87 (product(b, c, t)),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[56, 55])).
% 253.08/158.87 tff(58,plain,
% 253.08/158.87 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl(((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W)) <=> ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W)))),
% 253.08/158.87 inference(bind,[status(th)],[])).
% 253.08/158.87 tff(59,plain,
% 253.08/158.87 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))),
% 253.08/158.87 inference(quant_intro,[status(thm)],[58])).
% 253.08/158.87 tff(60,plain,
% 253.08/158.87 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))),
% 253.08/158.87 inference(rewrite,[status(thm)],[])).
% 253.08/158.87 tff(61,plain,
% 253.08/158.87 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((product(X, V, W) | (~product(X, Y, U))) <=> ((~product(X, Y, U)) | product(X, V, W))), (((product(X, V, W) | (~product(X, Y, U))) | (~product(Y, Z, V))) <=> (((~product(X, Y, U)) | product(X, V, W)) | (~product(Y, Z, V))))), rewrite((((~product(X, Y, U)) | product(X, V, W)) | (~product(Y, Z, V))) <=> ((~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))), (((product(X, V, W) | (~product(X, Y, U))) | (~product(Y, Z, V))) <=> ((~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W)))), ((((product(X, V, W) | (~product(X, Y, U))) | (~product(Y, Z, V))) | (~product(U, Z, W))) <=> (((~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W)) | (~product(U, Z, W))))), rewrite((((~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W)) | (~product(U, Z, W))) <=> ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))), ((((product(X, V, W) | (~product(X, Y, U))) | (~product(Y, Z, V))) | (~product(U, Z, W))) <=> ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))))),
% 253.08/158.87 inference(bind,[status(th)],[])).
% 253.08/158.87 tff(62,plain,
% 253.08/158.87 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((product(X, V, W) | (~product(X, Y, U))) | (~product(Y, Z, V))) | (~product(U, Z, W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))),
% 253.08/158.87 inference(quant_intro,[status(thm)],[61])).
% 253.08/158.87 tff(63,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((product(X, V, W) | (~product(X, Y, U))) | (~product(Y, Z, V))) | (~product(U, Z, W)))), file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax','associativity_multiplication_1')).
% 253.08/158.87 tff(64,plain,
% 253.08/158.87 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[63, 62])).
% 253.08/158.87 tff(65,plain,
% 253.08/158.87 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[64, 60])).
% 253.08/158.87 tff(66,plain,(
% 253.08/158.87 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))),
% 253.08/158.87 inference(skolemize,[status(sab)],[65])).
% 253.08/158.87 tff(67,plain,
% 253.08/158.87 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[66, 59])).
% 253.08/158.87 tff(68,plain,
% 253.08/158.87 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | ((~product(b, c, t)) | (~product(multiplicative_inverse(b), b, multiplicative_identity)) | (~product(multiplicative_identity, c, c)) | product(multiplicative_inverse(b), t, c))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | (~product(b, c, t)) | (~product(multiplicative_inverse(b), b, multiplicative_identity)) | (~product(multiplicative_identity, c, c)) | product(multiplicative_inverse(b), t, c))),
% 253.08/158.87 inference(rewrite,[status(thm)],[])).
% 253.08/158.87 tff(69,plain,
% 253.08/158.87 (((~product(multiplicative_identity, c, c)) | (~product(b, c, t)) | (~product(multiplicative_inverse(b), b, multiplicative_identity)) | product(multiplicative_inverse(b), t, c)) <=> ((~product(b, c, t)) | (~product(multiplicative_inverse(b), b, multiplicative_identity)) | (~product(multiplicative_identity, c, c)) | product(multiplicative_inverse(b), t, c))),
% 253.08/158.87 inference(rewrite,[status(thm)],[])).
% 253.08/158.87 tff(70,plain,
% 253.08/158.87 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | ((~product(multiplicative_identity, c, c)) | (~product(b, c, t)) | (~product(multiplicative_inverse(b), b, multiplicative_identity)) | product(multiplicative_inverse(b), t, c))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | ((~product(b, c, t)) | (~product(multiplicative_inverse(b), b, multiplicative_identity)) | (~product(multiplicative_identity, c, c)) | product(multiplicative_inverse(b), t, c)))),
% 253.08/158.87 inference(monotonicity,[status(thm)],[69])).
% 253.08/158.87 tff(71,plain,
% 253.08/158.87 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | ((~product(multiplicative_identity, c, c)) | (~product(b, c, t)) | (~product(multiplicative_inverse(b), b, multiplicative_identity)) | product(multiplicative_inverse(b), t, c))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | (~product(b, c, t)) | (~product(multiplicative_inverse(b), b, multiplicative_identity)) | (~product(multiplicative_identity, c, c)) | product(multiplicative_inverse(b), t, c))),
% 253.08/158.87 inference(transitivity,[status(thm)],[70, 68])).
% 253.08/158.87 tff(72,plain,
% 253.08/158.87 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | ((~product(multiplicative_identity, c, c)) | (~product(b, c, t)) | (~product(multiplicative_inverse(b), b, multiplicative_identity)) | product(multiplicative_inverse(b), t, c))),
% 253.08/158.87 inference(quant_inst,[status(thm)],[])).
% 253.08/158.87 tff(73,plain,
% 253.08/158.87 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | (~product(b, c, t)) | (~product(multiplicative_inverse(b), b, multiplicative_identity)) | (~product(multiplicative_identity, c, c)) | product(multiplicative_inverse(b), t, c)),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[72, 71])).
% 253.08/158.87 tff(74,plain,
% 253.08/158.87 (product(multiplicative_inverse(b), t, c)),
% 253.08/158.87 inference(unit_resolution,[status(thm)],[73, 67, 57, 54, 34])).
% 253.08/158.87 tff(75,plain,
% 253.08/158.87 (^[Z: $i, Y: $i, X: $i] : refl(((~product(X, Y, Z)) | product(Y, X, Z)) <=> ((~product(X, Y, Z)) | product(Y, X, Z)))),
% 253.08/158.87 inference(bind,[status(th)],[])).
% 253.08/158.87 tff(76,plain,
% 253.08/158.87 (![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))),
% 253.08/158.87 inference(quant_intro,[status(thm)],[75])).
% 253.08/158.87 tff(77,plain,
% 253.08/158.87 (![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))),
% 253.08/158.87 inference(rewrite,[status(thm)],[])).
% 253.08/158.87 tff(78,plain,
% 253.08/158.87 (^[Z: $i, Y: $i, X: $i] : rewrite((product(Y, X, Z) | (~product(X, Y, Z))) <=> ((~product(X, Y, Z)) | product(Y, X, Z)))),
% 253.08/158.87 inference(bind,[status(th)],[])).
% 253.08/158.87 tff(79,plain,
% 253.08/158.87 (![Z: $i, Y: $i, X: $i] : (product(Y, X, Z) | (~product(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))),
% 253.08/158.87 inference(quant_intro,[status(thm)],[78])).
% 253.08/158.87 tff(80,axiom,(![Z: $i, Y: $i, X: $i] : (product(Y, X, Z) | (~product(X, Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax','commutativity_multiplication')).
% 253.08/158.87 tff(81,plain,
% 253.08/158.87 (![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[80, 79])).
% 253.08/158.87 tff(82,plain,
% 253.08/158.87 (![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[81, 77])).
% 253.08/158.87 tff(83,plain,(
% 253.08/158.87 ![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))),
% 253.08/158.87 inference(skolemize,[status(sab)],[82])).
% 253.08/158.87 tff(84,plain,
% 253.08/158.87 (![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[83, 76])).
% 253.08/158.87 tff(85,plain,
% 253.08/158.87 (((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | ((~product(multiplicative_inverse(b), t, c)) | product(t, multiplicative_inverse(b), c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | (~product(multiplicative_inverse(b), t, c)) | product(t, multiplicative_inverse(b), c))),
% 253.08/158.87 inference(rewrite,[status(thm)],[])).
% 253.08/158.87 tff(86,plain,
% 253.08/158.87 ((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | ((~product(multiplicative_inverse(b), t, c)) | product(t, multiplicative_inverse(b), c))),
% 253.08/158.87 inference(quant_inst,[status(thm)],[])).
% 253.08/158.87 tff(87,plain,
% 253.08/158.87 ((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | (~product(multiplicative_inverse(b), t, c)) | product(t, multiplicative_inverse(b), c)),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[86, 85])).
% 253.08/158.87 tff(88,plain,
% 253.08/158.87 (product(t, multiplicative_inverse(b), c)),
% 253.08/158.87 inference(unit_resolution,[status(thm)],[87, 84, 74])).
% 253.08/158.87 tff(89,plain,
% 253.08/158.87 (product(a, c, s) <=> product(a, c, s)),
% 253.08/158.87 inference(rewrite,[status(thm)],[])).
% 253.08/158.87 tff(90,axiom,(product(a, c, s)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_10')).
% 253.08/158.87 tff(91,plain,
% 253.08/158.87 (product(a, c, s)),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[90, 89])).
% 253.08/158.87 tff(92,plain,
% 253.08/158.87 (((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | ((~product(a, c, s)) | product(c, a, s))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | (~product(a, c, s)) | product(c, a, s))),
% 253.08/158.87 inference(rewrite,[status(thm)],[])).
% 253.08/158.87 tff(93,plain,
% 253.08/158.87 ((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | ((~product(a, c, s)) | product(c, a, s))),
% 253.08/158.87 inference(quant_inst,[status(thm)],[])).
% 253.08/158.87 tff(94,plain,
% 253.08/158.87 ((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | (~product(a, c, s)) | product(c, a, s)),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[93, 92])).
