%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP230-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:32:04 PM UTC 2026
% Result : Unsatisfiable 10.61s 17.32s
% Output : CNFRefutation 10.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 36
% Syntax : Number of formulae : 256 ( 89 unt; 10 def)
% Number of atoms : 788 ( 456 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 349 ( 116 ~; 233 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 76 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c8 = multiply(sk_c3,sk_c4)
| inverse(sk_c1) = sk_c8 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c4 = inverse(sk_c3)
| inverse(sk_c1) = sk_c8 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| inverse(sk_c1) = sk_c8 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| inverse(sk_c1) = sk_c8 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| inverse(sk_c1) = sk_c8 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c8 = inverse(sk_c5)
| inverse(sk_c1) = sk_c8 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = multiply(sk_c3,sk_c4)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c3) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c4 = inverse(sk_c3)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c8 = multiply(sk_c3,sk_c4)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c3) = sk_c4
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c4 = inverse(sk_c3)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f33]) ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = multiply(sk_c3,sk_c4)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c3) = sk_c4
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c4 = inverse(sk_c3)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c8 = inverse(sk_c5)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X2) != X3
| multiply(X2,X3) != sk_c8
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk_c8 != inverse(X5)
| multiply(X5,sk_c8) != X4
| sk_c7 != multiply(sk_c8,X4)
| sk_c8 != multiply(X3,sk_c7)
| inverse(X2) != X3
| sk_c8 != multiply(X2,X3)
| sk_c7 != inverse(X1)
| sk_c8 != multiply(X1,sk_c7)
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c8 ),
inference(reorient_equations,[],[f53]) ).
fof(f55,plain,
! [X2,X0,X1,X4,X5] :
( sk_c8 != inverse(X5)
| multiply(X5,sk_c8) != X4
| sk_c7 != multiply(sk_c8,X4)
| sk_c8 != multiply(inverse(X2),sk_c7)
| sk_c8 != multiply(X2,inverse(X2))
| sk_c7 != inverse(X1)
| sk_c8 != multiply(X1,sk_c7)
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c8 ),
inference(equality_resolution,[],[f54]) ).
fof(f56,plain,
! [X2,X0,X1,X5] :
( sk_c8 != inverse(X5)
| sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| sk_c8 != multiply(inverse(X2),sk_c7)
| sk_c8 != multiply(X2,inverse(X2))
| sk_c7 != inverse(X1)
| sk_c8 != multiply(X1,sk_c7)
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c8 ),
inference(equality_resolution,[],[f55]) ).
tcf(c_77,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_78,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_80,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c3,sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_81,negated_conjecture,
( ( inverse(sk_c3) = sk_c4 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_82,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_83,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_84,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_85,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_86,negated_conjecture,
( ( multiply(sk_c3,sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c3) = sk_c4 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_88,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_89,negated_conjecture,
( ( multiply(sk_c8,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_90,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_92,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c3,sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c3) = sk_c4 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_94,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c3,sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c3) = sk_c4 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_104,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c8 )
| ( inverse(X2) != sk_c7 )
| ( inverse(X0) != sk_c8 )
| ( multiply(X2,sk_c7) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 )
| ( multiply(inverse(X1),sk_c7) != sk_c8 )
| ( multiply(X1,inverse(X1)) != sk_c8 )
| ( multiply(sk_c8,multiply(X3,sk_c8)) != sk_c7 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_341,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_104]) ).
tcf(c_342,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( multiply(inverse(X0),sk_c7) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_104]) ).
tcf(c_343,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_104]) ).
tcf(c_344,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_104]) ).
tcf(c_345,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_104]) ).
tcf(c_346,definition,
iPr_def_14 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_347,definition,
iPr_def_15 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_348,definition,
iPr_def_16 = multiply(sk_c5,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_349,definition,
iPr_def_17 = multiply(sk_c8,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_350,definition,
iPr_def_18 = multiply(sk_c4,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_351,definition,
iPr_def_19 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_352,definition,
iPr_def_20 = multiply(sk_c3,sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_353,definition,
iPr_def_21 = multiply(sk_c2,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_354,definition,
iPr_def_22 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_355,definition,
iPr_def_23 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_356,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_345]) ).
tcf(c_357,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_344]) ).
tcf(c_358,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_343]) ).
