TSTP Solution File: GRP197-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP197-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 22:26:45 EDT 2022
% Result : Unsatisfiable 0.18s 0.53s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP197-1 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n022.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 15:43:40 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.
% 0.18/0.53 % SZS status Unsatisfiable
% 0.18/0.53 % SZS output start Proof
% 0.18/0.53 tff(multiply_type, type, (
% 0.18/0.53 multiply: ( $i * $i ) > $i)).
% 0.18/0.53 tff(b_type, type, (
% 0.18/0.53 b: $i)).
% 0.18/0.53 tff(a_type, type, (
% 0.18/0.53 a: $i)).
% 0.18/0.53 tff(inj_0_type, type, (
% 0.18/0.53 inj_0: ( $i * $i ) > $i)).
% 0.18/0.53 tff(inj_1_type, type, (
% 0.18/0.53 inj_1: ( $i * $i ) > $i)).
% 0.18/0.53 tff(1,plain,
% 0.18/0.53 (![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(C, B))) | (A = C)) <=> ![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, multiply(Xk!1, Xk!0)) = Xk!1)),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(2,plain,
% 0.18/0.53 (![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(C, B))) | (A = C)) <=> ![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(C, B))) | (A = C))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(3,axiom,(![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(C, B))) | (A = C))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP008-1.ax','right_cancellation')).
% 0.18/0.53 tff(4,plain,
% 0.18/0.53 (![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(C, B))) | (A = C))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.18/0.53 tff(5,plain,(
% 0.18/0.53 ![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(C, B))) | (A = C))),
% 0.18/0.53 inference(skolemize,[status(sab)],[4])).
% 0.18/0.53 tff(6,plain,
% 0.18/0.53 (![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, multiply(Xk!1, Xk!0)) = Xk!1)),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.18/0.53 tff(7,plain,
% 0.18/0.53 ((~![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, multiply(Xk!1, Xk!0)) = Xk!1)) | (inj_0(multiply(a, b), multiply(multiply(a, multiply(b, multiply(a, multiply(a, b)))), multiply(a, b))) = multiply(a, multiply(b, multiply(a, multiply(a, b)))))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(8,plain,
% 0.18/0.53 (inj_0(multiply(a, b), multiply(multiply(a, multiply(b, multiply(a, multiply(a, b)))), multiply(a, b))) = multiply(a, multiply(b, multiply(a, multiply(a, b))))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[7, 6])).
% 0.18/0.53 tff(9,plain,
% 0.18/0.53 (^[Z: $i, Y: $i, X: $i] : refl((multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))) <=> (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))))),
% 0.18/0.53 inference(bind,[status(th)],[])).
% 0.18/0.53 tff(10,plain,
% 0.18/0.53 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.18/0.53 inference(quant_intro,[status(thm)],[9])).
% 0.18/0.53 tff(11,plain,
% 0.18/0.53 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(12,axiom,(![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP008-0.ax','associativity_of_multiply')).
% 0.18/0.53 tff(13,plain,
% 0.18/0.53 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.18/0.53 tff(14,plain,(
% 0.18/0.53 ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.18/0.53 inference(skolemize,[status(sab)],[13])).
% 0.18/0.53 tff(15,plain,
% 0.18/0.53 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.18/0.53 tff(16,plain,
% 0.18/0.53 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(a, multiply(b, a)), multiply(a, b)) = multiply(a, multiply(multiply(b, a), multiply(a, b))))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(17,plain,
% 0.18/0.53 (multiply(multiply(a, multiply(b, a)), multiply(a, b)) = multiply(a, multiply(multiply(b, a), multiply(a, b)))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.18/0.53 tff(18,plain,
% 0.18/0.53 (multiply(a, multiply(multiply(b, a), multiply(a, b))) = multiply(multiply(a, multiply(b, a)), multiply(a, b))),
% 0.18/0.53 inference(symmetry,[status(thm)],[17])).
% 0.18/0.53 tff(19,plain,
% 0.18/0.53 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(b, a), multiply(a, b)) = multiply(b, multiply(a, multiply(a, b))))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(20,plain,
% 0.18/0.53 (multiply(multiply(b, a), multiply(a, b)) = multiply(b, multiply(a, multiply(a, b)))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[19, 15])).
% 0.18/0.54 tff(21,plain,
% 0.18/0.54 (multiply(a, multiply(multiply(b, a), multiply(a, b))) = multiply(a, multiply(b, multiply(a, multiply(a, b))))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[20])).
% 0.18/0.54 tff(22,plain,
% 0.18/0.54 (multiply(a, multiply(b, multiply(a, multiply(a, b)))) = multiply(a, multiply(multiply(b, a), multiply(a, b)))),
% 0.18/0.54 inference(symmetry,[status(thm)],[21])).
% 0.18/0.54 tff(23,plain,
% 0.18/0.54 (multiply(a, multiply(b, multiply(a, multiply(a, b)))) = multiply(multiply(a, multiply(b, a)), multiply(a, b))),
% 0.18/0.54 inference(transitivity,[status(thm)],[22, 18])).
% 0.18/0.54 tff(24,plain,
% 0.18/0.54 (multiply(multiply(a, multiply(b, multiply(a, multiply(a, b)))), multiply(a, b)) = multiply(multiply(multiply(a, multiply(b, a)), multiply(a, b)), multiply(a, b))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[23])).
% 0.18/0.54 tff(25,plain,
% 0.18/0.54 (multiply(multiply(multiply(a, multiply(b, a)), multiply(a, b)), multiply(a, b)) = multiply(multiply(a, multiply(b, multiply(a, multiply(a, b)))), multiply(a, b))),
% 0.18/0.54 inference(symmetry,[status(thm)],[24])).
% 0.18/0.54 tff(26,plain,
% 0.18/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(a, multiply(b, a)), multiply(a, b)), multiply(a, b)) = multiply(multiply(a, multiply(b, a)), multiply(multiply(a, b), multiply(a, b))))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(27,plain,
% 0.18/0.54 (multiply(multiply(multiply(a, multiply(b, a)), multiply(a, b)), multiply(a, b)) = multiply(multiply(a, multiply(b, a)), multiply(multiply(a, b), multiply(a, b)))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[26, 15])).
% 0.18/0.54 tff(28,plain,
% 0.18/0.54 (multiply(multiply(a, multiply(b, a)), multiply(multiply(a, b), multiply(a, b))) = multiply(multiply(multiply(a, multiply(b, a)), multiply(a, b)), multiply(a, b))),
% 0.18/0.54 inference(symmetry,[status(thm)],[27])).
% 0.18/0.54 tff(29,plain,
% 0.18/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(a, b), a) = multiply(a, multiply(b, a)))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(30,plain,
% 0.18/0.54 (multiply(multiply(a, b), a) = multiply(a, multiply(b, a))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[29, 15])).
% 0.18/0.54 tff(31,plain,
% 0.18/0.54 (multiply(a, multiply(b, a)) = multiply(multiply(a, b), a)),
% 0.18/0.54 inference(symmetry,[status(thm)],[30])).
% 0.18/0.54 tff(32,plain,
% 0.18/0.54 (multiply(multiply(a, multiply(b, a)), multiply(multiply(a, b), multiply(a, b))) = multiply(multiply(multiply(a, b), a), multiply(multiply(a, b), multiply(a, b)))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[31])).
% 0.18/0.54 tff(33,plain,
% 0.18/0.54 (multiply(multiply(multiply(a, b), a), multiply(multiply(a, b), multiply(a, b))) = multiply(multiply(a, multiply(b, a)), multiply(multiply(a, b), multiply(a, b)))),
% 0.18/0.54 inference(symmetry,[status(thm)],[32])).
% 0.18/0.54 tff(34,plain,
% 0.18/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(a, b), a), multiply(multiply(a, b), multiply(a, b))) = multiply(multiply(a, b), multiply(a, multiply(multiply(a, b), multiply(a, b)))))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(35,plain,
% 0.18/0.54 (multiply(multiply(multiply(a, b), a), multiply(multiply(a, b), multiply(a, b))) = multiply(multiply(a, b), multiply(a, multiply(multiply(a, b), multiply(a, b))))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[34, 15])).
% 0.18/0.54 tff(36,plain,
% 0.18/0.54 (multiply(multiply(a, b), multiply(a, multiply(multiply(a, b), multiply(a, b)))) = multiply(multiply(multiply(a, b), a), multiply(multiply(a, b), multiply(a, b)))),
% 0.18/0.54 inference(symmetry,[status(thm)],[35])).
% 0.18/0.54 tff(37,plain,
% 0.18/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(b, a), b), multiply(a, a)) = multiply(multiply(b, a), multiply(b, multiply(a, a))))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(38,plain,
% 0.18/0.54 (multiply(multiply(multiply(b, a), b), multiply(a, a)) = multiply(multiply(b, a), multiply(b, multiply(a, a)))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[37, 15])).
% 0.18/0.54 tff(39,plain,
% 0.18/0.54 (multiply(multiply(b, a), multiply(b, multiply(a, a))) = multiply(multiply(multiply(b, a), b), multiply(a, a))),
% 0.18/0.54 inference(symmetry,[status(thm)],[38])).
% 0.18/0.54 tff(40,plain,
% 0.18/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(b, a), a) = multiply(b, multiply(a, a)))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(41,plain,
% 0.18/0.54 (multiply(multiply(b, a), a) = multiply(b, multiply(a, a))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[40, 15])).
% 0.18/0.54 tff(42,plain,
% 0.18/0.54 (multiply(b, multiply(a, a)) = multiply(multiply(b, a), a)),
% 0.18/0.54 inference(symmetry,[status(thm)],[41])).
% 0.18/0.54 tff(43,plain,
% 0.18/0.54 (multiply(multiply(b, a), multiply(b, multiply(a, a))) = multiply(multiply(b, a), multiply(multiply(b, a), a))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[42])).
% 0.18/0.54 tff(44,plain,
% 0.18/0.54 (multiply(multiply(b, a), multiply(multiply(b, a), a)) = multiply(multiply(b, a), multiply(b, multiply(a, a)))),
% 0.18/0.54 inference(symmetry,[status(thm)],[43])).
% 0.18/0.54 tff(45,plain,
% 0.18/0.54 ((~![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, multiply(Xk!1, Xk!0)) = Xk!1)) | (inj_0(multiply(a, multiply(a, multiply(b, b))), multiply(multiply(multiply(b, a), multiply(multiply(b, a), a)), multiply(a, multiply(a, multiply(b, b))))) = multiply(multiply(b, a), multiply(multiply(b, a), a)))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(46,plain,
% 0.18/0.54 (inj_0(multiply(a, multiply(a, multiply(b, b))), multiply(multiply(multiply(b, a), multiply(multiply(b, a), a)), multiply(a, multiply(a, multiply(b, b))))) = multiply(multiply(b, a), multiply(multiply(b, a), a))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[45, 6])).
% 0.18/0.54 tff(47,plain,
% 0.18/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(b, a), multiply(multiply(b, a), a)), multiply(a, multiply(a, multiply(b, b)))) = multiply(multiply(b, a), multiply(multiply(multiply(b, a), a), multiply(a, multiply(a, multiply(b, b))))))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(48,plain,
% 0.18/0.54 (multiply(multiply(multiply(b, a), multiply(multiply(b, a), a)), multiply(a, multiply(a, multiply(b, b)))) = multiply(multiply(b, a), multiply(multiply(multiply(b, a), a), multiply(a, multiply(a, multiply(b, b)))))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[47, 15])).
% 0.18/0.54 tff(49,plain,
% 0.18/0.54 (multiply(multiply(b, a), multiply(multiply(multiply(b, a), a), multiply(a, multiply(a, multiply(b, b))))) = multiply(multiply(multiply(b, a), multiply(multiply(b, a), a)), multiply(a, multiply(a, multiply(b, b))))),
% 0.18/0.54 inference(symmetry,[status(thm)],[48])).
% 0.18/0.54 tff(50,plain,
% 0.18/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(b, a), a), multiply(b, a)) = multiply(multiply(b, a), multiply(a, multiply(b, a))))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(51,plain,
% 0.18/0.54 (multiply(multiply(multiply(b, a), a), multiply(b, a)) = multiply(multiply(b, a), multiply(a, multiply(b, a)))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[50, 15])).