% 253.08/158.87 tff(95,plain,
% 253.08/158.87 (product(c, a, s)),
% 253.08/158.87 inference(unit_resolution,[status(thm)],[94, 84, 91])).
% 253.08/158.87 tff(96,plain,
% 253.08/158.87 (product(a, multiplicative_inverse(b), u) <=> product(a, multiplicative_inverse(b), u)),
% 253.08/158.87 inference(rewrite,[status(thm)],[])).
% 253.08/158.87 tff(97,axiom,(product(a, multiplicative_inverse(b), u)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_9')).
% 253.08/158.87 tff(98,plain,
% 253.08/158.87 (product(a, multiplicative_inverse(b), u)),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[97, 96])).
% 253.08/158.87 tff(99,plain,
% 253.08/158.87 (((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | ((~product(a, multiplicative_inverse(b), u)) | product(multiplicative_inverse(b), a, u))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | (~product(a, multiplicative_inverse(b), u)) | product(multiplicative_inverse(b), a, u))),
% 253.08/158.87 inference(rewrite,[status(thm)],[])).
% 253.08/158.87 tff(100,plain,
% 253.08/158.87 ((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | ((~product(a, multiplicative_inverse(b), u)) | product(multiplicative_inverse(b), a, u))),
% 253.08/158.87 inference(quant_inst,[status(thm)],[])).
% 253.08/158.87 tff(101,plain,
% 253.08/158.87 ((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | (~product(a, multiplicative_inverse(b), u)) | product(multiplicative_inverse(b), a, u)),
% 253.08/158.87 inference(modus_ponens,[status(thm)],[100, 99])).
% 253.08/158.87 tff(102,plain,
% 253.08/158.87 (product(multiplicative_inverse(b), a, u)),
% 253.08/158.87 inference(unit_resolution,[status(thm)],[101, 84, 98])).
% 253.08/158.87 tff(103,plain,
% 253.08/158.87 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | ((~product(c, a, s)) | (~product(multiplicative_inverse(b), a, u)) | (~product(t, multiplicative_inverse(b), c)) | product(t, u, s))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | (~product(c, a, s)) | (~product(multiplicative_inverse(b), a, u)) | (~product(t, multiplicative_inverse(b), c)) | product(t, u, s))),
% 253.08/158.88 inference(rewrite,[status(thm)],[])).
% 253.08/158.88 tff(104,plain,
% 253.08/158.88 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | ((~product(c, a, s)) | (~product(multiplicative_inverse(b), a, u)) | (~product(t, multiplicative_inverse(b), c)) | product(t, u, s))),
% 253.08/158.88 inference(quant_inst,[status(thm)],[])).
% 253.08/158.88 tff(105,plain,
% 253.08/158.88 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | (~product(c, a, s)) | (~product(multiplicative_inverse(b), a, u)) | (~product(t, multiplicative_inverse(b), c)) | product(t, u, s)),
% 253.08/158.88 inference(modus_ponens,[status(thm)],[104, 103])).
% 253.08/158.88 tff(106,plain,
% 253.08/158.88 (product(t, u, s)),
% 253.08/158.88 inference(unit_resolution,[status(thm)],[105, 67, 102, 95, 88])).
% 253.08/158.88 tff(107,plain,
% 253.08/158.88 ((~product(s, multiplicative_inverse(t), u)) <=> (~product(s, multiplicative_inverse(t), u))),
% 253.08/158.88 inference(rewrite,[status(thm)],[])).
% 253.08/158.88 tff(108,axiom,(~product(s, multiplicative_inverse(t), u)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_product_12')).
% 253.08/158.88 tff(109,plain,
% 253.08/158.88 (~product(s, multiplicative_inverse(t), u)),
% 253.08/158.88 inference(modus_ponens,[status(thm)],[108, 107])).
% 253.08/158.88 tff(110,plain,
% 253.08/158.88 (((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | ((~product(multiplicative_inverse(t), s, u)) | product(s, multiplicative_inverse(t), u))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | (~product(multiplicative_inverse(t), s, u)) | product(s, multiplicative_inverse(t), u))),
% 253.08/158.88 inference(rewrite,[status(thm)],[])).
% 253.08/158.88 tff(111,plain,
% 253.08/158.88 ((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | ((~product(multiplicative_inverse(t), s, u)) | product(s, multiplicative_inverse(t), u))),
% 253.13/158.88 inference(quant_inst,[status(thm)],[])).
% 253.13/158.88 tff(112,plain,
% 253.13/158.88 ((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | (~product(multiplicative_inverse(t), s, u)) | product(s, multiplicative_inverse(t), u)),
% 253.13/158.88 inference(modus_ponens,[status(thm)],[111, 110])).
% 253.13/158.88 tff(113,plain,
% 253.13/158.88 (~product(multiplicative_inverse(t), s, u)),
% 253.13/158.88 inference(unit_resolution,[status(thm)],[112, 84, 109])).
% 253.13/158.88 tff(114,assumption,(product(multiplicative_inverse(t), t, multiplicative_identity)), introduced(assumption)).
% 253.13/158.88 tff(115,plain,
% 253.13/158.88 (defined(u) <=> defined(u)),
% 253.13/158.88 inference(rewrite,[status(thm)],[])).
% 253.13/158.88 tff(116,axiom,(defined(u)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','u_is_defined')).
% 253.13/158.88 tff(117,plain,
% 253.13/158.88 (defined(u)),
% 253.13/158.88 inference(modus_ponens,[status(thm)],[116, 115])).
% 253.13/158.88 tff(118,plain,
% 253.13/158.88 (((~![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))) | ((~defined(u)) | product(multiplicative_identity, u, u))) <=> ((~![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))) | (~defined(u)) | product(multiplicative_identity, u, u))),
% 253.13/158.88 inference(rewrite,[status(thm)],[])).
% 253.13/158.88 tff(119,plain,
% 253.13/158.88 ((~![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))) | ((~defined(u)) | product(multiplicative_identity, u, u))),
% 253.13/158.88 inference(quant_inst,[status(thm)],[])).
% 253.13/158.88 tff(120,plain,
% 253.13/158.88 ((~![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))) | (~defined(u)) | product(multiplicative_identity, u, u)),
% 253.13/158.88 inference(modus_ponens,[status(thm)],[119, 118])).
% 253.13/158.88 tff(121,plain,
% 253.13/158.88 (product(multiplicative_identity, u, u)),
% 253.13/158.88 inference(unit_resolution,[status(thm)],[120, 30, 117])).
% 253.13/158.88 tff(122,plain,
% 253.13/158.88 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | ((~product(multiplicative_identity, u, u)) | (~product(t, u, s)) | (~product(multiplicative_inverse(t), t, multiplicative_identity)) | product(multiplicative_inverse(t), s, u))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | (~product(multiplicative_identity, u, u)) | (~product(t, u, s)) | (~product(multiplicative_inverse(t), t, multiplicative_identity)) | product(multiplicative_inverse(t), s, u))),
% 253.13/158.88 inference(rewrite,[status(thm)],[])).
% 253.13/158.88 tff(123,plain,
% 253.13/158.88 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | ((~product(multiplicative_identity, u, u)) | (~product(t, u, s)) | (~product(multiplicative_inverse(t), t, multiplicative_identity)) | product(multiplicative_inverse(t), s, u))),
% 253.13/158.88 inference(quant_inst,[status(thm)],[])).
% 253.13/158.88 tff(124,plain,
% 253.13/158.88 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | (~product(multiplicative_identity, u, u)) | (~product(t, u, s)) | (~product(multiplicative_inverse(t), t, multiplicative_identity)) | product(multiplicative_inverse(t), s, u)),
% 253.13/158.88 inference(modus_ponens,[status(thm)],[123, 122])).
% 253.13/158.88 tff(125,plain,
% 253.13/158.88 ($false),
% 253.13/158.88 inference(unit_resolution,[status(thm)],[124, 67, 121, 114, 113, 106])).
% 253.13/158.88 tff(126,plain,(~product(multiplicative_inverse(t), t, multiplicative_identity)), inference(lemma,lemma(discharge,[]))).
% 253.13/158.88 tff(127,plain,
% 253.13/158.88 (((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))) | ((~defined(t)) | sum(additive_identity, t, additive_identity) | product(multiplicative_inverse(t), t, multiplicative_identity))) <=> ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))) | (~defined(t)) | sum(additive_identity, t, additive_identity) | product(multiplicative_inverse(t), t, multiplicative_identity))),
% 253.13/158.88 inference(rewrite,[status(thm)],[])).
% 253.13/158.88 tff(128,plain,
% 253.13/158.88 ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))) | ((~defined(t)) | sum(additive_identity, t, additive_identity) | product(multiplicative_inverse(t), t, multiplicative_identity))),
% 253.13/158.88 inference(quant_inst,[status(thm)],[])).
% 253.13/158.88 tff(129,plain,
% 253.13/158.88 ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))) | (~defined(t)) | sum(additive_identity, t, additive_identity) | product(multiplicative_inverse(t), t, multiplicative_identity)),
% 253.13/158.88 inference(modus_ponens,[status(thm)],[128, 127])).
% 253.13/158.88 tff(130,plain,
% 253.13/158.88 (sum(additive_identity, t, additive_identity) | product(multiplicative_inverse(t), t, multiplicative_identity)),
% 253.13/158.88 inference(unit_resolution,[status(thm)],[129, 50, 3])).
% 253.13/158.88 tff(131,plain,
% 253.13/158.88 (sum(additive_identity, t, additive_identity)),
% 253.13/158.88 inference(unit_resolution,[status(thm)],[130, 126])).
