%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP267-1 : 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 : n006.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 01:32:39 PM UTC 2026
% Result : Unsatisfiable 1.17s 6.29s
% Output : CNFRefutation 4.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 33
% Syntax : Number of formulae : 253 ( 68 unt; 10 def)
% Number of atoms : 861 ( 456 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 361 ( 106 ~; 255 |; 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 : 65 ( 0 sgn 65 !; 0 ?; 45 :)
% 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_c5,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c7 = multiply(sk_c5,sk_c8)
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c8 = inverse(sk_c5)
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c7 = inverse(sk_c6)
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c7 = multiply(sk_c5,sk_c8)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c7 = inverse(sk_c6)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = multiply(sk_c5,sk_c8)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = inverse(sk_c5)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = inverse(sk_c6)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = multiply(sk_c5,sk_c8)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = inverse(sk_c5)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c6)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f27]) ).
fof(f31,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = inverse(sk_c5)
| sk_c6 = multiply(sk_c7,sk_c4) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c6)
| sk_c6 = multiply(sk_c7,sk_c4) ),
inference(reorient_equations,[],[f33]) ).
fof(f37,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = inverse(sk_c5)
| sk_c4 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = inverse(sk_c6)
| sk_c4 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c5,sk_c8)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = inverse(sk_c5)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = inverse(sk_c6)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(sk_c6) != sk_c7
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != X2
| multiply(sk_c7,X2) != sk_c6
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
! [X2,X3,X0,X1,X4] :
( sk_c7 != inverse(sk_c6)
| sk_c8 != inverse(X4)
| sk_c7 != multiply(X4,sk_c8)
| sk_c7 != inverse(X3)
| multiply(X3,sk_c7) != X2
| sk_c6 != multiply(sk_c7,X2)
| sk_c6 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,plain,
! [X3,X0,X1,X4] :
( sk_c7 != inverse(sk_c6)
| sk_c8 != inverse(X4)
| sk_c7 != multiply(X4,sk_c8)
| sk_c7 != inverse(X3)
| sk_c6 != multiply(sk_c7,multiply(X3,sk_c7))
| sk_c6 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8) ),
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_c5,sk_c8) = sk_c7 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_78,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_79,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_80,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_81,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_82,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_83,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( multiply(sk_c5,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_84,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_85,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_86,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c5,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c7,sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c3,sk_c7) = sk_c4 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c3,sk_c7) = sk_c4 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c5,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_98,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(sk_c6) != sk_c7 )
| ( inverse(X3) != sk_c7 )
| ( inverse(X2) != sk_c6 )
| ( inverse(X1) != sk_c8 )
| ( inverse(X0) != sk_c8 )
| ( multiply(X2,sk_c6) != sk_c7 )
| ( multiply(X1,sk_c8) != sk_c7 )
| ( multiply(X0,sk_c8) != sk_c7 )
| ( multiply(sk_c7,multiply(X3,sk_c7)) != sk_c6 ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_315,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_98]) ).
tcf(c_316,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_98]) ).
tcf(c_317,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_98]) ).
tcf(c_318,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_98]) ).
tcf(c_319,definition,
iPr_def_13 = inverse(sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_320,definition,
iPr_def_14 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_321,definition,
iPr_def_15 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_322,definition,
iPr_def_16 = multiply(sk_c5,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_323,definition,
iPr_def_17 = multiply(sk_c3,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_324,definition,
iPr_def_18 = multiply(sk_c7,sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_325,definition,
iPr_def_19 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_326,definition,
iPr_def_20 = multiply(sk_c2,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_327,definition,
iPr_def_21 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_328,definition,
iPr_def_22 = multiply(sk_c1,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_329,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_13 != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_318,c_319]) ).
tcf(c_330,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_317]) ).
tcf(c_331,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_316]) ).
tcf(c_333,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_315]) ).
tcf(c_334,negated_conjecture,
( ( iPr_def_14 = sk_c7 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_97,c_320]) ).