% 0.18/0.54 tff(52,plain,
% 0.18/0.54 (multiply(multiply(b, a), multiply(multiply(multiply(b, a), a), multiply(b, a))) = multiply(multiply(b, a), multiply(multiply(b, a), multiply(a, multiply(b, a))))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[51])).
% 0.18/0.54 tff(53,plain,
% 0.18/0.54 (multiply(multiply(b, a), multiply(multiply(b, a), multiply(a, multiply(b, a)))) = multiply(multiply(b, a), multiply(multiply(multiply(b, a), a), multiply(b, a)))),
% 0.18/0.54 inference(symmetry,[status(thm)],[52])).
% 0.18/0.54 tff(54,plain,
% 0.18/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(b, a), multiply(a, multiply(b, a))) = multiply(b, multiply(a, multiply(a, multiply(b, a)))))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(55,plain,
% 0.18/0.54 (multiply(multiply(b, a), multiply(a, multiply(b, a))) = multiply(b, multiply(a, multiply(a, multiply(b, a))))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[54, 15])).
% 0.18/0.54 tff(56,plain,
% 0.18/0.54 (multiply(b, multiply(a, multiply(a, multiply(b, a)))) = multiply(multiply(b, a), multiply(a, multiply(b, a)))),
% 0.18/0.54 inference(symmetry,[status(thm)],[55])).
% 0.18/0.54 tff(57,plain,
% 0.18/0.54 (^[Y: $i, X: $i] : refl((multiply(X, multiply(X, multiply(X, multiply(Y, Y)))) = multiply(Y, multiply(X, multiply(X, multiply(Y, X))))) <=> (multiply(X, multiply(X, multiply(X, multiply(Y, Y)))) = multiply(Y, multiply(X, multiply(X, multiply(Y, X))))))),
% 0.18/0.54 inference(bind,[status(th)],[])).
% 0.18/0.54 tff(58,plain,
% 0.18/0.54 (![Y: $i, X: $i] : (multiply(X, multiply(X, multiply(X, multiply(Y, Y)))) = multiply(Y, multiply(X, multiply(X, multiply(Y, X))))) <=> ![Y: $i, X: $i] : (multiply(X, multiply(X, multiply(X, multiply(Y, Y)))) = multiply(Y, multiply(X, multiply(X, multiply(Y, X)))))),
% 0.18/0.54 inference(quant_intro,[status(thm)],[57])).
% 0.18/0.54 tff(59,plain,
% 0.18/0.54 (![Y: $i, X: $i] : (multiply(X, multiply(X, multiply(X, multiply(Y, Y)))) = multiply(Y, multiply(X, multiply(X, multiply(Y, X))))) <=> ![Y: $i, X: $i] : (multiply(X, multiply(X, multiply(X, multiply(Y, Y)))) = multiply(Y, multiply(X, multiply(X, multiply(Y, X)))))),
% 0.18/0.54 inference(rewrite,[status(thm)],[])).
% 0.18/0.54 tff(60,axiom,(![Y: $i, X: $i] : (multiply(X, multiply(X, multiply(X, multiply(Y, Y)))) = multiply(Y, multiply(X, multiply(X, multiply(Y, X)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','condition')).
% 0.18/0.54 tff(61,plain,
% 0.18/0.54 (![Y: $i, X: $i] : (multiply(X, multiply(X, multiply(X, multiply(Y, Y)))) = multiply(Y, multiply(X, multiply(X, multiply(Y, X)))))),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.18/0.54 tff(62,plain,(
% 0.18/0.54 ![Y: $i, X: $i] : (multiply(X, multiply(X, multiply(X, multiply(Y, Y)))) = multiply(Y, multiply(X, multiply(X, multiply(Y, X)))))),
% 0.18/0.54 inference(skolemize,[status(sab)],[61])).
% 0.18/0.54 tff(63,plain,
% 0.18/0.54 (![Y: $i, X: $i] : (multiply(X, multiply(X, multiply(X, multiply(Y, Y)))) = multiply(Y, multiply(X, multiply(X, multiply(Y, X)))))),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.18/0.54 tff(64,plain,
% 0.18/0.54 ((~![Y: $i, X: $i] : (multiply(X, multiply(X, multiply(X, multiply(Y, Y)))) = multiply(Y, multiply(X, multiply(X, multiply(Y, X)))))) | (multiply(a, multiply(a, multiply(a, multiply(b, b)))) = multiply(b, multiply(a, multiply(a, multiply(b, a)))))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(65,plain,
% 0.18/0.54 (multiply(a, multiply(a, multiply(a, multiply(b, b)))) = multiply(b, multiply(a, multiply(a, multiply(b, a))))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.18/0.54 tff(66,plain,
% 0.18/0.54 (multiply(a, multiply(a, multiply(a, multiply(b, b)))) = multiply(multiply(b, a), multiply(a, multiply(b, a)))),
% 0.18/0.54 inference(transitivity,[status(thm)],[65, 56])).
% 0.18/0.54 tff(67,plain,
% 0.18/0.54 (multiply(multiply(b, a), multiply(a, multiply(a, multiply(a, multiply(b, b))))) = multiply(multiply(b, a), multiply(multiply(b, a), multiply(a, multiply(b, a))))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[66])).
% 0.18/0.54 tff(68,plain,
% 0.18/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(b, a), a), multiply(a, multiply(a, multiply(b, b)))) = multiply(multiply(b, a), multiply(a, multiply(a, multiply(a, multiply(b, b))))))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(69,plain,
% 0.18/0.54 (multiply(multiply(multiply(b, a), a), multiply(a, multiply(a, multiply(b, b)))) = multiply(multiply(b, a), multiply(a, multiply(a, multiply(a, multiply(b, b)))))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[68, 15])).
% 0.18/0.54 tff(70,plain,
% 0.18/0.54 (multiply(multiply(multiply(b, a), a), multiply(a, multiply(a, multiply(b, b)))) = multiply(multiply(b, a), multiply(multiply(multiply(b, a), a), multiply(b, a)))),
% 0.18/0.54 inference(transitivity,[status(thm)],[69, 67, 53])).
% 0.18/0.54 tff(71,plain,
% 0.18/0.54 (multiply(multiply(b, a), multiply(multiply(multiply(b, a), a), multiply(a, multiply(a, multiply(b, b))))) = multiply(multiply(b, a), multiply(multiply(b, a), multiply(multiply(multiply(b, a), a), multiply(b, a))))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[70])).
% 0.18/0.54 tff(72,plain,
% 0.18/0.54 (multiply(multiply(b, a), multiply(multiply(b, a), multiply(multiply(multiply(b, a), a), multiply(b, a)))) = multiply(multiply(b, a), multiply(multiply(multiply(b, a), a), multiply(a, multiply(a, multiply(b, b)))))),
% 0.18/0.54 inference(symmetry,[status(thm)],[71])).
% 0.18/0.54 tff(73,plain,
% 0.18/0.54 (multiply(multiply(b, a), multiply(multiply(b, a), multiply(multiply(multiply(b, a), a), multiply(b, a)))) = multiply(multiply(b, a), multiply(multiply(b, a), multiply(multiply(b, a), multiply(a, multiply(b, a)))))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[52])).
% 0.18/0.54 tff(74,plain,
% 0.18/0.54 (multiply(multiply(b, a), multiply(multiply(b, a), multiply(multiply(b, a), multiply(a, multiply(b, a))))) = multiply(multiply(b, a), multiply(multiply(b, a), multiply(multiply(multiply(b, a), a), multiply(b, a))))),
% 0.18/0.54 inference(symmetry,[status(thm)],[73])).
% 0.18/0.54 tff(75,plain,
% 0.18/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(b, a), multiply(multiply(b, a), multiply(multiply(b, a), multiply(a, multiply(b, a))))) = multiply(b, multiply(a, multiply(multiply(b, a), multiply(multiply(b, a), multiply(a, multiply(b, a)))))))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(76,plain,
% 0.18/0.54 (multiply(multiply(b, a), multiply(multiply(b, a), multiply(multiply(b, a), multiply(a, multiply(b, a))))) = multiply(b, multiply(a, multiply(multiply(b, a), multiply(multiply(b, a), multiply(a, multiply(b, a))))))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[75, 15])).
% 0.18/0.54 tff(77,plain,
% 0.18/0.54 (multiply(b, multiply(a, multiply(multiply(b, a), multiply(multiply(b, a), multiply(a, multiply(b, a)))))) = multiply(multiply(b, a), multiply(multiply(b, a), multiply(multiply(b, a), multiply(a, multiply(b, a)))))),
% 0.18/0.54 inference(symmetry,[status(thm)],[76])).
% 0.18/0.54 tff(78,plain,
% 0.18/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a))) = multiply(a, multiply(multiply(b, a), multiply(a, multiply(b, a)))))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(79,plain,
% 0.18/0.54 (multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a))) = multiply(a, multiply(multiply(b, a), multiply(a, multiply(b, a))))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[78, 15])).
% 0.18/0.54 tff(80,plain,
% 0.18/0.54 (multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a)))) = multiply(multiply(a, b), multiply(a, multiply(multiply(b, a), multiply(a, multiply(b, a)))))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[79])).
% 0.18/0.54 tff(81,plain,
% 0.18/0.54 (multiply(multiply(a, b), multiply(a, multiply(multiply(b, a), multiply(a, multiply(b, a))))) = multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a))))),
% 0.18/0.54 inference(symmetry,[status(thm)],[80])).
% 0.18/0.54 tff(82,plain,
% 0.18/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(a, b), a), multiply(multiply(b, a), multiply(a, multiply(b, a)))) = multiply(multiply(a, b), multiply(a, multiply(multiply(b, a), multiply(a, multiply(b, a))))))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(83,plain,
% 0.18/0.54 (multiply(multiply(multiply(a, b), a), multiply(multiply(b, a), multiply(a, multiply(b, a)))) = multiply(multiply(a, b), multiply(a, multiply(multiply(b, a), multiply(a, multiply(b, a)))))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[82, 15])).
% 0.18/0.54 tff(84,plain,
% 0.18/0.54 (multiply(multiply(multiply(a, b), a), multiply(multiply(b, a), multiply(a, multiply(b, a)))) = multiply(multiply(a, multiply(b, a)), multiply(multiply(b, a), multiply(a, multiply(b, a))))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[30])).
% 0.18/0.54 tff(85,plain,
% 0.18/0.54 (multiply(multiply(a, multiply(b, a)), multiply(multiply(b, a), multiply(a, multiply(b, a)))) = multiply(multiply(multiply(a, b), a), multiply(multiply(b, a), multiply(a, multiply(b, a))))),
% 0.18/0.54 inference(symmetry,[status(thm)],[84])).
% 0.18/0.54 tff(86,plain,
% 0.18/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(a, multiply(b, a)), multiply(multiply(b, a), multiply(a, multiply(b, a)))) = multiply(a, multiply(multiply(b, a), multiply(multiply(b, a), multiply(a, multiply(b, a))))))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(87,plain,
% 0.18/0.54 (multiply(multiply(a, multiply(b, a)), multiply(multiply(b, a), multiply(a, multiply(b, a)))) = multiply(a, multiply(multiply(b, a), multiply(multiply(b, a), multiply(a, multiply(b, a)))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[86, 15])).
% 0.18/0.55 tff(88,plain,
% 0.18/0.55 (multiply(a, multiply(multiply(b, a), multiply(multiply(b, a), multiply(a, multiply(b, a))))) = multiply(multiply(a, multiply(b, a)), multiply(multiply(b, a), multiply(a, multiply(b, a))))),
% 0.18/0.55 inference(symmetry,[status(thm)],[87])).
% 0.18/0.55 tff(89,plain,
% 0.18/0.55 (multiply(a, multiply(multiply(b, a), multiply(multiply(b, a), multiply(a, multiply(b, a))))) = multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a))))),
% 0.18/0.55 inference(transitivity,[status(thm)],[88, 85, 83, 81])).
% 0.18/0.55 tff(90,plain,
% 0.18/0.55 (multiply(b, multiply(a, multiply(multiply(b, a), multiply(multiply(b, a), multiply(a, multiply(b, a)))))) = multiply(b, multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a)))))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[89])).