tcf(c_359,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( multiply(inverse(X0),sk_c7) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_342]) ).
tcf(c_360,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_341]) ).
tcf(c_361,negated_conjecture,
( ( iPr_def_15 = sk_c7 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_103,c_347,c_346]) ).
tcf(c_362,negated_conjecture,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_102,c_348]) ).
tcf(c_363,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_101,c_349]) ).
tcf(c_364,negated_conjecture,
( ( iPr_def_18 = sk_c8 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_100,c_350]) ).
tcf(c_365,negated_conjecture,
( ( iPr_def_19 = sk_c4 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_99,c_351]) ).
tcf(c_366,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_98,c_352]) ).
tcf(c_367,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_97,c_353]) ).
tcf(c_370,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_371,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_19 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_372,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_373,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_91,c_354]) ).
tcf(c_374,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_375,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_376,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_377,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_19 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_378,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_379,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_85,c_355]) ).
tcf(c_380,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_381,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_382,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_383,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_19 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_384,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_685,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(sk_c3,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_371,c_352]) ).
tcf(c_696,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c5,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_372,c_348]) ).
tcf(c_711,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(sk_c5,iPr_def_22) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_373,c_348]) ).
tcf(c_712,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_373,c_367]) ).
tcf(c_729,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(sk_c8,iPr_def_16) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_374,c_349]) ).
tcf(c_739,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(sk_c4,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_375,c_350]) ).
tcf(c_797,plain,
multiply(iPr_def_23,sk_c1) = identity,
inference(superposition,[status(thm)],[c_355,c_78]) ).
tcf(c_798,plain,
multiply(iPr_def_19,sk_c3) = identity,
inference(superposition,[status(thm)],[c_351,c_78]) ).
tcf(c_799,plain,
multiply(iPr_def_14,sk_c5) = identity,
inference(superposition,[status(thm)],[c_346,c_78]) ).
tcf(c_800,plain,
multiply(iPr_def_15,sk_c2) = identity,
inference(superposition,[status(thm)],[c_347,c_78]) ).
tcf(c_822,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( sk_c8 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_376,c_370]) ).
tcf(c_855,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_377,c_352]) ).
tcf(c_871,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c5,iPr_def_22) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_378,c_348]) ).
tcf(c_891,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_379,c_373]) ).
tcf(c_896,plain,
( ( iPr_def_21 = iPr_def_23 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_379,c_367]) ).
tcf(c_982,plain,
( ( iPr_def_21 = iPr_def_23 )
| ( sk_c8 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_382,c_370]) ).
tcf(c_1009,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(sk_c3,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_383,c_352]) ).
tcf(c_1031,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( sk_c8 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_384,c_378]) ).
tcf(c_1037,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c5,iPr_def_23) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_384,c_348]) ).
tcf(c_1062,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_18 )
| ( inverse(sk_c4) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_350,c_358]) ).
tcf(c_1066,plain,
( ~ iPr_def_12
| ( sk_c8 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_78,c_358]) ).
tcf(c_1158,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c4,X0)) = multiply(iPr_def_20,X0),
inference(superposition,[status(thm)],[c_352,c_79]) ).
tcf(c_1160,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c6,X0)) = multiply(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_349,c_79]) ).
tcf(c_1161,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c8,X0)) = multiply(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_348,c_79]) ).
tcf(c_1165,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_78,c_79]) ).
tcf(c_1167,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_797,c_79]) ).
tcf(c_1168,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_798,c_79]) ).
tcf(c_1169,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_799,c_79]) ).
tcf(c_1170,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_800,c_79]) ).
tcf(c_1173,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1170,c_77]) ).
tcf(c_1174,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1169,c_77]) ).
tcf(c_1175,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1168,c_77]) ).
tcf(c_1176,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1167,c_77]) ).
tcf(c_1289,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( iPr_def_14 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_822,c_712]) ).
tcf(c_1515,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( multiply(sk_c5,iPr_def_14) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_891,c_348]) ).
tcf(c_1819,plain,
( ( iPr_def_21 = iPr_def_23 )
| ( iPr_def_14 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_982,c_896]) ).
tcf(c_1911,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_22 )
| ( inverse(sk_c1) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_354,c_360]) ).
tcf(c_1913,plain,
( ~ iPr_def_10
| ( sk_c8 != sk_c7 )
| ( inverse(identity) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_77,c_360]) ).
