TSTP Solution File: GRP039-4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP039-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 22:25:37 EDT 2022
% Result : Unsatisfiable 15.76s 10.37s
% Output : Proof 15.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP039-4 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n004.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 14:13:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 15.76/10.37 % SZS status Unsatisfiable
% 15.76/10.37 % SZS output start Proof
% 15.76/10.37 tff(subgroup_member_type, type, (
% 15.76/10.37 subgroup_member: $i > $o)).
% 15.76/10.37 tff(inverse_type, type, (
% 15.76/10.37 inverse: $i > $i)).
% 15.76/10.37 tff(element_in_O2_type, type, (
% 15.76/10.37 element_in_O2: ( $i * $i ) > $i)).
% 15.76/10.37 tff(a_type, type, (
% 15.76/10.37 a: $i)).
% 15.76/10.37 tff(multiply_type, type, (
% 15.76/10.37 multiply: ( $i * $i ) > $i)).
% 15.76/10.37 tff(c_type, type, (
% 15.76/10.37 c: $i)).
% 15.76/10.37 tff(identity_type, type, (
% 15.76/10.37 identity: $i)).
% 15.76/10.37 tff(d_type, type, (
% 15.76/10.37 d: $i)).
% 15.76/10.37 tff(product_type, type, (
% 15.76/10.37 product: ( $i * $i * $i ) > $o)).
% 15.76/10.37 tff(b_type, type, (
% 15.76/10.37 b: $i)).
% 15.76/10.37 tff(1,plain,
% 15.76/10.37 (^[X: $i] : refl(product(identity, X, X) <=> product(identity, X, X))),
% 15.76/10.37 inference(bind,[status(th)],[])).
% 15.76/10.37 tff(2,plain,
% 15.76/10.37 (![X: $i] : product(identity, X, X) <=> ![X: $i] : product(identity, X, X)),
% 15.76/10.37 inference(quant_intro,[status(thm)],[1])).
% 15.76/10.37 tff(3,plain,
% 15.76/10.37 (![X: $i] : product(identity, X, X) <=> ![X: $i] : product(identity, X, X)),
% 15.76/10.37 inference(rewrite,[status(thm)],[])).
% 15.76/10.37 tff(4,axiom,(![X: $i] : product(identity, X, X)), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','left_identity')).
% 15.76/10.37 tff(5,plain,
% 15.76/10.37 (![X: $i] : product(identity, X, X)),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 15.76/10.37 tff(6,plain,(
% 15.76/10.37 ![X: $i] : product(identity, X, X)),
% 15.76/10.37 inference(skolemize,[status(sab)],[5])).
% 15.76/10.37 tff(7,plain,
% 15.76/10.37 (![X: $i] : product(identity, X, X)),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 15.76/10.37 tff(8,plain,
% 15.76/10.37 ((~![X: $i] : product(identity, X, X)) | product(identity, inverse(element_in_O2(multiply(identity, c), inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))))),
% 15.76/10.37 inference(quant_inst,[status(thm)],[])).
% 15.76/10.37 tff(9,plain,
% 15.76/10.37 (product(identity, inverse(element_in_O2(multiply(identity, c), inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))))),
% 15.76/10.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 15.76/10.37 tff(10,plain,
% 15.76/10.37 (^[X: $i] : refl(product(inverse(X), X, identity) <=> product(inverse(X), X, identity))),
% 15.76/10.37 inference(bind,[status(th)],[])).
% 15.76/10.37 tff(11,plain,
% 15.76/10.37 (![X: $i] : product(inverse(X), X, identity) <=> ![X: $i] : product(inverse(X), X, identity)),
% 15.76/10.37 inference(quant_intro,[status(thm)],[10])).
% 15.76/10.37 tff(12,plain,
% 15.76/10.37 (![X: $i] : product(inverse(X), X, identity) <=> ![X: $i] : product(inverse(X), X, identity)),
% 15.76/10.37 inference(rewrite,[status(thm)],[])).
% 15.76/10.37 tff(13,axiom,(![X: $i] : product(inverse(X), X, identity)), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','left_inverse')).
% 15.76/10.37 tff(14,plain,
% 15.76/10.37 (![X: $i] : product(inverse(X), X, identity)),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[13, 12])).
% 15.76/10.37 tff(15,plain,(
% 15.76/10.37 ![X: $i] : product(inverse(X), X, identity)),
% 15.76/10.37 inference(skolemize,[status(sab)],[14])).
% 15.76/10.37 tff(16,plain,
% 15.76/10.37 (![X: $i] : product(inverse(X), X, identity)),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[15, 11])).
% 15.76/10.37 tff(17,plain,
% 15.76/10.37 ((~![X: $i] : product(inverse(X), X, identity)) | product(inverse(inverse(a)), inverse(a), identity)),
% 15.76/10.37 inference(quant_inst,[status(thm)],[])).
% 15.76/10.37 tff(18,plain,
% 15.76/10.37 (product(inverse(inverse(a)), inverse(a), identity)),
% 15.76/10.37 inference(unit_resolution,[status(thm)],[17, 16])).
% 15.76/10.37 tff(19,plain,
% 15.76/10.37 ((~![X: $i] : product(identity, X, X)) | product(identity, a, a)),
% 15.76/10.37 inference(quant_inst,[status(thm)],[])).
% 15.76/10.37 tff(20,plain,
% 15.76/10.37 (product(identity, a, a)),
% 15.76/10.37 inference(unit_resolution,[status(thm)],[19, 7])).
% 15.76/10.37 tff(21,plain,
% 15.76/10.37 ((~![X: $i] : product(inverse(X), X, identity)) | product(inverse(a), a, identity)),
% 15.76/10.37 inference(quant_inst,[status(thm)],[])).
% 15.76/10.37 tff(22,plain,
% 15.76/10.37 (product(inverse(a), a, identity)),
% 15.76/10.37 inference(unit_resolution,[status(thm)],[21, 16])).
% 15.76/10.37 tff(23,plain,
% 15.76/10.37 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl((product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) <=> (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))))),
% 15.76/10.37 inference(bind,[status(th)],[])).
% 15.76/10.37 tff(24,plain,
% 15.76/10.37 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 15.76/10.37 inference(quant_intro,[status(thm)],[23])).
% 15.76/10.37 tff(25,plain,
% 15.76/10.37 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 15.76/10.37 inference(rewrite,[status(thm)],[])).
% 15.76/10.37 tff(26,plain,
% 15.76/10.37 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(rewrite((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(U, Z, W))) <=> ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))), (((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(U, Z, W))) | product(X, V, W)) <=> (((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) | product(X, V, W)))), rewrite((((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) | product(X, V, W)) <=> (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))), (((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(U, Z, W))) | product(X, V, W)) <=> (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))))),
% 15.76/10.37 inference(bind,[status(th)],[])).
% 15.76/10.37 tff(27,plain,
% 15.76/10.37 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(U, Z, W))) | product(X, V, W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 15.76/10.37 inference(quant_intro,[status(thm)],[26])).
% 15.76/10.37 tff(28,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(U, Z, W))) | product(X, V, W))), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','associativity1')).
% 15.76/10.37 tff(29,plain,
% 15.76/10.37 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[28, 27])).
% 15.76/10.37 tff(30,plain,
% 15.76/10.37 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[29, 25])).
% 15.76/10.37 tff(31,plain,(
% 15.76/10.37 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 15.76/10.37 inference(skolemize,[status(sab)],[30])).
% 15.76/10.37 tff(32,plain,
% 15.76/10.37 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[31, 24])).
% 15.76/10.37 tff(33,plain,
% 15.76/10.37 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(inverse(inverse(a)), identity, a) | (~product(identity, a, a)) | (~product(inverse(a), a, identity)) | (~product(inverse(inverse(a)), inverse(a), identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | product(inverse(inverse(a)), identity, a) | (~product(identity, a, a)) | (~product(inverse(a), a, identity)) | (~product(inverse(inverse(a)), inverse(a), identity)))),
% 15.76/10.37 inference(rewrite,[status(thm)],[])).
% 15.76/10.37 tff(34,plain,
% 15.76/10.37 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(inverse(inverse(a)), identity, a) | (~product(identity, a, a)) | (~product(inverse(a), a, identity)) | (~product(inverse(inverse(a)), inverse(a), identity)))),
% 15.76/10.37 inference(quant_inst,[status(thm)],[])).
% 15.76/10.37 tff(35,plain,
% 15.76/10.37 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | product(inverse(inverse(a)), identity, a) | (~product(identity, a, a)) | (~product(inverse(a), a, identity)) | (~product(inverse(inverse(a)), inverse(a), identity))),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[34, 33])).
% 15.76/10.37 tff(36,plain,
% 15.76/10.37 (product(inverse(inverse(a)), identity, a)),
% 15.76/10.37 inference(unit_resolution,[status(thm)],[35, 32, 22, 20, 18])).
% 15.76/10.37 tff(37,plain,
% 15.76/10.37 (^[X: $i] : refl(product(X, identity, X) <=> product(X, identity, X))),
% 15.76/10.37 inference(bind,[status(th)],[])).
% 15.76/10.37 tff(38,plain,
% 15.76/10.37 (![X: $i] : product(X, identity, X) <=> ![X: $i] : product(X, identity, X)),
% 15.76/10.37 inference(quant_intro,[status(thm)],[37])).
% 15.76/10.37 tff(39,plain,
% 15.76/10.37 (![X: $i] : product(X, identity, X) <=> ![X: $i] : product(X, identity, X)),
% 15.76/10.37 inference(rewrite,[status(thm)],[])).
% 15.76/10.37 tff(40,axiom,(![X: $i] : product(X, identity, X)), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','right_identity')).
% 15.76/10.37 tff(41,plain,
% 15.76/10.37 (![X: $i] : product(X, identity, X)),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[40, 39])).
% 15.76/10.37 tff(42,plain,(
% 15.76/10.37 ![X: $i] : product(X, identity, X)),
% 15.76/10.37 inference(skolemize,[status(sab)],[41])).
% 15.76/10.37 tff(43,plain,
% 15.76/10.37 (![X: $i] : product(X, identity, X)),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[42, 38])).
% 15.76/10.37 tff(44,plain,
% 15.76/10.37 ((~![X: $i] : product(X, identity, X)) | product(inverse(inverse(a)), identity, inverse(inverse(a)))),
% 15.76/10.37 inference(quant_inst,[status(thm)],[])).
% 15.76/10.37 tff(45,plain,
% 15.76/10.37 (product(inverse(inverse(a)), identity, inverse(inverse(a)))),
% 15.76/10.37 inference(unit_resolution,[status(thm)],[44, 43])).
% 15.76/10.37 tff(46,plain,
% 15.76/10.37 (^[W: $i, Z: $i, Y: $i, X: $i] : refl(((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))) <=> ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))))),
% 15.76/10.37 inference(bind,[status(th)],[])).
% 15.76/10.37 tff(47,plain,
% 15.76/10.37 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 15.76/10.37 inference(quant_intro,[status(thm)],[46])).
% 15.76/10.37 tff(48,plain,
% 15.76/10.37 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 15.76/10.37 inference(rewrite,[status(thm)],[])).
% 15.76/10.37 tff(49,plain,
% 15.76/10.37 (^[W: $i, Z: $i, Y: $i, X: $i] : rewrite((((~product(X, Y, Z)) | (~product(X, Y, W))) | (Z = W)) <=> ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))))),
% 15.76/10.37 inference(bind,[status(th)],[])).
% 15.76/10.37 tff(50,plain,
% 15.76/10.37 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, Z)) | (~product(X, Y, W))) | (Z = W)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 15.76/10.37 inference(quant_intro,[status(thm)],[49])).
% 15.76/10.37 tff(51,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, Z)) | (~product(X, Y, W))) | (Z = W))), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','total_function2')).
% 15.76/10.37 tff(52,plain,
% 15.76/10.37 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[51, 50])).
% 15.76/10.37 tff(53,plain,
% 15.76/10.37 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[52, 48])).
% 15.76/10.37 tff(54,plain,(
% 15.76/10.37 ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 15.76/10.37 inference(skolemize,[status(sab)],[53])).
% 15.76/10.37 tff(55,plain,
% 15.76/10.37 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[54, 47])).
% 15.76/10.37 tff(56,plain,
% 15.76/10.37 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((~product(inverse(inverse(a)), identity, inverse(inverse(a)))) | (~product(inverse(inverse(a)), identity, a)) | (a = inverse(inverse(a))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(inverse(inverse(a)), identity, inverse(inverse(a)))) | (~product(inverse(inverse(a)), identity, a)) | (a = inverse(inverse(a))))),
% 15.76/10.37 inference(rewrite,[status(thm)],[])).