% 253.13/158.88 tff(132,plain,
% 253.13/158.88 (defined(additive_identity) <=> defined(additive_identity)),
% 253.13/158.88 inference(rewrite,[status(thm)],[])).
% 253.13/158.88 tff(133,axiom,(defined(additive_identity)), file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax','well_definedness_of_additive_identity')).
% 253.13/158.88 tff(134,plain,
% 253.13/158.88 (defined(additive_identity)),
% 253.13/158.88 inference(modus_ponens,[status(thm)],[133, 132])).
% 253.13/158.88 tff(135,plain,
% 253.13/158.88 (((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))) | ((~defined(additive_identity)) | sum(additive_identity, additive_identity, additive_identity))) <=> ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))) | (~defined(additive_identity)) | sum(additive_identity, additive_identity, additive_identity))),
% 253.13/158.88 inference(rewrite,[status(thm)],[])).
% 253.13/158.88 tff(136,plain,
% 253.13/158.88 ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))) | ((~defined(additive_identity)) | sum(additive_identity, additive_identity, additive_identity))),
% 253.13/158.88 inference(quant_inst,[status(thm)],[])).
% 253.13/158.88 tff(137,plain,
% 253.13/158.88 ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))) | (~defined(additive_identity)) | sum(additive_identity, additive_identity, additive_identity)),
% 253.13/158.88 inference(modus_ponens,[status(thm)],[136, 135])).
% 253.13/158.88 tff(138,plain,
% 253.13/158.88 (sum(additive_identity, additive_identity, additive_identity)),
% 253.13/158.88 inference(unit_resolution,[status(thm)],[137, 13, 134])).
% 253.13/158.88 tff(139,plain,
% 253.13/158.88 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl(((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W)) <=> ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W)))),
% 253.13/158.88 inference(bind,[status(th)],[])).
% 253.13/158.88 tff(140,plain,
% 253.13/158.88 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))),
% 253.13/158.88 inference(quant_intro,[status(thm)],[139])).
% 253.13/158.88 tff(141,plain,
% 253.13/158.88 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))),
% 253.13/158.88 inference(rewrite,[status(thm)],[])).
% 253.13/158.88 tff(142,plain,
% 253.13/158.88 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((sum(X, V, W) | (~sum(X, Y, U))) <=> ((~sum(X, Y, U)) | sum(X, V, W))), (((sum(X, V, W) | (~sum(X, Y, U))) | (~sum(Y, Z, V))) <=> (((~sum(X, Y, U)) | sum(X, V, W)) | (~sum(Y, Z, V))))), rewrite((((~sum(X, Y, U)) | sum(X, V, W)) | (~sum(Y, Z, V))) <=> ((~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))), (((sum(X, V, W) | (~sum(X, Y, U))) | (~sum(Y, Z, V))) <=> ((~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W)))), ((((sum(X, V, W) | (~sum(X, Y, U))) | (~sum(Y, Z, V))) | (~sum(U, Z, W))) <=> (((~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W)) | (~sum(U, Z, W))))), rewrite((((~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W)) | (~sum(U, Z, W))) <=> ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))), ((((sum(X, V, W) | (~sum(X, Y, U))) | (~sum(Y, Z, V))) | (~sum(U, Z, W))) <=> ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))))),
% 253.13/158.88 inference(bind,[status(th)],[])).
% 253.13/158.88 tff(143,plain,
% 253.13/158.88 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((sum(X, V, W) | (~sum(X, Y, U))) | (~sum(Y, Z, V))) | (~sum(U, Z, W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))),
% 253.13/158.88 inference(quant_intro,[status(thm)],[142])).
% 253.13/158.88 tff(144,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((sum(X, V, W) | (~sum(X, Y, U))) | (~sum(Y, Z, V))) | (~sum(U, Z, W)))), file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax','associativity_addition_1')).
% 253.13/158.88 tff(145,plain,
% 253.13/158.88 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))),
% 253.13/158.88 inference(modus_ponens,[status(thm)],[144, 143])).
% 253.13/158.88 tff(146,plain,
% 253.13/158.88 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))),
% 253.13/158.88 inference(modus_ponens,[status(thm)],[145, 141])).
% 253.13/158.88 tff(147,plain,(
% 253.13/158.88 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))),
% 253.13/158.88 inference(skolemize,[status(sab)],[146])).
% 253.13/158.88 tff(148,plain,
% 253.13/158.88 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))),
% 253.13/158.88 inference(modus_ponens,[status(thm)],[147, 140])).
% 253.13/158.88 tff(149,plain,
% 253.13/158.88 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | ((~sum(additive_identity, additive_identity, additive_identity)) | (~sum(additive_identity, t, t)) | (~sum(additive_identity, t, additive_identity)) | sum(additive_identity, additive_identity, t))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | (~sum(additive_identity, additive_identity, additive_identity)) | (~sum(additive_identity, t, t)) | (~sum(additive_identity, t, additive_identity)) | sum(additive_identity, additive_identity, t))),
% 253.13/158.88 inference(rewrite,[status(thm)],[])).
% 253.13/158.88 tff(150,plain,
% 253.13/158.88 (((~sum(additive_identity, t, t)) | (~sum(additive_identity, t, additive_identity)) | (~sum(additive_identity, additive_identity, additive_identity)) | sum(additive_identity, additive_identity, t)) <=> ((~sum(additive_identity, additive_identity, additive_identity)) | (~sum(additive_identity, t, t)) | (~sum(additive_identity, t, additive_identity)) | sum(additive_identity, additive_identity, t))),
% 253.13/158.88 inference(rewrite,[status(thm)],[])).
% 253.13/158.88 tff(151,plain,
% 253.13/158.88 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | ((~sum(additive_identity, t, t)) | (~sum(additive_identity, t, additive_identity)) | (~sum(additive_identity, additive_identity, additive_identity)) | sum(additive_identity, additive_identity, t))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | ((~sum(additive_identity, additive_identity, additive_identity)) | (~sum(additive_identity, t, t)) | (~sum(additive_identity, t, additive_identity)) | sum(additive_identity, additive_identity, t)))),
% 253.13/158.88 inference(monotonicity,[status(thm)],[150])).
% 253.13/158.88 tff(152,plain,
% 253.13/158.88 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | ((~sum(additive_identity, t, t)) | (~sum(additive_identity, t, additive_identity)) | (~sum(additive_identity, additive_identity, additive_identity)) | sum(additive_identity, additive_identity, t))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | (~sum(additive_identity, additive_identity, additive_identity)) | (~sum(additive_identity, t, t)) | (~sum(additive_identity, t, additive_identity)) | sum(additive_identity, additive_identity, t))),
% 253.13/158.88 inference(transitivity,[status(thm)],[151, 149])).
% 253.13/158.88 tff(153,plain,
% 253.13/158.88 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | ((~sum(additive_identity, t, t)) | (~sum(additive_identity, t, additive_identity)) | (~sum(additive_identity, additive_identity, additive_identity)) | sum(additive_identity, additive_identity, t))),
% 253.13/158.88 inference(quant_inst,[status(thm)],[])).
% 253.13/158.88 tff(154,plain,
% 253.13/158.88 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | (~sum(additive_identity, additive_identity, additive_identity)) | (~sum(additive_identity, t, t)) | (~sum(additive_identity, t, additive_identity)) | sum(additive_identity, additive_identity, t)),
% 253.13/158.88 inference(modus_ponens,[status(thm)],[153, 152])).
% 253.13/158.88 tff(155,plain,
% 253.13/158.88 (sum(additive_identity, additive_identity, t)),
% 253.13/158.88 inference(unit_resolution,[status(thm)],[154, 148, 138, 131, 17])).
% 253.13/158.88 tff(156,plain,
% 253.13/158.88 (defined(a) <=> defined(a)),
% 253.13/158.88 inference(rewrite,[status(thm)],[])).
% 253.13/158.88 tff(157,axiom,(defined(a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_is_defined')).
% 253.13/158.88 tff(158,plain,
% 253.13/158.88 (defined(a)),
% 253.13/158.88 inference(modus_ponens,[status(thm)],[157, 156])).
% 253.13/158.88 tff(159,plain,
% 253.13/158.88 (((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))) | ((~defined(a)) | sum(additive_identity, a, a))) <=> ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))) | (~defined(a)) | sum(additive_identity, a, a))),
% 253.13/158.88 inference(rewrite,[status(thm)],[])).
% 253.13/158.88 tff(160,plain,
% 253.13/158.88 ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))) | ((~defined(a)) | sum(additive_identity, a, a))),
% 253.13/158.88 inference(quant_inst,[status(thm)],[])).
% 253.13/158.88 tff(161,plain,
% 253.13/158.88 ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))) | (~defined(a)) | sum(additive_identity, a, a)),
% 253.13/158.88 inference(modus_ponens,[status(thm)],[160, 159])).
% 253.13/158.88 tff(162,plain,
% 253.13/158.88 (sum(additive_identity, a, a)),
% 253.13/158.88 inference(unit_resolution,[status(thm)],[161, 13, 158])).
% 253.13/158.88 tff(163,plain,
% 253.13/158.88 (^[Z: $i, Y: $i, X: $i] : refl(((~sum(X, Y, Z)) | sum(Y, X, Z)) <=> ((~sum(X, Y, Z)) | sum(Y, X, Z)))),
% 253.13/158.88 inference(bind,[status(th)],[])).
% 253.13/158.88 tff(164,plain,
% 253.13/158.88 (![Z: $i, Y: $i, X: $i] : ((~sum(X, Y, Z)) | sum(Y, X, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~sum(X, Y, Z)) | sum(Y, X, Z))),
% 253.13/158.88 inference(quant_intro,[status(thm)],[163])).