tcf(c_1931,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_23 )
| ( sk_c8 != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_1911,c_355]) ).
tcf(c_2038,plain,
( ~ iPr_def_13
| ( inverse(sk_c5) != sk_c8 )
| ( multiply(sk_c8,iPr_def_16) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_348,c_357]) ).
tcf(c_2040,plain,
( ~ iPr_def_13
| ( multiply(sk_c8,identity) != sk_c7 )
| ( inverse(inverse(sk_c8)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_78,c_357]) ).
tcf(c_2061,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_14 )
| ( multiply(sk_c8,iPr_def_16) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_2038,c_346]) ).
tcf(c_2217,plain,
( ~ iPr_def_11
| ( inverse(identity) != sk_c8 )
| ( multiply(inverse(identity),sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_77,c_359]) ).
tcf(c_2290,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( multiply(iPr_def_20,sk_c6) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_1031,c_349]) ).
tcf(c_2697,plain,
multiply(iPr_def_15,iPr_def_21) = sk_c7,
inference(superposition,[status(thm)],[c_353,c_1173]) ).
tcf(c_2700,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(iPr_def_21,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_2697,c_79]) ).
tcf(c_2706,plain,
multiply(iPr_def_14,iPr_def_16) = sk_c8,
inference(superposition,[status(thm)],[c_348,c_1174]) ).
tcf(c_2712,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_16,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2706,c_79]) ).
tcf(c_2714,plain,
multiply(iPr_def_19,iPr_def_20) = sk_c4,
inference(superposition,[status(thm)],[c_352,c_1175]) ).
tcf(c_2717,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(iPr_def_20,X0)) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2714,c_79]) ).
tcf(c_2808,plain,
multiply(iPr_def_23,iPr_def_22) = sk_c7,
inference(superposition,[status(thm)],[c_354,c_1176]) ).
tcf(c_2817,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(iPr_def_22,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_2808,c_79]) ).
tcf(c_3247,plain,
( ( iPr_def_14 = iPr_def_18 )
| ( multiply(iPr_def_23,iPr_def_21) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_1289,c_2808]) ).
tcf(c_3524,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(iPr_def_19,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_377,c_739]) ).
tcf(c_3864,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_14,iPr_def_16) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_871,c_1174]) ).
tcf(c_3865,plain,
( ( sk_c8 = iPr_def_22 )
| ( sk_c8 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_3864,c_2706]) ).
tcf(c_4510,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_14,iPr_def_16) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1037,c_1174]) ).
tcf(c_4511,plain,
( ( sk_c8 = iPr_def_23 )
| ( sk_c8 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_4510,c_2706]) ).
tcf(c_4698,plain,
multiply(sk_c3,iPr_def_18) = multiply(iPr_def_20,sk_c7),
inference(superposition,[status(thm)],[c_350,c_1158]) ).
tcf(c_5033,plain,
multiply(sk_c5,iPr_def_17) = multiply(iPr_def_16,sk_c6),
inference(superposition,[status(thm)],[c_349,c_1161]) ).
tcf(c_5338,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1165,c_77]) ).
tcf(c_5344,plain,
multiply(inverse(sk_c4),iPr_def_18) = sk_c7,
inference(superposition,[status(thm)],[c_350,c_5338]) ).
tcf(c_5346,plain,
multiply(inverse(sk_c5),iPr_def_16) = sk_c8,
inference(superposition,[status(thm)],[c_348,c_5338]) ).
tcf(c_5349,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_77,c_5338]) ).
tcf(c_5350,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_78,c_5338]) ).
tcf(c_5352,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(inverse(sk_c5),iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_696,c_5338]) ).
tcf(c_5359,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(inverse(sk_c8),iPr_def_17) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_729,c_5338]) ).
tcf(c_5380,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(inverse(sk_c5),iPr_def_16) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_871,c_5338]) ).
tcf(c_5382,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(inverse(sk_c5),iPr_def_16) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_711,c_5338]) ).
tcf(c_5404,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(inverse(sk_c5),iPr_def_16) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1037,c_5338]) ).
tcf(c_5414,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_1176,c_5338]) ).
tcf(c_5415,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_1175,c_5338]) ).
tcf(c_5416,plain,
! [X0: $i] : multiply(inverse(iPr_def_14),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_1174,c_5338]) ).