% 15.76/10.37 tff(57,plain,
% 15.76/10.37 (((a = inverse(inverse(a))) | (~product(inverse(inverse(a)), identity, inverse(inverse(a)))) | (~product(inverse(inverse(a)), identity, a))) <=> ((~product(inverse(inverse(a)), identity, inverse(inverse(a)))) | (~product(inverse(inverse(a)), identity, a)) | (a = inverse(inverse(a))))),
% 15.76/10.37 inference(rewrite,[status(thm)],[])).
% 15.76/10.37 tff(58,plain,
% 15.76/10.37 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((a = inverse(inverse(a))) | (~product(inverse(inverse(a)), identity, inverse(inverse(a)))) | (~product(inverse(inverse(a)), identity, a)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((~product(inverse(inverse(a)), identity, inverse(inverse(a)))) | (~product(inverse(inverse(a)), identity, a)) | (a = inverse(inverse(a)))))),
% 15.76/10.37 inference(monotonicity,[status(thm)],[57])).
% 15.76/10.37 tff(59,plain,
% 15.76/10.37 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((a = inverse(inverse(a))) | (~product(inverse(inverse(a)), identity, inverse(inverse(a)))) | (~product(inverse(inverse(a)), identity, a)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(inverse(inverse(a)), identity, inverse(inverse(a)))) | (~product(inverse(inverse(a)), identity, a)) | (a = inverse(inverse(a))))),
% 15.76/10.37 inference(transitivity,[status(thm)],[58, 56])).
% 15.76/10.37 tff(60,plain,
% 15.76/10.37 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((a = inverse(inverse(a))) | (~product(inverse(inverse(a)), identity, inverse(inverse(a)))) | (~product(inverse(inverse(a)), identity, a)))),
% 15.76/10.37 inference(quant_inst,[status(thm)],[])).
% 15.76/10.37 tff(61,plain,
% 15.76/10.37 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(inverse(inverse(a)), identity, inverse(inverse(a)))) | (~product(inverse(inverse(a)), identity, a)) | (a = inverse(inverse(a)))),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[60, 59])).
% 15.76/10.37 tff(62,plain,
% 15.76/10.37 (a = inverse(inverse(a))),
% 15.76/10.37 inference(unit_resolution,[status(thm)],[61, 55, 45, 36])).
% 15.76/10.37 tff(63,plain,
% 15.76/10.37 (inverse(a) = inverse(inverse(inverse(a)))),
% 15.76/10.37 inference(monotonicity,[status(thm)],[62])).
% 15.76/10.37 tff(64,plain,
% 15.76/10.37 (inverse(inverse(inverse(a))) = inverse(a)),
% 15.76/10.37 inference(symmetry,[status(thm)],[63])).
% 15.76/10.37 tff(65,plain,
% 15.76/10.37 (product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(inverse(inverse(a)))) <=> product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(a))),
% 15.76/10.37 inference(monotonicity,[status(thm)],[64])).
% 15.76/10.37 tff(66,plain,
% 15.76/10.37 (product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(a)) <=> product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(inverse(inverse(a))))),
% 15.76/10.37 inference(symmetry,[status(thm)],[65])).
% 15.76/10.37 tff(67,assumption,(subgroup_member(multiply(identity, c))), introduced(assumption)).
% 15.76/10.37 tff(68,plain,
% 15.76/10.37 (^[Y: $i, X: $i] : refl(product(X, Y, multiply(X, Y)) <=> product(X, Y, multiply(X, Y)))),
% 15.76/10.37 inference(bind,[status(th)],[])).
% 15.76/10.37 tff(69,plain,
% 15.76/10.37 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y)) <=> ![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 15.76/10.37 inference(quant_intro,[status(thm)],[68])).
% 15.76/10.37 tff(70,plain,
% 15.76/10.37 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y)) <=> ![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 15.76/10.37 inference(rewrite,[status(thm)],[])).
% 15.76/10.37 tff(71,axiom,(![Y: $i, X: $i] : product(X, Y, multiply(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','total_function1')).
% 15.76/10.37 tff(72,plain,
% 15.76/10.37 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[71, 70])).
% 15.76/10.37 tff(73,plain,(
% 15.76/10.37 ![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 15.76/10.37 inference(skolemize,[status(sab)],[72])).
% 15.76/10.37 tff(74,plain,
% 15.76/10.37 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[73, 69])).
% 15.76/10.37 tff(75,plain,
% 15.76/10.37 ((~![Y: $i, X: $i] : product(X, Y, multiply(X, Y))) | product(identity, c, multiply(identity, c))),
% 15.76/10.37 inference(quant_inst,[status(thm)],[])).
% 15.76/10.37 tff(76,plain,
% 15.76/10.37 (product(identity, c, multiply(identity, c))),
% 15.76/10.37 inference(unit_resolution,[status(thm)],[75, 74])).
% 15.76/10.37 tff(77,plain,
% 15.76/10.37 ((~![X: $i] : product(identity, X, X)) | product(identity, c, c)),
% 15.76/10.37 inference(quant_inst,[status(thm)],[])).
% 15.76/10.37 tff(78,plain,
% 15.76/10.37 (product(identity, c, c)),
% 15.76/10.37 inference(unit_resolution,[status(thm)],[77, 7])).
% 15.76/10.37 tff(79,plain,
% 15.76/10.37 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((c = multiply(identity, c)) | (~product(identity, c, multiply(identity, c))) | (~product(identity, c, c)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (c = multiply(identity, c)) | (~product(identity, c, multiply(identity, c))) | (~product(identity, c, c)))),
% 15.76/10.37 inference(rewrite,[status(thm)],[])).
% 15.76/10.37 tff(80,plain,
% 15.76/10.37 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((c = multiply(identity, c)) | (~product(identity, c, multiply(identity, c))) | (~product(identity, c, c)))),
% 15.76/10.37 inference(quant_inst,[status(thm)],[])).
% 15.76/10.37 tff(81,plain,
% 15.76/10.37 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (c = multiply(identity, c)) | (~product(identity, c, multiply(identity, c))) | (~product(identity, c, c))),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[80, 79])).
% 15.76/10.37 tff(82,plain,
% 15.76/10.37 (c = multiply(identity, c)),
% 15.76/10.37 inference(unit_resolution,[status(thm)],[81, 55, 78, 76])).
% 15.76/10.37 tff(83,plain,
% 15.76/10.37 (multiply(identity, c) = c),
% 15.76/10.37 inference(symmetry,[status(thm)],[82])).
% 15.76/10.37 tff(84,plain,
% 15.76/10.37 ((~![X: $i] : product(X, identity, X)) | product(b, identity, b)),
% 15.76/10.37 inference(quant_inst,[status(thm)],[])).
% 15.76/10.37 tff(85,plain,
% 15.76/10.37 (product(b, identity, b)),
% 15.76/10.37 inference(unit_resolution,[status(thm)],[84, 43])).
% 15.76/10.37 tff(86,plain,
% 15.76/10.37 ((~![Y: $i, X: $i] : product(X, Y, multiply(X, Y))) | product(b, identity, multiply(b, identity))),
% 15.76/10.37 inference(quant_inst,[status(thm)],[])).
% 15.76/10.37 tff(87,plain,
% 15.76/10.37 (product(b, identity, multiply(b, identity))),
% 15.76/10.37 inference(unit_resolution,[status(thm)],[86, 74])).
% 15.76/10.37 tff(88,plain,
% 15.76/10.37 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((~product(b, identity, multiply(b, identity))) | (~product(b, identity, b)) | (b = multiply(b, identity)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(b, identity, multiply(b, identity))) | (~product(b, identity, b)) | (b = multiply(b, identity)))),
% 15.76/10.37 inference(rewrite,[status(thm)],[])).
% 15.76/10.37 tff(89,plain,
% 15.76/10.37 (((b = multiply(b, identity)) | (~product(b, identity, multiply(b, identity))) | (~product(b, identity, b))) <=> ((~product(b, identity, multiply(b, identity))) | (~product(b, identity, b)) | (b = multiply(b, identity)))),
% 15.76/10.37 inference(rewrite,[status(thm)],[])).
% 15.76/10.37 tff(90,plain,
% 15.76/10.37 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((b = multiply(b, identity)) | (~product(b, identity, multiply(b, identity))) | (~product(b, identity, b)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((~product(b, identity, multiply(b, identity))) | (~product(b, identity, b)) | (b = multiply(b, identity))))),
% 15.76/10.37 inference(monotonicity,[status(thm)],[89])).
% 15.76/10.37 tff(91,plain,
% 15.76/10.37 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((b = multiply(b, identity)) | (~product(b, identity, multiply(b, identity))) | (~product(b, identity, b)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(b, identity, multiply(b, identity))) | (~product(b, identity, b)) | (b = multiply(b, identity)))),
% 15.76/10.37 inference(transitivity,[status(thm)],[90, 88])).
% 15.76/10.37 tff(92,plain,
% 15.76/10.37 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((b = multiply(b, identity)) | (~product(b, identity, multiply(b, identity))) | (~product(b, identity, b)))),
% 15.76/10.37 inference(quant_inst,[status(thm)],[])).
% 15.76/10.37 tff(93,plain,
% 15.76/10.37 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(b, identity, multiply(b, identity))) | (~product(b, identity, b)) | (b = multiply(b, identity))),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[92, 91])).
% 15.76/10.37 tff(94,plain,
% 15.76/10.37 (b = multiply(b, identity)),
% 15.76/10.37 inference(unit_resolution,[status(thm)],[93, 55, 87, 85])).
% 15.76/10.37 tff(95,plain,
% 15.76/10.37 (multiply(b, identity) = b),
% 15.76/10.37 inference(symmetry,[status(thm)],[94])).
% 15.76/10.37 tff(96,plain,
% 15.76/10.37 (product(multiply(b, identity), inverse(a), multiply(identity, c)) <=> product(b, inverse(a), c)),
% 15.76/10.37 inference(monotonicity,[status(thm)],[95, 83])).
% 15.76/10.37 tff(97,plain,
% 15.76/10.37 (product(b, inverse(a), c) <=> product(multiply(b, identity), inverse(a), multiply(identity, c))),
% 15.76/10.37 inference(symmetry,[status(thm)],[96])).
% 15.76/10.37 tff(98,plain,
% 15.76/10.37 (product(b, inverse(a), c) <=> product(b, inverse(a), c)),
% 15.76/10.37 inference(rewrite,[status(thm)],[])).
% 15.76/10.37 tff(99,axiom,(product(b, inverse(a), c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','b_times_a_inverse_is_c')).
% 15.76/10.37 tff(100,plain,
% 15.76/10.37 (product(b, inverse(a), c)),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[99, 98])).
% 15.76/10.37 tff(101,plain,
% 15.76/10.37 (product(multiply(b, identity), inverse(a), multiply(identity, c))),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[100, 97])).
% 15.76/10.37 tff(102,plain,
% 15.76/10.37 ((~![X: $i] : product(inverse(X), X, identity)) | product(inverse(multiply(b, identity)), multiply(b, identity), identity)),
% 15.76/10.37 inference(quant_inst,[status(thm)],[])).
% 15.76/10.37 tff(103,plain,
% 15.76/10.37 (product(inverse(multiply(b, identity)), multiply(b, identity), identity)),
% 15.76/10.37 inference(unit_resolution,[status(thm)],[102, 16])).
% 15.76/10.37 tff(104,plain,
% 15.76/10.37 ((~![X: $i] : product(X, identity, X)) | product(inverse(a), identity, inverse(a))),
% 15.76/10.37 inference(quant_inst,[status(thm)],[])).
% 15.76/10.37 tff(105,plain,
% 15.76/10.37 (product(inverse(a), identity, inverse(a))),
% 15.76/10.37 inference(unit_resolution,[status(thm)],[104, 43])).
% 15.76/10.37 tff(106,plain,
% 15.76/10.37 (^[X: $i] : refl(product(X, inverse(X), identity) <=> product(X, inverse(X), identity))),
% 15.76/10.37 inference(bind,[status(th)],[])).
% 15.76/10.37 tff(107,plain,
% 15.76/10.37 (![X: $i] : product(X, inverse(X), identity) <=> ![X: $i] : product(X, inverse(X), identity)),
% 15.76/10.37 inference(quant_intro,[status(thm)],[106])).