% 253.13/158.88 tff(165,plain,
% 253.13/158.88 (![Z: $i, Y: $i, X: $i] : ((~sum(X, Y, Z)) | sum(Y, X, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~sum(X, Y, Z)) | sum(Y, X, Z))),
% 253.13/158.88 inference(rewrite,[status(thm)],[])).
% 253.13/158.88 tff(166,plain,
% 253.13/158.88 (^[Z: $i, Y: $i, X: $i] : rewrite((sum(Y, X, Z) | (~sum(X, Y, Z))) <=> ((~sum(X, Y, Z)) | sum(Y, X, Z)))),
% 253.13/158.88 inference(bind,[status(th)],[])).
% 253.13/158.88 tff(167,plain,
% 253.13/158.88 (![Z: $i, Y: $i, X: $i] : (sum(Y, X, Z) | (~sum(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~sum(X, Y, Z)) | sum(Y, X, Z))),
% 253.13/158.88 inference(quant_intro,[status(thm)],[166])).
% 253.13/158.88 tff(168,axiom,(![Z: $i, Y: $i, X: $i] : (sum(Y, X, Z) | (~sum(X, Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax','commutativity_addition')).
% 253.13/158.88 tff(169,plain,
% 253.13/158.88 (![Z: $i, Y: $i, X: $i] : ((~sum(X, Y, Z)) | sum(Y, X, Z))),
% 253.13/158.88 inference(modus_ponens,[status(thm)],[168, 167])).
% 253.13/158.88 tff(170,plain,
% 253.13/158.88 (![Z: $i, Y: $i, X: $i] : ((~sum(X, Y, Z)) | sum(Y, X, Z))),
% 253.13/158.88 inference(modus_ponens,[status(thm)],[169, 165])).
% 253.13/158.88 tff(171,plain,(
% 253.13/158.88 ![Z: $i, Y: $i, X: $i] : ((~sum(X, Y, Z)) | sum(Y, X, Z))),
% 253.13/158.88 inference(skolemize,[status(sab)],[170])).
% 253.13/158.88 tff(172,plain,
% 253.13/158.88 (![Z: $i, Y: $i, X: $i] : ((~sum(X, Y, Z)) | sum(Y, X, Z))),
% 253.13/158.88 inference(modus_ponens,[status(thm)],[171, 164])).
% 253.13/158.88 tff(173,plain,
% 253.13/158.88 (((~![Z: $i, Y: $i, X: $i] : ((~sum(X, Y, Z)) | sum(Y, X, Z))) | ((~sum(additive_identity, a, a)) | sum(a, additive_identity, a))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~sum(X, Y, Z)) | sum(Y, X, Z))) | (~sum(additive_identity, a, a)) | sum(a, additive_identity, a))),
% 253.13/158.88 inference(rewrite,[status(thm)],[])).
% 253.13/158.88 tff(174,plain,
% 253.13/158.88 ((~![Z: $i, Y: $i, X: $i] : ((~sum(X, Y, Z)) | sum(Y, X, Z))) | ((~sum(additive_identity, a, a)) | sum(a, additive_identity, a))),
% 253.13/158.88 inference(quant_inst,[status(thm)],[])).
% 253.13/158.88 tff(175,plain,
% 253.13/158.88 ((~![Z: $i, Y: $i, X: $i] : ((~sum(X, Y, Z)) | sum(Y, X, Z))) | (~sum(additive_identity, a, a)) | sum(a, additive_identity, a)),
% 253.13/158.88 inference(modus_ponens,[status(thm)],[174, 173])).
% 253.13/158.88 tff(176,plain,
% 253.13/158.88 (sum(a, additive_identity, a)),
% 253.13/158.88 inference(unit_resolution,[status(thm)],[175, 172, 162])).
% 253.13/158.88 tff(177,plain,
% 253.13/158.88 (^[X: $i] : refl(((~defined(X)) | sum(additive_inverse(X), X, additive_identity)) <=> ((~defined(X)) | sum(additive_inverse(X), X, additive_identity)))),
% 253.13/158.88 inference(bind,[status(th)],[])).
% 253.13/158.88 tff(178,plain,
% 253.13/158.88 (![X: $i] : ((~defined(X)) | sum(additive_inverse(X), X, additive_identity)) <=> ![X: $i] : ((~defined(X)) | sum(additive_inverse(X), X, additive_identity))),
% 253.13/158.88 inference(quant_intro,[status(thm)],[177])).
% 253.13/158.88 tff(179,plain,
% 253.13/158.88 (![X: $i] : ((~defined(X)) | sum(additive_inverse(X), X, additive_identity)) <=> ![X: $i] : ((~defined(X)) | sum(additive_inverse(X), X, additive_identity))),
% 253.13/158.88 inference(rewrite,[status(thm)],[])).
% 253.13/158.88 tff(180,plain,
% 253.13/158.88 (^[X: $i] : rewrite((sum(additive_inverse(X), X, additive_identity) | (~defined(X))) <=> ((~defined(X)) | sum(additive_inverse(X), X, additive_identity)))),
% 253.13/158.88 inference(bind,[status(th)],[])).
% 253.13/158.88 tff(181,plain,
% 253.13/158.88 (![X: $i] : (sum(additive_inverse(X), X, additive_identity) | (~defined(X))) <=> ![X: $i] : ((~defined(X)) | sum(additive_inverse(X), X, additive_identity))),
% 253.13/158.88 inference(quant_intro,[status(thm)],[180])).
% 253.13/158.88 tff(182,axiom,(![X: $i] : (sum(additive_inverse(X), X, additive_identity) | (~defined(X)))), file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax','existence_of_inverse_addition')).
% 253.13/158.88 tff(183,plain,
% 253.13/158.88 (![X: $i] : ((~defined(X)) | sum(additive_inverse(X), X, additive_identity))),
% 253.13/158.88 inference(modus_ponens,[status(thm)],[182, 181])).
% 253.13/158.88 tff(184,plain,
% 253.13/158.88 (![X: $i] : ((~defined(X)) | sum(additive_inverse(X), X, additive_identity))),
% 253.13/158.88 inference(modus_ponens,[status(thm)],[183, 179])).
% 253.13/158.88 tff(185,plain,(
% 253.13/158.88 ![X: $i] : ((~defined(X)) | sum(additive_inverse(X), X, additive_identity))),
% 253.13/158.88 inference(skolemize,[status(sab)],[184])).
% 253.13/158.88 tff(186,plain,
% 253.13/158.88 (![X: $i] : ((~defined(X)) | sum(additive_inverse(X), X, additive_identity))),
% 253.13/158.88 inference(modus_ponens,[status(thm)],[185, 178])).
% 253.13/158.89 tff(187,plain,
% 253.13/158.89 (((~![X: $i] : ((~defined(X)) | sum(additive_inverse(X), X, additive_identity))) | ((~defined(a)) | sum(additive_inverse(a), a, additive_identity))) <=> ((~![X: $i] : ((~defined(X)) | sum(additive_inverse(X), X, additive_identity))) | (~defined(a)) | sum(additive_inverse(a), a, additive_identity))),
% 253.13/158.89 inference(rewrite,[status(thm)],[])).
% 253.13/158.89 tff(188,plain,
% 253.13/158.89 ((~![X: $i] : ((~defined(X)) | sum(additive_inverse(X), X, additive_identity))) | ((~defined(a)) | sum(additive_inverse(a), a, additive_identity))),
% 253.13/158.89 inference(quant_inst,[status(thm)],[])).
% 253.13/158.89 tff(189,plain,
% 253.13/158.89 ((~![X: $i] : ((~defined(X)) | sum(additive_inverse(X), X, additive_identity))) | (~defined(a)) | sum(additive_inverse(a), a, additive_identity)),
% 253.13/158.89 inference(modus_ponens,[status(thm)],[188, 187])).
% 253.13/158.89 tff(190,plain,
% 253.13/158.89 (sum(additive_inverse(a), a, additive_identity)),
% 253.13/158.89 inference(unit_resolution,[status(thm)],[189, 186, 158])).
% 253.13/158.89 tff(191,plain,
% 253.13/158.89 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | ((~sum(additive_inverse(a), a, additive_identity)) | (~sum(a, additive_identity, a)) | (~sum(additive_identity, additive_identity, t)) | sum(additive_inverse(a), a, t))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | (~sum(additive_inverse(a), a, additive_identity)) | (~sum(a, additive_identity, a)) | (~sum(additive_identity, additive_identity, t)) | sum(additive_inverse(a), a, t))),
% 253.13/158.89 inference(rewrite,[status(thm)],[])).
% 253.13/158.89 tff(192,plain,
% 253.13/158.89 (((~sum(additive_identity, additive_identity, t)) | (~sum(a, additive_identity, a)) | (~sum(additive_inverse(a), a, additive_identity)) | sum(additive_inverse(a), a, t)) <=> ((~sum(additive_inverse(a), a, additive_identity)) | (~sum(a, additive_identity, a)) | (~sum(additive_identity, additive_identity, t)) | sum(additive_inverse(a), a, t))),
% 253.13/158.89 inference(rewrite,[status(thm)],[])).
% 253.13/158.89 tff(193,plain,
% 253.13/158.89 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | ((~sum(additive_identity, additive_identity, t)) | (~sum(a, additive_identity, a)) | (~sum(additive_inverse(a), a, additive_identity)) | sum(additive_inverse(a), a, t))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | ((~sum(additive_inverse(a), a, additive_identity)) | (~sum(a, additive_identity, a)) | (~sum(additive_identity, additive_identity, t)) | sum(additive_inverse(a), a, t)))),
% 253.13/158.89 inference(monotonicity,[status(thm)],[192])).