tcf(c_335,negated_conjecture,
( ( iPr_def_15 = sk_c8 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_96,c_321]) ).
tcf(c_336,negated_conjecture,
( ( iPr_def_16 = sk_c7 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_95,c_322]) ).
tcf(c_337,negated_conjecture,
( ( iPr_def_17 = sk_c4 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_94,c_323]) ).
tcf(c_338,negated_conjecture,
( ( iPr_def_17 = sk_c4 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_340,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_91,c_324]) ).
tcf(c_341,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_343,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_88,c_325]) ).
tcf(c_344,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_345,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_346,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_85,c_326]) ).
tcf(c_347,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_348,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_349,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_82,c_327]) ).
tcf(c_350,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_351,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_352,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_79,c_328]) ).
tcf(c_353,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_354,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_568,plain,
( ( sk_c7 = iPr_def_13 )
| ( inverse(iPr_def_18) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_340,c_319]) ).
tcf(c_581,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(iPr_def_14,sk_c4) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_334,c_324]) ).
tcf(c_584,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(sk_c7,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_337,c_324]) ).
tcf(c_635,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c8 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_344,c_341]) ).
tcf(c_667,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(sk_c3,iPr_def_20) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_346,c_323]) ).
tcf(c_670,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_13 )
| ( iPr_def_13 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_346,c_329]) ).
tcf(c_689,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c5,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_347,c_322]) ).
tcf(c_699,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c3,iPr_def_20) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_348,c_323]) ).
tcf(c_718,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_345,c_326]) ).
tcf(c_720,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(sk_c2,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_343,c_326]) ).
tcf(c_750,plain,
multiply(iPr_def_15,sk_c5) = identity,
inference(superposition,[status(thm)],[c_321,c_75]) ).
tcf(c_751,plain,
multiply(iPr_def_13,sk_c6) = identity,
inference(superposition,[status(thm)],[c_319,c_75]) ).
tcf(c_752,plain,
multiply(iPr_def_21,sk_c1) = identity,
inference(superposition,[status(thm)],[c_327,c_75]) ).
tcf(c_753,plain,
multiply(iPr_def_19,sk_c2) = identity,
inference(superposition,[status(thm)],[c_325,c_75]) ).
tcf(c_754,plain,
multiply(iPr_def_14,sk_c3) = identity,
inference(superposition,[status(thm)],[c_320,c_75]) ).
tcf(c_775,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_349,c_328]) ).
tcf(c_814,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_350,c_328]) ).
tcf(c_833,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(iPr_def_13,iPr_def_18) = identity ) ),
inference(superposition,[status(thm)],[c_340,c_751]) ).
tcf(c_852,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_351,c_328]) ).
tcf(c_883,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c7 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_352,c_346]) ).
tcf(c_885,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(sk_c3,iPr_def_22) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_352,c_323]) ).
tcf(c_934,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(sk_c1,iPr_def_15) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_353,c_328]) ).
tcf(c_966,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c3,iPr_def_22) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_354,c_323]) ).
tcf(c_999,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_20 )
| ( inverse(sk_c2) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_326,c_331]) ).
tcf(c_1002,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( inverse(iPr_def_13) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_751,c_331]) ).
tcf(c_1015,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_19 )
| ( sk_c7 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_999,c_325]) ).
tcf(c_1068,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_22 )
| ( inverse(sk_c1) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_328,c_333]) ).
tcf(c_1069,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_16 )
| ( inverse(sk_c5) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_322,c_333]) ).
tcf(c_1081,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_16 )
| ( sk_c8 != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_1069,c_321]) ).
tcf(c_1085,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_22 )
| ( sk_c8 != iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_1068,c_327]) ).
tcf(c_1158,plain,
( ~ iPr_def_12
| ( inverse(sk_c3) != sk_c7 )
| ( multiply(sk_c7,iPr_def_17) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_323,c_330]) ).
tcf(c_1170,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_14 )
| ( multiply(sk_c7,iPr_def_17) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_1158,c_320]) ).
