%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP306-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n026.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 01:32:47 PM UTC 2026
% Result : Unsatisfiable 19.11s 3.53s
% Output : CNFRefutation 19.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 37
% Syntax : Number of formulae : 276 ( 100 unt; 10 def)
% Number of atoms : 904 ( 497 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 432 ( 161 ~; 271 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 15 ( 13 usr; 14 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn 85 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
multiply(sk_c8,sk_c7) = sk_c6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c8 = inverse(sk_c3)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c8 = inverse(sk_c4)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c8 = multiply(sk_c1,sk_c2) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = multiply(sk_c1,sk_c2) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c8 = multiply(sk_c1,sk_c2) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c8 = multiply(sk_c1,sk_c2) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c1,sk_c2) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c8 = inverse(sk_c3)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c8 = inverse(sk_c4)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
! [X2,X3,X0,X1,X4] :
( sk_c8 != inverse(X4)
| multiply(X4,sk_c8) != X3
| sk_c7 != multiply(sk_c8,X3)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != multiply(X1,sk_c7)
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8
| sk_c6 != inverse(sk_c8)
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(reorient_equations,[],[f46]) ).
fof(f48,plain,
! [X2,X3,X0,X4] :
( sk_c8 != inverse(X4)
| multiply(X4,sk_c8) != X3
| sk_c7 != multiply(sk_c8,X3)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != multiply(inverse(X0),sk_c7)
| sk_c8 != multiply(X0,inverse(X0))
| sk_c6 != inverse(sk_c8)
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(equality_resolution,[],[f47]) ).
fof(f49,plain,
! [X2,X0,X4] :
( sk_c8 != inverse(X4)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X2)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != multiply(inverse(X0),sk_c7)
| sk_c8 != multiply(X0,inverse(X0))
| sk_c6 != inverse(sk_c8)
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(equality_resolution,[],[f48]) ).
tcf(c_74,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_75,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_77,negated_conjecture,
multiply(sk_c8,sk_c7) = sk_c6,
inference(cnf_transformation,[],[f5]) ).
tcf(c_78,negated_conjecture,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_79,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_80,negated_conjecture,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_81,negated_conjecture,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_82,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_83,negated_conjecture,
( ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_84,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_85,negated_conjecture,
( ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_86,negated_conjecture,
( ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( inverse(sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_93,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_95,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_96,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_98,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(sk_c8) != sk_c6 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c8 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( multiply(X2,sk_c8) != sk_c7 )
| ( multiply(inverse(X0),sk_c7) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 )
| ( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7 ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(sk_c8) != sk_c6 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c8 )
| ( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7 )
| ( multiply(X0,inverse(X0)) != sk_c8 )
| ( multiply(inverse(X0),sk_c7) != sk_c8 )
| ( multiply(X2,sk_c8) != sk_c7 ) ),
inference(global_subsumption_just,[status(thm)],[c_98,c_77,c_98]) ).
tcf(c_104,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(sk_c8) != sk_c6 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X0) != sk_c8 )
| ( multiply(X2,sk_c8) != sk_c7 )
| ( multiply(inverse(X1),sk_c7) != sk_c8 )
| ( multiply(X1,inverse(X1)) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(renaming,[status(thm)],[c_103]) ).
tcf(c_304,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( multiply(inverse(X0),sk_c7) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_104]) ).
tcf(c_305,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_104]) ).
tcf(c_306,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_104]) ).
tcf(c_307,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c8) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_104]) ).
tcf(c_308,definition,
iPr_def_13 = inverse(sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_309,definition,
iPr_def_14 = multiply(sk_c2,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_310,definition,
iPr_def_15 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_311,definition,
iPr_def_16 = multiply(sk_c4,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_312,definition,
iPr_def_17 = multiply(sk_c8,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_313,definition,
iPr_def_18 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_314,definition,
iPr_def_19 = multiply(sk_c3,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_315,definition,
iPr_def_20 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_316,definition,
iPr_def_21 = multiply(sk_c1,sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_317,definition,
iPr_def_22 = multiply(sk_c8,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_318,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_13 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_307,c_308]) ).
tcf(c_319,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_306]) ).
tcf(c_320,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_305]) ).