% 15.76/10.37 tff(108,plain,
% 15.76/10.37 (![X: $i] : product(X, inverse(X), identity) <=> ![X: $i] : product(X, inverse(X), identity)),
% 15.76/10.37 inference(rewrite,[status(thm)],[])).
% 15.76/10.37 tff(109,axiom,(![X: $i] : product(X, inverse(X), identity)), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','right_inverse')).
% 15.76/10.37 tff(110,plain,
% 15.76/10.37 (![X: $i] : product(X, inverse(X), identity)),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[109, 108])).
% 15.76/10.37 tff(111,plain,(
% 15.76/10.37 ![X: $i] : product(X, inverse(X), identity)),
% 15.76/10.37 inference(skolemize,[status(sab)],[110])).
% 15.76/10.37 tff(112,plain,
% 15.76/10.37 (![X: $i] : product(X, inverse(X), identity)),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[111, 107])).
% 15.76/10.37 tff(113,plain,
% 15.76/10.37 ((~![X: $i] : product(X, inverse(X), identity)) | product(a, inverse(a), identity)),
% 15.76/10.37 inference(quant_inst,[status(thm)],[])).
% 15.76/10.37 tff(114,plain,
% 15.76/10.37 (product(a, inverse(a), identity)),
% 15.76/10.37 inference(unit_resolution,[status(thm)],[113, 112])).
% 15.76/10.37 tff(115,plain,
% 15.76/10.37 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl((product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))) <=> (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))))),
% 15.76/10.37 inference(bind,[status(th)],[])).
% 15.76/10.37 tff(116,plain,
% 15.76/10.37 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 15.76/10.37 inference(quant_intro,[status(thm)],[115])).
% 15.76/10.37 tff(117,plain,
% 15.76/10.37 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 15.76/10.37 inference(rewrite,[status(thm)],[])).
% 15.76/10.37 tff(118,plain,
% 15.76/10.37 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(rewrite((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) <=> ((~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))), (((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) | product(U, Z, W)) <=> (((~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))) | product(U, Z, W)))), rewrite((((~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))) | product(U, Z, W)) <=> (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))), (((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) | product(U, Z, W)) <=> (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))))),
% 15.76/10.37 inference(bind,[status(th)],[])).
% 15.76/10.37 tff(119,plain,
% 15.76/10.37 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) | product(U, Z, W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 15.76/10.37 inference(quant_intro,[status(thm)],[118])).
% 15.76/10.37 tff(120,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) | product(U, Z, W))), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','associativity2')).
% 15.76/10.37 tff(121,plain,
% 15.76/10.37 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[120, 119])).
% 15.76/10.37 tff(122,plain,
% 15.76/10.37 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[121, 117])).
% 15.76/10.37 tff(123,plain,(
% 15.76/10.37 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 15.76/10.37 inference(skolemize,[status(sab)],[122])).
% 15.76/10.37 tff(124,plain,
% 15.76/10.37 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 15.76/10.37 inference(modus_ponens,[status(thm)],[123, 116])).
% 15.76/10.37 tff(125,plain,
% 15.76/10.37 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | ((~product(inverse(a), identity, inverse(a))) | (~product(inverse(a), a, identity)) | product(identity, inverse(a), inverse(a)) | (~product(a, inverse(a), identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (~product(inverse(a), identity, inverse(a))) | (~product(inverse(a), a, identity)) | product(identity, inverse(a), inverse(a)) | (~product(a, inverse(a), identity)))),
% 15.76/10.37 inference(rewrite,[status(thm)],[])).
% 15.76/10.37 tff(126,plain,
% 15.76/10.37 ((product(identity, inverse(a), inverse(a)) | (~product(a, inverse(a), identity)) | (~product(inverse(a), a, identity)) | (~product(inverse(a), identity, inverse(a)))) <=> ((~product(inverse(a), identity, inverse(a))) | (~product(inverse(a), a, identity)) | product(identity, inverse(a), inverse(a)) | (~product(a, inverse(a), identity)))),
% 15.76/10.37 inference(rewrite,[status(thm)],[])).
% 15.76/10.37 tff(127,plain,
% 15.76/10.37 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(identity, inverse(a), inverse(a)) | (~product(a, inverse(a), identity)) | (~product(inverse(a), a, identity)) | (~product(inverse(a), identity, inverse(a))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | ((~product(inverse(a), identity, inverse(a))) | (~product(inverse(a), a, identity)) | product(identity, inverse(a), inverse(a)) | (~product(a, inverse(a), identity))))),
% 15.76/10.37 inference(monotonicity,[status(thm)],[126])).
% 15.76/10.37 tff(128,plain,
% 15.76/10.37 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(identity, inverse(a), inverse(a)) | (~product(a, inverse(a), identity)) | (~product(inverse(a), a, identity)) | (~product(inverse(a), identity, inverse(a))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (~product(inverse(a), identity, inverse(a))) | (~product(inverse(a), a, identity)) | product(identity, inverse(a), inverse(a)) | (~product(a, inverse(a), identity)))),
% 15.76/10.38 inference(transitivity,[status(thm)],[127, 125])).
% 15.76/10.38 tff(129,plain,
% 15.76/10.38 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(identity, inverse(a), inverse(a)) | (~product(a, inverse(a), identity)) | (~product(inverse(a), a, identity)) | (~product(inverse(a), identity, inverse(a))))),
% 15.76/10.38 inference(quant_inst,[status(thm)],[])).
% 15.76/10.38 tff(130,plain,
% 15.76/10.38 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (~product(inverse(a), identity, inverse(a))) | (~product(inverse(a), a, identity)) | product(identity, inverse(a), inverse(a)) | (~product(a, inverse(a), identity))),
% 15.76/10.38 inference(modus_ponens,[status(thm)],[129, 128])).
% 15.76/10.38 tff(131,plain,
% 15.76/10.38 (product(identity, inverse(a), inverse(a))),
% 15.76/10.38 inference(unit_resolution,[status(thm)],[130, 124, 22, 114, 105])).
% 15.76/10.38 tff(132,plain,
% 15.76/10.38 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | ((~product(multiply(b, identity), inverse(a), multiply(identity, c))) | product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a)) | (~product(identity, inverse(a), inverse(a))) | (~product(inverse(multiply(b, identity)), multiply(b, identity), identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (~product(multiply(b, identity), inverse(a), multiply(identity, c))) | product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a)) | (~product(identity, inverse(a), inverse(a))) | (~product(inverse(multiply(b, identity)), multiply(b, identity), identity)))),
% 15.76/10.38 inference(rewrite,[status(thm)],[])).
% 15.76/10.38 tff(133,plain,
% 15.76/10.38 ((product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a)) | (~product(identity, inverse(a), inverse(a))) | (~product(multiply(b, identity), inverse(a), multiply(identity, c))) | (~product(inverse(multiply(b, identity)), multiply(b, identity), identity))) <=> ((~product(multiply(b, identity), inverse(a), multiply(identity, c))) | product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a)) | (~product(identity, inverse(a), inverse(a))) | (~product(inverse(multiply(b, identity)), multiply(b, identity), identity)))),
% 15.76/10.38 inference(rewrite,[status(thm)],[])).
% 15.76/10.38 tff(134,plain,
% 15.76/10.38 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a)) | (~product(identity, inverse(a), inverse(a))) | (~product(multiply(b, identity), inverse(a), multiply(identity, c))) | (~product(inverse(multiply(b, identity)), multiply(b, identity), identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | ((~product(multiply(b, identity), inverse(a), multiply(identity, c))) | product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a)) | (~product(identity, inverse(a), inverse(a))) | (~product(inverse(multiply(b, identity)), multiply(b, identity), identity))))),
% 15.76/10.38 inference(monotonicity,[status(thm)],[133])).
% 15.76/10.38 tff(135,plain,
% 15.76/10.38 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a)) | (~product(identity, inverse(a), inverse(a))) | (~product(multiply(b, identity), inverse(a), multiply(identity, c))) | (~product(inverse(multiply(b, identity)), multiply(b, identity), identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (~product(multiply(b, identity), inverse(a), multiply(identity, c))) | product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a)) | (~product(identity, inverse(a), inverse(a))) | (~product(inverse(multiply(b, identity)), multiply(b, identity), identity)))),
% 15.76/10.38 inference(transitivity,[status(thm)],[134, 132])).
% 15.76/10.38 tff(136,plain,
% 15.76/10.38 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a)) | (~product(identity, inverse(a), inverse(a))) | (~product(multiply(b, identity), inverse(a), multiply(identity, c))) | (~product(inverse(multiply(b, identity)), multiply(b, identity), identity)))),
% 15.76/10.38 inference(quant_inst,[status(thm)],[])).
% 15.76/10.38 tff(137,plain,
% 15.76/10.38 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (~product(multiply(b, identity), inverse(a), multiply(identity, c))) | product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a)) | (~product(identity, inverse(a), inverse(a))) | (~product(inverse(multiply(b, identity)), multiply(b, identity), identity))),
% 15.76/10.38 inference(modus_ponens,[status(thm)],[136, 135])).
% 15.76/10.38 tff(138,plain,
% 15.76/10.38 ((~product(multiply(b, identity), inverse(a), multiply(identity, c))) | product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a))),
% 15.76/10.38 inference(unit_resolution,[status(thm)],[137, 32, 131, 103])).
% 15.76/10.38 tff(139,plain,
% 15.76/10.38 (product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a))),
% 15.76/10.38 inference(unit_resolution,[status(thm)],[138, 101])).
% 15.76/10.38 tff(140,plain,
% 15.76/10.38 (subgroup_member(b) <=> subgroup_member(b)),
% 15.76/10.38 inference(rewrite,[status(thm)],[])).
% 15.76/10.38 tff(141,axiom,(subgroup_member(b)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','b_is_in_subgroup')).
% 15.76/10.38 tff(142,plain,
% 15.76/10.38 (subgroup_member(b)),
% 15.76/10.38 inference(modus_ponens,[status(thm)],[141, 140])).
% 15.76/10.38 tff(143,plain,
% 15.76/10.38 (subgroup_member(identity) <=> subgroup_member(identity)),
% 15.76/10.38 inference(rewrite,[status(thm)],[])).
% 15.76/10.38 tff(144,axiom,(subgroup_member(identity)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','identity_is_in_subgroup')).
% 15.76/10.38 tff(145,plain,
% 15.76/10.38 (subgroup_member(identity)),
% 15.76/10.38 inference(modus_ponens,[status(thm)],[144, 143])).
% 15.76/10.38 tff(146,plain,
% 15.76/10.38 (^[B: $i, A: $i, C: $i] : refl((subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A))) <=> (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A))))),
% 15.76/10.38 inference(bind,[status(th)],[])).
% 15.76/10.38 tff(147,plain,
% 15.76/10.38 (![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A))) <=> ![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))),
% 15.76/10.38 inference(quant_intro,[status(thm)],[146])).
% 15.76/10.38 tff(148,plain,
% 15.76/10.38 (![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A))) <=> ![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))),
% 15.76/10.38 inference(rewrite,[status(thm)],[])).
% 15.76/10.38 tff(149,plain,
% 15.76/10.38 (^[B: $i, A: $i, C: $i] : trans(monotonicity(rewrite((((~subgroup_member(A)) | (~subgroup_member(B))) | (~product(A, B, C))) <=> ((~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))), (((((~subgroup_member(A)) | (~subgroup_member(B))) | (~product(A, B, C))) | subgroup_member(C)) <=> (((~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A))) | subgroup_member(C)))), rewrite((((~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A))) | subgroup_member(C)) <=> (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))), (((((~subgroup_member(A)) | (~subgroup_member(B))) | (~product(A, B, C))) | subgroup_member(C)) <=> (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))))),
% 15.76/10.38 inference(bind,[status(th)],[])).
% 15.76/10.38 tff(150,plain,
% 15.76/10.38 (![B: $i, A: $i, C: $i] : ((((~subgroup_member(A)) | (~subgroup_member(B))) | (~product(A, B, C))) | subgroup_member(C)) <=> ![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))),
% 15.76/10.38 inference(quant_intro,[status(thm)],[149])).
% 15.76/10.38 tff(151,axiom,(![B: $i, A: $i, C: $i] : ((((~subgroup_member(A)) | (~subgroup_member(B))) | (~product(A, B, C))) | subgroup_member(C))), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-1.ax','closure_of_product')).
% 15.76/10.38 tff(152,plain,
% 15.76/10.38 (![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))),
% 15.76/10.38 inference(modus_ponens,[status(thm)],[151, 150])).