tcf(c_1380,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c4,X0)) = multiply(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_324,c_76]) ).
tcf(c_1381,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c7,X0)) = multiply(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_323,c_76]) ).
tcf(c_1383,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_75,c_76]) ).
tcf(c_1385,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_750,c_76]) ).
tcf(c_1386,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(sk_c6,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_751,c_76]) ).
tcf(c_1387,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_752,c_76]) ).
tcf(c_1388,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_753,c_76]) ).
tcf(c_1393,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1388,c_74]) ).
tcf(c_1394,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1387,c_74]) ).
tcf(c_1395,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(sk_c6,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1386,c_74]) ).
tcf(c_1396,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1385,c_74]) ).
tcf(c_1462,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_754,c_76]) ).
tcf(c_1463,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1462,c_74]) ).
tcf(c_1477,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(sk_c5,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_635,c_322]) ).
tcf(c_1729,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_20 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_883,c_329]) ).
tcf(c_2094,plain,
multiply(iPr_def_19,iPr_def_20) = sk_c6,
inference(superposition,[status(thm)],[c_326,c_1393]) ).
tcf(c_2104,plain,
multiply(iPr_def_21,iPr_def_22) = sk_c8,
inference(superposition,[status(thm)],[c_328,c_1394]) ).
tcf(c_2117,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_13,multiply(iPr_def_19,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_345,c_1395]) ).
tcf(c_2118,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_13,multiply(iPr_def_19,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_344,c_1395]) ).
tcf(c_2119,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_13 )
| ( multiply(iPr_def_13,multiply(iPr_def_19,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_343,c_1395]) ).
tcf(c_2122,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_13 )
| ( multiply(iPr_def_13,multiply(iPr_def_18,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_340,c_1395]) ).
tcf(c_2152,plain,
multiply(iPr_def_15,iPr_def_16) = sk_c8,
inference(superposition,[status(thm)],[c_322,c_1396]) ).
tcf(c_2164,plain,
multiply(iPr_def_14,iPr_def_17) = sk_c7,
inference(superposition,[status(thm)],[c_323,c_1463]) ).
tcf(c_2233,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(iPr_def_14,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_337,c_581]) ).
tcf(c_2235,plain,
( ( sk_c7 = iPr_def_18 )
| ( sk_c7 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_2233,c_2164]) ).
tcf(c_2401,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_17,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_2164,c_76]) ).
tcf(c_2419,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(iPr_def_18,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_2235,c_584]) ).
tcf(c_2430,plain,
( ( iPr_def_18 = iPr_def_22 )
| ( sk_c7 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_2235,c_352]) ).
tcf(c_2433,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(iPr_def_18,sk_c4) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_2235,c_324]) ).
tcf(c_2558,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_18 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_2430,c_329]) ).
tcf(c_2912,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(iPr_def_14,iPr_def_17) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_667,c_1463]) ).
tcf(c_2913,plain,
( ( sk_c7 = iPr_def_20 )
| ( sk_c7 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_2912,c_2164]) ).
tcf(c_3014,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_718,c_1393]) ).
tcf(c_3015,plain,
( ( sk_c6 = iPr_def_19 )
| ( sk_c7 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_3014,c_2094]) ).
tcf(c_3119,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_720,c_1393]) ).
tcf(c_3120,plain,
( ( sk_c6 = iPr_def_19 )
| ( sk_c7 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_3119,c_2094]) ).
tcf(c_3355,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_775,c_1394]) ).
tcf(c_3356,plain,
( ( sk_c7 = iPr_def_13 )
| ( sk_c8 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_3355,c_2104]) ).
tcf(c_3377,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_814,c_1394]) ).
tcf(c_3378,plain,
( ( sk_c8 = iPr_def_21 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_3377,c_2104]) ).
tcf(c_3538,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_852,c_1394]) ).
tcf(c_3539,plain,
( ( sk_c7 = iPr_def_16 )
| ( sk_c8 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_3538,c_2104]) ).
tcf(c_3591,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(iPr_def_14,iPr_def_17) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_885,c_1463]) ).