% 253.13/158.89 tff(194,plain,
% 253.13/158.89 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | ((~sum(additive_identity, additive_identity, t)) | (~sum(a, additive_identity, a)) | (~sum(additive_inverse(a), a, additive_identity)) | sum(additive_inverse(a), a, t))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | (~sum(additive_inverse(a), a, additive_identity)) | (~sum(a, additive_identity, a)) | (~sum(additive_identity, additive_identity, t)) | sum(additive_inverse(a), a, t))),
% 253.13/158.89 inference(transitivity,[status(thm)],[193, 191])).
% 253.13/158.89 tff(195,plain,
% 253.13/158.89 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | ((~sum(additive_identity, additive_identity, t)) | (~sum(a, additive_identity, a)) | (~sum(additive_inverse(a), a, additive_identity)) | sum(additive_inverse(a), a, t))),
% 253.13/158.89 inference(quant_inst,[status(thm)],[])).
% 253.13/158.89 tff(196,plain,
% 253.13/158.89 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | (~sum(additive_inverse(a), a, additive_identity)) | (~sum(a, additive_identity, a)) | (~sum(additive_identity, additive_identity, t)) | sum(additive_inverse(a), a, t)),
% 253.13/158.89 inference(modus_ponens,[status(thm)],[195, 194])).
% 253.13/158.89 tff(197,plain,
% 253.13/158.89 (sum(additive_inverse(a), a, t)),
% 253.13/158.89 inference(unit_resolution,[status(thm)],[196, 148, 190, 176, 155])).
% 253.13/158.89 tff(198,plain,
% 253.13/158.89 (((~![Z: $i, Y: $i, X: $i] : ((~sum(X, Y, Z)) | sum(Y, X, Z))) | ((~sum(additive_identity, t, additive_identity)) | sum(t, additive_identity, additive_identity))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~sum(X, Y, Z)) | sum(Y, X, Z))) | (~sum(additive_identity, t, additive_identity)) | sum(t, additive_identity, additive_identity))),
% 253.13/158.89 inference(rewrite,[status(thm)],[])).
% 253.13/158.89 tff(199,plain,
% 253.13/158.89 ((~![Z: $i, Y: $i, X: $i] : ((~sum(X, Y, Z)) | sum(Y, X, Z))) | ((~sum(additive_identity, t, additive_identity)) | sum(t, additive_identity, additive_identity))),
% 253.13/158.89 inference(quant_inst,[status(thm)],[])).
% 253.13/158.89 tff(200,plain,
% 253.13/158.89 ((~![Z: $i, Y: $i, X: $i] : ((~sum(X, Y, Z)) | sum(Y, X, Z))) | (~sum(additive_identity, t, additive_identity)) | sum(t, additive_identity, additive_identity)),
% 253.13/158.89 inference(modus_ponens,[status(thm)],[199, 198])).
% 253.13/158.89 tff(201,plain,
% 253.13/158.89 (sum(t, additive_identity, additive_identity)),
% 253.13/158.89 inference(unit_resolution,[status(thm)],[200, 172, 131])).
% 253.13/158.89 tff(202,plain,
% 253.13/158.89 (((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))) | ((~defined(b)) | sum(additive_identity, b, b))) <=> ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))) | (~defined(b)) | sum(additive_identity, b, b))),
% 253.13/158.89 inference(rewrite,[status(thm)],[])).
% 253.13/158.89 tff(203,plain,
% 253.13/158.89 ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))) | ((~defined(b)) | sum(additive_identity, b, b))),
% 253.13/158.89 inference(quant_inst,[status(thm)],[])).
% 253.13/158.89 tff(204,plain,
% 253.13/158.89 ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))) | (~defined(b)) | sum(additive_identity, b, b)),
% 253.13/158.89 inference(modus_ponens,[status(thm)],[203, 202])).
% 253.13/158.89 tff(205,plain,
% 253.13/158.89 (sum(additive_identity, b, b)),
% 253.13/158.89 inference(unit_resolution,[status(thm)],[204, 13, 40])).
% 253.13/158.89 tff(206,plain,
% 253.13/158.89 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl((sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W))) <=> (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W))))),
% 253.13/158.89 inference(bind,[status(th)],[])).
% 253.13/158.89 tff(207,plain,
% 253.13/158.89 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W)))),
% 253.13/158.89 inference(quant_intro,[status(thm)],[206])).
% 253.13/158.89 tff(208,plain,
% 253.13/158.89 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W)))),
% 253.13/158.89 inference(rewrite,[status(thm)],[])).
% 253.13/158.89 tff(209,plain,
% 253.13/158.89 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((sum(U, Z, W) | (~sum(X, Y, U))) <=> (sum(U, Z, W) | (~sum(X, Y, U)))), (((sum(U, Z, W) | (~sum(X, Y, U))) | (~sum(Y, Z, V))) <=> ((sum(U, Z, W) | (~sum(X, Y, U))) | (~sum(Y, Z, V))))), rewrite(((sum(U, Z, W) | (~sum(X, Y, U))) | (~sum(Y, Z, V))) <=> (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)))), (((sum(U, Z, W) | (~sum(X, Y, U))) | (~sum(Y, Z, V))) <=> (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U))))), ((((sum(U, Z, W) | (~sum(X, Y, U))) | (~sum(Y, Z, V))) | (~sum(X, V, W))) <=> ((sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U))) | (~sum(X, V, W))))), rewrite(((sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U))) | (~sum(X, V, W))) <=> (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W)))), ((((sum(U, Z, W) | (~sum(X, Y, U))) | (~sum(Y, Z, V))) | (~sum(X, V, W))) <=> (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W)))))),
% 253.13/158.89 inference(bind,[status(th)],[])).
% 253.13/158.89 tff(210,plain,
% 253.13/158.89 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((sum(U, Z, W) | (~sum(X, Y, U))) | (~sum(Y, Z, V))) | (~sum(X, V, W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W)))),
% 253.13/158.89 inference(quant_intro,[status(thm)],[209])).
% 253.13/158.89 tff(211,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((sum(U, Z, W) | (~sum(X, Y, U))) | (~sum(Y, Z, V))) | (~sum(X, V, W)))), file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax','associativity_addition_2')).
% 253.13/158.89 tff(212,plain,
% 253.13/158.89 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W)))),
% 253.13/158.89 inference(modus_ponens,[status(thm)],[211, 210])).
% 253.13/158.89 tff(213,plain,
% 253.13/158.89 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W)))),
% 253.13/158.89 inference(modus_ponens,[status(thm)],[212, 208])).
% 253.13/158.89 tff(214,plain,(
% 253.13/158.89 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W)))),
% 253.13/158.89 inference(skolemize,[status(sab)],[213])).
% 253.13/158.89 tff(215,plain,
% 253.13/158.89 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W)))),
% 253.13/158.89 inference(modus_ponens,[status(thm)],[214, 207])).
% 253.13/158.89 tff(216,plain,
% 253.13/158.89 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W)))) | (sum(additive_identity, b, additive_identity) | (~sum(additive_identity, b, b)) | (~sum(t, additive_identity, additive_identity)) | (~sum(t, b, additive_identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W)))) | sum(additive_identity, b, additive_identity) | (~sum(additive_identity, b, b)) | (~sum(t, additive_identity, additive_identity)) | (~sum(t, b, additive_identity)))),
% 253.13/158.89 inference(rewrite,[status(thm)],[])).
% 253.13/158.89 tff(217,plain,
% 253.13/158.89 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W)))) | (sum(additive_identity, b, additive_identity) | (~sum(additive_identity, b, b)) | (~sum(t, additive_identity, additive_identity)) | (~sum(t, b, additive_identity)))),
% 253.13/158.89 inference(quant_inst,[status(thm)],[])).
% 253.13/158.89 tff(218,plain,
% 253.13/158.89 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W)))) | sum(additive_identity, b, additive_identity) | (~sum(additive_identity, b, b)) | (~sum(t, additive_identity, additive_identity)) | (~sum(t, b, additive_identity))),
% 253.13/158.89 inference(modus_ponens,[status(thm)],[217, 216])).
% 253.13/158.89 tff(219,plain,
% 253.13/158.89 (~sum(t, b, additive_identity)),
% 253.13/158.89 inference(unit_resolution,[status(thm)],[218, 215, 37, 205, 201])).
% 253.13/158.89 tff(220,plain,
% 253.13/158.89 (defined(s) <=> defined(s)),
% 253.13/158.89 inference(rewrite,[status(thm)],[])).
% 253.13/158.89 tff(221,axiom,(defined(s)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s_is_defined')).
% 253.13/158.89 tff(222,plain,
% 253.13/158.89 (defined(s)),
% 253.13/158.89 inference(modus_ponens,[status(thm)],[221, 220])).
% 253.13/158.89 tff(223,plain,
% 253.13/158.89 (((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))) | ((~defined(s)) | sum(additive_identity, s, s))) <=> ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))) | (~defined(s)) | sum(additive_identity, s, s))),
% 253.13/158.89 inference(rewrite,[status(thm)],[])).
% 253.13/158.89 tff(224,plain,
% 253.13/158.89 ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))) | ((~defined(s)) | sum(additive_identity, s, s))),
% 253.13/158.89 inference(quant_inst,[status(thm)],[])).
% 253.13/158.89 tff(225,plain,
% 253.13/158.89 ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, X))) | (~defined(s)) | sum(additive_identity, s, s)),
% 253.13/158.89 inference(modus_ponens,[status(thm)],[224, 223])).
% 253.13/158.89 tff(226,plain,
% 253.13/158.89 (sum(additive_identity, s, s)),
% 253.13/158.89 inference(unit_resolution,[status(thm)],[225, 13, 222])).