tcf(c_321,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( multiply(inverse(X0),sk_c7) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_304]) ).
tcf(c_322,negated_conjecture,
( ( iPr_def_15 = sk_c8 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_97,c_310,c_309]) ).
tcf(c_323,negated_conjecture,
( ( iPr_def_16 = sk_c5 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_96,c_311]) ).
tcf(c_324,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_95,c_312]) ).
tcf(c_325,negated_conjecture,
( ( iPr_def_18 = sk_c8 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_94,c_313]) ).
tcf(c_326,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_93,c_314]) ).
tcf(c_327,negated_conjecture,
( ( iPr_def_20 = sk_c2 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_92,c_315]) ).
tcf(c_328,negated_conjecture,
( ( iPr_def_20 = sk_c2 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_329,negated_conjecture,
( ( iPr_def_20 = sk_c2 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_330,negated_conjecture,
( ( iPr_def_20 = sk_c2 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_331,negated_conjecture,
( ( iPr_def_20 = sk_c2 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_332,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_87,c_316]) ).
tcf(c_333,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_334,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_335,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_336,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_337,negated_conjecture,
( ( iPr_def_15 = sk_c8 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_338,negated_conjecture,
( ( iPr_def_16 = sk_c5 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_339,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_340,negated_conjecture,
( ( iPr_def_18 = sk_c8 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_341,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_342,negated_conjecture,
iPr_def_22 = sk_c6,
inference(demodulation,[status(thm)],[c_77,c_317]) ).
tcf(c_343,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_344,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_505,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_13 != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_318,c_342]) ).
tcf(c_526,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_322,c_325]) ).
tcf(c_534,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_324,c_326]) ).
tcf(c_564,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(iPr_def_15,sk_c5) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_322,c_312]) ).
tcf(c_636,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(sk_c8,iPr_def_16) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_333,c_312]) ).
tcf(c_689,plain,
! [X0: $i] :
( ( iPr_def_13 = sk_c6 )
| ( iPr_def_13 != X0 )
| ( sk_c6 != X0 ) ),
inference(instantiation,[status(thm)],[c_344]) ).
tcf(c_692,plain,
! [X0: $i,X1: $i] :
( ( sk_c6 = X0 )
| ( sk_c6 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_344]) ).
tcf(c_695,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(iPr_def_18,sk_c7) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_325,c_317]) ).
tcf(c_714,plain,
! [X0: $i] :
( ( sk_c6 = X0 )
| ( sk_c6 != sk_c6 )
| ( X0 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_692]) ).
tcf(c_715,plain,
sk_c6 = sk_c6,
inference(instantiation,[status(thm)],[c_343]) ).
tcf(c_725,plain,
( ( sk_c6 = iPr_def_22 )
| ( iPr_def_22 != sk_c6 )
| ( sk_c6 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_714]) ).
tcf(c_727,plain,
multiply(iPr_def_13,sk_c8) = identity,
inference(superposition,[status(thm)],[c_308,c_75]) ).
tcf(c_728,plain,
multiply(iPr_def_18,sk_c3) = identity,
inference(superposition,[status(thm)],[c_313,c_75]) ).
tcf(c_729,plain,
multiply(iPr_def_15,sk_c4) = identity,
inference(superposition,[status(thm)],[c_310,c_75]) ).
tcf(c_730,plain,
multiply(iPr_def_20,sk_c1) = identity,
inference(superposition,[status(thm)],[c_315,c_75]) ).
tcf(c_731,plain,
( ( iPr_def_13 = sk_c6 )
| ( iPr_def_13 != iPr_def_22 )
| ( sk_c6 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_689]) ).
tcf(c_741,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( sk_c8 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_336,c_334]) ).
tcf(c_753,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_337,c_342]) ).
tcf(c_767,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( multiply(iPr_def_15,sk_c5) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_753,c_312]) ).
tcf(c_800,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_13,iPr_def_21) = identity ) ),
inference(superposition,[status(thm)],[c_335,c_727]) ).
tcf(c_835,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( sk_c5 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_338,c_342]) ).
tcf(c_845,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( sk_c7 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_339,c_342]) ).
tcf(c_868,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( sk_c8 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_340,c_342]) ).