% 0.18/0.55 tff(91,plain,
% 0.18/0.55 (multiply(b, multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a))))) = multiply(b, multiply(a, multiply(multiply(b, a), multiply(multiply(b, a), multiply(a, multiply(b, a))))))),
% 0.18/0.55 inference(symmetry,[status(thm)],[90])).
% 0.18/0.55 tff(92,plain,
% 0.18/0.55 (![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(A, C))) | (B = C)) <=> ![Xk!0: $i, Xk!1: $i] : (inj_1(Xk!1, multiply(Xk!1, Xk!0)) = Xk!0)),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(93,plain,
% 0.18/0.55 (![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(A, C))) | (B = C)) <=> ![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(A, C))) | (B = C))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(94,axiom,(![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(A, C))) | (B = C))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP008-1.ax','left_cancellation')).
% 0.18/0.55 tff(95,plain,
% 0.18/0.55 (![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(A, C))) | (B = C))),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.18/0.55 tff(96,plain,(
% 0.18/0.55 ![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(A, C))) | (B = C))),
% 0.18/0.55 inference(skolemize,[status(sab)],[95])).
% 0.18/0.55 tff(97,plain,
% 0.18/0.55 (![Xk!0: $i, Xk!1: $i] : (inj_1(Xk!1, multiply(Xk!1, Xk!0)) = Xk!0)),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.18/0.55 tff(98,plain,
% 0.18/0.55 ((~![Xk!0: $i, Xk!1: $i] : (inj_1(Xk!1, multiply(Xk!1, Xk!0)) = Xk!0)) | (inj_1(a, multiply(a, multiply(b, multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a))))))) = multiply(b, multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a))))))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(99,plain,
% 0.18/0.55 (inj_1(a, multiply(a, multiply(b, multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a))))))) = multiply(b, multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a)))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.18/0.55 tff(100,plain,
% 0.18/0.55 ((~![Xk!0: $i, Xk!1: $i] : (inj_1(Xk!1, multiply(Xk!1, Xk!0)) = Xk!0)) | (inj_1(multiply(a, b), multiply(multiply(a, b), multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b))))))) = multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b))))))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(101,plain,
% 0.18/0.55 (inj_1(multiply(a, b), multiply(multiply(a, b), multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b))))))) = multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b)))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[100, 97])).
% 0.18/0.55 tff(102,plain,
% 0.18/0.55 ((~![Y: $i, X: $i] : (multiply(X, multiply(X, multiply(X, multiply(Y, Y)))) = multiply(Y, multiply(X, multiply(X, multiply(Y, X)))))) | (multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a)))))) = multiply(multiply(a, multiply(b, a)), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b))))))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(103,plain,
% 0.18/0.55 (multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a)))))) = multiply(multiply(a, multiply(b, a)), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b)))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[102, 63])).
% 0.18/0.55 tff(104,plain,
% 0.18/0.55 (multiply(multiply(a, multiply(b, a)), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b))))) = multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a))))))),
% 0.18/0.55 inference(symmetry,[status(thm)],[103])).
% 0.18/0.55 tff(105,plain,
% 0.18/0.55 (multiply(multiply(multiply(a, b), a), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b))))) = multiply(multiply(a, multiply(b, a)), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b)))))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[30])).
% 0.18/0.55 tff(106,plain,
% 0.18/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(a, b), a), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b))))) = multiply(multiply(a, b), multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b)))))))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(107,plain,
% 0.18/0.55 (multiply(multiply(multiply(a, b), a), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b))))) = multiply(multiply(a, b), multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b))))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[106, 15])).
% 0.18/0.55 tff(108,plain,
% 0.18/0.55 (multiply(multiply(a, b), multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b)))))) = multiply(multiply(multiply(a, b), a), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b)))))),
% 0.18/0.55 inference(symmetry,[status(thm)],[107])).
% 0.18/0.55 tff(109,plain,
% 0.18/0.55 (multiply(multiply(a, b), multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b)))))) = multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a))))))),
% 0.18/0.55 inference(transitivity,[status(thm)],[108, 105, 104])).
% 0.18/0.55 tff(110,plain,
% 0.18/0.55 (inj_1(multiply(a, b), multiply(multiply(a, b), multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b))))))) = inj_1(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a)))))))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[109])).
% 0.18/0.55 tff(111,plain,
% 0.18/0.55 (inj_1(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a))))))) = inj_1(multiply(a, b), multiply(multiply(a, b), multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b)))))))),
% 0.18/0.55 inference(symmetry,[status(thm)],[110])).
% 0.18/0.55 tff(112,plain,
% 0.18/0.55 ((~![Xk!0: $i, Xk!1: $i] : (inj_1(Xk!1, multiply(Xk!1, Xk!0)) = Xk!0)) | (inj_1(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a))))))) = multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a))))))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(113,plain,
% 0.18/0.55 (inj_1(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a))))))) = multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a)))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[112, 97])).
% 0.18/0.55 tff(114,plain,
% 0.18/0.55 (multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a))))) = inj_1(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a)))))))),
% 0.18/0.55 inference(symmetry,[status(thm)],[113])).
% 0.18/0.55 tff(115,plain,
% 0.18/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a))))) = multiply(a, multiply(b, multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a)))))))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(116,plain,
% 0.18/0.55 (multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a))))) = multiply(a, multiply(b, multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a))))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[115, 15])).
% 0.18/0.55 tff(117,plain,
% 0.18/0.55 (multiply(a, multiply(b, multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a)))))) = multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a)))))),
% 0.18/0.55 inference(symmetry,[status(thm)],[116])).
% 0.18/0.55 tff(118,plain,
% 0.18/0.55 (multiply(a, multiply(b, multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a)))))) = multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b)))))),
% 0.18/0.55 inference(transitivity,[status(thm)],[117, 114, 111, 101])).
% 0.18/0.55 tff(119,plain,
% 0.18/0.55 (inj_1(a, multiply(a, multiply(b, multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a))))))) = inj_1(a, multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b))))))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[118])).
% 0.18/0.55 tff(120,plain,
% 0.18/0.55 (inj_1(a, multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b)))))) = inj_1(a, multiply(a, multiply(b, multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, multiply(b, a)))))))),
% 0.18/0.55 inference(symmetry,[status(thm)],[119])).
% 0.18/0.55 tff(121,plain,
% 0.18/0.55 ((~![Xk!0: $i, Xk!1: $i] : (inj_1(Xk!1, multiply(Xk!1, Xk!0)) = Xk!0)) | (inj_1(a, multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b)))))) = multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b)))))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(122,plain,
% 0.18/0.55 (inj_1(a, multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b)))))) = multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[121, 97])).
% 0.18/0.55 tff(123,plain,
% 0.18/0.55 (multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b)))) = inj_1(a, multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b))))))),
% 0.18/0.55 inference(symmetry,[status(thm)],[122])).
% 0.18/0.55 tff(124,plain,
% 0.18/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(a, b), multiply(a, multiply(a, b))) = multiply(a, multiply(b, multiply(a, multiply(a, b)))))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(125,plain,
% 0.18/0.55 (multiply(multiply(a, b), multiply(a, multiply(a, b))) = multiply(a, multiply(b, multiply(a, multiply(a, b))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[124, 15])).
% 0.18/0.55 tff(126,plain,
% 0.18/0.55 (multiply(a, multiply(b, multiply(a, multiply(a, b)))) = multiply(multiply(a, b), multiply(a, multiply(a, b)))),
% 0.18/0.55 inference(symmetry,[status(thm)],[125])).
% 0.18/0.55 tff(127,plain,
% 0.18/0.55 (multiply(multiply(a, multiply(b, a)), multiply(a, b)) = multiply(multiply(a, b), multiply(a, multiply(a, b)))),
% 0.18/0.55 inference(transitivity,[status(thm)],[17, 21, 126])).
% 0.18/0.55 tff(128,plain,
% 0.18/0.55 (multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b))) = multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, multiply(a, b))))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[127])).
% 0.18/0.55 tff(129,plain,
% 0.18/0.55 (multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, multiply(a, b)))) = multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b)))),
% 0.18/0.55 inference(symmetry,[status(thm)],[128])).
% 0.18/0.55 tff(130,plain,
% 0.18/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(a, a), b) = multiply(a, multiply(a, b)))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(131,plain,
% 0.18/0.55 (multiply(multiply(a, a), b) = multiply(a, multiply(a, b))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[130, 15])).
% 0.18/0.55 tff(132,plain,
% 0.18/0.55 (multiply(multiply(a, b), multiply(multiply(a, a), b)) = multiply(multiply(a, b), multiply(a, multiply(a, b)))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[131])).
% 0.18/0.55 tff(133,plain,
% 0.18/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(a, b), multiply(a, a)), b) = multiply(multiply(a, b), multiply(multiply(a, a), b)))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(134,plain,
% 0.18/0.55 (multiply(multiply(multiply(a, b), multiply(a, a)), b) = multiply(multiply(a, b), multiply(multiply(a, a), b))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[133, 15])).
% 0.18/0.55 tff(135,plain,
% 0.18/0.55 (multiply(multiply(multiply(a, b), multiply(a, a)), b) = multiply(multiply(a, b), multiply(a, multiply(a, b)))),
% 0.18/0.55 inference(transitivity,[status(thm)],[134, 132])).
% 0.18/0.55 tff(136,plain,
% 0.18/0.55 (multiply(multiply(a, b), multiply(multiply(multiply(a, b), multiply(a, a)), b)) = multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, multiply(a, b))))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[135])).
% 0.18/0.55 tff(137,plain,
% 0.18/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, a))), b) = multiply(multiply(a, b), multiply(multiply(multiply(a, b), multiply(a, a)), b)))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(138,plain,
% 0.18/0.55 (multiply(multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, a))), b) = multiply(multiply(a, b), multiply(multiply(multiply(a, b), multiply(a, a)), b))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[137, 15])).
% 0.18/0.55 tff(139,plain,
% 0.18/0.55 (multiply(multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, a))), b) = multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b)))),
% 0.18/0.55 inference(transitivity,[status(thm)],[138, 136, 129])).
% 0.18/0.55 tff(140,plain,
% 0.18/0.55 (multiply(multiply(a, b), multiply(multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, a))), b)) = multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, multiply(b, a)), multiply(a, b))))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[139])).
% 0.18/0.55 tff(141,plain,
% 0.18/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, a)))), b) = multiply(multiply(a, b), multiply(multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, a))), b)))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(142,plain,
% 0.18/0.55 (multiply(multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, a)))), b) = multiply(multiply(a, b), multiply(multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, a))), b))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[141, 15])).
% 0.18/0.55 tff(143,plain,
% 0.18/0.56 ((~![Y: $i, X: $i] : (multiply(X, multiply(X, multiply(X, multiply(Y, Y)))) = multiply(Y, multiply(X, multiply(X, multiply(Y, X)))))) | (multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, a)))) = multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, multiply(a, b))))))),
% 0.18/0.56 inference(quant_inst,[status(thm)],[])).
% 0.18/0.56 tff(144,plain,
% 0.18/0.56 (multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, a)))) = multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, multiply(a, b)))))),
% 0.18/0.56 inference(unit_resolution,[status(thm)],[143, 63])).
% 0.18/0.56 tff(145,plain,
% 0.18/0.56 (multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, multiply(a, b))))) = multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, a))))),
% 0.18/0.56 inference(symmetry,[status(thm)],[144])).
% 0.18/0.56 tff(146,plain,
% 0.18/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(a, b), multiply(a, b)), multiply(a, multiply(a, b))) = multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, multiply(a, b)))))),
% 0.18/0.56 inference(quant_inst,[status(thm)],[])).
% 0.18/0.56 tff(147,plain,
% 0.18/0.56 (multiply(multiply(multiply(a, b), multiply(a, b)), multiply(a, multiply(a, b))) = multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, multiply(a, b))))),
% 0.18/0.56 inference(unit_resolution,[status(thm)],[146, 15])).
% 0.18/0.56 tff(148,plain,
% 0.18/0.56 (multiply(a, multiply(multiply(multiply(a, b), multiply(a, b)), multiply(a, multiply(a, b)))) = multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, multiply(a, b)))))),
% 0.18/0.56 inference(monotonicity,[status(thm)],[147])).