% 15.76/10.38 tff(153,plain,
% 15.76/10.38 (![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))),
% 15.76/10.38 inference(modus_ponens,[status(thm)],[152, 148])).
% 15.76/10.38 tff(154,plain,(
% 15.76/10.38 ![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))),
% 15.76/10.38 inference(skolemize,[status(sab)],[153])).
% 15.76/10.38 tff(155,plain,
% 15.76/10.38 (![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))),
% 15.76/10.38 inference(modus_ponens,[status(thm)],[154, 147])).
% 15.76/10.38 tff(156,plain,
% 15.76/10.38 (((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | ((~subgroup_member(b)) | (~subgroup_member(identity)) | subgroup_member(multiply(b, identity)) | (~product(b, identity, multiply(b, identity))))) <=> ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (~subgroup_member(b)) | (~subgroup_member(identity)) | subgroup_member(multiply(b, identity)) | (~product(b, identity, multiply(b, identity))))),
% 15.76/10.38 inference(rewrite,[status(thm)],[])).
% 15.76/10.38 tff(157,plain,
% 15.76/10.38 ((subgroup_member(multiply(b, identity)) | (~product(b, identity, multiply(b, identity))) | (~subgroup_member(identity)) | (~subgroup_member(b))) <=> ((~subgroup_member(b)) | (~subgroup_member(identity)) | subgroup_member(multiply(b, identity)) | (~product(b, identity, multiply(b, identity))))),
% 15.76/10.38 inference(rewrite,[status(thm)],[])).
% 15.76/10.38 tff(158,plain,
% 15.76/10.38 (((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (subgroup_member(multiply(b, identity)) | (~product(b, identity, multiply(b, identity))) | (~subgroup_member(identity)) | (~subgroup_member(b)))) <=> ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | ((~subgroup_member(b)) | (~subgroup_member(identity)) | subgroup_member(multiply(b, identity)) | (~product(b, identity, multiply(b, identity)))))),
% 15.76/10.38 inference(monotonicity,[status(thm)],[157])).
% 15.76/10.38 tff(159,plain,
% 15.76/10.38 (((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (subgroup_member(multiply(b, identity)) | (~product(b, identity, multiply(b, identity))) | (~subgroup_member(identity)) | (~subgroup_member(b)))) <=> ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (~subgroup_member(b)) | (~subgroup_member(identity)) | subgroup_member(multiply(b, identity)) | (~product(b, identity, multiply(b, identity))))),
% 15.76/10.38 inference(transitivity,[status(thm)],[158, 156])).
% 15.76/10.38 tff(160,plain,
% 15.76/10.38 ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (subgroup_member(multiply(b, identity)) | (~product(b, identity, multiply(b, identity))) | (~subgroup_member(identity)) | (~subgroup_member(b)))),
% 15.76/10.38 inference(quant_inst,[status(thm)],[])).
% 15.76/10.38 tff(161,plain,
% 15.76/10.38 ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (~subgroup_member(b)) | (~subgroup_member(identity)) | subgroup_member(multiply(b, identity)) | (~product(b, identity, multiply(b, identity)))),
% 15.76/10.38 inference(modus_ponens,[status(thm)],[160, 159])).
% 15.76/10.38 tff(162,plain,
% 15.76/10.38 (subgroup_member(multiply(b, identity))),
% 15.76/10.38 inference(unit_resolution,[status(thm)],[161, 155, 145, 142, 87])).
% 15.76/10.38 tff(163,plain,
% 15.76/10.38 (^[X: $i] : refl(((~subgroup_member(X)) | subgroup_member(inverse(X))) <=> ((~subgroup_member(X)) | subgroup_member(inverse(X))))),
% 15.76/10.38 inference(bind,[status(th)],[])).
% 15.76/10.38 tff(164,plain,
% 15.76/10.38 (![X: $i] : ((~subgroup_member(X)) | subgroup_member(inverse(X))) <=> ![X: $i] : ((~subgroup_member(X)) | subgroup_member(inverse(X)))),
% 15.76/10.38 inference(quant_intro,[status(thm)],[163])).
% 15.76/10.38 tff(165,plain,
% 15.76/10.38 (![X: $i] : ((~subgroup_member(X)) | subgroup_member(inverse(X))) <=> ![X: $i] : ((~subgroup_member(X)) | subgroup_member(inverse(X)))),
% 15.76/10.38 inference(rewrite,[status(thm)],[])).
% 15.76/10.38 tff(166,axiom,(![X: $i] : ((~subgroup_member(X)) | subgroup_member(inverse(X)))), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-1.ax','closure_of_inverse')).
% 15.76/10.38 tff(167,plain,
% 15.76/10.38 (![X: $i] : ((~subgroup_member(X)) | subgroup_member(inverse(X)))),
% 15.76/10.38 inference(modus_ponens,[status(thm)],[166, 165])).
% 15.76/10.38 tff(168,plain,(
% 15.76/10.38 ![X: $i] : ((~subgroup_member(X)) | subgroup_member(inverse(X)))),
% 15.76/10.38 inference(skolemize,[status(sab)],[167])).
% 15.76/10.38 tff(169,plain,
% 15.76/10.38 (![X: $i] : ((~subgroup_member(X)) | subgroup_member(inverse(X)))),
% 15.76/10.38 inference(modus_ponens,[status(thm)],[168, 164])).
% 15.76/10.38 tff(170,plain,
% 15.76/10.38 (((~![X: $i] : ((~subgroup_member(X)) | subgroup_member(inverse(X)))) | ((~subgroup_member(multiply(b, identity))) | subgroup_member(inverse(multiply(b, identity))))) <=> ((~![X: $i] : ((~subgroup_member(X)) | subgroup_member(inverse(X)))) | (~subgroup_member(multiply(b, identity))) | subgroup_member(inverse(multiply(b, identity))))),
% 15.76/10.38 inference(rewrite,[status(thm)],[])).
% 15.76/10.38 tff(171,plain,
% 15.76/10.38 ((~![X: $i] : ((~subgroup_member(X)) | subgroup_member(inverse(X)))) | ((~subgroup_member(multiply(b, identity))) | subgroup_member(inverse(multiply(b, identity))))),
% 15.76/10.38 inference(quant_inst,[status(thm)],[])).
% 15.76/10.38 tff(172,plain,
% 15.76/10.38 ((~![X: $i] : ((~subgroup_member(X)) | subgroup_member(inverse(X)))) | (~subgroup_member(multiply(b, identity))) | subgroup_member(inverse(multiply(b, identity)))),
% 15.76/10.38 inference(modus_ponens,[status(thm)],[171, 170])).
% 15.76/10.38 tff(173,plain,
% 15.76/10.38 (subgroup_member(inverse(multiply(b, identity)))),
% 15.76/10.38 inference(unit_resolution,[status(thm)],[172, 169, 162])).
% 15.76/10.38 tff(174,plain,
% 15.76/10.38 (((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (subgroup_member(inverse(a)) | (~subgroup_member(multiply(identity, c))) | (~subgroup_member(inverse(multiply(b, identity)))) | (~product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a))))) <=> ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | subgroup_member(inverse(a)) | (~subgroup_member(multiply(identity, c))) | (~subgroup_member(inverse(multiply(b, identity)))) | (~product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a))))),
% 15.76/10.38 inference(rewrite,[status(thm)],[])).
% 15.76/10.38 tff(175,plain,
% 15.76/10.38 ((subgroup_member(inverse(a)) | (~product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a))) | (~subgroup_member(multiply(identity, c))) | (~subgroup_member(inverse(multiply(b, identity))))) <=> (subgroup_member(inverse(a)) | (~subgroup_member(multiply(identity, c))) | (~subgroup_member(inverse(multiply(b, identity)))) | (~product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a))))),
% 15.76/10.38 inference(rewrite,[status(thm)],[])).
% 15.76/10.38 tff(176,plain,
% 15.76/10.38 (((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (subgroup_member(inverse(a)) | (~product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a))) | (~subgroup_member(multiply(identity, c))) | (~subgroup_member(inverse(multiply(b, identity)))))) <=> ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (subgroup_member(inverse(a)) | (~subgroup_member(multiply(identity, c))) | (~subgroup_member(inverse(multiply(b, identity)))) | (~product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a)))))),
% 15.76/10.38 inference(monotonicity,[status(thm)],[175])).
% 15.76/10.38 tff(177,plain,
% 15.76/10.38 (((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (subgroup_member(inverse(a)) | (~product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a))) | (~subgroup_member(multiply(identity, c))) | (~subgroup_member(inverse(multiply(b, identity)))))) <=> ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | subgroup_member(inverse(a)) | (~subgroup_member(multiply(identity, c))) | (~subgroup_member(inverse(multiply(b, identity)))) | (~product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a))))),
% 15.76/10.38 inference(transitivity,[status(thm)],[176, 174])).
% 15.76/10.38 tff(178,plain,
% 15.76/10.38 ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (subgroup_member(inverse(a)) | (~product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a))) | (~subgroup_member(multiply(identity, c))) | (~subgroup_member(inverse(multiply(b, identity)))))),
% 15.76/10.38 inference(quant_inst,[status(thm)],[])).
% 15.76/10.38 tff(179,plain,
% 15.76/10.38 ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | subgroup_member(inverse(a)) | (~subgroup_member(multiply(identity, c))) | (~subgroup_member(inverse(multiply(b, identity)))) | (~product(inverse(multiply(b, identity)), multiply(identity, c), inverse(a)))),
% 15.76/10.38 inference(modus_ponens,[status(thm)],[178, 177])).
% 15.76/10.38 tff(180,plain,
% 15.76/10.38 (subgroup_member(inverse(a)) | (~subgroup_member(multiply(identity, c)))),
% 15.76/10.38 inference(unit_resolution,[status(thm)],[179, 155, 173, 139])).
% 15.76/10.38 tff(181,plain,
% 15.76/10.38 (subgroup_member(inverse(a))),
% 15.76/10.38 inference(unit_resolution,[status(thm)],[180, 67])).
% 15.76/10.38 tff(182,plain,
% 15.76/10.38 ((~![X: $i] : product(identity, X, X)) | product(identity, d, d)),
% 15.76/10.38 inference(quant_inst,[status(thm)],[])).
% 15.76/10.38 tff(183,plain,
% 15.76/10.38 (product(identity, d, d)),
% 15.76/10.38 inference(unit_resolution,[status(thm)],[182, 7])).
% 15.76/10.38 tff(184,plain,
% 15.76/10.38 (product(identity, multiply(identity, c), multiply(identity, c)) <=> product(identity, c, c)),
% 15.76/10.38 inference(monotonicity,[status(thm)],[83, 83])).
% 15.76/10.38 tff(185,plain,
% 15.76/10.38 (product(identity, c, c) <=> product(identity, multiply(identity, c), multiply(identity, c))),
% 15.76/10.38 inference(symmetry,[status(thm)],[184])).
% 15.76/10.38 tff(186,plain,
% 15.76/10.38 (product(identity, multiply(identity, c), multiply(identity, c))),
% 15.76/10.38 inference(modus_ponens,[status(thm)],[78, 185])).
% 15.76/10.38 tff(187,plain,
% 15.76/10.38 (product(a, multiply(identity, c), d) <=> product(a, c, d)),
% 15.76/10.38 inference(monotonicity,[status(thm)],[83])).
% 15.76/10.38 tff(188,plain,
% 15.76/10.38 (product(a, c, d) <=> product(a, multiply(identity, c), d)),
% 15.76/10.38 inference(symmetry,[status(thm)],[187])).
% 15.76/10.38 tff(189,plain,
% 15.76/10.38 (product(a, c, d) <=> product(a, c, d)),
% 15.76/10.38 inference(rewrite,[status(thm)],[])).
% 15.76/10.38 tff(190,axiom,(product(a, c, d)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a_times_c_is_d')).
% 15.76/10.38 tff(191,plain,
% 15.76/10.38 (product(a, c, d)),
% 15.76/10.38 inference(modus_ponens,[status(thm)],[190, 189])).
% 15.76/10.38 tff(192,plain,
% 15.76/10.38 (product(a, multiply(identity, c), d)),
% 15.76/10.38 inference(modus_ponens,[status(thm)],[191, 188])).
% 15.76/10.38 tff(193,plain,
% 15.76/10.38 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | ((~product(a, multiply(identity, c), d)) | (~product(identity, multiply(identity, c), multiply(identity, c))) | (~product(inverse(a), a, identity)) | product(inverse(a), d, multiply(identity, c)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (~product(a, multiply(identity, c), d)) | (~product(identity, multiply(identity, c), multiply(identity, c))) | (~product(inverse(a), a, identity)) | product(inverse(a), d, multiply(identity, c)))),
% 15.76/10.38 inference(rewrite,[status(thm)],[])).