tcf(c_881,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( multiply(iPr_def_18,sk_c7) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_868,c_317]) ).
tcf(c_915,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_341,c_342]) ).
tcf(c_952,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( inverse(iPr_def_13) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_727,c_320]) ).
tcf(c_1026,plain,
( ~ iPr_def_12
| ( inverse(sk_c3) != sk_c8 )
| ( multiply(sk_c8,iPr_def_19) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_314,c_319]) ).
tcf(c_1028,plain,
( ~ iPr_def_12
| ( inverse(identity) != sk_c8 )
| ( multiply(sk_c8,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_74,c_319]) ).
tcf(c_1030,plain,
( ~ iPr_def_12
| ( inverse(iPr_def_13) != sk_c8 )
| ( multiply(sk_c8,identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_727,c_319]) ).
tcf(c_1047,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_18 )
| ( multiply(sk_c8,iPr_def_19) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_1026,c_313]) ).
tcf(c_1105,plain,
( ~ iPr_def_10
| ( inverse(identity) != sk_c8 )
| ( multiply(inverse(identity),sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_74,c_321]) ).
tcf(c_1106,plain,
( ~ iPr_def_10
| ( multiply(sk_c8,iPr_def_13) != sk_c8 )
| ( multiply(inverse(sk_c8),sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_308,c_321]) ).
tcf(c_1160,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_21 )
| ( sk_c8 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_526,c_335]) ).
tcf(c_1161,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_21 )
| ( sk_c8 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_526,c_332]) ).
tcf(c_1356,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c8,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_314,c_76]) ).
tcf(c_1358,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c8,X0)) = multiply(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_311,c_76]) ).
tcf(c_1359,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c2,X0)) = multiply(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_316,c_76]) ).
tcf(c_1360,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c7,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_309,c_76]) ).
tcf(c_1362,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_75,c_76]) ).
tcf(c_1364,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(sk_c8,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_727,c_76]) ).
tcf(c_1365,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_728,c_76]) ).
tcf(c_1366,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_729,c_76]) ).
tcf(c_1367,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_730,c_76]) ).
tcf(c_1372,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1367,c_74]) ).
tcf(c_1373,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1366,c_74]) ).
tcf(c_1374,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1365,c_74]) ).
tcf(c_1375,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(sk_c8,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1364,c_74]) ).
tcf(c_1435,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_741,c_534]) ).
tcf(c_1551,plain,
multiply(iPr_def_20,iPr_def_21) = sk_c2,
inference(superposition,[status(thm)],[c_316,c_1372]) ).
tcf(c_1748,plain,
multiply(iPr_def_15,iPr_def_16) = sk_c8,
inference(superposition,[status(thm)],[c_311,c_1373]) ).
tcf(c_1769,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(iPr_def_16,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_1748,c_76]) ).
tcf(c_1797,plain,
multiply(iPr_def_18,iPr_def_19) = sk_c8,
inference(superposition,[status(thm)],[c_314,c_1374]) ).
tcf(c_1800,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_19,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_1797,c_76]) ).
tcf(c_1809,plain,
multiply(iPr_def_13,iPr_def_22) = sk_c7,
inference(superposition,[status(thm)],[c_317,c_1375]) ).
tcf(c_1810,plain,
multiply(iPr_def_13,iPr_def_17) = sk_c5,
inference(superposition,[status(thm)],[c_312,c_1375]) ).
tcf(c_1881,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(iPr_def_17,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_1810,c_76]) ).
tcf(c_1892,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( multiply(iPr_def_20,iPr_def_14) = sk_c2 ) ),
inference(superposition,[status(thm)],[c_1435,c_1551]) ).
tcf(c_1941,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(iPr_def_15,iPr_def_16) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_323,c_564]) ).
tcf(c_1943,plain,
( ( sk_c8 = iPr_def_17 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_1941,c_1748]) ).
tcf(c_3359,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(iPr_def_18,iPr_def_19) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_326,c_695]) ).
tcf(c_3364,plain,
( ( sk_c8 = iPr_def_22 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_3359,c_1797]) ).
tcf(c_3436,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(iPr_def_13,iPr_def_22) = identity ) ),
inference(superposition,[status(thm)],[c_3364,c_727]) ).