% 253.13/158.89 tff(227,plain,
% 253.13/158.89 (((~![Z: $i, Y: $i, X: $i] : ((~sum(X, Y, Z)) | sum(Y, X, Z))) | ((~sum(additive_identity, s, s)) | sum(s, additive_identity, s))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~sum(X, Y, Z)) | sum(Y, X, Z))) | (~sum(additive_identity, s, s)) | sum(s, additive_identity, s))),
% 253.13/158.89 inference(rewrite,[status(thm)],[])).
% 253.13/158.89 tff(228,plain,
% 253.13/158.89 ((~![Z: $i, Y: $i, X: $i] : ((~sum(X, Y, Z)) | sum(Y, X, Z))) | ((~sum(additive_identity, s, s)) | sum(s, additive_identity, s))),
% 253.13/158.89 inference(quant_inst,[status(thm)],[])).
% 253.13/158.89 tff(229,plain,
% 253.13/158.89 ((~![Z: $i, Y: $i, X: $i] : ((~sum(X, Y, Z)) | sum(Y, X, Z))) | (~sum(additive_identity, s, s)) | sum(s, additive_identity, s)),
% 253.13/158.89 inference(modus_ponens,[status(thm)],[228, 227])).
% 253.13/158.89 tff(230,plain,
% 253.13/158.89 (sum(s, additive_identity, s)),
% 253.13/158.89 inference(unit_resolution,[status(thm)],[229, 172, 226])).
% 253.13/158.89 tff(231,plain,
% 253.13/158.89 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | (sum(s, t, s) | (~sum(s, additive_identity, s)) | (~sum(additive_identity, additive_identity, t)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | sum(s, t, s) | (~sum(s, additive_identity, s)) | (~sum(additive_identity, additive_identity, t)))),
% 253.13/158.89 inference(rewrite,[status(thm)],[])).
% 253.13/158.89 tff(232,plain,
% 253.13/158.89 (((~sum(s, additive_identity, s)) | (~sum(additive_identity, additive_identity, t)) | (~sum(s, additive_identity, s)) | sum(s, t, s)) <=> (sum(s, t, s) | (~sum(s, additive_identity, s)) | (~sum(additive_identity, additive_identity, t)))),
% 253.13/158.89 inference(rewrite,[status(thm)],[])).
% 253.13/158.89 tff(233,plain,
% 253.13/158.89 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | ((~sum(s, additive_identity, s)) | (~sum(additive_identity, additive_identity, t)) | (~sum(s, additive_identity, s)) | sum(s, t, s))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | (sum(s, t, s) | (~sum(s, additive_identity, s)) | (~sum(additive_identity, additive_identity, t))))),
% 253.13/158.89 inference(monotonicity,[status(thm)],[232])).
% 253.13/158.89 tff(234,plain,
% 253.13/158.89 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | ((~sum(s, additive_identity, s)) | (~sum(additive_identity, additive_identity, t)) | (~sum(s, additive_identity, s)) | sum(s, t, s))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | sum(s, t, s) | (~sum(s, additive_identity, s)) | (~sum(additive_identity, additive_identity, t)))),
% 253.13/158.89 inference(transitivity,[status(thm)],[233, 231])).
% 253.13/158.89 tff(235,plain,
% 253.13/158.89 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | ((~sum(s, additive_identity, s)) | (~sum(additive_identity, additive_identity, t)) | (~sum(s, additive_identity, s)) | sum(s, t, s))),
% 253.13/158.89 inference(quant_inst,[status(thm)],[])).
% 253.13/158.89 tff(236,plain,
% 253.13/158.89 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | sum(X, V, W))) | sum(s, t, s) | (~sum(s, additive_identity, s)) | (~sum(additive_identity, additive_identity, t))),
% 253.13/158.89 inference(modus_ponens,[status(thm)],[235, 234])).
% 253.13/158.89 tff(237,plain,
% 253.13/158.89 (sum(s, t, s)),
% 253.13/158.89 inference(unit_resolution,[status(thm)],[236, 148, 230, 155])).
% 253.13/158.89 tff(238,plain,
% 253.13/158.89 (((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | ((~product(b, c, t)) | product(c, b, t))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | (~product(b, c, t)) | product(c, b, t))),
% 253.13/158.89 inference(rewrite,[status(thm)],[])).
% 253.13/158.89 tff(239,plain,
% 253.13/158.89 ((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | ((~product(b, c, t)) | product(c, b, t))),
% 253.13/158.89 inference(quant_inst,[status(thm)],[])).
% 253.13/158.89 tff(240,plain,
% 253.13/158.89 ((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | (~product(b, c, t)) | product(c, b, t)),
% 253.13/158.89 inference(modus_ponens,[status(thm)],[239, 238])).
% 253.13/158.89 tff(241,plain,
% 253.13/158.89 (product(c, b, t)),
% 253.13/158.89 inference(unit_resolution,[status(thm)],[240, 84, 57])).
% 253.13/158.89 tff(242,plain,
% 253.13/158.89 (((~![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))) | ((~defined(b)) | product(multiplicative_identity, b, b))) <=> ((~![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))) | (~defined(b)) | product(multiplicative_identity, b, b))),
% 253.13/158.89 inference(rewrite,[status(thm)],[])).
% 253.13/158.89 tff(243,plain,
% 253.13/158.89 ((~![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))) | ((~defined(b)) | product(multiplicative_identity, b, b))),
% 253.13/158.89 inference(quant_inst,[status(thm)],[])).
% 253.13/158.89 tff(244,plain,
% 253.13/158.89 ((~![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))) | (~defined(b)) | product(multiplicative_identity, b, b)),
% 253.13/158.89 inference(modus_ponens,[status(thm)],[243, 242])).
% 253.13/158.89 tff(245,plain,
% 253.13/158.89 (product(multiplicative_identity, b, b)),
% 253.13/158.89 inference(unit_resolution,[status(thm)],[244, 30, 40])).
% 253.13/158.89 tff(246,plain,
% 253.13/158.89 ((~sum(additive_identity, c, additive_identity)) <=> (~sum(additive_identity, c, additive_identity))),
% 253.13/158.89 inference(rewrite,[status(thm)],[])).
% 253.13/158.89 tff(247,axiom,(~sum(additive_identity, c, additive_identity)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_sum_8')).
% 253.13/158.89 tff(248,plain,
% 253.13/158.89 (~sum(additive_identity, c, additive_identity)),
% 253.13/158.89 inference(modus_ponens,[status(thm)],[247, 246])).
% 253.13/158.89 tff(249,plain,
% 253.13/158.89 (((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))) | ((~defined(c)) | sum(additive_identity, c, additive_identity) | product(multiplicative_inverse(c), c, multiplicative_identity))) <=> ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))) | (~defined(c)) | sum(additive_identity, c, additive_identity) | product(multiplicative_inverse(c), c, multiplicative_identity))),
% 253.13/158.89 inference(rewrite,[status(thm)],[])).
% 253.13/158.89 tff(250,plain,
% 253.13/158.89 ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))) | ((~defined(c)) | sum(additive_identity, c, additive_identity) | product(multiplicative_inverse(c), c, multiplicative_identity))),
% 253.13/158.89 inference(quant_inst,[status(thm)],[])).
% 253.13/158.89 tff(251,plain,
% 253.13/158.89 ((~![X: $i] : ((~defined(X)) | sum(additive_identity, X, additive_identity) | product(multiplicative_inverse(X), X, multiplicative_identity))) | (~defined(c)) | sum(additive_identity, c, additive_identity) | product(multiplicative_inverse(c), c, multiplicative_identity)),
% 253.13/158.89 inference(modus_ponens,[status(thm)],[250, 249])).
% 253.13/158.89 tff(252,plain,
% 253.13/158.89 (product(multiplicative_inverse(c), c, multiplicative_identity)),
% 253.13/158.89 inference(unit_resolution,[status(thm)],[251, 50, 20, 248])).
% 253.13/158.89 tff(253,plain,
% 253.13/158.89 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | ((~product(multiplicative_identity, b, b)) | (~product(c, b, t)) | (~product(multiplicative_inverse(c), c, multiplicative_identity)) | product(multiplicative_inverse(c), t, b))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | (~product(multiplicative_identity, b, b)) | (~product(c, b, t)) | (~product(multiplicative_inverse(c), c, multiplicative_identity)) | product(multiplicative_inverse(c), t, b))),
% 253.13/158.89 inference(rewrite,[status(thm)],[])).
% 253.13/158.89 tff(254,plain,
% 253.13/158.89 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | ((~product(multiplicative_identity, b, b)) | (~product(c, b, t)) | (~product(multiplicative_inverse(c), c, multiplicative_identity)) | product(multiplicative_inverse(c), t, b))),
% 253.13/158.89 inference(quant_inst,[status(thm)],[])).
% 253.13/158.89 tff(255,plain,
% 253.13/158.89 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | (~product(multiplicative_identity, b, b)) | (~product(c, b, t)) | (~product(multiplicative_inverse(c), c, multiplicative_identity)) | product(multiplicative_inverse(c), t, b)),
% 253.13/158.89 inference(modus_ponens,[status(thm)],[254, 253])).
% 253.13/158.89 tff(256,plain,
% 253.13/158.89 (product(multiplicative_inverse(c), t, b)),
% 253.13/158.89 inference(unit_resolution,[status(thm)],[255, 67, 252, 245, 241])).
% 253.13/158.89 tff(257,plain,
% 253.13/158.89 (((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | ((~product(multiplicative_inverse(c), t, b)) | product(t, multiplicative_inverse(c), b))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | (~product(multiplicative_inverse(c), t, b)) | product(t, multiplicative_inverse(c), b))),
% 253.13/158.90 inference(rewrite,[status(thm)],[])).