% 0.18/0.56 tff(149,plain,
% 0.18/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(a, multiply(multiply(a, b), multiply(a, b))), multiply(a, multiply(a, b))) = multiply(a, multiply(multiply(multiply(a, b), multiply(a, b)), multiply(a, multiply(a, b)))))),
% 0.18/0.56 inference(quant_inst,[status(thm)],[])).
% 0.18/0.56 tff(150,plain,
% 0.18/0.56 (multiply(multiply(a, multiply(multiply(a, b), multiply(a, b))), multiply(a, multiply(a, b))) = multiply(a, multiply(multiply(multiply(a, b), multiply(a, b)), multiply(a, multiply(a, b))))),
% 0.18/0.56 inference(unit_resolution,[status(thm)],[149, 15])).
% 0.18/0.56 tff(151,plain,
% 0.18/0.56 (multiply(multiply(a, multiply(multiply(a, b), multiply(a, b))), multiply(a, multiply(a, b))) = multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, a))))),
% 0.18/0.56 inference(transitivity,[status(thm)],[150, 148, 145])).
% 0.18/0.56 tff(152,plain,
% 0.18/0.56 (multiply(multiply(multiply(a, multiply(multiply(a, b), multiply(a, b))), multiply(a, multiply(a, b))), b) = multiply(multiply(multiply(a, b), multiply(multiply(a, b), multiply(multiply(a, b), multiply(a, a)))), b)),
% 0.18/0.56 inference(monotonicity,[status(thm)],[151])).
% 0.18/0.56 tff(153,plain,
% 0.18/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(a, multiply(multiply(a, b), multiply(a, b))), multiply(a, multiply(a, b))), b) = multiply(multiply(a, multiply(multiply(a, b), multiply(a, b))), multiply(multiply(a, multiply(a, b)), b)))),
% 0.18/0.56 inference(quant_inst,[status(thm)],[])).
% 0.18/0.56 tff(154,plain,
% 0.18/0.56 (multiply(multiply(multiply(a, multiply(multiply(a, b), multiply(a, b))), multiply(a, multiply(a, b))), b) = multiply(multiply(a, multiply(multiply(a, b), multiply(a, b))), multiply(multiply(a, multiply(a, b)), b))),
% 0.18/0.56 inference(unit_resolution,[status(thm)],[153, 15])).
% 0.18/0.56 tff(155,plain,
% 0.18/0.56 (multiply(multiply(a, multiply(multiply(a, b), multiply(a, b))), multiply(multiply(a, multiply(a, b)), b)) = multiply(multiply(multiply(a, multiply(multiply(a, b), multiply(a, b))), multiply(a, multiply(a, b))), b)),
% 0.18/0.56 inference(symmetry,[status(thm)],[154])).
% 0.18/0.56 tff(156,plain,
% 0.18/0.56 (multiply(a, multiply(a, b)) = multiply(multiply(a, a), b)),
% 0.18/0.56 inference(symmetry,[status(thm)],[131])).
% 0.18/0.56 tff(157,plain,
% 0.18/0.56 (multiply(multiply(a, multiply(a, b)), b) = multiply(multiply(multiply(a, a), b), b)),
% 0.18/0.56 inference(monotonicity,[status(thm)],[156])).
% 0.18/0.56 tff(158,plain,
% 0.18/0.56 (multiply(multiply(multiply(a, a), b), b) = multiply(multiply(a, multiply(a, b)), b)),
% 0.18/0.56 inference(symmetry,[status(thm)],[157])).
% 0.18/0.56 tff(159,plain,
% 0.18/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(a, a), b), b) = multiply(multiply(a, a), multiply(b, b)))),
% 0.18/0.56 inference(quant_inst,[status(thm)],[])).
% 0.18/0.56 tff(160,plain,
% 0.18/0.56 (multiply(multiply(multiply(a, a), b), b) = multiply(multiply(a, a), multiply(b, b))),
% 0.18/0.56 inference(unit_resolution,[status(thm)],[159, 15])).
% 0.18/0.56 tff(161,plain,
% 0.18/0.56 (multiply(multiply(a, a), multiply(b, b)) = multiply(multiply(multiply(a, a), b), b)),
% 0.18/0.56 inference(symmetry,[status(thm)],[160])).
% 0.18/0.56 tff(162,plain,
% 0.18/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(a, a), multiply(b, b)) = multiply(a, multiply(a, multiply(b, b))))),
% 0.18/0.56 inference(quant_inst,[status(thm)],[])).
% 0.18/0.56 tff(163,plain,
% 0.18/0.56 (multiply(multiply(a, a), multiply(b, b)) = multiply(a, multiply(a, multiply(b, b)))),
% 0.18/0.56 inference(unit_resolution,[status(thm)],[162, 15])).
% 0.18/0.56 tff(164,plain,
% 0.18/0.56 (multiply(a, multiply(a, multiply(b, b))) = multiply(multiply(a, a), multiply(b, b))),
% 0.18/0.56 inference(symmetry,[status(thm)],[163])).
% 0.18/0.56 tff(165,plain,
% 0.18/0.56 (multiply(a, multiply(a, multiply(b, b))) = multiply(multiply(a, multiply(a, b)), b)),
% 0.18/0.56 inference(transitivity,[status(thm)],[164, 161, 158])).
% 0.18/0.56 tff(166,plain,
% 0.18/0.56 (multiply(multiply(a, multiply(multiply(a, b), multiply(a, b))), multiply(a, multiply(a, multiply(b, b)))) = multiply(multiply(a, multiply(multiply(a, b), multiply(a, b))), multiply(multiply(a, multiply(a, b)), b))),
% 0.18/0.56 inference(monotonicity,[status(thm)],[165])).
% 0.18/0.56 tff(167,plain,
% 0.18/0.56 (multiply(multiply(a, multiply(multiply(a, b), multiply(a, b))), multiply(a, multiply(a, multiply(b, b)))) = multiply(multiply(multiply(b, a), multiply(multiply(b, a), a)), multiply(a, multiply(a, multiply(b, b))))),
% 0.18/0.56 inference(transitivity,[status(thm)],[166, 155, 152, 142, 140, 123, 120, 99, 91, 77, 74, 72, 49])).
% 0.18/0.56 tff(168,plain,
% 0.18/0.56 (inj_0(multiply(a, multiply(a, multiply(b, b))), multiply(multiply(a, multiply(multiply(a, b), multiply(a, b))), multiply(a, multiply(a, multiply(b, b))))) = inj_0(multiply(a, multiply(a, multiply(b, b))), multiply(multiply(multiply(b, a), multiply(multiply(b, a), a)), multiply(a, multiply(a, multiply(b, b)))))),
% 0.18/0.56 inference(monotonicity,[status(thm)],[167])).
% 0.18/0.56 tff(169,plain,
% 0.18/0.56 ((~![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, multiply(Xk!1, Xk!0)) = Xk!1)) | (inj_0(multiply(a, multiply(a, multiply(b, b))), multiply(multiply(a, multiply(multiply(a, b), multiply(a, b))), multiply(a, multiply(a, multiply(b, b))))) = multiply(a, multiply(multiply(a, b), multiply(a, b))))),
% 0.18/0.56 inference(quant_inst,[status(thm)],[])).
% 0.18/0.56 tff(170,plain,
% 0.18/0.56 (inj_0(multiply(a, multiply(a, multiply(b, b))), multiply(multiply(a, multiply(multiply(a, b), multiply(a, b))), multiply(a, multiply(a, multiply(b, b))))) = multiply(a, multiply(multiply(a, b), multiply(a, b)))),
% 0.18/0.56 inference(unit_resolution,[status(thm)],[169, 6])).
% 0.18/0.56 tff(171,plain,
% 0.18/0.56 (multiply(a, multiply(multiply(a, b), multiply(a, b))) = inj_0(multiply(a, multiply(a, multiply(b, b))), multiply(multiply(a, multiply(multiply(a, b), multiply(a, b))), multiply(a, multiply(a, multiply(b, b)))))),
% 0.18/0.56 inference(symmetry,[status(thm)],[170])).
% 0.18/0.56 tff(172,plain,
% 0.18/0.56 (multiply(a, multiply(multiply(a, b), multiply(a, b))) = multiply(multiply(multiply(b, a), b), multiply(a, a))),
% 0.18/0.56 inference(transitivity,[status(thm)],[171, 168, 46, 44, 39])).
% 0.18/0.56 tff(173,plain,
% 0.18/0.56 (multiply(multiply(a, b), multiply(a, multiply(multiply(a, b), multiply(a, b)))) = multiply(multiply(a, b), multiply(multiply(multiply(b, a), b), multiply(a, a)))),
% 0.18/0.56 inference(monotonicity,[status(thm)],[172])).
% 0.18/0.56 tff(174,plain,
% 0.18/0.56 (multiply(multiply(a, b), multiply(multiply(multiply(b, a), b), multiply(a, a))) = multiply(multiply(a, b), multiply(a, multiply(multiply(a, b), multiply(a, b))))),
% 0.18/0.56 inference(symmetry,[status(thm)],[173])).
% 0.18/0.56 tff(175,plain,
% 0.18/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(a, b), multiply(multiply(b, a), b)), multiply(a, a)) = multiply(multiply(a, b), multiply(multiply(multiply(b, a), b), multiply(a, a))))),
% 0.18/0.56 inference(quant_inst,[status(thm)],[])).
% 0.18/0.56 tff(176,plain,
% 0.18/0.56 (multiply(multiply(multiply(a, b), multiply(multiply(b, a), b)), multiply(a, a)) = multiply(multiply(a, b), multiply(multiply(multiply(b, a), b), multiply(a, a)))),
% 0.18/0.56 inference(unit_resolution,[status(thm)],[175, 15])).
% 0.18/0.56 tff(177,plain,
% 0.18/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(b, b), multiply(multiply(b, a), a)) = multiply(b, multiply(b, multiply(multiply(b, a), a))))),
% 0.18/0.56 inference(quant_inst,[status(thm)],[])).
% 0.18/0.56 tff(178,plain,
% 0.18/0.56 (multiply(multiply(b, b), multiply(multiply(b, a), a)) = multiply(b, multiply(b, multiply(multiply(b, a), a)))),
% 0.18/0.56 inference(unit_resolution,[status(thm)],[177, 15])).
% 0.18/0.56 tff(179,plain,
% 0.18/0.56 (multiply(b, multiply(b, multiply(multiply(b, a), a))) = multiply(multiply(b, b), multiply(multiply(b, a), a))),
% 0.18/0.56 inference(symmetry,[status(thm)],[178])).
% 0.18/0.56 tff(180,plain,
% 0.18/0.56 (multiply(b, multiply(multiply(b, a), a)) = multiply(b, multiply(b, multiply(a, a)))),
% 0.18/0.56 inference(monotonicity,[status(thm)],[41])).
% 0.18/0.56 tff(181,plain,
% 0.18/0.56 (multiply(b, multiply(b, multiply(multiply(b, a), a))) = multiply(b, multiply(b, multiply(b, multiply(a, a))))),
% 0.18/0.56 inference(monotonicity,[status(thm)],[180])).
% 0.18/0.56 tff(182,plain,
% 0.18/0.56 (multiply(b, multiply(b, multiply(b, multiply(a, a)))) = multiply(b, multiply(b, multiply(multiply(b, a), a)))),
% 0.18/0.56 inference(symmetry,[status(thm)],[181])).
% 0.18/0.56 tff(183,plain,
% 0.18/0.56 ((~![Y: $i, X: $i] : (multiply(X, multiply(X, multiply(X, multiply(Y, Y)))) = multiply(Y, multiply(X, multiply(X, multiply(Y, X)))))) | (multiply(b, multiply(b, multiply(b, multiply(a, a)))) = multiply(a, multiply(b, multiply(b, multiply(a, b)))))),
% 0.18/0.56 inference(quant_inst,[status(thm)],[])).
% 0.18/0.56 tff(184,plain,
% 0.18/0.56 (multiply(b, multiply(b, multiply(b, multiply(a, a)))) = multiply(a, multiply(b, multiply(b, multiply(a, b))))),
% 0.18/0.56 inference(unit_resolution,[status(thm)],[183, 63])).