tcf(c_3463,plain,
( ( sk_c7 = identity )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_3436,c_1809]) ).
tcf(c_4685,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(sk_c2,identity) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_3463,c_309]) ).
tcf(c_4687,plain,
( ( identity = iPr_def_17 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_3463,c_324]) ).
tcf(c_5474,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1161,c_1160]) ).
tcf(c_5547,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( multiply(iPr_def_15,iPr_def_16) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_835,c_767]) ).
tcf(c_5552,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( sk_c8 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_5547,c_1748]) ).
tcf(c_5615,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( multiply(iPr_def_17,sk_c7) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_5552,c_317]) ).
tcf(c_5621,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( inverse(iPr_def_17) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_5552,c_308]) ).
tcf(c_6241,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( multiply(iPr_def_18,iPr_def_19) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_915,c_881]) ).
tcf(c_6248,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( sk_c8 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_6241,c_1797]) ).
tcf(c_7055,plain,
( ( iPr_def_17 = iPr_def_22 )
| ( iPr_def_13 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_6248,c_5552]) ).
tcf(c_7083,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( multiply(iPr_def_13,iPr_def_22) = identity ) ),
inference(superposition,[status(thm)],[c_6248,c_727]) ).
tcf(c_7091,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( inverse(iPr_def_22) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_6248,c_308]) ).
tcf(c_7110,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( sk_c7 = identity ) ),
inference(light_normalisation,[status(thm)],[c_7083,c_1809]) ).
tcf(c_7381,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_13 = iPr_def_22 )
| ( iPr_def_13 != iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_7055,c_505]) ).
tcf(c_7419,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( identity = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_7110,c_845]) ).
tcf(c_8352,plain,
! [X0: $i] :
( ( iPr_def_13 = iPr_def_22 )
| ( multiply(iPr_def_17,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_7419,c_74]) ).
tcf(c_11562,plain,
multiply(sk_c1,iPr_def_14) = multiply(iPr_def_21,sk_c7),
inference(superposition,[status(thm)],[c_309,c_1359]) ).
tcf(c_11675,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1362,c_74]) ).
tcf(c_11706,plain,
multiply(inverse(sk_c2),iPr_def_14) = sk_c7,
inference(superposition,[status(thm)],[c_309,c_11675]) ).
tcf(c_11707,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_74,c_11675]) ).
tcf(c_11708,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_75,c_11675]) ).
tcf(c_11785,plain,
! [X0: $i] : multiply(inverse(iPr_def_13),X0) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_1375,c_11675]) ).
tcf(c_11786,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_1374,c_11675]) ).
tcf(c_11787,plain,
! [X0: $i] : multiply(inverse(iPr_def_15),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_1373,c_11675]) ).
tcf(c_11788,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_1372,c_11675]) ).
tcf(c_11789,plain,
multiply(inverse(iPr_def_20),sk_c2) = iPr_def_21,
inference(superposition,[status(thm)],[c_1551,c_11675]) ).
tcf(c_11807,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_11675,c_11675]) ).
tcf(c_12140,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_11708,c_11807]) ).
tcf(c_12151,plain,
multiply(sk_c2,sk_c7) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_12140,c_1360]) ).
tcf(c_12165,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_12140,c_11707]) ).
tcf(c_12243,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( inverse(iPr_def_17) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_7419,c_12165]) ).
tcf(c_12248,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_12165,c_75]) ).
tcf(c_12687,plain,
( ~ iPr_def_12
| ( sk_c8 != sk_c7 )
| ( inverse(iPr_def_13) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_1030,c_12140]) ).
tcf(c_13560,plain,
( ~ iPr_def_10
| ( sk_c8 != identity )
| ( multiply(identity,sk_c7) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_1105,c_12165]) ).
tcf(c_13561,plain,
( ~ iPr_def_10
| ( sk_c8 != identity )
| ( sk_c8 != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_13560,c_74]) ).
tcf(c_13602,plain,
( ( sk_c8 = iPr_def_14 )
| ~ iPr_def_10
| ( identity != iPr_def_17 )
| ( sk_c8 != sk_c7 ) ),
inference(superposition,[status(thm)],[c_1943,c_13561]) ).