% 253.13/158.90 tff(258,plain,
% 253.13/158.90 ((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | ((~product(multiplicative_inverse(c), t, b)) | product(t, multiplicative_inverse(c), b))),
% 253.13/158.90 inference(quant_inst,[status(thm)],[])).
% 253.13/158.90 tff(259,plain,
% 253.13/158.90 ((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | (~product(multiplicative_inverse(c), t, b)) | product(t, multiplicative_inverse(c), b)),
% 253.13/158.90 inference(modus_ponens,[status(thm)],[258, 257])).
% 253.13/158.90 tff(260,plain,
% 253.13/158.90 (product(t, multiplicative_inverse(c), b)),
% 253.13/158.90 inference(unit_resolution,[status(thm)],[259, 84, 256])).
% 253.13/158.90 tff(261,plain,
% 253.13/158.90 (((~![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))) | ((~defined(a)) | product(multiplicative_identity, a, a))) <=> ((~![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))) | (~defined(a)) | product(multiplicative_identity, a, a))),
% 253.13/158.90 inference(rewrite,[status(thm)],[])).
% 253.13/158.90 tff(262,plain,
% 253.13/158.90 ((~![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))) | ((~defined(a)) | product(multiplicative_identity, a, a))),
% 253.13/158.90 inference(quant_inst,[status(thm)],[])).
% 253.13/158.90 tff(263,plain,
% 253.13/158.90 ((~![X: $i] : ((~defined(X)) | product(multiplicative_identity, X, X))) | (~defined(a)) | product(multiplicative_identity, a, a)),
% 253.13/158.90 inference(modus_ponens,[status(thm)],[262, 261])).
% 253.13/158.90 tff(264,plain,
% 253.13/158.90 (product(multiplicative_identity, a, a)),
% 253.13/158.90 inference(unit_resolution,[status(thm)],[263, 30, 158])).
% 253.13/158.90 tff(265,plain,
% 253.13/158.90 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | ((~product(multiplicative_inverse(c), c, multiplicative_identity)) | (~product(multiplicative_identity, a, a)) | (~product(c, a, s)) | product(multiplicative_inverse(c), s, a))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | (~product(multiplicative_inverse(c), c, multiplicative_identity)) | (~product(multiplicative_identity, a, a)) | (~product(c, a, s)) | product(multiplicative_inverse(c), s, a))),
% 253.13/158.90 inference(rewrite,[status(thm)],[])).
% 253.13/158.90 tff(266,plain,
% 253.13/158.90 (((~product(multiplicative_identity, a, a)) | (~product(c, a, s)) | (~product(multiplicative_inverse(c), c, multiplicative_identity)) | product(multiplicative_inverse(c), s, a)) <=> ((~product(multiplicative_inverse(c), c, multiplicative_identity)) | (~product(multiplicative_identity, a, a)) | (~product(c, a, s)) | product(multiplicative_inverse(c), s, a))),
% 253.13/158.90 inference(rewrite,[status(thm)],[])).
% 253.13/158.90 tff(267,plain,
% 253.13/158.90 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | ((~product(multiplicative_identity, a, a)) | (~product(c, a, s)) | (~product(multiplicative_inverse(c), c, multiplicative_identity)) | product(multiplicative_inverse(c), s, a))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | ((~product(multiplicative_inverse(c), c, multiplicative_identity)) | (~product(multiplicative_identity, a, a)) | (~product(c, a, s)) | product(multiplicative_inverse(c), s, a)))),
% 253.13/158.90 inference(monotonicity,[status(thm)],[266])).
% 253.13/158.90 tff(268,plain,
% 253.13/158.90 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | ((~product(multiplicative_identity, a, a)) | (~product(c, a, s)) | (~product(multiplicative_inverse(c), c, multiplicative_identity)) | product(multiplicative_inverse(c), s, a))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | (~product(multiplicative_inverse(c), c, multiplicative_identity)) | (~product(multiplicative_identity, a, a)) | (~product(c, a, s)) | product(multiplicative_inverse(c), s, a))),
% 253.13/158.90 inference(transitivity,[status(thm)],[267, 265])).
% 253.13/158.90 tff(269,plain,
% 253.13/158.90 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | ((~product(multiplicative_identity, a, a)) | (~product(c, a, s)) | (~product(multiplicative_inverse(c), c, multiplicative_identity)) | product(multiplicative_inverse(c), s, a))),
% 253.13/158.90 inference(quant_inst,[status(thm)],[])).
% 253.13/158.90 tff(270,plain,
% 253.13/158.90 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)) | product(X, V, W))) | (~product(multiplicative_inverse(c), c, multiplicative_identity)) | (~product(multiplicative_identity, a, a)) | (~product(c, a, s)) | product(multiplicative_inverse(c), s, a)),
% 253.13/158.90 inference(modus_ponens,[status(thm)],[269, 268])).
% 253.13/158.90 tff(271,plain,
% 253.13/158.90 (product(multiplicative_inverse(c), s, a)),
% 253.13/158.90 inference(unit_resolution,[status(thm)],[270, 67, 252, 264, 95])).
% 253.13/158.90 tff(272,plain,
% 253.13/158.90 (((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | ((~product(multiplicative_inverse(c), s, a)) | product(s, multiplicative_inverse(c), a))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | (~product(multiplicative_inverse(c), s, a)) | product(s, multiplicative_inverse(c), a))),
% 253.13/158.90 inference(rewrite,[status(thm)],[])).
% 253.13/158.90 tff(273,plain,
% 253.13/158.90 ((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | ((~product(multiplicative_inverse(c), s, a)) | product(s, multiplicative_inverse(c), a))),
% 253.13/158.90 inference(quant_inst,[status(thm)],[])).
% 253.13/158.90 tff(274,plain,
% 253.13/158.90 ((~![Z: $i, Y: $i, X: $i] : ((~product(X, Y, Z)) | product(Y, X, Z))) | (~product(multiplicative_inverse(c), s, a)) | product(s, multiplicative_inverse(c), a)),
% 253.13/158.90 inference(modus_ponens,[status(thm)],[273, 272])).
% 253.13/158.90 tff(275,plain,
% 253.13/158.90 (product(s, multiplicative_inverse(c), a)),
% 253.13/158.90 inference(unit_resolution,[status(thm)],[274, 84, 271])).
% 253.13/158.90 tff(276,plain,
% 253.13/158.90 (^[B: $i, D: $i, Z: $i, Y: $i, A: $i, X: $i, C: $i] : refl(((~product(Y, Z, D)) | (~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B)) <=> ((~product(Y, Z, D)) | (~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B)))),
% 253.13/158.90 inference(bind,[status(th)],[])).
% 253.13/158.90 tff(277,plain,
% 253.13/158.90 (![B: $i, D: $i, Z: $i, Y: $i, A: $i, X: $i, C: $i] : ((~product(Y, Z, D)) | (~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B)) <=> ![B: $i, D: $i, Z: $i, Y: $i, A: $i, X: $i, C: $i] : ((~product(Y, Z, D)) | (~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B))),
% 253.13/158.90 inference(quant_intro,[status(thm)],[276])).
% 253.13/158.90 tff(278,plain,
% 253.13/158.90 (![B: $i, D: $i, Z: $i, Y: $i, A: $i, X: $i, C: $i] : ((~product(Y, Z, D)) | (~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B)) <=> ![B: $i, D: $i, Z: $i, Y: $i, A: $i, X: $i, C: $i] : ((~product(Y, Z, D)) | (~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B))),
% 253.13/158.90 inference(rewrite,[status(thm)],[])).
% 253.13/158.90 tff(279,plain,
% 253.13/158.90 (^[B: $i, D: $i, Z: $i, Y: $i, A: $i, X: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((sum(C, D, B) | (~sum(X, Y, A))) <=> ((~sum(X, Y, A)) | sum(C, D, B))), (((sum(C, D, B) | (~sum(X, Y, A))) | (~product(A, Z, B))) <=> (((~sum(X, Y, A)) | sum(C, D, B)) | (~product(A, Z, B))))), rewrite((((~sum(X, Y, A)) | sum(C, D, B)) | (~product(A, Z, B))) <=> ((~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B))), (((sum(C, D, B) | (~sum(X, Y, A))) | (~product(A, Z, B))) <=> ((~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B)))), ((((sum(C, D, B) | (~sum(X, Y, A))) | (~product(A, Z, B))) | (~product(X, Z, C))) <=> (((~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B)) | (~product(X, Z, C))))), rewrite((((~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B)) | (~product(X, Z, C))) <=> ((~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B))), ((((sum(C, D, B) | (~sum(X, Y, A))) | (~product(A, Z, B))) | (~product(X, Z, C))) <=> ((~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B)))), (((((sum(C, D, B) | (~sum(X, Y, A))) | (~product(A, Z, B))) | (~product(X, Z, C))) | (~product(Y, Z, D))) <=> (((~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B)) | (~product(Y, Z, D))))), rewrite((((~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B)) | (~product(Y, Z, D))) <=> ((~product(Y, Z, D)) | (~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B))), (((((sum(C, D, B) | (~sum(X, Y, A))) | (~product(A, Z, B))) | (~product(X, Z, C))) | (~product(Y, Z, D))) <=> ((~product(Y, Z, D)) | (~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B))))),
% 253.13/158.90 inference(bind,[status(th)],[])).
% 253.13/158.90 tff(280,plain,
% 253.13/158.90 (![B: $i, D: $i, Z: $i, Y: $i, A: $i, X: $i, C: $i] : ((((sum(C, D, B) | (~sum(X, Y, A))) | (~product(A, Z, B))) | (~product(X, Z, C))) | (~product(Y, Z, D))) <=> ![B: $i, D: $i, Z: $i, Y: $i, A: $i, X: $i, C: $i] : ((~product(Y, Z, D)) | (~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B))),
% 253.13/158.90 inference(quant_intro,[status(thm)],[279])).