% 0.18/0.56 tff(185,plain,
% 0.18/0.56 (multiply(a, multiply(b, multiply(b, multiply(a, b)))) = multiply(b, multiply(b, multiply(b, multiply(a, a))))),
% 0.18/0.56 inference(symmetry,[status(thm)],[184])).
% 0.18/0.56 tff(186,plain,
% 0.18/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(a, b), multiply(b, multiply(a, b))) = multiply(a, multiply(b, multiply(b, multiply(a, b)))))),
% 0.18/0.56 inference(quant_inst,[status(thm)],[])).
% 0.18/0.56 tff(187,plain,
% 0.18/0.56 (multiply(multiply(a, b), multiply(b, multiply(a, b))) = multiply(a, multiply(b, multiply(b, multiply(a, b))))),
% 0.18/0.56 inference(unit_resolution,[status(thm)],[186, 15])).
% 0.18/0.56 tff(188,plain,
% 0.18/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(b, a), b) = multiply(b, multiply(a, b)))),
% 0.18/0.56 inference(quant_inst,[status(thm)],[])).
% 0.18/0.56 tff(189,plain,
% 0.18/0.56 (multiply(multiply(b, a), b) = multiply(b, multiply(a, b))),
% 0.18/0.56 inference(unit_resolution,[status(thm)],[188, 15])).
% 0.18/0.56 tff(190,plain,
% 0.18/0.56 (multiply(multiply(a, b), multiply(multiply(b, a), b)) = multiply(multiply(a, b), multiply(b, multiply(a, b)))),
% 0.18/0.56 inference(monotonicity,[status(thm)],[189])).
% 0.18/0.56 tff(191,plain,
% 0.18/0.56 (multiply(multiply(a, b), multiply(multiply(b, a), b)) = multiply(multiply(b, b), multiply(multiply(b, a), a))),
% 0.18/0.56 inference(transitivity,[status(thm)],[190, 187, 185, 182, 179])).
% 0.18/0.56 tff(192,plain,
% 0.18/0.56 (multiply(multiply(multiply(a, b), multiply(multiply(b, a), b)), multiply(a, a)) = multiply(multiply(multiply(b, b), multiply(multiply(b, a), a)), multiply(a, a))),
% 0.18/0.56 inference(monotonicity,[status(thm)],[191])).
% 0.18/0.56 tff(193,plain,
% 0.18/0.56 (multiply(multiply(multiply(b, b), multiply(multiply(b, a), a)), multiply(a, a)) = multiply(multiply(multiply(a, b), multiply(multiply(b, a), b)), multiply(a, a))),
% 0.18/0.56 inference(symmetry,[status(thm)],[192])).
% 0.18/0.56 tff(194,plain,
% 0.18/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(b, b), multiply(multiply(b, a), a)), multiply(a, a)) = multiply(multiply(b, b), multiply(multiply(multiply(b, a), a), multiply(a, a))))),
% 0.18/0.56 inference(quant_inst,[status(thm)],[])).
% 0.18/0.56 tff(195,plain,
% 0.18/0.56 (multiply(multiply(multiply(b, b), multiply(multiply(b, a), a)), multiply(a, a)) = multiply(multiply(b, b), multiply(multiply(multiply(b, a), a), multiply(a, a)))),
% 0.18/0.56 inference(unit_resolution,[status(thm)],[194, 15])).
% 0.18/0.56 tff(196,plain,
% 0.18/0.56 (multiply(multiply(b, b), multiply(multiply(multiply(b, a), a), multiply(a, a))) = multiply(multiply(multiply(b, b), multiply(multiply(b, a), a)), multiply(a, a))),
% 0.18/0.56 inference(symmetry,[status(thm)],[195])).
% 0.18/0.56 tff(197,plain,
% 0.18/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(b, multiply(a, a)), multiply(a, a)) = multiply(b, multiply(multiply(a, a), multiply(a, a))))),
% 0.18/0.56 inference(quant_inst,[status(thm)],[])).
% 0.18/0.56 tff(198,plain,
% 0.18/0.56 (multiply(multiply(b, multiply(a, a)), multiply(a, a)) = multiply(b, multiply(multiply(a, a), multiply(a, a)))),
% 0.18/0.56 inference(unit_resolution,[status(thm)],[197, 15])).
% 0.18/0.56 tff(199,plain,
% 0.18/0.56 (multiply(multiply(multiply(b, a), a), multiply(a, a)) = multiply(multiply(b, multiply(a, a)), multiply(a, a))),
% 0.18/0.56 inference(monotonicity,[status(thm)],[41])).
% 0.18/0.56 tff(200,plain,
% 0.18/0.56 (multiply(multiply(multiply(b, a), a), multiply(a, a)) = multiply(b, multiply(multiply(a, a), multiply(a, a)))),
% 0.18/0.56 inference(transitivity,[status(thm)],[199, 198])).
% 0.18/0.56 tff(201,plain,
% 0.18/0.56 (multiply(multiply(b, b), multiply(multiply(multiply(b, a), a), multiply(a, a))) = multiply(multiply(b, b), multiply(b, multiply(multiply(a, a), multiply(a, a))))),
% 0.18/0.56 inference(monotonicity,[status(thm)],[200])).
% 0.18/0.56 tff(202,plain,
% 0.18/0.56 (multiply(multiply(b, b), multiply(b, multiply(multiply(a, a), multiply(a, a)))) = multiply(multiply(b, b), multiply(multiply(multiply(b, a), a), multiply(a, a)))),
% 0.18/0.56 inference(symmetry,[status(thm)],[201])).
% 0.18/0.56 tff(203,plain,
% 0.18/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(b, b), multiply(b, multiply(multiply(a, a), multiply(a, a)))) = multiply(b, multiply(b, multiply(b, multiply(multiply(a, a), multiply(a, a))))))),
% 0.18/0.56 inference(quant_inst,[status(thm)],[])).
% 0.18/0.56 tff(204,plain,
% 0.18/0.56 (multiply(multiply(b, b), multiply(b, multiply(multiply(a, a), multiply(a, a)))) = multiply(b, multiply(b, multiply(b, multiply(multiply(a, a), multiply(a, a)))))),
% 0.18/0.56 inference(unit_resolution,[status(thm)],[203, 15])).
% 0.18/0.56 tff(205,plain,
% 0.18/0.56 (multiply(b, multiply(b, multiply(b, multiply(multiply(a, a), multiply(a, a))))) = multiply(multiply(b, b), multiply(b, multiply(multiply(a, a), multiply(a, a))))),
% 0.18/0.56 inference(symmetry,[status(thm)],[204])).
% 0.18/0.56 tff(206,plain,
% 0.18/0.56 ((~![Y: $i, X: $i] : (multiply(X, multiply(X, multiply(X, multiply(Y, Y)))) = multiply(Y, multiply(X, multiply(X, multiply(Y, X)))))) | (multiply(b, multiply(b, multiply(b, multiply(multiply(a, a), multiply(a, a))))) = multiply(multiply(a, a), multiply(b, multiply(b, multiply(multiply(a, a), b)))))),
% 0.18/0.56 inference(quant_inst,[status(thm)],[])).
% 0.18/0.56 tff(207,plain,
% 0.18/0.56 (multiply(b, multiply(b, multiply(b, multiply(multiply(a, a), multiply(a, a))))) = multiply(multiply(a, a), multiply(b, multiply(b, multiply(multiply(a, a), b))))),
% 0.18/0.56 inference(unit_resolution,[status(thm)],[206, 63])).
% 0.18/0.56 tff(208,plain,
% 0.18/0.56 (multiply(multiply(a, a), multiply(b, multiply(b, multiply(multiply(a, a), b)))) = multiply(b, multiply(b, multiply(b, multiply(multiply(a, a), multiply(a, a)))))),
% 0.18/0.56 inference(symmetry,[status(thm)],[207])).
% 0.18/0.56 tff(209,plain,
% 0.18/0.56 (multiply(b, multiply(multiply(a, a), b)) = multiply(b, multiply(a, multiply(a, b)))),
% 0.18/0.56 inference(monotonicity,[status(thm)],[131])).
% 0.18/0.56 tff(210,plain,
% 0.18/0.56 (multiply(b, multiply(a, multiply(a, b))) = multiply(b, multiply(multiply(a, a), b))),
% 0.18/0.56 inference(symmetry,[status(thm)],[209])).
% 0.18/0.56 tff(211,plain,
% 0.18/0.56 (multiply(b, multiply(b, multiply(a, multiply(a, b)))) = multiply(b, multiply(b, multiply(multiply(a, a), b)))),
% 0.18/0.56 inference(monotonicity,[status(thm)],[210])).
% 0.18/0.57 tff(212,plain,
% 0.18/0.57 (multiply(multiply(a, a), multiply(b, multiply(b, multiply(a, multiply(a, b))))) = multiply(multiply(a, a), multiply(b, multiply(b, multiply(multiply(a, a), b))))),
% 0.18/0.57 inference(monotonicity,[status(thm)],[211])).
% 0.18/0.57 tff(213,plain,
% 0.18/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(a, a), b), multiply(b, multiply(a, multiply(a, b)))) = multiply(multiply(a, a), multiply(b, multiply(b, multiply(a, multiply(a, b))))))),
% 0.18/0.57 inference(quant_inst,[status(thm)],[])).
% 0.18/0.57 tff(214,plain,
% 0.18/0.57 (multiply(multiply(multiply(a, a), b), multiply(b, multiply(a, multiply(a, b)))) = multiply(multiply(a, a), multiply(b, multiply(b, multiply(a, multiply(a, b)))))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[213, 15])).
% 0.18/0.57 tff(215,plain,
% 0.18/0.57 (multiply(multiply(a, multiply(a, b)), multiply(multiply(b, a), multiply(a, b))) = multiply(multiply(multiply(a, a), b), multiply(b, multiply(a, multiply(a, b))))),
% 0.18/0.57 inference(monotonicity,[status(thm)],[156, 20])).
% 0.18/0.57 tff(216,plain,
% 0.18/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(a, multiply(a, b)), multiply(b, a)), multiply(a, b)) = multiply(multiply(a, multiply(a, b)), multiply(multiply(b, a), multiply(a, b))))),
% 0.18/0.57 inference(quant_inst,[status(thm)],[])).
% 0.18/0.57 tff(217,plain,
% 0.18/0.57 (multiply(multiply(multiply(a, multiply(a, b)), multiply(b, a)), multiply(a, b)) = multiply(multiply(a, multiply(a, b)), multiply(multiply(b, a), multiply(a, b)))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[216, 15])).
% 0.18/0.57 tff(218,plain,
% 0.18/0.57 (multiply(multiply(multiply(a, multiply(a, b)), multiply(b, a)), multiply(a, b)) = multiply(multiply(a, multiply(b, multiply(a, multiply(a, b)))), multiply(a, b))),
% 0.18/0.57 inference(transitivity,[status(thm)],[217, 215, 214, 212, 208, 205, 202, 196, 193, 176, 174, 36, 33, 28, 25])).
% 0.18/0.57 tff(219,plain,
% 0.18/0.57 (inj_0(multiply(a, b), multiply(multiply(multiply(a, multiply(a, b)), multiply(b, a)), multiply(a, b))) = inj_0(multiply(a, b), multiply(multiply(a, multiply(b, multiply(a, multiply(a, b)))), multiply(a, b)))),
% 0.18/0.57 inference(monotonicity,[status(thm)],[218])).
% 0.18/0.57 tff(220,plain,
% 0.18/0.57 ((~![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, multiply(Xk!1, Xk!0)) = Xk!1)) | (inj_0(multiply(a, b), multiply(multiply(multiply(a, multiply(a, b)), multiply(b, a)), multiply(a, b))) = multiply(multiply(a, multiply(a, b)), multiply(b, a)))),
% 0.18/0.57 inference(quant_inst,[status(thm)],[])).
% 0.18/0.57 tff(221,plain,
% 0.18/0.57 (inj_0(multiply(a, b), multiply(multiply(multiply(a, multiply(a, b)), multiply(b, a)), multiply(a, b))) = multiply(multiply(a, multiply(a, b)), multiply(b, a))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[220, 6])).