tcf(c_13610,plain,
( ( sk_c8 = iPr_def_14 )
| ~ iPr_def_10
| ( identity != iPr_def_18 )
| ( sk_c8 != sk_c7 ) ),
inference(superposition,[status(thm)],[c_325,c_13561]) ).
tcf(c_14053,plain,
multiply(sk_c5,identity) = multiply(iPr_def_13,iPr_def_17),
inference(superposition,[status(thm)],[c_12140,c_1881]) ).
tcf(c_14056,plain,
multiply(sk_c5,identity) = sk_c5,
inference(light_normalisation,[status(thm)],[c_14053,c_1810]) ).
tcf(c_14442,plain,
multiply(sk_c8,iPr_def_13) = identity,
inference(superposition,[status(thm)],[c_11785,c_75]) ).
tcf(c_14446,plain,
! [X0: $i] : multiply(sk_c8,multiply(iPr_def_13,X0)) = X0,
inference(superposition,[status(thm)],[c_11785,c_11675]) ).
tcf(c_14447,plain,
multiply(sk_c8,identity) = inverse(iPr_def_13),
inference(superposition,[status(thm)],[c_11785,c_12140]) ).
tcf(c_14533,plain,
multiply(sk_c4,identity) = multiply(iPr_def_16,iPr_def_13),
inference(superposition,[status(thm)],[c_14442,c_1358]) ).
tcf(c_14534,plain,
multiply(sk_c3,identity) = multiply(iPr_def_19,iPr_def_13),
inference(superposition,[status(thm)],[c_14442,c_1356]) ).
tcf(c_14695,plain,
inverse(iPr_def_13) = sk_c8,
inference(demodulation,[status(thm)],[c_14447,c_12140]) ).
tcf(c_14697,plain,
( ~ iPr_def_12
| ( sk_c8 != sk_c7 )
| ( sk_c8 != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_12687,c_14695]) ).
tcf(c_14698,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( sk_c8 != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_952,c_14695]) ).
tcf(c_14699,plain,
( ~ iPr_def_11
| ( sk_c7 != identity ) ),
inference(equality_resolution_simp,[status(thm)],[c_14698]) ).
tcf(c_14702,plain,
( ~ iPr_def_12
| ( sk_c8 != sk_c7 ) ),
inference(equality_resolution_simp,[status(thm)],[c_14697]) ).
tcf(c_14722,plain,
( ( sk_c8 = iPr_def_14 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_3463,c_14699]) ).
tcf(c_15025,plain,
( ( sk_c8 = iPr_def_14 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_324,c_14702]) ).
tcf(c_15132,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(sk_c8,identity) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_800,c_14446]) ).
tcf(c_16312,plain,
multiply(iPr_def_16,iPr_def_13) = sk_c4,
inference(demodulation,[status(thm)],[c_14533,c_12140]) ).
tcf(c_16363,plain,
( ( sk_c8 = iPr_def_14 )
| ~ iPr_def_10
| ( sk_c8 != sk_c7 ) ),
inference(global_subsumption_just,[status(thm)],[c_13610,c_4687,c_13602]) ).
tcf(c_16383,plain,
( ( sk_c8 = iPr_def_14 )
| ~ iPr_def_10
| ( sk_c8 != iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_324,c_16363]) ).
tcf(c_16779,plain,
multiply(iPr_def_19,iPr_def_13) = sk_c3,
inference(demodulation,[status(thm)],[c_14534,c_12140]) ).
tcf(c_16783,plain,
multiply(sk_c8,iPr_def_13) = multiply(iPr_def_18,sk_c3),
inference(superposition,[status(thm)],[c_16779,c_1800]) ).
tcf(c_17522,plain,
multiply(sk_c3,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_11786,c_75]) ).
tcf(c_17525,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_18)) != sk_c8 )
| ( multiply(sk_c3,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_11786,c_320]) ).
tcf(c_17527,plain,
multiply(sk_c3,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_11786,c_12140]) ).
tcf(c_17530,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_19 )
| ( inverse(inverse(iPr_def_18)) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_17525,c_314]) ).
tcf(c_17573,plain,
inverse(iPr_def_18) = sk_c3,
inference(demodulation,[status(thm)],[c_17527,c_12140]) ).