tcf(c_5417,plain,
! [X0: $i] : multiply(inverse(iPr_def_15),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_1173,c_5338]) ).
tcf(c_5419,plain,
multiply(inverse(iPr_def_15),sk_c7) = iPr_def_21,
inference(superposition,[status(thm)],[c_2697,c_5338]) ).
tcf(c_5428,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_5338,c_5338]) ).
tcf(c_5817,plain,
( ~ iPr_def_10
| ( sk_c8 != sk_c7 )
| ( inverse(inverse(identity)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_5349,c_360]) ).
tcf(c_5892,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_5350,c_5428]) ).
tcf(c_5904,plain,
multiply(sk_c8,sk_c6) = multiply(iPr_def_17,identity),
inference(superposition,[status(thm)],[c_5892,c_1160]) ).
tcf(c_5910,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_5892,c_5349]) ).
tcf(c_5912,plain,
multiply(iPr_def_17,identity) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_5904,c_349]) ).
tcf(c_5922,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_5910,c_78]) ).
tcf(c_6372,plain,
multiply(sk_c1,iPr_def_23) = identity,
inference(superposition,[status(thm)],[c_5414,c_78]) ).
tcf(c_6376,plain,
multiply(sk_c1,identity) = inverse(iPr_def_23),
inference(superposition,[status(thm)],[c_5414,c_5892]) ).
tcf(c_6438,plain,
multiply(iPr_def_23,identity) = iPr_def_23,
inference(superposition,[status(thm)],[c_6372,c_1176]) ).
tcf(c_6488,plain,
multiply(sk_c7,identity) = multiply(iPr_def_15,iPr_def_21),
inference(superposition,[status(thm)],[c_5892,c_2700]) ).
tcf(c_6491,plain,
multiply(sk_c7,identity) = sk_c7,
inference(light_normalisation,[status(thm)],[c_6488,c_2697]) ).
tcf(c_6514,plain,
inverse(iPr_def_23) = sk_c1,
inference(demodulation,[status(thm)],[c_6376,c_5892]) ).
tcf(c_6647,plain,
multiply(sk_c3,iPr_def_19) = identity,
inference(superposition,[status(thm)],[c_5415,c_78]) ).
tcf(c_6650,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_19,X0)) = X0,
inference(superposition,[status(thm)],[c_5415,c_5338]) ).
tcf(c_6651,plain,
multiply(sk_c3,identity) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_5415,c_5892]) ).
tcf(c_6664,plain,
( ( identity = iPr_def_20 )
| ( sk_c8 = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_1009,c_6647]) ).
tcf(c_6665,plain,
( ( identity = iPr_def_20 )
| ( sk_c8 = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_855,c_6647]) ).
tcf(c_6666,plain,
( ( identity = iPr_def_20 )
| ( sk_c8 = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_685,c_6647]) ).
tcf(c_6766,plain,
multiply(iPr_def_19,identity) = iPr_def_19,
inference(superposition,[status(thm)],[c_6647,c_1175]) ).
tcf(c_7060,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( identity = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_6665,c_6664]) ).
tcf(c_7218,plain,
( ( identity = iPr_def_20 )
| ( multiply(sk_c5,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_6666,c_348]) ).
tcf(c_7356,plain,
inverse(iPr_def_19) = sk_c3,
inference(demodulation,[status(thm)],[c_6651,c_5892]) ).
tcf(c_7369,plain,
multiply(sk_c3,identity) = sk_c3,
inference(superposition,[status(thm)],[c_798,c_6650]) ).
tcf(c_7370,plain,
multiply(sk_c3,sk_c4) = iPr_def_20,
inference(superposition,[status(thm)],[c_2714,c_6650]) ).
tcf(c_7372,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_18) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_3524,c_6650]) ).
tcf(c_7385,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(iPr_def_20,sk_c7) = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_7372,c_4698]) ).
tcf(c_7504,plain,
multiply(sk_c8,identity) = multiply(iPr_def_14,iPr_def_16),
inference(superposition,[status(thm)],[c_5892,c_2712]) ).
tcf(c_7507,plain,
multiply(sk_c8,identity) = sk_c8,
inference(light_normalisation,[status(thm)],[c_7504,c_2706]) ).