% 0.18/0.57 tff(222,plain,
% 0.18/0.57 (multiply(multiply(a, multiply(a, b)), multiply(b, a)) = inj_0(multiply(a, b), multiply(multiply(multiply(a, multiply(a, b)), multiply(b, a)), multiply(a, b)))),
% 0.18/0.57 inference(symmetry,[status(thm)],[221])).
% 0.18/0.57 tff(223,plain,
% 0.18/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(a, multiply(a, b)), multiply(b, a)) = multiply(a, multiply(multiply(a, b), multiply(b, a))))),
% 0.18/0.57 inference(quant_inst,[status(thm)],[])).
% 0.18/0.57 tff(224,plain,
% 0.18/0.57 (multiply(multiply(a, multiply(a, b)), multiply(b, a)) = multiply(a, multiply(multiply(a, b), multiply(b, a)))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[223, 15])).
% 0.18/0.57 tff(225,plain,
% 0.18/0.57 (multiply(a, multiply(multiply(a, b), multiply(b, a))) = multiply(multiply(a, multiply(a, b)), multiply(b, a))),
% 0.18/0.57 inference(symmetry,[status(thm)],[224])).
% 0.18/0.57 tff(226,plain,
% 0.18/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(a, b), multiply(b, a)) = multiply(a, multiply(b, multiply(b, a))))),
% 0.18/0.57 inference(quant_inst,[status(thm)],[])).
% 0.18/0.57 tff(227,plain,
% 0.18/0.57 (multiply(multiply(a, b), multiply(b, a)) = multiply(a, multiply(b, multiply(b, a)))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[226, 15])).
% 0.18/0.57 tff(228,plain,
% 0.18/0.57 (multiply(a, multiply(b, multiply(b, a))) = multiply(multiply(a, b), multiply(b, a))),
% 0.18/0.57 inference(symmetry,[status(thm)],[227])).
% 0.18/0.57 tff(229,plain,
% 0.18/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(b, b), a) = multiply(b, multiply(b, a)))),
% 0.18/0.57 inference(quant_inst,[status(thm)],[])).
% 0.18/0.57 tff(230,plain,
% 0.18/0.57 (multiply(multiply(b, b), a) = multiply(b, multiply(b, a))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[229, 15])).
% 0.18/0.57 tff(231,plain,
% 0.18/0.57 (multiply(b, multiply(b, a)) = multiply(multiply(b, b), a)),
% 0.18/0.57 inference(symmetry,[status(thm)],[230])).
% 0.18/0.57 tff(232,plain,
% 0.18/0.57 (multiply(a, multiply(b, multiply(b, a))) = multiply(a, multiply(multiply(b, b), a))),
% 0.18/0.57 inference(monotonicity,[status(thm)],[231])).
% 0.18/0.57 tff(233,plain,
% 0.18/0.57 (multiply(a, multiply(multiply(b, b), a)) = multiply(a, multiply(b, multiply(b, a)))),
% 0.18/0.57 inference(symmetry,[status(thm)],[232])).
% 0.18/0.57 tff(234,plain,
% 0.18/0.57 (multiply(a, multiply(multiply(b, b), a)) = multiply(multiply(a, b), multiply(b, a))),
% 0.18/0.57 inference(transitivity,[status(thm)],[233, 228])).
% 0.18/0.57 tff(235,plain,
% 0.18/0.57 (multiply(a, multiply(a, multiply(multiply(b, b), a))) = multiply(a, multiply(multiply(a, b), multiply(b, a)))),
% 0.18/0.57 inference(monotonicity,[status(thm)],[234])).
% 0.18/0.57 tff(236,plain,
% 0.18/0.57 ((~![Xk!0: $i, Xk!1: $i] : (inj_1(Xk!1, multiply(Xk!1, Xk!0)) = Xk!0)) | (inj_1(multiply(multiply(a, multiply(multiply(b, b), a)), multiply(b, b)), multiply(multiply(multiply(a, multiply(multiply(b, b), a)), multiply(b, b)), multiply(a, multiply(a, multiply(multiply(b, b), a))))) = multiply(a, multiply(a, multiply(multiply(b, b), a))))),
% 0.18/0.57 inference(quant_inst,[status(thm)],[])).
% 0.18/0.57 tff(237,plain,
% 0.18/0.57 (inj_1(multiply(multiply(a, multiply(multiply(b, b), a)), multiply(b, b)), multiply(multiply(multiply(a, multiply(multiply(b, b), a)), multiply(b, b)), multiply(a, multiply(a, multiply(multiply(b, b), a))))) = multiply(a, multiply(a, multiply(multiply(b, b), a)))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[236, 97])).
% 0.18/0.57 tff(238,plain,
% 0.18/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(a, multiply(multiply(b, b), a)), multiply(b, b)), multiply(a, multiply(a, multiply(multiply(b, b), a)))) = multiply(multiply(a, multiply(multiply(b, b), a)), multiply(multiply(b, b), multiply(a, multiply(a, multiply(multiply(b, b), a))))))),
% 0.18/0.57 inference(quant_inst,[status(thm)],[])).
% 0.18/0.57 tff(239,plain,
% 0.18/0.57 (multiply(multiply(multiply(a, multiply(multiply(b, b), a)), multiply(b, b)), multiply(a, multiply(a, multiply(multiply(b, b), a)))) = multiply(multiply(a, multiply(multiply(b, b), a)), multiply(multiply(b, b), multiply(a, multiply(a, multiply(multiply(b, b), a)))))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[238, 15])).
% 0.18/0.57 tff(240,plain,
% 0.18/0.57 (multiply(multiply(a, multiply(multiply(b, b), a)), multiply(multiply(b, b), multiply(a, multiply(a, multiply(multiply(b, b), a))))) = multiply(multiply(multiply(a, multiply(multiply(b, b), a)), multiply(b, b)), multiply(a, multiply(a, multiply(multiply(b, b), a))))),
% 0.18/0.57 inference(symmetry,[status(thm)],[239])).
% 0.18/0.57 tff(241,plain,
% 0.18/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(b, b), a), multiply(a, multiply(multiply(b, b), a))) = multiply(multiply(b, b), multiply(a, multiply(a, multiply(multiply(b, b), a)))))),
% 0.18/0.57 inference(quant_inst,[status(thm)],[])).
% 0.18/0.57 tff(242,plain,
% 0.18/0.57 (multiply(multiply(multiply(b, b), a), multiply(a, multiply(multiply(b, b), a))) = multiply(multiply(b, b), multiply(a, multiply(a, multiply(multiply(b, b), a))))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[241, 15])).
% 0.18/0.57 tff(243,plain,
% 0.18/0.57 (multiply(multiply(b, b), multiply(a, multiply(a, multiply(multiply(b, b), a)))) = multiply(multiply(multiply(b, b), a), multiply(a, multiply(multiply(b, b), a)))),
% 0.18/0.57 inference(symmetry,[status(thm)],[242])).
% 0.18/0.57 tff(244,plain,
% 0.18/0.57 (multiply(multiply(a, multiply(multiply(b, b), a)), multiply(multiply(b, b), multiply(a, multiply(a, multiply(multiply(b, b), a))))) = multiply(multiply(a, multiply(multiply(b, b), a)), multiply(multiply(multiply(b, b), a), multiply(a, multiply(multiply(b, b), a))))),
% 0.18/0.57 inference(monotonicity,[status(thm)],[243])).
% 0.18/0.57 tff(245,plain,
% 0.18/0.57 (multiply(multiply(a, multiply(multiply(b, b), a)), multiply(multiply(multiply(b, b), a), multiply(a, multiply(multiply(b, b), a)))) = multiply(multiply(a, multiply(multiply(b, b), a)), multiply(multiply(b, b), multiply(a, multiply(a, multiply(multiply(b, b), a)))))),
% 0.18/0.57 inference(symmetry,[status(thm)],[244])).
% 0.18/0.57 tff(246,plain,
% 0.18/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(a, multiply(multiply(b, b), a)), multiply(multiply(multiply(b, b), a), multiply(a, multiply(multiply(b, b), a)))) = multiply(a, multiply(multiply(multiply(b, b), a), multiply(multiply(multiply(b, b), a), multiply(a, multiply(multiply(b, b), a))))))),
% 0.18/0.57 inference(quant_inst,[status(thm)],[])).
% 0.18/0.57 tff(247,plain,
% 0.18/0.57 (multiply(multiply(a, multiply(multiply(b, b), a)), multiply(multiply(multiply(b, b), a), multiply(a, multiply(multiply(b, b), a)))) = multiply(a, multiply(multiply(multiply(b, b), a), multiply(multiply(multiply(b, b), a), multiply(a, multiply(multiply(b, b), a)))))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[246, 15])).
% 0.18/0.57 tff(248,plain,
% 0.18/0.57 (multiply(a, multiply(multiply(multiply(b, b), a), multiply(multiply(multiply(b, b), a), multiply(a, multiply(multiply(b, b), a))))) = multiply(multiply(a, multiply(multiply(b, b), a)), multiply(multiply(multiply(b, b), a), multiply(a, multiply(multiply(b, b), a))))),
% 0.18/0.57 inference(symmetry,[status(thm)],[247])).
% 0.18/0.57 tff(249,plain,
% 0.18/0.57 ((~![Y: $i, X: $i] : (multiply(X, multiply(X, multiply(X, multiply(Y, Y)))) = multiply(Y, multiply(X, multiply(X, multiply(Y, X)))))) | (multiply(multiply(multiply(b, b), a), multiply(multiply(multiply(b, b), a), multiply(multiply(multiply(b, b), a), multiply(a, a)))) = multiply(a, multiply(multiply(multiply(b, b), a), multiply(multiply(multiply(b, b), a), multiply(a, multiply(multiply(b, b), a))))))),
% 0.18/0.57 inference(quant_inst,[status(thm)],[])).
% 0.18/0.57 tff(250,plain,
% 0.18/0.57 (multiply(multiply(multiply(b, b), a), multiply(multiply(multiply(b, b), a), multiply(multiply(multiply(b, b), a), multiply(a, a)))) = multiply(a, multiply(multiply(multiply(b, b), a), multiply(multiply(multiply(b, b), a), multiply(a, multiply(multiply(b, b), a)))))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[249, 63])).
% 0.18/0.57 tff(251,plain,
% 0.18/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(b, b), a), multiply(a, a)) = multiply(multiply(b, b), multiply(a, multiply(a, a))))),
% 0.18/0.57 inference(quant_inst,[status(thm)],[])).
% 0.18/0.57 tff(252,plain,
% 0.18/0.57 (multiply(multiply(multiply(b, b), a), multiply(a, a)) = multiply(multiply(b, b), multiply(a, multiply(a, a)))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[251, 15])).
% 0.18/0.57 tff(253,plain,
% 0.18/0.57 (multiply(multiply(b, b), multiply(a, multiply(a, a))) = multiply(multiply(multiply(b, b), a), multiply(a, a))),
% 0.18/0.57 inference(symmetry,[status(thm)],[252])).
% 0.18/0.57 tff(254,plain,
% 0.18/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(b, b), multiply(a, multiply(a, a))) = multiply(b, multiply(b, multiply(a, multiply(a, a)))))),
% 0.18/0.57 inference(quant_inst,[status(thm)],[])).
% 0.18/0.57 tff(255,plain,
% 0.18/0.57 (multiply(multiply(b, b), multiply(a, multiply(a, a))) = multiply(b, multiply(b, multiply(a, multiply(a, a))))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[254, 15])).
% 0.18/0.57 tff(256,plain,
% 0.18/0.57 (multiply(b, multiply(b, multiply(a, multiply(a, a)))) = multiply(multiply(b, b), multiply(a, multiply(a, a)))),
% 0.18/0.57 inference(symmetry,[status(thm)],[255])).
% 0.18/0.57 tff(257,plain,
% 0.18/0.57 (multiply(b, multiply(b, multiply(a, multiply(a, a)))) = multiply(multiply(multiply(b, b), a), multiply(a, a))),
% 0.18/0.57 inference(transitivity,[status(thm)],[256, 253])).
% 0.18/0.57 tff(258,plain,
% 0.18/0.57 (multiply(multiply(multiply(b, b), a), multiply(b, multiply(b, multiply(a, multiply(a, a))))) = multiply(multiply(multiply(b, b), a), multiply(multiply(multiply(b, b), a), multiply(a, a)))),
% 0.18/0.57 inference(monotonicity,[status(thm)],[257])).