tcf(c_18218,plain,
multiply(sk_c4,iPr_def_15) = identity,
inference(superposition,[status(thm)],[c_11787,c_75]) ).
tcf(c_21987,plain,
multiply(sk_c1,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_11788,c_75]) ).
tcf(c_22005,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_11788,c_11675]) ).
tcf(c_22007,plain,
multiply(sk_c1,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_11788,c_12140]) ).
tcf(c_22194,plain,
inverse(iPr_def_20) = sk_c1,
inference(demodulation,[status(thm)],[c_22007,c_12140]) ).
tcf(c_24257,plain,
multiply(sk_c1,sk_c2) = iPr_def_21,
inference(superposition,[status(thm)],[c_1551,c_22005]) ).
tcf(c_24847,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( iPr_def_13 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_12243,c_5621]) ).
tcf(c_25110,plain,
sk_c8 = iPr_def_14,
inference(global_subsumption_just,[status(thm)],[c_4685,c_318,c_342,c_715,c_725,c_731,c_1943,c_7381,c_14722,c_15025,c_16383,c_24847]) ).
tcf(c_25177,plain,
inverse(iPr_def_13) = iPr_def_14,
inference(demodulation,[status(thm)],[c_14695,c_25110]) ).
tcf(c_25178,plain,
multiply(iPr_def_14,iPr_def_13) = identity,
inference(demodulation,[status(thm)],[c_14442,c_25110]) ).
tcf(c_25183,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_19,X0)) = multiply(iPr_def_14,X0),
inference(demodulation,[status(thm)],[c_1800,c_25110]) ).
tcf(c_25184,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(iPr_def_16,X0)) = multiply(iPr_def_14,X0),
inference(demodulation,[status(thm)],[c_1769,c_25110]) ).
tcf(c_25260,plain,
multiply(iPr_def_15,iPr_def_16) = iPr_def_14,
inference(demodulation,[status(thm)],[c_1748,c_25110]) ).
tcf(c_25268,plain,
! [X0: $i] :
( ~ iPr_def_10
| ( multiply(inverse(X0),sk_c7) != iPr_def_14 )
| ( multiply(X0,inverse(X0)) != iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_321,c_25110]) ).
tcf(c_25275,plain,
multiply(iPr_def_14,sk_c7) = iPr_def_22,
inference(demodulation,[status(thm)],[c_317,c_25110]) ).
tcf(c_25281,plain,
multiply(sk_c3,iPr_def_14) = iPr_def_19,
inference(demodulation,[status(thm)],[c_314,c_25110]) ).
tcf(c_25282,plain,
multiply(iPr_def_14,sk_c5) = iPr_def_17,
inference(demodulation,[status(thm)],[c_312,c_25110]) ).
tcf(c_25283,plain,
multiply(sk_c4,iPr_def_14) = iPr_def_16,
inference(demodulation,[status(thm)],[c_311,c_25110]) ).
tcf(c_25284,plain,
inverse(iPr_def_14) = iPr_def_13,
inference(demodulation,[status(thm)],[c_308,c_25110]) ).
tcf(c_25819,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_13 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_24847,c_505]) ).
tcf(c_25836,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_25819,c_318,c_342,c_715,c_725,c_731,c_7381,c_25819]) ).
tcf(c_25908,plain,
( ~ iPr_def_10
| ( multiply(sk_c1,iPr_def_20) != iPr_def_14 )
| ( multiply(inverse(sk_c1),sk_c7) != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_315,c_25268]) ).
tcf(c_25944,plain,
( ~ iPr_def_10
| ( identity != iPr_def_14 )
| ( multiply(iPr_def_20,sk_c7) != iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_25908,c_315,c_21987]) ).
tcf(c_28421,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( sk_c7 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_8352,c_5615]) ).
tcf(c_28514,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_28421,c_7110]) ).
tcf(c_28693,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( multiply(inverse(iPr_def_20),sk_c2) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1892,c_11675]) ).
tcf(c_28825,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( inverse(iPr_def_22) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_28514,c_12165]) ).
tcf(c_33216,plain,
iPr_def_13 = iPr_def_22,
inference(superposition,[status(thm)],[c_28825,c_7091]) ).