% 253.13/158.90 tff(281,axiom,(![B: $i, D: $i, Z: $i, Y: $i, A: $i, X: $i, C: $i] : ((((sum(C, D, B) | (~sum(X, Y, A))) | (~product(A, Z, B))) | (~product(X, Z, C))) | (~product(Y, Z, D)))), file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax','distributivity_1')).
% 253.13/158.90 tff(282,plain,
% 253.13/158.90 (![B: $i, D: $i, Z: $i, Y: $i, A: $i, X: $i, C: $i] : ((~product(Y, Z, D)) | (~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B))),
% 253.13/158.90 inference(modus_ponens,[status(thm)],[281, 280])).
% 253.13/158.90 tff(283,plain,
% 253.13/158.90 (![B: $i, D: $i, Z: $i, Y: $i, A: $i, X: $i, C: $i] : ((~product(Y, Z, D)) | (~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B))),
% 253.13/158.90 inference(modus_ponens,[status(thm)],[282, 278])).
% 253.13/158.90 tff(284,plain,(
% 253.13/158.90 ![B: $i, D: $i, Z: $i, Y: $i, A: $i, X: $i, C: $i] : ((~product(Y, Z, D)) | (~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B))),
% 253.13/158.90 inference(skolemize,[status(sab)],[283])).
% 253.13/158.90 tff(285,plain,
% 253.13/158.90 (![B: $i, D: $i, Z: $i, Y: $i, A: $i, X: $i, C: $i] : ((~product(Y, Z, D)) | (~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B))),
% 253.13/158.90 inference(modus_ponens,[status(thm)],[284, 277])).
% 253.13/158.90 tff(286,plain,
% 253.13/158.90 (((~![B: $i, D: $i, Z: $i, Y: $i, A: $i, X: $i, C: $i] : ((~product(Y, Z, D)) | (~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B))) | (sum(a, b, a) | (~sum(s, t, s)) | (~product(s, multiplicative_inverse(c), a)) | (~product(t, multiplicative_inverse(c), b)))) <=> ((~![B: $i, D: $i, Z: $i, Y: $i, A: $i, X: $i, C: $i] : ((~product(Y, Z, D)) | (~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B))) | sum(a, b, a) | (~sum(s, t, s)) | (~product(s, multiplicative_inverse(c), a)) | (~product(t, multiplicative_inverse(c), b)))),
% 253.13/158.90 inference(rewrite,[status(thm)],[])).
% 253.13/158.90 tff(287,plain,
% 253.13/158.90 (((~product(t, multiplicative_inverse(c), b)) | (~product(s, multiplicative_inverse(c), a)) | (~product(s, multiplicative_inverse(c), a)) | (~sum(s, t, s)) | sum(a, b, a)) <=> (sum(a, b, a) | (~sum(s, t, s)) | (~product(s, multiplicative_inverse(c), a)) | (~product(t, multiplicative_inverse(c), b)))),
% 253.13/158.90 inference(rewrite,[status(thm)],[])).
% 253.13/158.90 tff(288,plain,
% 253.13/158.90 (((~![B: $i, D: $i, Z: $i, Y: $i, A: $i, X: $i, C: $i] : ((~product(Y, Z, D)) | (~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B))) | ((~product(t, multiplicative_inverse(c), b)) | (~product(s, multiplicative_inverse(c), a)) | (~product(s, multiplicative_inverse(c), a)) | (~sum(s, t, s)) | sum(a, b, a))) <=> ((~![B: $i, D: $i, Z: $i, Y: $i, A: $i, X: $i, C: $i] : ((~product(Y, Z, D)) | (~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B))) | (sum(a, b, a) | (~sum(s, t, s)) | (~product(s, multiplicative_inverse(c), a)) | (~product(t, multiplicative_inverse(c), b))))),
% 253.13/158.90 inference(monotonicity,[status(thm)],[287])).
% 253.13/158.90 tff(289,plain,
% 253.13/158.90 (((~![B: $i, D: $i, Z: $i, Y: $i, A: $i, X: $i, C: $i] : ((~product(Y, Z, D)) | (~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B))) | ((~product(t, multiplicative_inverse(c), b)) | (~product(s, multiplicative_inverse(c), a)) | (~product(s, multiplicative_inverse(c), a)) | (~sum(s, t, s)) | sum(a, b, a))) <=> ((~![B: $i, D: $i, Z: $i, Y: $i, A: $i, X: $i, C: $i] : ((~product(Y, Z, D)) | (~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B))) | sum(a, b, a) | (~sum(s, t, s)) | (~product(s, multiplicative_inverse(c), a)) | (~product(t, multiplicative_inverse(c), b)))),
% 253.13/158.90 inference(transitivity,[status(thm)],[288, 286])).
% 253.13/158.90 tff(290,plain,
% 253.13/158.90 ((~![B: $i, D: $i, Z: $i, Y: $i, A: $i, X: $i, C: $i] : ((~product(Y, Z, D)) | (~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B))) | ((~product(t, multiplicative_inverse(c), b)) | (~product(s, multiplicative_inverse(c), a)) | (~product(s, multiplicative_inverse(c), a)) | (~sum(s, t, s)) | sum(a, b, a))),
% 253.13/158.90 inference(quant_inst,[status(thm)],[])).
% 253.13/158.90 tff(291,plain,
% 253.13/158.90 ((~![B: $i, D: $i, Z: $i, Y: $i, A: $i, X: $i, C: $i] : ((~product(Y, Z, D)) | (~product(X, Z, C)) | (~product(A, Z, B)) | (~sum(X, Y, A)) | sum(C, D, B))) | sum(a, b, a) | (~sum(s, t, s)) | (~product(s, multiplicative_inverse(c), a)) | (~product(t, multiplicative_inverse(c), b))),
% 253.13/158.90 inference(modus_ponens,[status(thm)],[290, 289])).
% 253.13/158.90 tff(292,plain,
% 253.13/158.90 (sum(a, b, a) | (~sum(s, t, s))),
% 253.13/158.90 inference(unit_resolution,[status(thm)],[291, 285, 275, 260])).
% 253.13/158.90 tff(293,plain,
% 253.13/158.90 (sum(a, b, a)),
% 253.13/158.90 inference(unit_resolution,[status(thm)],[292, 237])).
% 253.13/158.90 tff(294,plain,
% 253.13/158.90 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W)))) | ((~sum(a, b, a)) | (~sum(additive_inverse(a), a, additive_identity)) | sum(t, b, additive_identity) | (~sum(additive_inverse(a), a, t)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W)))) | (~sum(a, b, a)) | (~sum(additive_inverse(a), a, additive_identity)) | sum(t, b, additive_identity) | (~sum(additive_inverse(a), a, t)))),
% 253.13/158.90 inference(rewrite,[status(thm)],[])).
% 253.13/158.90 tff(295,plain,
% 253.13/158.90 ((sum(t, b, additive_identity) | (~sum(a, b, a)) | (~sum(additive_inverse(a), a, t)) | (~sum(additive_inverse(a), a, additive_identity))) <=> ((~sum(a, b, a)) | (~sum(additive_inverse(a), a, additive_identity)) | sum(t, b, additive_identity) | (~sum(additive_inverse(a), a, t)))),
% 253.13/158.90 inference(rewrite,[status(thm)],[])).
% 253.13/158.90 tff(296,plain,
% 253.13/158.90 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W)))) | (sum(t, b, additive_identity) | (~sum(a, b, a)) | (~sum(additive_inverse(a), a, t)) | (~sum(additive_inverse(a), a, additive_identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W)))) | ((~sum(a, b, a)) | (~sum(additive_inverse(a), a, additive_identity)) | sum(t, b, additive_identity) | (~sum(additive_inverse(a), a, t))))),
% 253.13/158.90 inference(monotonicity,[status(thm)],[295])).
% 253.13/158.90 tff(297,plain,
% 253.13/158.90 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W)))) | (sum(t, b, additive_identity) | (~sum(a, b, a)) | (~sum(additive_inverse(a), a, t)) | (~sum(additive_inverse(a), a, additive_identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W)))) | (~sum(a, b, a)) | (~sum(additive_inverse(a), a, additive_identity)) | sum(t, b, additive_identity) | (~sum(additive_inverse(a), a, t)))),
% 253.13/158.90 inference(transitivity,[status(thm)],[296, 294])).
% 253.13/158.90 tff(298,plain,
% 253.13/158.90 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W)))) | (sum(t, b, additive_identity) | (~sum(a, b, a)) | (~sum(additive_inverse(a), a, t)) | (~sum(additive_inverse(a), a, additive_identity)))),
% 253.13/158.90 inference(quant_inst,[status(thm)],[])).
% 253.13/158.90 tff(299,plain,
% 253.13/158.90 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(U, Z, W) | (~sum(Y, Z, V)) | (~sum(X, Y, U)) | (~sum(X, V, W)))) | (~sum(a, b, a)) | (~sum(additive_inverse(a), a, additive_identity)) | sum(t, b, additive_identity) | (~sum(additive_inverse(a), a, t))),
% 253.13/158.92 inference(modus_ponens,[status(thm)],[298, 297])).
% 253.13/158.92 tff(300,plain,
% 253.13/158.92 ($false),
% 253.13/158.92 inference(unit_resolution,[status(thm)],[299, 215, 190, 293, 219, 197])).
% 253.13/158.92 % SZS output end Proof
%------------------------------------------------------------------------------