% 15.76/10.38 tff(194,plain,
% 15.76/10.38 ((product(inverse(a), d, multiply(identity, c)) | (~product(identity, multiply(identity, c), multiply(identity, c))) | (~product(a, multiply(identity, c), d)) | (~product(inverse(a), a, identity))) <=> ((~product(a, multiply(identity, c), d)) | (~product(identity, multiply(identity, c), multiply(identity, c))) | (~product(inverse(a), a, identity)) | product(inverse(a), d, multiply(identity, c)))),
% 15.76/10.38 inference(rewrite,[status(thm)],[])).
% 15.76/10.38 tff(195,plain,
% 15.76/10.38 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(inverse(a), d, multiply(identity, c)) | (~product(identity, multiply(identity, c), multiply(identity, c))) | (~product(a, multiply(identity, c), d)) | (~product(inverse(a), a, identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | ((~product(a, multiply(identity, c), d)) | (~product(identity, multiply(identity, c), multiply(identity, c))) | (~product(inverse(a), a, identity)) | product(inverse(a), d, multiply(identity, c))))),
% 15.76/10.38 inference(monotonicity,[status(thm)],[194])).
% 15.76/10.38 tff(196,plain,
% 15.76/10.38 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(inverse(a), d, multiply(identity, c)) | (~product(identity, multiply(identity, c), multiply(identity, c))) | (~product(a, multiply(identity, c), d)) | (~product(inverse(a), a, identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (~product(a, multiply(identity, c), d)) | (~product(identity, multiply(identity, c), multiply(identity, c))) | (~product(inverse(a), a, identity)) | product(inverse(a), d, multiply(identity, c)))),
% 15.76/10.38 inference(transitivity,[status(thm)],[195, 193])).
% 15.76/10.38 tff(197,plain,
% 15.76/10.38 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(inverse(a), d, multiply(identity, c)) | (~product(identity, multiply(identity, c), multiply(identity, c))) | (~product(a, multiply(identity, c), d)) | (~product(inverse(a), a, identity)))),
% 15.76/10.38 inference(quant_inst,[status(thm)],[])).
% 15.76/10.38 tff(198,plain,
% 15.76/10.38 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (~product(a, multiply(identity, c), d)) | (~product(identity, multiply(identity, c), multiply(identity, c))) | (~product(inverse(a), a, identity)) | product(inverse(a), d, multiply(identity, c))),
% 15.76/10.38 inference(modus_ponens,[status(thm)],[197, 196])).
% 15.76/10.38 tff(199,plain,
% 15.76/10.38 ((~product(a, multiply(identity, c), d)) | (~product(identity, multiply(identity, c), multiply(identity, c))) | product(inverse(a), d, multiply(identity, c))),
% 15.76/10.38 inference(unit_resolution,[status(thm)],[198, 32, 22])).
% 15.76/10.38 tff(200,plain,
% 15.76/10.38 (product(inverse(a), d, multiply(identity, c))),
% 15.76/10.38 inference(unit_resolution,[status(thm)],[199, 192, 186])).
% 15.76/10.38 tff(201,plain,
% 15.76/10.38 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(inverse(inverse(a)), multiply(identity, c), d) | (~product(identity, d, d)) | (~product(inverse(a), d, multiply(identity, c))) | (~product(inverse(inverse(a)), inverse(a), identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | product(inverse(inverse(a)), multiply(identity, c), d) | (~product(identity, d, d)) | (~product(inverse(a), d, multiply(identity, c))) | (~product(inverse(inverse(a)), inverse(a), identity)))),
% 15.76/10.38 inference(rewrite,[status(thm)],[])).
% 15.76/10.38 tff(202,plain,
% 15.76/10.38 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(inverse(inverse(a)), multiply(identity, c), d) | (~product(identity, d, d)) | (~product(inverse(a), d, multiply(identity, c))) | (~product(inverse(inverse(a)), inverse(a), identity)))),
% 15.76/10.38 inference(quant_inst,[status(thm)],[])).
% 15.76/10.38 tff(203,plain,
% 15.76/10.38 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | product(inverse(inverse(a)), multiply(identity, c), d) | (~product(identity, d, d)) | (~product(inverse(a), d, multiply(identity, c))) | (~product(inverse(inverse(a)), inverse(a), identity))),
% 15.76/10.38 inference(modus_ponens,[status(thm)],[202, 201])).
% 15.76/10.38 tff(204,plain,
% 15.76/10.38 (product(inverse(inverse(a)), multiply(identity, c), d)),
% 15.76/10.38 inference(unit_resolution,[status(thm)],[203, 32, 200, 183, 18])).
% 15.76/10.38 tff(205,plain,
% 15.76/10.38 ((~subgroup_member(d)) <=> (~subgroup_member(d))),
% 15.76/10.38 inference(rewrite,[status(thm)],[])).
% 15.76/10.38 tff(206,axiom,(~subgroup_member(d)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_d_is_in_subgroup')).
% 15.76/10.38 tff(207,plain,
% 15.76/10.38 (~subgroup_member(d)),
% 15.76/10.38 inference(modus_ponens,[status(thm)],[206, 205])).
% 15.76/10.38 tff(208,plain,
% 15.76/10.38 (((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (subgroup_member(d) | (~subgroup_member(multiply(identity, c))) | (~subgroup_member(inverse(inverse(a)))) | (~product(inverse(inverse(a)), multiply(identity, c), d)))) <=> ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | subgroup_member(d) | (~subgroup_member(multiply(identity, c))) | (~subgroup_member(inverse(inverse(a)))) | (~product(inverse(inverse(a)), multiply(identity, c), d)))),
% 15.76/10.38 inference(rewrite,[status(thm)],[])).
% 15.76/10.38 tff(209,plain,
% 15.76/10.38 ((subgroup_member(d) | (~product(inverse(inverse(a)), multiply(identity, c), d)) | (~subgroup_member(multiply(identity, c))) | (~subgroup_member(inverse(inverse(a))))) <=> (subgroup_member(d) | (~subgroup_member(multiply(identity, c))) | (~subgroup_member(inverse(inverse(a)))) | (~product(inverse(inverse(a)), multiply(identity, c), d)))),
% 15.76/10.38 inference(rewrite,[status(thm)],[])).
% 15.76/10.38 tff(210,plain,
% 15.76/10.38 (((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (subgroup_member(d) | (~product(inverse(inverse(a)), multiply(identity, c), d)) | (~subgroup_member(multiply(identity, c))) | (~subgroup_member(inverse(inverse(a)))))) <=> ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (subgroup_member(d) | (~subgroup_member(multiply(identity, c))) | (~subgroup_member(inverse(inverse(a)))) | (~product(inverse(inverse(a)), multiply(identity, c), d))))),
% 15.76/10.38 inference(monotonicity,[status(thm)],[209])).
% 15.76/10.38 tff(211,plain,
% 15.76/10.38 (((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (subgroup_member(d) | (~product(inverse(inverse(a)), multiply(identity, c), d)) | (~subgroup_member(multiply(identity, c))) | (~subgroup_member(inverse(inverse(a)))))) <=> ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | subgroup_member(d) | (~subgroup_member(multiply(identity, c))) | (~subgroup_member(inverse(inverse(a)))) | (~product(inverse(inverse(a)), multiply(identity, c), d)))),
% 15.76/10.38 inference(transitivity,[status(thm)],[210, 208])).
% 15.76/10.38 tff(212,plain,
% 15.76/10.38 ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (subgroup_member(d) | (~product(inverse(inverse(a)), multiply(identity, c), d)) | (~subgroup_member(multiply(identity, c))) | (~subgroup_member(inverse(inverse(a)))))),
% 15.76/10.38 inference(quant_inst,[status(thm)],[])).
% 15.76/10.38 tff(213,plain,
% 15.76/10.38 ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | subgroup_member(d) | (~subgroup_member(multiply(identity, c))) | (~subgroup_member(inverse(inverse(a)))) | (~product(inverse(inverse(a)), multiply(identity, c), d))),
% 15.76/10.38 inference(modus_ponens,[status(thm)],[212, 211])).
% 15.76/10.39 tff(214,plain,
% 15.76/10.39 ((~subgroup_member(multiply(identity, c))) | (~subgroup_member(inverse(inverse(a))))),
% 15.76/10.39 inference(unit_resolution,[status(thm)],[213, 155, 207, 204])).
% 15.76/10.39 tff(215,plain,
% 15.76/10.39 (~subgroup_member(inverse(inverse(a)))),
% 15.76/10.39 inference(unit_resolution,[status(thm)],[214, 67])).
% 15.76/10.39 tff(216,plain,
% 15.76/10.39 (((~![X: $i] : ((~subgroup_member(X)) | subgroup_member(inverse(X)))) | ((~subgroup_member(inverse(a))) | subgroup_member(inverse(inverse(a))))) <=> ((~![X: $i] : ((~subgroup_member(X)) | subgroup_member(inverse(X)))) | (~subgroup_member(inverse(a))) | subgroup_member(inverse(inverse(a))))),
% 15.76/10.39 inference(rewrite,[status(thm)],[])).
% 15.76/10.39 tff(217,plain,
% 15.76/10.39 ((~![X: $i] : ((~subgroup_member(X)) | subgroup_member(inverse(X)))) | ((~subgroup_member(inverse(a))) | subgroup_member(inverse(inverse(a))))),
% 15.76/10.39 inference(quant_inst,[status(thm)],[])).
% 15.76/10.39 tff(218,plain,
% 15.76/10.39 ((~![X: $i] : ((~subgroup_member(X)) | subgroup_member(inverse(X)))) | (~subgroup_member(inverse(a))) | subgroup_member(inverse(inverse(a)))),
% 15.76/10.39 inference(modus_ponens,[status(thm)],[217, 216])).
% 15.76/10.39 tff(219,plain,
% 15.76/10.39 ((~subgroup_member(inverse(a))) | subgroup_member(inverse(inverse(a)))),
% 15.76/10.39 inference(unit_resolution,[status(thm)],[218, 169])).
% 15.76/10.39 tff(220,plain,
% 15.76/10.39 ($false),
% 15.76/10.39 inference(unit_resolution,[status(thm)],[219, 215, 181])).
% 15.76/10.39 tff(221,plain,(~subgroup_member(multiply(identity, c))), inference(lemma,lemma(discharge,[]))).
% 15.76/10.39 tff(222,plain,
% 15.76/10.39 (((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | ((~subgroup_member(c)) | subgroup_member(multiply(identity, c)) | (~product(identity, c, multiply(identity, c))) | (~subgroup_member(identity)))) <=> ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (~subgroup_member(c)) | subgroup_member(multiply(identity, c)) | (~product(identity, c, multiply(identity, c))) | (~subgroup_member(identity)))),
% 15.76/10.39 inference(rewrite,[status(thm)],[])).
% 15.76/10.39 tff(223,plain,
% 15.76/10.39 ((subgroup_member(multiply(identity, c)) | (~product(identity, c, multiply(identity, c))) | (~subgroup_member(c)) | (~subgroup_member(identity))) <=> ((~subgroup_member(c)) | subgroup_member(multiply(identity, c)) | (~product(identity, c, multiply(identity, c))) | (~subgroup_member(identity)))),
% 15.76/10.39 inference(rewrite,[status(thm)],[])).
% 15.76/10.39 tff(224,plain,
% 15.76/10.39 (((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (subgroup_member(multiply(identity, c)) | (~product(identity, c, multiply(identity, c))) | (~subgroup_member(c)) | (~subgroup_member(identity)))) <=> ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | ((~subgroup_member(c)) | subgroup_member(multiply(identity, c)) | (~product(identity, c, multiply(identity, c))) | (~subgroup_member(identity))))),
% 15.76/10.39 inference(monotonicity,[status(thm)],[223])).
% 15.76/10.39 tff(225,plain,
% 15.76/10.39 (((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (subgroup_member(multiply(identity, c)) | (~product(identity, c, multiply(identity, c))) | (~subgroup_member(c)) | (~subgroup_member(identity)))) <=> ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (~subgroup_member(c)) | subgroup_member(multiply(identity, c)) | (~product(identity, c, multiply(identity, c))) | (~subgroup_member(identity)))),
% 15.76/10.39 inference(transitivity,[status(thm)],[224, 222])).