tcf(c_7513,plain,
multiply(sk_c4,identity) = multiply(iPr_def_19,iPr_def_20),
inference(superposition,[status(thm)],[c_5892,c_2717]) ).
tcf(c_7517,plain,
multiply(sk_c4,identity) = sk_c4,
inference(light_normalisation,[status(thm)],[c_7513,c_2714]) ).
tcf(c_7545,plain,
multiply(sk_c7,identity) = multiply(iPr_def_23,iPr_def_22),
inference(superposition,[status(thm)],[c_5892,c_2817]) ).
tcf(c_7696,plain,
! [X0: $i] :
( ( iPr_def_22 = iPr_def_23 )
| ( multiply(iPr_def_20,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_7060,c_77]) ).
tcf(c_7801,plain,
multiply(sk_c5,iPr_def_14) = identity,
inference(superposition,[status(thm)],[c_5416,c_78]) ).
tcf(c_7804,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_14,X0)) = X0,
inference(superposition,[status(thm)],[c_5416,c_5338]) ).
tcf(c_7805,plain,
multiply(sk_c5,identity) = inverse(iPr_def_14),
inference(superposition,[status(thm)],[c_5416,c_5892]) ).
tcf(c_7820,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( identity = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_1515,c_7801]) ).
tcf(c_7923,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( iPr_def_16 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_7820,c_7060]) ).
tcf(c_7975,plain,
inverse(iPr_def_14) = sk_c5,
inference(demodulation,[status(thm)],[c_7805,c_5892]) ).
tcf(c_7984,plain,
multiply(sk_c5,identity) = sk_c5,
inference(superposition,[status(thm)],[c_799,c_7804]) ).
tcf(c_7988,plain,
multiply(sk_c5,sk_c8) = iPr_def_16,
inference(superposition,[status(thm)],[c_2706,c_7804]) ).
tcf(c_8201,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( multiply(iPr_def_22,iPr_def_22) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_7923,c_2808]) ).
tcf(c_8315,plain,
multiply(sk_c2,iPr_def_15) = identity,
inference(superposition,[status(thm)],[c_5417,c_78]) ).
tcf(c_8318,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_15,X0)) = X0,
inference(superposition,[status(thm)],[c_5417,c_5338]) ).
tcf(c_8319,plain,
multiply(sk_c2,identity) = inverse(iPr_def_15),
inference(superposition,[status(thm)],[c_5417,c_5892]) ).
tcf(c_9156,plain,
inverse(iPr_def_15) = sk_c2,
inference(demodulation,[status(thm)],[c_8319,c_5892]) ).
tcf(c_9159,plain,
( ~ iPr_def_11
| ( multiply(iPr_def_15,sk_c2) != sk_c8 )
| ( multiply(inverse(iPr_def_15),sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_9156,c_359]) ).
tcf(c_9166,plain,
multiply(sk_c2,sk_c7) = iPr_def_21,
inference(superposition,[status(thm)],[c_2697,c_8318]) ).
tcf(c_9268,plain,
( ~ iPr_def_10
| ( sk_c8 != identity )
| ( sk_c8 != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_1913,c_5910]) ).
tcf(c_9547,plain,
( ( identity = iPr_def_20 )
| ( multiply(inverse(sk_c5),iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_7218,c_5338]) ).
tcf(c_9806,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( sk_c6 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_7696,c_2290]) ).
tcf(c_10034,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( iPr_def_16 = iPr_def_17 )
| ( sk_c8 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_9806,c_380]) ).
tcf(c_10035,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( iPr_def_16 = iPr_def_17 )
| ( sk_c8 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_9806,c_374]) ).
tcf(c_10660,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( iPr_def_16 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_10035,c_10034]) ).
tcf(c_11352,plain,
( ( iPr_def_16 = iPr_def_17 )
| ( multiply(iPr_def_22,iPr_def_22) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_10660,c_2808]) ).
tcf(c_15806,plain,
( ~ iPr_def_13
| ( sk_c8 != sk_c7 )
| ( inverse(inverse(sk_c8)) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_2040,c_5892]) ).
tcf(c_15840,plain,
( ( sk_c8 = iPr_def_20 )
| ~ iPr_def_13
| ( sk_c8 != sk_c7 )
| ( inverse(inverse(iPr_def_23)) != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_384,c_15806]) ).