tcf(c_33226,plain,
multiply(iPr_def_14,sk_c7) = iPr_def_13,
inference(demodulation,[status(thm)],[c_25275,c_33216]) ).
tcf(c_34304,plain,
multiply(iPr_def_14,identity) = multiply(iPr_def_18,iPr_def_19),
inference(superposition,[status(thm)],[c_12140,c_25183]) ).
tcf(c_34305,plain,
multiply(iPr_def_14,iPr_def_13) = multiply(iPr_def_18,sk_c3),
inference(superposition,[status(thm)],[c_16779,c_25183]) ).
tcf(c_34363,plain,
multiply(iPr_def_14,identity) = multiply(iPr_def_15,iPr_def_16),
inference(superposition,[status(thm)],[c_12140,c_25184]) ).
tcf(c_34364,plain,
multiply(iPr_def_14,iPr_def_13) = multiply(iPr_def_15,sk_c4),
inference(superposition,[status(thm)],[c_16312,c_25184]) ).
tcf(c_34495,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_34364,c_34363,c_34305,c_34304,c_33226,c_33216,c_28693,c_25944,c_25836,c_25284,c_25260,c_25178,c_25177,c_25282,c_25281,c_25283,c_25110,c_24257,c_22194,c_21987,c_18218,c_17573,c_17530,c_17522,c_16783,c_15132,c_14699,c_14447,c_14056,c_14053,c_12151,c_12165,c_11789,c_11706,c_11562,c_5474,c_12248,c_1106,c_1047,c_1028,c_636,c_336,c_331,c_330,c_329,c_328,c_327,c_313,c_308]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP306-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.42 % Computer : n026.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Wed Sep 23 14:27:54 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.48 Running first-order theorem proving
% 0.15/0.48 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.50
% 0.15/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.50
% 0.23/0.50 % Detected problem language: tptp
% 0.23/0.52 % Proving...
% 19.11/3.53 % SZS status Started for theBenchmark.p
% 19.11/3.53 % SZS status Unsatisfiable for theBenchmark.p
% 19.11/3.53
% 19.11/3.53 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 19.11/3.53
% 19.11/3.53 % ------ iProver source info
% 19.11/3.53
% 19.11/3.53 % git: date: 2026-07-19 20:42:38 +0200
% 19.11/3.53 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 19.11/3.53 % git: non_committed_changes: false
% 19.11/3.53
% 19.11/3.53 % ------ Parsing...% successful
% 19.11/3.53
% 19.11/3.53
% 19.11/3.53 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 19.11/3.53
% 19.11/3.53 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 19.11/3.53
% 19.11/3.53 % ------ Preprocessing... gs_s sp: 3 0s gs_e snvd_s sp: 0 0s snvd_e %
% 19.11/3.53
% 19.11/3.53 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 19.11/3.53 % ------ Proving...
% 19.11/3.53 % ------ Problem Properties
% 19.11/3.53
% 19.11/3.53 %
% 19.11/3.53 % clauses 38
% 19.11/3.53 % conjectures 25
% 19.11/3.53 % EPR 22
% 19.11/3.53 % Horn 17
% 19.11/3.53 % unary 14
% 19.11/3.53 % binary 20
% 19.11/3.53 % lits 67
% 19.11/3.53 % lits eq 61
% 19.11/3.53 % fd_pure 0
% 19.11/3.53 % fd_pseudo 0
% 19.11/3.53 % fd_cond 0
% 19.11/3.53 % fd_pseudo_cond 0
% 19.11/3.53 % AC symbols 0
% 19.11/3.53
% 19.11/3.53 % ------ Schedule dynamic 5 is on
% 19.11/3.53
% 19.11/3.53 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 19.11/3.53
% 19.11/3.53
% 19.11/3.53 % ------
% 19.11/3.53 % Current options:
% 19.11/3.53 % ------
% 19.11/3.53
% 19.11/3.53
% 19.11/3.53 %
% 19.11/3.53
% 19.11/3.53 % ------ Proving...
% 19.11/3.53 %
% 19.11/3.53
% 19.11/3.53 % SZS status Unsatisfiable for theBenchmark.p
% 19.11/3.53
% 19.11/3.53 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 19.11/3.54
% 19.11/3.54
%------------------------------------------------------------------------------