% 15.76/10.39 tff(226,plain,
% 15.76/10.39 ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (subgroup_member(multiply(identity, c)) | (~product(identity, c, multiply(identity, c))) | (~subgroup_member(c)) | (~subgroup_member(identity)))),
% 15.76/10.39 inference(quant_inst,[status(thm)],[])).
% 15.76/10.39 tff(227,plain,
% 15.76/10.39 ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (~subgroup_member(c)) | subgroup_member(multiply(identity, c)) | (~product(identity, c, multiply(identity, c))) | (~subgroup_member(identity))),
% 15.76/10.39 inference(modus_ponens,[status(thm)],[226, 225])).
% 15.76/10.39 tff(228,plain,
% 15.76/10.39 ((~subgroup_member(c)) | subgroup_member(multiply(identity, c))),
% 15.76/10.39 inference(unit_resolution,[status(thm)],[227, 155, 145, 76])).
% 15.76/10.39 tff(229,plain,
% 15.76/10.39 (~subgroup_member(c)),
% 15.76/10.39 inference(unit_resolution,[status(thm)],[228, 221])).
% 15.76/10.39 tff(230,plain,
% 15.76/10.39 (((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (subgroup_member(c) | (~product(b, inverse(a), c)) | (~subgroup_member(inverse(a))) | (~subgroup_member(b)))) <=> ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | subgroup_member(c) | (~product(b, inverse(a), c)) | (~subgroup_member(inverse(a))) | (~subgroup_member(b)))),
% 15.76/10.39 inference(rewrite,[status(thm)],[])).
% 15.76/10.39 tff(231,plain,
% 15.76/10.39 ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (subgroup_member(c) | (~product(b, inverse(a), c)) | (~subgroup_member(inverse(a))) | (~subgroup_member(b)))),
% 15.76/10.39 inference(quant_inst,[status(thm)],[])).
% 15.76/10.39 tff(232,plain,
% 15.76/10.39 ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, B, C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | subgroup_member(c) | (~product(b, inverse(a), c)) | (~subgroup_member(inverse(a))) | (~subgroup_member(b))),
% 15.76/10.39 inference(modus_ponens,[status(thm)],[231, 230])).
% 15.76/10.39 tff(233,plain,
% 15.76/10.39 (subgroup_member(c) | (~subgroup_member(inverse(a)))),
% 15.76/10.39 inference(unit_resolution,[status(thm)],[232, 155, 142, 100])).
% 15.76/10.39 tff(234,plain,
% 15.76/10.39 (~subgroup_member(inverse(a))),
% 15.76/10.39 inference(unit_resolution,[status(thm)],[233, 229])).
% 15.76/10.39 tff(235,plain,
% 15.76/10.39 (^[B: $i, A: $i] : refl((subgroup_member(A) | subgroup_member(B) | product(A, element_in_O2(A, B), B)) <=> (subgroup_member(A) | subgroup_member(B) | product(A, element_in_O2(A, B), B)))),
% 15.76/10.39 inference(bind,[status(th)],[])).
% 15.76/10.39 tff(236,plain,
% 15.76/10.39 (![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(B) | product(A, element_in_O2(A, B), B)) <=> ![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(B) | product(A, element_in_O2(A, B), B))),
% 15.76/10.39 inference(quant_intro,[status(thm)],[235])).
% 15.76/10.39 tff(237,plain,
% 15.76/10.39 (![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(B) | product(A, element_in_O2(A, B), B)) <=> ![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(B) | product(A, element_in_O2(A, B), B))),
% 15.76/10.39 inference(rewrite,[status(thm)],[])).
% 15.76/10.39 tff(238,plain,
% 15.76/10.39 (^[B: $i, A: $i] : trans(monotonicity(rewrite((product(A, element_in_O2(A, B), B) | subgroup_member(B)) <=> (subgroup_member(B) | product(A, element_in_O2(A, B), B))), (((product(A, element_in_O2(A, B), B) | subgroup_member(B)) | subgroup_member(A)) <=> ((subgroup_member(B) | product(A, element_in_O2(A, B), B)) | subgroup_member(A)))), rewrite(((subgroup_member(B) | product(A, element_in_O2(A, B), B)) | subgroup_member(A)) <=> (subgroup_member(A) | subgroup_member(B) | product(A, element_in_O2(A, B), B))), (((product(A, element_in_O2(A, B), B) | subgroup_member(B)) | subgroup_member(A)) <=> (subgroup_member(A) | subgroup_member(B) | product(A, element_in_O2(A, B), B))))),
% 15.76/10.39 inference(bind,[status(th)],[])).
% 15.76/10.39 tff(239,plain,
% 15.76/10.39 (![B: $i, A: $i] : ((product(A, element_in_O2(A, B), B) | subgroup_member(B)) | subgroup_member(A)) <=> ![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(B) | product(A, element_in_O2(A, B), B))),
% 15.76/10.39 inference(quant_intro,[status(thm)],[238])).
% 15.76/10.39 tff(240,axiom,(![B: $i, A: $i] : ((product(A, element_in_O2(A, B), B) | subgroup_member(B)) | subgroup_member(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','property_of_O2')).
% 15.76/10.39 tff(241,plain,
% 15.76/10.39 (![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(B) | product(A, element_in_O2(A, B), B))),
% 15.76/10.39 inference(modus_ponens,[status(thm)],[240, 239])).
% 15.76/10.39 tff(242,plain,
% 15.76/10.39 (![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(B) | product(A, element_in_O2(A, B), B))),
% 15.76/10.39 inference(modus_ponens,[status(thm)],[241, 237])).
% 15.76/10.39 tff(243,plain,(
% 15.76/10.39 ![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(B) | product(A, element_in_O2(A, B), B))),
% 15.76/10.39 inference(skolemize,[status(sab)],[242])).
% 15.76/10.39 tff(244,plain,
% 15.76/10.39 (![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(B) | product(A, element_in_O2(A, B), B))),
% 15.76/10.39 inference(modus_ponens,[status(thm)],[243, 236])).
% 15.76/10.39 tff(245,plain,
% 15.76/10.39 (((~![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(B) | product(A, element_in_O2(A, B), B))) | (subgroup_member(inverse(a)) | subgroup_member(multiply(identity, c)) | product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(a)))) <=> ((~![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(B) | product(A, element_in_O2(A, B), B))) | subgroup_member(inverse(a)) | subgroup_member(multiply(identity, c)) | product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(a)))),
% 15.76/10.39 inference(rewrite,[status(thm)],[])).
% 15.76/10.39 tff(246,plain,
% 15.76/10.39 ((subgroup_member(multiply(identity, c)) | subgroup_member(inverse(a)) | product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(a))) <=> (subgroup_member(inverse(a)) | subgroup_member(multiply(identity, c)) | product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(a)))),
% 15.76/10.39 inference(rewrite,[status(thm)],[])).
% 15.76/10.39 tff(247,plain,
% 15.76/10.39 (((~![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(B) | product(A, element_in_O2(A, B), B))) | (subgroup_member(multiply(identity, c)) | subgroup_member(inverse(a)) | product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(a)))) <=> ((~![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(B) | product(A, element_in_O2(A, B), B))) | (subgroup_member(inverse(a)) | subgroup_member(multiply(identity, c)) | product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(a))))),
% 15.76/10.39 inference(monotonicity,[status(thm)],[246])).
% 15.76/10.39 tff(248,plain,
% 15.76/10.39 (((~![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(B) | product(A, element_in_O2(A, B), B))) | (subgroup_member(multiply(identity, c)) | subgroup_member(inverse(a)) | product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(a)))) <=> ((~![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(B) | product(A, element_in_O2(A, B), B))) | subgroup_member(inverse(a)) | subgroup_member(multiply(identity, c)) | product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(a)))),
% 15.76/10.39 inference(transitivity,[status(thm)],[247, 245])).
% 15.76/10.39 tff(249,plain,
% 15.76/10.39 ((~![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(B) | product(A, element_in_O2(A, B), B))) | (subgroup_member(multiply(identity, c)) | subgroup_member(inverse(a)) | product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(a)))),
% 15.76/10.39 inference(quant_inst,[status(thm)],[])).
% 15.76/10.39 tff(250,plain,
% 15.76/10.39 ((~![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(B) | product(A, element_in_O2(A, B), B))) | subgroup_member(inverse(a)) | subgroup_member(multiply(identity, c)) | product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(a))),
% 15.76/10.39 inference(modus_ponens,[status(thm)],[249, 248])).
% 15.76/10.39 tff(251,plain,
% 15.76/10.39 (subgroup_member(inverse(a)) | subgroup_member(multiply(identity, c)) | product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(a))),
% 15.76/10.39 inference(unit_resolution,[status(thm)],[250, 244])).
% 15.76/10.39 tff(252,plain,
% 15.76/10.39 (product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(a))),
% 15.76/10.39 inference(unit_resolution,[status(thm)],[251, 234, 221])).
% 15.76/10.39 tff(253,plain,
% 15.76/10.39 (product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(inverse(inverse(a))))),
% 15.76/10.39 inference(modus_ponens,[status(thm)],[252, 66])).
% 15.76/10.39 tff(254,plain,
% 15.76/10.39 ((~![X: $i] : product(X, inverse(X), identity)) | product(element_in_O2(multiply(identity, c), inverse(a)), inverse(element_in_O2(multiply(identity, c), inverse(a))), identity)),
% 15.76/10.39 inference(quant_inst,[status(thm)],[])).
% 15.76/10.39 tff(255,plain,
% 15.76/10.39 (product(element_in_O2(multiply(identity, c), inverse(a)), inverse(element_in_O2(multiply(identity, c), inverse(a))), identity)),
% 15.76/10.39 inference(unit_resolution,[status(thm)],[254, 112])).
% 15.76/10.39 tff(256,plain,
% 15.76/10.39 (product(b, inverse(a), multiply(identity, c)) <=> product(b, inverse(a), c)),
% 15.76/10.39 inference(monotonicity,[status(thm)],[83])).
% 15.76/10.39 tff(257,plain,
% 15.76/10.39 (product(b, inverse(a), c) <=> product(b, inverse(a), multiply(identity, c))),
% 15.76/10.39 inference(symmetry,[status(thm)],[256])).
% 15.76/10.39 tff(258,plain,
% 15.76/10.39 (product(b, inverse(a), multiply(identity, c))),
% 15.76/10.39 inference(modus_ponens,[status(thm)],[100, 257])).
% 15.76/10.39 tff(259,plain,
% 15.76/10.39 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | ((~product(inverse(a), identity, inverse(a))) | (~product(b, inverse(a), multiply(identity, c))) | product(multiply(identity, c), identity, multiply(identity, c)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (~product(inverse(a), identity, inverse(a))) | (~product(b, inverse(a), multiply(identity, c))) | product(multiply(identity, c), identity, multiply(identity, c)))),
% 15.76/10.39 inference(rewrite,[status(thm)],[])).
% 15.76/10.39 tff(260,plain,
% 15.76/10.39 ((product(multiply(identity, c), identity, multiply(identity, c)) | (~product(inverse(a), identity, inverse(a))) | (~product(b, inverse(a), multiply(identity, c))) | (~product(b, inverse(a), multiply(identity, c)))) <=> ((~product(inverse(a), identity, inverse(a))) | (~product(b, inverse(a), multiply(identity, c))) | product(multiply(identity, c), identity, multiply(identity, c)))),
% 15.76/10.39 inference(rewrite,[status(thm)],[])).
% 15.76/10.39 tff(261,plain,
% 15.76/10.39 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(multiply(identity, c), identity, multiply(identity, c)) | (~product(inverse(a), identity, inverse(a))) | (~product(b, inverse(a), multiply(identity, c))) | (~product(b, inverse(a), multiply(identity, c))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | ((~product(inverse(a), identity, inverse(a))) | (~product(b, inverse(a), multiply(identity, c))) | product(multiply(identity, c), identity, multiply(identity, c))))),
% 15.76/10.39 inference(monotonicity,[status(thm)],[260])).
% 15.76/10.39 tff(262,plain,
% 15.76/10.39 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(multiply(identity, c), identity, multiply(identity, c)) | (~product(inverse(a), identity, inverse(a))) | (~product(b, inverse(a), multiply(identity, c))) | (~product(b, inverse(a), multiply(identity, c))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (~product(inverse(a), identity, inverse(a))) | (~product(b, inverse(a), multiply(identity, c))) | product(multiply(identity, c), identity, multiply(identity, c)))),
% 15.76/10.39 inference(transitivity,[status(thm)],[261, 259])).