tcf(c_15881,plain,
( ( sk_c8 = iPr_def_20 )
| ~ iPr_def_13
| ( sk_c8 != sk_c7 ) ),
inference(ground_joinability,[status(thm)],[c_15840,c_355,c_6514]) ).
tcf(c_15921,plain,
( ~ iPr_def_11
| ( sk_c8 != identity )
| ( multiply(identity,sk_c7) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_2217,c_5910]) ).
tcf(c_16996,plain,
( ( iPr_def_14 = iPr_def_18 )
| ( multiply(iPr_def_21,iPr_def_21) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_1819,c_3247]) ).
tcf(c_20569,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_16996,c_15921,c_15881,c_15806,c_11352,c_9547,c_9268,c_9166,c_9159,c_9156,c_8315,c_8201,c_7988,c_7984,c_7975,c_7545,c_7517,c_7513,c_7507,c_7504,c_7385,c_7370,c_7369,c_7356,c_6766,c_6647,c_6491,c_6438,c_5912,c_5904,c_5910,c_5817,c_5419,c_5404,c_5382,c_5380,c_5359,c_5352,c_5346,c_5344,c_5033,c_4698,c_4511,c_3865,c_5922,c_2061,c_1931,c_1066,c_1062,c_800,c_381,c_366,c_365,c_364,c_363,c_362,c_361,c_347,c_356]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP230-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/15.40 % Computer : n007.cluster.edu
% 0.12/15.40 % Model : x86_64 x86_64
% 0.12/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/15.40 % Memory : 8046.5625MB
% 0.12/15.40 % OS : Linux 6.8.0-71-generic
% 0.12/15.40 % CPULimit : 300
% 0.12/15.40 % WCLimit : 300
% 0.12/15.40 % DateTime : Wed Sep 23 14:10:39 UTC 2026
% 0.12/15.40 % CPUTime :
% 0.12/15.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/15.44 Running first-order theorem proving
% 0.12/15.44 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/15.45
% 0.12/15.45 % ======== iProver multi-core TPTP/SMT =========
% 0.12/15.45
% 0.12/15.46 % Detected problem language: tptp
% 0.12/15.47 % Proving...
% 10.61/17.32 % SZS status Started for theBenchmark.p
% 10.61/17.32 % SZS status Unsatisfiable for theBenchmark.p
% 10.61/17.32
% 10.61/17.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.61/17.32
% 10.61/17.32 % ------ iProver source info
% 10.61/17.32
% 10.61/17.32 % git: date: 2026-07-19 20:42:38 +0200
% 10.61/17.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.61/17.32 % git: non_committed_changes: false
% 10.61/17.32
% 10.61/17.32 % ------ Parsing...% successful
% 10.61/17.32
% 10.61/17.32
% 10.61/17.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.61/17.32
% 10.61/17.32 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.61/17.32
% 10.61/17.32 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.61/17.32
% 10.61/17.32 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.61/17.32 % ------ Proving...
% 10.61/17.32 % ------ Problem Properties
% 10.61/17.32
% 10.61/17.32 %
% 10.61/17.32 % clauses 42
% 10.61/17.32 % conjectures 29
% 10.61/17.32 % EPR 25
% 10.61/17.32 % Horn 17
% 10.61/17.32 % unary 13
% 10.61/17.32 % binary 24
% 10.61/17.32 % lits 77
% 10.61/17.32 % lits eq 69
% 10.61/17.32 % fd_pure 0
% 10.61/17.32 % fd_pseudo 0
% 10.61/17.32 % fd_cond 0
% 10.61/17.32 % fd_pseudo_cond 0
% 10.61/17.32 % AC symbols 0
% 10.61/17.32
% 10.61/17.32 % ------ Schedule dynamic 5 is on
% 10.61/17.32
% 10.61/17.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.61/17.32
% 10.61/17.32
% 10.61/17.32 % ------
% 10.61/17.32 % Current options:
% 10.61/17.32 % ------
% 10.61/17.32
% 10.61/17.32
% 10.61/17.32 %
% 10.61/17.32
% 10.61/17.32 % ------ Proving...
% 10.61/17.32 %
% 10.61/17.32
% 10.61/17.32 % SZS status Unsatisfiable for theBenchmark.p
% 10.61/17.32
% 10.61/17.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.61/17.33
% 10.61/17.33
%------------------------------------------------------------------------------