% 0.18/0.57 tff(259,plain,
% 0.18/0.57 (multiply(multiply(multiply(b, b), a), multiply(multiply(multiply(b, b), a), multiply(b, multiply(b, multiply(a, multiply(a, a)))))) = multiply(multiply(multiply(b, b), a), multiply(multiply(multiply(b, b), a), multiply(multiply(multiply(b, b), a), multiply(a, a))))),
% 0.18/0.57 inference(monotonicity,[status(thm)],[258])).
% 0.18/0.57 tff(260,plain,
% 0.18/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(multiply(b, b), a), multiply(multiply(b, b), a)), multiply(b, multiply(b, multiply(a, multiply(a, a))))) = multiply(multiply(multiply(b, b), a), multiply(multiply(multiply(b, b), a), multiply(b, multiply(b, multiply(a, multiply(a, a)))))))),
% 0.18/0.57 inference(quant_inst,[status(thm)],[])).
% 0.18/0.57 tff(261,plain,
% 0.18/0.57 (multiply(multiply(multiply(multiply(b, b), a), multiply(multiply(b, b), a)), multiply(b, multiply(b, multiply(a, multiply(a, a))))) = multiply(multiply(multiply(b, b), a), multiply(multiply(multiply(b, b), a), multiply(b, multiply(b, multiply(a, multiply(a, a))))))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[260, 15])).
% 0.18/0.57 tff(262,plain,
% 0.18/0.57 (multiply(multiply(multiply(multiply(b, b), a), multiply(multiply(b, b), a)), multiply(b, multiply(b, multiply(a, multiply(a, a))))) = multiply(multiply(multiply(a, multiply(multiply(b, b), a)), multiply(b, b)), multiply(a, multiply(a, multiply(multiply(b, b), a))))),
% 0.18/0.57 inference(transitivity,[status(thm)],[261, 259, 250, 248, 245, 240])).
% 0.18/0.57 tff(263,plain,
% 0.18/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(a, multiply(multiply(b, b), a)), multiply(b, b)) = multiply(a, multiply(multiply(multiply(b, b), a), multiply(b, b))))),
% 0.18/0.57 inference(quant_inst,[status(thm)],[])).
% 0.18/0.57 tff(264,plain,
% 0.18/0.57 (multiply(multiply(a, multiply(multiply(b, b), a)), multiply(b, b)) = multiply(a, multiply(multiply(multiply(b, b), a), multiply(b, b)))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[263, 15])).
% 0.18/0.57 tff(265,plain,
% 0.18/0.57 (multiply(a, multiply(multiply(multiply(b, b), a), multiply(b, b))) = multiply(multiply(a, multiply(multiply(b, b), a)), multiply(b, b))),
% 0.18/0.57 inference(symmetry,[status(thm)],[264])).
% 0.18/0.57 tff(266,plain,
% 0.18/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(b, b), a), multiply(b, b)) = multiply(multiply(b, b), multiply(a, multiply(b, b))))),
% 0.18/0.57 inference(quant_inst,[status(thm)],[])).
% 0.18/0.57 tff(267,plain,
% 0.18/0.57 (multiply(multiply(multiply(b, b), a), multiply(b, b)) = multiply(multiply(b, b), multiply(a, multiply(b, b)))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[266, 15])).
% 0.18/0.57 tff(268,plain,
% 0.18/0.57 (multiply(a, multiply(multiply(multiply(b, b), a), multiply(b, b))) = multiply(a, multiply(multiply(b, b), multiply(a, multiply(b, b))))),
% 0.18/0.57 inference(monotonicity,[status(thm)],[267])).
% 0.18/0.57 tff(269,plain,
% 0.18/0.57 (multiply(a, multiply(multiply(b, b), multiply(a, multiply(b, b)))) = multiply(a, multiply(multiply(multiply(b, b), a), multiply(b, b)))),
% 0.18/0.57 inference(symmetry,[status(thm)],[268])).
% 0.18/0.57 tff(270,plain,
% 0.18/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(b, b), multiply(a, b)) = multiply(b, multiply(b, multiply(a, b))))),
% 0.18/0.57 inference(quant_inst,[status(thm)],[])).
% 0.18/0.57 tff(271,plain,
% 0.18/0.57 (multiply(multiply(b, b), multiply(a, b)) = multiply(b, multiply(b, multiply(a, b)))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[270, 15])).
% 0.18/0.57 tff(272,plain,
% 0.18/0.57 (multiply(b, multiply(b, multiply(a, b))) = multiply(multiply(b, b), multiply(a, b))),
% 0.18/0.57 inference(symmetry,[status(thm)],[271])).
% 0.18/0.57 tff(273,plain,
% 0.18/0.57 (multiply(multiply(b, multiply(b, multiply(a, b))), b) = multiply(multiply(multiply(b, b), multiply(a, b)), b)),
% 0.18/0.57 inference(monotonicity,[status(thm)],[272])).
% 0.18/0.57 tff(274,plain,
% 0.18/0.57 (multiply(multiply(multiply(b, b), multiply(a, b)), b) = multiply(multiply(b, multiply(b, multiply(a, b))), b)),
% 0.18/0.57 inference(symmetry,[status(thm)],[273])).
% 0.18/0.57 tff(275,plain,
% 0.18/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(b, b), multiply(a, b)), b) = multiply(multiply(b, b), multiply(multiply(a, b), b)))),
% 0.18/0.58 inference(quant_inst,[status(thm)],[])).
% 0.18/0.58 tff(276,plain,
% 0.18/0.58 (multiply(multiply(multiply(b, b), multiply(a, b)), b) = multiply(multiply(b, b), multiply(multiply(a, b), b))),
% 0.18/0.58 inference(unit_resolution,[status(thm)],[275, 15])).
% 0.18/0.58 tff(277,plain,
% 0.18/0.58 (multiply(multiply(b, b), multiply(multiply(a, b), b)) = multiply(multiply(multiply(b, b), multiply(a, b)), b)),
% 0.18/0.58 inference(symmetry,[status(thm)],[276])).
% 0.18/0.58 tff(278,plain,
% 0.18/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(a, b), b) = multiply(a, multiply(b, b)))),
% 0.18/0.58 inference(quant_inst,[status(thm)],[])).
% 0.18/0.58 tff(279,plain,
% 0.18/0.58 (multiply(multiply(a, b), b) = multiply(a, multiply(b, b))),
% 0.18/0.58 inference(unit_resolution,[status(thm)],[278, 15])).
% 0.18/0.58 tff(280,plain,
% 0.18/0.58 (multiply(multiply(b, b), multiply(multiply(a, b), b)) = multiply(multiply(b, b), multiply(a, multiply(b, b)))),
% 0.18/0.58 inference(monotonicity,[status(thm)],[279])).
% 0.18/0.58 tff(281,plain,
% 0.18/0.58 (multiply(multiply(b, b), multiply(a, multiply(b, b))) = multiply(multiply(b, b), multiply(multiply(a, b), b))),
% 0.18/0.58 inference(symmetry,[status(thm)],[280])).
% 0.18/0.58 tff(282,plain,
% 0.18/0.58 (multiply(multiply(b, b), multiply(a, multiply(b, b))) = multiply(multiply(b, multiply(b, multiply(a, b))), b)),
% 0.18/0.58 inference(transitivity,[status(thm)],[281, 277, 274])).
% 0.18/0.58 tff(283,plain,
% 0.18/0.58 (multiply(a, multiply(multiply(b, b), multiply(a, multiply(b, b)))) = multiply(a, multiply(multiply(b, multiply(b, multiply(a, b))), b))),
% 0.18/0.58 inference(monotonicity,[status(thm)],[282])).
% 0.18/0.58 tff(284,plain,
% 0.18/0.58 (multiply(a, multiply(multiply(b, multiply(b, multiply(a, b))), b)) = multiply(a, multiply(multiply(b, b), multiply(a, multiply(b, b))))),
% 0.18/0.58 inference(symmetry,[status(thm)],[283])).
% 0.18/0.58 tff(285,plain,
% 0.18/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(a, multiply(b, multiply(b, multiply(a, b)))), b) = multiply(a, multiply(multiply(b, multiply(b, multiply(a, b))), b)))),
% 0.18/0.58 inference(quant_inst,[status(thm)],[])).
% 0.18/0.58 tff(286,plain,
% 0.18/0.58 (multiply(multiply(a, multiply(b, multiply(b, multiply(a, b)))), b) = multiply(a, multiply(multiply(b, multiply(b, multiply(a, b))), b))),
% 0.18/0.58 inference(unit_resolution,[status(thm)],[285, 15])).
% 0.18/0.58 tff(287,plain,
% 0.18/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(b, b), multiply(a, a)) = multiply(b, multiply(b, multiply(a, a))))),
% 0.18/0.58 inference(quant_inst,[status(thm)],[])).
% 0.18/0.58 tff(288,plain,
% 0.18/0.58 (multiply(multiply(b, b), multiply(a, a)) = multiply(b, multiply(b, multiply(a, a)))),
% 0.18/0.58 inference(unit_resolution,[status(thm)],[287, 15])).
% 0.18/0.58 tff(289,plain,
% 0.18/0.58 (multiply(b, multiply(multiply(b, b), multiply(a, a))) = multiply(b, multiply(b, multiply(b, multiply(a, a))))),
% 0.18/0.58 inference(monotonicity,[status(thm)],[288])).
% 0.18/0.58 tff(290,plain,
% 0.18/0.58 (multiply(b, multiply(b, multiply(b, multiply(a, a)))) = multiply(b, multiply(multiply(b, b), multiply(a, a)))),
% 0.18/0.58 inference(symmetry,[status(thm)],[289])).
% 0.18/0.58 tff(291,plain,
% 0.18/0.58 (multiply(a, multiply(b, multiply(b, multiply(a, b)))) = multiply(b, multiply(multiply(b, b), multiply(a, a)))),
% 0.18/0.58 inference(transitivity,[status(thm)],[185, 290])).
% 0.18/0.58 tff(292,plain,
% 0.18/0.58 (multiply(multiply(a, multiply(b, multiply(b, multiply(a, b)))), b) = multiply(multiply(b, multiply(multiply(b, b), multiply(a, a))), b)),
% 0.18/0.58 inference(monotonicity,[status(thm)],[291])).
% 0.18/0.58 tff(293,plain,
% 0.18/0.58 (multiply(multiply(b, multiply(multiply(b, b), multiply(a, a))), b) = multiply(multiply(a, multiply(b, multiply(b, multiply(a, b)))), b)),
% 0.18/0.58 inference(symmetry,[status(thm)],[292])).
% 0.18/0.58 tff(294,plain,
% 0.18/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(b, multiply(multiply(b, b), multiply(a, a))), b) = multiply(b, multiply(multiply(multiply(b, b), multiply(a, a)), b)))),
% 0.18/0.58 inference(quant_inst,[status(thm)],[])).
% 0.18/0.58 tff(295,plain,
% 0.18/0.58 (multiply(multiply(b, multiply(multiply(b, b), multiply(a, a))), b) = multiply(b, multiply(multiply(multiply(b, b), multiply(a, a)), b))),
% 0.18/0.58 inference(unit_resolution,[status(thm)],[294, 15])).
% 0.18/0.58 tff(296,plain,
% 0.18/0.58 (multiply(b, multiply(multiply(multiply(b, b), multiply(a, a)), b)) = multiply(multiply(b, multiply(multiply(b, b), multiply(a, a))), b)),
% 0.18/0.58 inference(symmetry,[status(thm)],[295])).
% 0.18/0.58 tff(297,plain,
% 0.18/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(b, a), a), b) = multiply(multiply(b, a), multiply(a, b)))),
% 0.18/0.58 inference(quant_inst,[status(thm)],[])).
% 0.18/0.58 tff(298,plain,
% 0.18/0.58 (multiply(multiply(multiply(b, a), a), b) = multiply(multiply(b, a), multiply(a, b))),
% 0.18/0.58 inference(unit_resolution,[status(thm)],[297, 15])).
% 0.18/0.58 tff(299,plain,
% 0.18/0.58 (multiply(multiply(multiply(b, a), a), b) = multiply(b, multiply(multiply(a, a), b))),
% 0.18/0.58 inference(transitivity,[status(thm)],[298, 20, 210])).