% 15.76/10.39 tff(263,plain,
% 15.76/10.39 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(multiply(identity, c), identity, multiply(identity, c)) | (~product(inverse(a), identity, inverse(a))) | (~product(b, inverse(a), multiply(identity, c))) | (~product(b, inverse(a), multiply(identity, c))))),
% 15.76/10.39 inference(quant_inst,[status(thm)],[])).
% 15.76/10.39 tff(264,plain,
% 15.76/10.39 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (~product(inverse(a), identity, inverse(a))) | (~product(b, inverse(a), multiply(identity, c))) | product(multiply(identity, c), identity, multiply(identity, c))),
% 15.76/10.39 inference(modus_ponens,[status(thm)],[263, 262])).
% 15.76/10.39 tff(265,plain,
% 15.76/10.39 ((~product(b, inverse(a), multiply(identity, c))) | product(multiply(identity, c), identity, multiply(identity, c))),
% 15.76/10.39 inference(unit_resolution,[status(thm)],[264, 124, 105])).
% 15.76/10.39 tff(266,plain,
% 15.76/10.39 (product(multiply(identity, c), identity, multiply(identity, c))),
% 15.76/10.39 inference(unit_resolution,[status(thm)],[265, 258])).
% 15.76/10.39 tff(267,plain,
% 15.76/10.39 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | ((~product(multiply(identity, c), identity, multiply(identity, c))) | product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c)) | (~product(element_in_O2(multiply(identity, c), inverse(a)), inverse(element_in_O2(multiply(identity, c), inverse(a))), identity)) | (~product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(inverse(inverse(a))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (~product(multiply(identity, c), identity, multiply(identity, c))) | product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c)) | (~product(element_in_O2(multiply(identity, c), inverse(a)), inverse(element_in_O2(multiply(identity, c), inverse(a))), identity)) | (~product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(inverse(inverse(a))))))),
% 15.76/10.39 inference(rewrite,[status(thm)],[])).
% 15.76/10.39 tff(268,plain,
% 15.76/10.39 ((product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c)) | (~product(element_in_O2(multiply(identity, c), inverse(a)), inverse(element_in_O2(multiply(identity, c), inverse(a))), identity)) | (~product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(inverse(inverse(a))))) | (~product(multiply(identity, c), identity, multiply(identity, c)))) <=> ((~product(multiply(identity, c), identity, multiply(identity, c))) | product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c)) | (~product(element_in_O2(multiply(identity, c), inverse(a)), inverse(element_in_O2(multiply(identity, c), inverse(a))), identity)) | (~product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(inverse(inverse(a))))))),
% 15.76/10.39 inference(rewrite,[status(thm)],[])).
% 15.76/10.39 tff(269,plain,
% 15.76/10.39 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c)) | (~product(element_in_O2(multiply(identity, c), inverse(a)), inverse(element_in_O2(multiply(identity, c), inverse(a))), identity)) | (~product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(inverse(inverse(a))))) | (~product(multiply(identity, c), identity, multiply(identity, c))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | ((~product(multiply(identity, c), identity, multiply(identity, c))) | product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c)) | (~product(element_in_O2(multiply(identity, c), inverse(a)), inverse(element_in_O2(multiply(identity, c), inverse(a))), identity)) | (~product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(inverse(inverse(a)))))))),
% 15.76/10.39 inference(monotonicity,[status(thm)],[268])).
% 15.76/10.39 tff(270,plain,
% 15.76/10.39 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c)) | (~product(element_in_O2(multiply(identity, c), inverse(a)), inverse(element_in_O2(multiply(identity, c), inverse(a))), identity)) | (~product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(inverse(inverse(a))))) | (~product(multiply(identity, c), identity, multiply(identity, c))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (~product(multiply(identity, c), identity, multiply(identity, c))) | product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c)) | (~product(element_in_O2(multiply(identity, c), inverse(a)), inverse(element_in_O2(multiply(identity, c), inverse(a))), identity)) | (~product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(inverse(inverse(a))))))),
% 15.76/10.39 inference(transitivity,[status(thm)],[269, 267])).
% 15.76/10.39 tff(271,plain,
% 15.76/10.39 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c)) | (~product(element_in_O2(multiply(identity, c), inverse(a)), inverse(element_in_O2(multiply(identity, c), inverse(a))), identity)) | (~product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(inverse(inverse(a))))) | (~product(multiply(identity, c), identity, multiply(identity, c))))),
% 15.76/10.39 inference(quant_inst,[status(thm)],[])).
% 15.76/10.39 tff(272,plain,
% 15.76/10.39 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (~product(multiply(identity, c), identity, multiply(identity, c))) | product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c)) | (~product(element_in_O2(multiply(identity, c), inverse(a)), inverse(element_in_O2(multiply(identity, c), inverse(a))), identity)) | (~product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(inverse(inverse(a)))))),
% 15.76/10.39 inference(modus_ponens,[status(thm)],[271, 270])).
% 15.76/10.39 tff(273,plain,
% 15.76/10.39 (product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c)) | (~product(multiply(identity, c), element_in_O2(multiply(identity, c), inverse(a)), inverse(inverse(inverse(a)))))),
% 15.76/10.39 inference(unit_resolution,[status(thm)],[272, 124, 266, 255])).
% 15.76/10.39 tff(274,plain,
% 15.76/10.39 (product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c))),
% 15.76/10.39 inference(unit_resolution,[status(thm)],[273, 253])).
% 15.76/10.39 tff(275,plain,
% 15.76/10.39 ((~![X: $i] : product(X, inverse(X), identity)) | product(inverse(inverse(a)), inverse(inverse(inverse(a))), identity)),
% 15.76/10.39 inference(quant_inst,[status(thm)],[])).
% 15.76/10.39 tff(276,plain,
% 15.76/10.39 (product(inverse(inverse(a)), inverse(inverse(inverse(a))), identity)),
% 15.76/10.39 inference(unit_resolution,[status(thm)],[275, 112])).
% 15.76/10.39 tff(277,plain,
% 15.76/10.39 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | ((~product(inverse(inverse(a)), inverse(inverse(inverse(a))), identity)) | (~product(identity, inverse(element_in_O2(multiply(identity, c), inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))))) | (~product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c))) | product(inverse(inverse(a)), multiply(identity, c), inverse(element_in_O2(multiply(identity, c), inverse(a)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (~product(inverse(inverse(a)), inverse(inverse(inverse(a))), identity)) | (~product(identity, inverse(element_in_O2(multiply(identity, c), inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))))) | (~product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c))) | product(inverse(inverse(a)), multiply(identity, c), inverse(element_in_O2(multiply(identity, c), inverse(a)))))),
% 15.76/10.40 inference(rewrite,[status(thm)],[])).
% 15.76/10.40 tff(278,plain,
% 15.76/10.40 ((product(inverse(inverse(a)), multiply(identity, c), inverse(element_in_O2(multiply(identity, c), inverse(a)))) | (~product(identity, inverse(element_in_O2(multiply(identity, c), inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))))) | (~product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c))) | (~product(inverse(inverse(a)), inverse(inverse(inverse(a))), identity))) <=> ((~product(inverse(inverse(a)), inverse(inverse(inverse(a))), identity)) | (~product(identity, inverse(element_in_O2(multiply(identity, c), inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))))) | (~product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c))) | product(inverse(inverse(a)), multiply(identity, c), inverse(element_in_O2(multiply(identity, c), inverse(a)))))),
% 15.76/10.40 inference(rewrite,[status(thm)],[])).
% 15.76/10.40 tff(279,plain,
% 15.76/10.40 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(inverse(inverse(a)), multiply(identity, c), inverse(element_in_O2(multiply(identity, c), inverse(a)))) | (~product(identity, inverse(element_in_O2(multiply(identity, c), inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))))) | (~product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c))) | (~product(inverse(inverse(a)), inverse(inverse(inverse(a))), identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | ((~product(inverse(inverse(a)), inverse(inverse(inverse(a))), identity)) | (~product(identity, inverse(element_in_O2(multiply(identity, c), inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))))) | (~product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c))) | product(inverse(inverse(a)), multiply(identity, c), inverse(element_in_O2(multiply(identity, c), inverse(a))))))),
% 15.76/10.40 inference(monotonicity,[status(thm)],[278])).
% 15.76/10.40 tff(280,plain,
% 15.76/10.40 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(inverse(inverse(a)), multiply(identity, c), inverse(element_in_O2(multiply(identity, c), inverse(a)))) | (~product(identity, inverse(element_in_O2(multiply(identity, c), inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))))) | (~product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c))) | (~product(inverse(inverse(a)), inverse(inverse(inverse(a))), identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (~product(inverse(inverse(a)), inverse(inverse(inverse(a))), identity)) | (~product(identity, inverse(element_in_O2(multiply(identity, c), inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))))) | (~product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c))) | product(inverse(inverse(a)), multiply(identity, c), inverse(element_in_O2(multiply(identity, c), inverse(a)))))),
% 15.76/10.40 inference(transitivity,[status(thm)],[279, 277])).
% 15.76/10.40 tff(281,plain,
% 15.76/10.40 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(inverse(inverse(a)), multiply(identity, c), inverse(element_in_O2(multiply(identity, c), inverse(a)))) | (~product(identity, inverse(element_in_O2(multiply(identity, c), inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))))) | (~product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c))) | (~product(inverse(inverse(a)), inverse(inverse(inverse(a))), identity)))),
% 15.76/10.40 inference(quant_inst,[status(thm)],[])).
% 15.76/10.40 tff(282,plain,
% 15.76/10.40 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (~product(inverse(inverse(a)), inverse(inverse(inverse(a))), identity)) | (~product(identity, inverse(element_in_O2(multiply(identity, c), inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))))) | (~product(inverse(inverse(inverse(a))), inverse(element_in_O2(multiply(identity, c), inverse(a))), multiply(identity, c))) | product(inverse(inverse(a)), multiply(identity, c), inverse(element_in_O2(multiply(identity, c), inverse(a))))),
% 15.76/10.40 inference(modus_ponens,[status(thm)],[281, 280])).
% 15.76/10.40 tff(283,plain,
% 15.76/10.40 (product(inverse(inverse(a)), multiply(identity, c), inverse(element_in_O2(multiply(identity, c), inverse(a))))),
% 15.76/10.40 inference(unit_resolution,[status(thm)],[282, 32, 276, 274, 9])).
% 15.76/10.40 tff(284,plain,
% 15.76/10.40 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((~product(inverse(inverse(a)), multiply(identity, c), d)) | (inverse(element_in_O2(multiply(identity, c), inverse(a))) = d) | (~product(inverse(inverse(a)), multiply(identity, c), inverse(element_in_O2(multiply(identity, c), inverse(a))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(inverse(inverse(a)), multiply(identity, c), d)) | (inverse(element_in_O2(multiply(identity, c), inverse(a))) = d) | (~product(inverse(inverse(a)), multiply(identity, c), inverse(element_in_O2(multiply(identity, c), inverse(a))))))),
% 15.76/10.40 inference(rewrite,[status(thm)],[])).
% 15.76/10.40 tff(285,plain,
% 15.76/10.40 (((inverse(element_in_O2(multiply(identity, c), inverse(a))) = d) | (~product(inverse(inverse(a)), multiply(identity, c), d)) | (~product(inverse(inverse(a)), multiply(identity, c), inverse(element_in_O2(multiply(identity, c), inverse(a)))))) <=> ((~product(inverse(inverse(a)), multiply(identity, c), d)) | (inverse(element_in_O2(multiply(identity, c), inverse(a))) = d) | (~product(inverse(inverse(a)), multiply(identity, c), inverse(element_in_O2(multiply(identity, c), inverse(a))))))),
% 15.76/10.40 inference(rewrite,[status(thm)],[])).
% 15.76/10.40 tff(286,plain,
% 15.76/10.40 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((inverse(element_in_O2(multiply(identity, c), inverse(a))) = d) | (~product(inverse(inverse(a)), multiply(identity, c), d)) | (~product(inverse(inverse(a)), multiply(identity, c), inverse(element_in_O2(multiply(identity, c), inverse(a))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((~product(inverse(inverse(a)), multiply(identity, c), d)) | (inverse(element_in_O2(multiply(identity, c), inverse(a))) = d) | (~product(inverse(inverse(a)), multiply(identity, c), inverse(element_in_O2(multiply(identity, c), inverse(a)))))))),
% 15.76/10.40 inference(monotonicity,[status(thm)],[285])).