% 0.18/0.58 tff(300,plain,
% 0.18/0.58 (multiply(b, multiply(multiply(multiply(b, a), a), b)) = multiply(b, multiply(b, multiply(multiply(a, a), b)))),
% 0.18/0.58 inference(monotonicity,[status(thm)],[299])).
% 0.18/0.58 tff(301,plain,
% 0.18/0.58 (multiply(b, multiply(b, multiply(multiply(a, a), b))) = multiply(b, multiply(multiply(multiply(b, a), a), b))),
% 0.18/0.58 inference(symmetry,[status(thm)],[300])).
% 0.18/0.58 tff(302,plain,
% 0.18/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(b, multiply(a, a)), b) = multiply(b, multiply(multiply(a, a), b)))),
% 0.18/0.58 inference(quant_inst,[status(thm)],[])).
% 0.18/0.58 tff(303,plain,
% 0.18/0.58 (multiply(multiply(b, multiply(a, a)), b) = multiply(b, multiply(multiply(a, a), b))),
% 0.18/0.58 inference(unit_resolution,[status(thm)],[302, 15])).
% 0.18/0.58 tff(304,plain,
% 0.18/0.58 (multiply(b, multiply(multiply(b, multiply(a, a)), b)) = multiply(b, multiply(b, multiply(multiply(a, a), b)))),
% 0.18/0.58 inference(monotonicity,[status(thm)],[303])).
% 0.18/0.58 tff(305,plain,
% 0.18/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(b, multiply(b, multiply(a, a))), b) = multiply(b, multiply(multiply(b, multiply(a, a)), b)))),
% 0.18/0.58 inference(quant_inst,[status(thm)],[])).
% 0.18/0.58 tff(306,plain,
% 0.18/0.58 (multiply(multiply(b, multiply(b, multiply(a, a))), b) = multiply(b, multiply(multiply(b, multiply(a, a)), b))),
% 0.18/0.58 inference(unit_resolution,[status(thm)],[305, 15])).
% 0.18/0.58 tff(307,plain,
% 0.18/0.58 (multiply(multiply(multiply(b, b), multiply(a, a)), b) = multiply(multiply(b, multiply(b, multiply(a, a))), b)),
% 0.18/0.58 inference(monotonicity,[status(thm)],[288])).
% 0.18/0.58 tff(308,plain,
% 0.18/0.58 (multiply(multiply(multiply(b, b), multiply(a, a)), b) = multiply(b, multiply(multiply(multiply(b, a), a), b))),
% 0.18/0.58 inference(transitivity,[status(thm)],[307, 306, 304, 301])).
% 0.18/0.58 tff(309,plain,
% 0.18/0.58 (multiply(b, multiply(multiply(multiply(b, b), multiply(a, a)), b)) = multiply(b, multiply(b, multiply(multiply(multiply(b, a), a), b)))),
% 0.18/0.58 inference(monotonicity,[status(thm)],[308])).
% 0.18/0.58 tff(310,plain,
% 0.18/0.58 (multiply(b, multiply(b, multiply(multiply(multiply(b, a), a), b))) = multiply(b, multiply(multiply(multiply(b, b), multiply(a, a)), b))),
% 0.18/0.58 inference(symmetry,[status(thm)],[309])).
% 0.18/0.58 tff(311,plain,
% 0.18/0.58 (multiply(b, multiply(b, multiply(a, multiply(a, b)))) = multiply(b, multiply(multiply(multiply(b, a), a), b))),
% 0.18/0.58 inference(transitivity,[status(thm)],[211, 301])).
% 0.18/0.58 tff(312,plain,
% 0.18/0.58 (multiply(b, multiply(b, multiply(b, multiply(a, multiply(a, b))))) = multiply(b, multiply(b, multiply(multiply(multiply(b, a), a), b)))),
% 0.18/0.58 inference(monotonicity,[status(thm)],[311])).
% 0.18/0.58 tff(313,plain,
% 0.18/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(b, b), multiply(b, multiply(a, multiply(a, b)))) = multiply(b, multiply(b, multiply(b, multiply(a, multiply(a, b))))))),
% 0.18/0.58 inference(quant_inst,[status(thm)],[])).
% 0.18/0.58 tff(314,plain,
% 0.18/0.58 (multiply(multiply(b, b), multiply(b, multiply(a, multiply(a, b)))) = multiply(b, multiply(b, multiply(b, multiply(a, multiply(a, b)))))),
% 0.18/0.58 inference(unit_resolution,[status(thm)],[313, 15])).
% 0.18/0.58 tff(315,plain,
% 0.18/0.58 ((~![Xk!0: $i, Xk!1: $i] : (inj_1(Xk!1, multiply(Xk!1, Xk!0)) = Xk!0)) | (inj_1(a, multiply(a, multiply(b, multiply(a, multiply(a, b))))) = multiply(b, multiply(a, multiply(a, b))))),
% 0.18/0.58 inference(quant_inst,[status(thm)],[])).
% 0.18/0.58 tff(316,plain,
% 0.18/0.58 (inj_1(a, multiply(a, multiply(b, multiply(a, multiply(a, b))))) = multiply(b, multiply(a, multiply(a, b)))),
% 0.18/0.58 inference(unit_resolution,[status(thm)],[315, 97])).
% 0.18/0.58 tff(317,plain,
% 0.18/0.58 (multiply(a, multiply(a, multiply(multiply(b, b), a))) = multiply(a, multiply(b, multiply(a, multiply(a, b))))),
% 0.18/0.58 inference(transitivity,[status(thm)],[235, 225, 222, 219, 8])).
% 0.18/0.58 tff(318,plain,
% 0.18/0.58 (inj_1(a, multiply(a, multiply(a, multiply(multiply(b, b), a)))) = inj_1(a, multiply(a, multiply(b, multiply(a, multiply(a, b)))))),
% 0.18/0.58 inference(monotonicity,[status(thm)],[317])).
% 0.18/0.58 tff(319,plain,
% 0.18/0.58 ((~![Xk!0: $i, Xk!1: $i] : (inj_1(Xk!1, multiply(Xk!1, Xk!0)) = Xk!0)) | (inj_1(a, multiply(a, multiply(a, multiply(multiply(b, b), a)))) = multiply(a, multiply(multiply(b, b), a)))),
% 0.18/0.58 inference(quant_inst,[status(thm)],[])).
% 0.18/0.58 tff(320,plain,
% 0.18/0.58 (inj_1(a, multiply(a, multiply(a, multiply(multiply(b, b), a)))) = multiply(a, multiply(multiply(b, b), a))),
% 0.18/0.58 inference(unit_resolution,[status(thm)],[319, 97])).
% 0.18/0.58 tff(321,plain,
% 0.18/0.58 (multiply(a, multiply(multiply(b, b), a)) = inj_1(a, multiply(a, multiply(a, multiply(multiply(b, b), a))))),
% 0.18/0.58 inference(symmetry,[status(thm)],[320])).
% 0.18/0.58 tff(322,plain,
% 0.18/0.58 (multiply(a, multiply(multiply(b, b), a)) = multiply(b, multiply(a, multiply(a, b)))),
% 0.18/0.58 inference(transitivity,[status(thm)],[321, 318, 316])).
% 0.18/0.58 tff(323,plain,
% 0.18/0.58 (multiply(multiply(b, b), multiply(a, multiply(multiply(b, b), a))) = multiply(multiply(b, b), multiply(b, multiply(a, multiply(a, b))))),
% 0.18/0.58 inference(monotonicity,[status(thm)],[322])).
% 0.18/0.58 tff(324,plain,
% 0.18/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(b, b), a), multiply(multiply(b, b), a)) = multiply(multiply(b, b), multiply(a, multiply(multiply(b, b), a))))),
% 0.18/0.58 inference(quant_inst,[status(thm)],[])).
% 0.18/0.58 tff(325,plain,
% 0.18/0.58 (multiply(multiply(multiply(b, b), a), multiply(multiply(b, b), a)) = multiply(multiply(b, b), multiply(a, multiply(multiply(b, b), a)))),
% 0.18/0.58 inference(unit_resolution,[status(thm)],[324, 15])).
% 0.18/0.58 tff(326,plain,
% 0.18/0.58 (multiply(multiply(multiply(b, b), a), multiply(multiply(b, b), a)) = multiply(multiply(a, multiply(multiply(b, b), a)), multiply(b, b))),
% 0.18/0.58 inference(transitivity,[status(thm)],[325, 323, 314, 312, 310, 296, 293, 286, 284, 269, 265])).
% 0.18/0.58 tff(327,plain,
% 0.18/0.58 (inj_1(multiply(multiply(multiply(b, b), a), multiply(multiply(b, b), a)), multiply(multiply(multiply(multiply(b, b), a), multiply(multiply(b, b), a)), multiply(b, multiply(b, multiply(a, multiply(a, a)))))) = inj_1(multiply(multiply(a, multiply(multiply(b, b), a)), multiply(b, b)), multiply(multiply(multiply(a, multiply(multiply(b, b), a)), multiply(b, b)), multiply(a, multiply(a, multiply(multiply(b, b), a)))))),
% 0.18/0.58 inference(monotonicity,[status(thm)],[326, 262])).
% 0.18/0.58 tff(328,plain,
% 0.18/0.58 ((~![Xk!0: $i, Xk!1: $i] : (inj_1(Xk!1, multiply(Xk!1, Xk!0)) = Xk!0)) | (inj_1(multiply(multiply(multiply(b, b), a), multiply(multiply(b, b), a)), multiply(multiply(multiply(multiply(b, b), a), multiply(multiply(b, b), a)), multiply(b, multiply(b, multiply(a, multiply(a, a)))))) = multiply(b, multiply(b, multiply(a, multiply(a, a)))))),
% 0.18/0.58 inference(quant_inst,[status(thm)],[])).
% 0.18/0.58 tff(329,plain,
% 0.18/0.58 (inj_1(multiply(multiply(multiply(b, b), a), multiply(multiply(b, b), a)), multiply(multiply(multiply(multiply(b, b), a), multiply(multiply(b, b), a)), multiply(b, multiply(b, multiply(a, multiply(a, a)))))) = multiply(b, multiply(b, multiply(a, multiply(a, a))))),
% 0.18/0.58 inference(unit_resolution,[status(thm)],[328, 97])).
% 0.18/0.58 tff(330,plain,
% 0.18/0.58 (multiply(b, multiply(b, multiply(a, multiply(a, a)))) = inj_1(multiply(multiply(multiply(b, b), a), multiply(multiply(b, b), a)), multiply(multiply(multiply(multiply(b, b), a), multiply(multiply(b, b), a)), multiply(b, multiply(b, multiply(a, multiply(a, a))))))),
% 0.18/0.58 inference(symmetry,[status(thm)],[329])).
% 0.18/0.58 tff(331,plain,
% 0.18/0.58 (multiply(b, multiply(b, multiply(a, multiply(a, a)))) = multiply(a, multiply(b, multiply(a, multiply(a, b))))),
% 0.18/0.59 inference(transitivity,[status(thm)],[330, 327, 237, 235, 225, 222, 219, 8])).
% 0.18/0.59 tff(332,plain,
% 0.18/0.59 ((~(multiply(b, multiply(b, multiply(a, multiply(a, a)))) = multiply(a, multiply(b, multiply(a, multiply(a, b)))))) <=> (~(multiply(b, multiply(b, multiply(a, multiply(a, a)))) = multiply(a, multiply(b, multiply(a, multiply(a, b))))))),
% 0.18/0.59 inference(rewrite,[status(thm)],[])).
% 0.18/0.59 tff(333,axiom,(~(multiply(b, multiply(b, multiply(a, multiply(a, a)))) = multiply(a, multiply(b, multiply(a, multiply(a, b)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.18/0.59 tff(334,plain,
% 0.18/0.59 (~(multiply(b, multiply(b, multiply(a, multiply(a, a)))) = multiply(a, multiply(b, multiply(a, multiply(a, b)))))),
% 0.18/0.59 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.18/0.59 tff(335,plain,
% 0.18/0.59 ($false),
% 0.18/0.59 inference(unit_resolution,[status(thm)],[334, 331])).
% 0.18/0.59 % SZS output end Proof
%------------------------------------------------------------------------------