% 15.76/10.40 tff(287,plain,
% 15.76/10.40 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((inverse(element_in_O2(multiply(identity, c), inverse(a))) = d) | (~product(inverse(inverse(a)), multiply(identity, c), d)) | (~product(inverse(inverse(a)), multiply(identity, c), inverse(element_in_O2(multiply(identity, c), inverse(a))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(inverse(inverse(a)), multiply(identity, c), d)) | (inverse(element_in_O2(multiply(identity, c), inverse(a))) = d) | (~product(inverse(inverse(a)), multiply(identity, c), inverse(element_in_O2(multiply(identity, c), inverse(a))))))),
% 15.76/10.40 inference(transitivity,[status(thm)],[286, 284])).
% 15.76/10.40 tff(288,plain,
% 15.76/10.40 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((inverse(element_in_O2(multiply(identity, c), inverse(a))) = d) | (~product(inverse(inverse(a)), multiply(identity, c), d)) | (~product(inverse(inverse(a)), multiply(identity, c), inverse(element_in_O2(multiply(identity, c), inverse(a))))))),
% 15.76/10.40 inference(quant_inst,[status(thm)],[])).
% 15.76/10.40 tff(289,plain,
% 15.76/10.40 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(inverse(inverse(a)), multiply(identity, c), d)) | (inverse(element_in_O2(multiply(identity, c), inverse(a))) = d) | (~product(inverse(inverse(a)), multiply(identity, c), inverse(element_in_O2(multiply(identity, c), inverse(a)))))),
% 15.76/10.40 inference(modus_ponens,[status(thm)],[288, 287])).
% 15.76/10.40 tff(290,plain,
% 15.76/10.40 (inverse(element_in_O2(multiply(identity, c), inverse(a))) = d),
% 15.76/10.40 inference(unit_resolution,[status(thm)],[289, 55, 204, 283])).
% 15.76/10.40 tff(291,plain,
% 15.76/10.40 (subgroup_member(inverse(element_in_O2(multiply(identity, c), inverse(a)))) <=> subgroup_member(d)),
% 15.76/10.40 inference(monotonicity,[status(thm)],[290])).
% 15.76/10.40 tff(292,plain,
% 15.76/10.40 (subgroup_member(d) <=> subgroup_member(inverse(element_in_O2(multiply(identity, c), inverse(a))))),
% 15.76/10.40 inference(symmetry,[status(thm)],[291])).
% 15.76/10.40 tff(293,plain,
% 15.76/10.40 ((~subgroup_member(d)) <=> (~subgroup_member(inverse(element_in_O2(multiply(identity, c), inverse(a)))))),
% 15.76/10.40 inference(monotonicity,[status(thm)],[292])).
% 15.76/10.40 tff(294,plain,
% 15.76/10.40 (~subgroup_member(inverse(element_in_O2(multiply(identity, c), inverse(a))))),
% 15.76/10.40 inference(modus_ponens,[status(thm)],[207, 293])).
% 15.76/10.40 tff(295,plain,
% 15.76/10.40 (^[B: $i, A: $i] : refl((subgroup_member(A) | subgroup_member(element_in_O2(A, B)) | subgroup_member(B)) <=> (subgroup_member(A) | subgroup_member(element_in_O2(A, B)) | subgroup_member(B)))),
% 15.76/10.40 inference(bind,[status(th)],[])).
% 15.76/10.40 tff(296,plain,
% 15.76/10.40 (![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(element_in_O2(A, B)) | subgroup_member(B)) <=> ![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(element_in_O2(A, B)) | subgroup_member(B))),
% 15.76/10.40 inference(quant_intro,[status(thm)],[295])).
% 15.76/10.40 tff(297,plain,
% 15.76/10.40 (![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(element_in_O2(A, B)) | subgroup_member(B)) <=> ![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(element_in_O2(A, B)) | subgroup_member(B))),
% 15.76/10.40 inference(rewrite,[status(thm)],[])).
% 15.76/10.40 tff(298,plain,
% 15.76/10.40 (^[B: $i, A: $i] : trans(monotonicity(rewrite((subgroup_member(element_in_O2(A, B)) | subgroup_member(B)) <=> (subgroup_member(element_in_O2(A, B)) | subgroup_member(B))), (((subgroup_member(element_in_O2(A, B)) | subgroup_member(B)) | subgroup_member(A)) <=> ((subgroup_member(element_in_O2(A, B)) | subgroup_member(B)) | subgroup_member(A)))), rewrite(((subgroup_member(element_in_O2(A, B)) | subgroup_member(B)) | subgroup_member(A)) <=> (subgroup_member(A) | subgroup_member(element_in_O2(A, B)) | subgroup_member(B))), (((subgroup_member(element_in_O2(A, B)) | subgroup_member(B)) | subgroup_member(A)) <=> (subgroup_member(A) | subgroup_member(element_in_O2(A, B)) | subgroup_member(B))))),
% 15.76/10.40 inference(bind,[status(th)],[])).
% 15.76/10.40 tff(299,plain,
% 15.76/10.40 (![B: $i, A: $i] : ((subgroup_member(element_in_O2(A, B)) | subgroup_member(B)) | subgroup_member(A)) <=> ![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(element_in_O2(A, B)) | subgroup_member(B))),
% 15.76/10.40 inference(quant_intro,[status(thm)],[298])).
% 15.76/10.40 tff(300,axiom,(![B: $i, A: $i] : ((subgroup_member(element_in_O2(A, B)) | subgroup_member(B)) | subgroup_member(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','an_element_in_O2')).
% 15.76/10.40 tff(301,plain,
% 15.76/10.40 (![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(element_in_O2(A, B)) | subgroup_member(B))),
% 15.76/10.40 inference(modus_ponens,[status(thm)],[300, 299])).
% 15.76/10.40 tff(302,plain,
% 15.76/10.40 (![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(element_in_O2(A, B)) | subgroup_member(B))),
% 15.76/10.40 inference(modus_ponens,[status(thm)],[301, 297])).
% 15.76/10.40 tff(303,plain,(
% 15.76/10.40 ![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(element_in_O2(A, B)) | subgroup_member(B))),
% 15.76/10.40 inference(skolemize,[status(sab)],[302])).
% 15.76/10.40 tff(304,plain,
% 15.76/10.40 (![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(element_in_O2(A, B)) | subgroup_member(B))),
% 15.76/10.40 inference(modus_ponens,[status(thm)],[303, 296])).
% 15.76/10.40 tff(305,plain,
% 15.76/10.40 (((~![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(element_in_O2(A, B)) | subgroup_member(B))) | (subgroup_member(inverse(a)) | subgroup_member(multiply(identity, c)) | subgroup_member(element_in_O2(multiply(identity, c), inverse(a))))) <=> ((~![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(element_in_O2(A, B)) | subgroup_member(B))) | subgroup_member(inverse(a)) | subgroup_member(multiply(identity, c)) | subgroup_member(element_in_O2(multiply(identity, c), inverse(a))))),
% 15.76/10.40 inference(rewrite,[status(thm)],[])).
% 15.76/10.40 tff(306,plain,
% 15.76/10.40 ((subgroup_member(multiply(identity, c)) | subgroup_member(element_in_O2(multiply(identity, c), inverse(a))) | subgroup_member(inverse(a))) <=> (subgroup_member(inverse(a)) | subgroup_member(multiply(identity, c)) | subgroup_member(element_in_O2(multiply(identity, c), inverse(a))))),
% 15.76/10.40 inference(rewrite,[status(thm)],[])).
% 15.76/10.40 tff(307,plain,
% 15.76/10.40 (((~![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(element_in_O2(A, B)) | subgroup_member(B))) | (subgroup_member(multiply(identity, c)) | subgroup_member(element_in_O2(multiply(identity, c), inverse(a))) | subgroup_member(inverse(a)))) <=> ((~![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(element_in_O2(A, B)) | subgroup_member(B))) | (subgroup_member(inverse(a)) | subgroup_member(multiply(identity, c)) | subgroup_member(element_in_O2(multiply(identity, c), inverse(a)))))),
% 15.76/10.40 inference(monotonicity,[status(thm)],[306])).
% 15.76/10.40 tff(308,plain,
% 15.76/10.40 (((~![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(element_in_O2(A, B)) | subgroup_member(B))) | (subgroup_member(multiply(identity, c)) | subgroup_member(element_in_O2(multiply(identity, c), inverse(a))) | subgroup_member(inverse(a)))) <=> ((~![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(element_in_O2(A, B)) | subgroup_member(B))) | subgroup_member(inverse(a)) | subgroup_member(multiply(identity, c)) | subgroup_member(element_in_O2(multiply(identity, c), inverse(a))))),
% 15.76/10.40 inference(transitivity,[status(thm)],[307, 305])).
% 15.76/10.40 tff(309,plain,
% 15.76/10.40 ((~![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(element_in_O2(A, B)) | subgroup_member(B))) | (subgroup_member(multiply(identity, c)) | subgroup_member(element_in_O2(multiply(identity, c), inverse(a))) | subgroup_member(inverse(a)))),
% 15.76/10.40 inference(quant_inst,[status(thm)],[])).
% 15.76/10.40 tff(310,plain,
% 15.76/10.40 ((~![B: $i, A: $i] : (subgroup_member(A) | subgroup_member(element_in_O2(A, B)) | subgroup_member(B))) | subgroup_member(inverse(a)) | subgroup_member(multiply(identity, c)) | subgroup_member(element_in_O2(multiply(identity, c), inverse(a)))),
% 15.76/10.40 inference(modus_ponens,[status(thm)],[309, 308])).
% 15.76/10.40 tff(311,plain,
% 15.76/10.40 (subgroup_member(inverse(a)) | subgroup_member(multiply(identity, c)) | subgroup_member(element_in_O2(multiply(identity, c), inverse(a)))),
% 15.76/10.40 inference(unit_resolution,[status(thm)],[310, 304])).
% 15.76/10.40 tff(312,plain,
% 15.76/10.40 (subgroup_member(element_in_O2(multiply(identity, c), inverse(a)))),
% 15.76/10.40 inference(unit_resolution,[status(thm)],[311, 234, 221])).
% 15.76/10.40 tff(313,plain,
% 15.76/10.40 (((~![X: $i] : ((~subgroup_member(X)) | subgroup_member(inverse(X)))) | ((~subgroup_member(element_in_O2(multiply(identity, c), inverse(a)))) | subgroup_member(inverse(element_in_O2(multiply(identity, c), inverse(a)))))) <=> ((~![X: $i] : ((~subgroup_member(X)) | subgroup_member(inverse(X)))) | (~subgroup_member(element_in_O2(multiply(identity, c), inverse(a)))) | subgroup_member(inverse(element_in_O2(multiply(identity, c), inverse(a)))))),
% 15.76/10.40 inference(rewrite,[status(thm)],[])).
% 15.76/10.40 tff(314,plain,
% 15.76/10.40 ((~![X: $i] : ((~subgroup_member(X)) | subgroup_member(inverse(X)))) | ((~subgroup_member(element_in_O2(multiply(identity, c), inverse(a)))) | subgroup_member(inverse(element_in_O2(multiply(identity, c), inverse(a)))))),
% 15.76/10.40 inference(quant_inst,[status(thm)],[])).
% 15.76/10.40 tff(315,plain,
% 15.76/10.40 ((~![X: $i] : ((~subgroup_member(X)) | subgroup_member(inverse(X)))) | (~subgroup_member(element_in_O2(multiply(identity, c), inverse(a)))) | subgroup_member(inverse(element_in_O2(multiply(identity, c), inverse(a))))),
% 15.76/10.40 inference(modus_ponens,[status(thm)],[314, 313])).
% 15.76/10.40 tff(316,plain,
% 15.76/10.40 ((~subgroup_member(element_in_O2(multiply(identity, c), inverse(a)))) | subgroup_member(inverse(element_in_O2(multiply(identity, c), inverse(a))))),
% 15.76/10.40 inference(unit_resolution,[status(thm)],[315, 169])).
% 15.76/10.40 tff(317,plain,
% 15.76/10.40 (subgroup_member(inverse(element_in_O2(multiply(identity, c), inverse(a))))),
% 15.76/10.40 inference(unit_resolution,[status(thm)],[316, 312])).
% 15.76/10.40 tff(318,plain,
% 15.76/10.40 ($false),
% 15.76/10.40 inference(unit_resolution,[status(thm)],[317, 294])).
% 15.76/10.40 % SZS output end Proof
%------------------------------------------------------------------------------