tcf(c_3592,plain,
( ( sk_c7 = iPr_def_22 )
| ( sk_c7 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_3591,c_2164]) ).
tcf(c_3603,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_934,c_1394]) ).
tcf(c_3604,plain,
( ( sk_c7 = iPr_def_22 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_3603,c_2104]) ).
tcf(c_3654,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_14,iPr_def_17) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_966,c_1463]) ).
tcf(c_3655,plain,
( ( sk_c7 = iPr_def_22 )
| ( sk_c7 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_3654,c_2164]) ).
tcf(c_3830,plain,
( iPr_def_12
| ( sk_c7 = iPr_def_13 )
| ( iPr_def_13 != iPr_def_20 ) ),
inference(global_subsumption_just,[status(thm)],[c_670,c_670,c_1015,c_1085,c_2913,c_3120,c_3356,c_3592]) ).
tcf(c_3988,plain,
multiply(sk_c3,iPr_def_18) = multiply(iPr_def_17,sk_c4),
inference(superposition,[status(thm)],[c_324,c_1381]) ).
tcf(c_5025,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1383,c_74]) ).
tcf(c_5039,plain,
multiply(inverse(sk_c2),iPr_def_20) = sk_c6,
inference(superposition,[status(thm)],[c_326,c_5025]) ).
tcf(c_5040,plain,
multiply(inverse(sk_c7),iPr_def_18) = sk_c4,
inference(superposition,[status(thm)],[c_324,c_5025]) ).
tcf(c_5041,plain,
multiply(inverse(sk_c3),iPr_def_17) = sk_c7,
inference(superposition,[status(thm)],[c_323,c_5025]) ).
tcf(c_5042,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_74,c_5025]) ).
tcf(c_5043,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_75,c_5025]) ).
tcf(c_5062,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(inverse(sk_c3),iPr_def_17) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_699,c_5025]) ).
tcf(c_5075,plain,
multiply(inverse(iPr_def_13),identity) = sk_c6,
inference(superposition,[status(thm)],[c_751,c_5025]) ).
tcf(c_5078,plain,
multiply(inverse(iPr_def_14),identity) = sk_c3,
inference(superposition,[status(thm)],[c_754,c_5025]) ).
tcf(c_5088,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(inverse(iPr_def_13),identity) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_833,c_5025]) ).
tcf(c_5115,plain,
! [X0: $i] : multiply(inverse(iPr_def_15),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_1396,c_5025]) ).
tcf(c_5116,plain,
! [X0: $i] : multiply(inverse(iPr_def_13),X0) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_1395,c_5025]) ).
tcf(c_5126,plain,
multiply(inverse(iPr_def_14),sk_c7) = iPr_def_17,
inference(superposition,[status(thm)],[c_2164,c_5025]) ).
tcf(c_5140,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_5025,c_5025]) ).
tcf(c_5717,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_5043,c_5140]) ).
tcf(c_5741,plain,
multiply(sk_c7,sk_c4) = multiply(iPr_def_18,identity),
inference(superposition,[status(thm)],[c_5717,c_1380]) ).
tcf(c_5742,plain,
multiply(sk_c7,identity) = multiply(iPr_def_14,iPr_def_17),
inference(superposition,[status(thm)],[c_5717,c_2401]) ).
tcf(c_5748,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_5717,c_5042]) ).
tcf(c_5750,plain,
multiply(sk_c7,identity) = sk_c7,
inference(light_normalisation,[status(thm)],[c_5742,c_2164]) ).
tcf(c_5751,plain,
multiply(iPr_def_18,identity) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_5741,c_324]) ).
tcf(c_5786,plain,
( ( sk_c7 = iPr_def_16 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_348,c_1015]) ).
tcf(c_5918,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_5748,c_75]) ).
tcf(c_5920,plain,
( ( sk_c7 = iPr_def_16 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_5786,c_3015,c_5786]) ).
tcf(c_6367,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_16 ) ),
inference(global_subsumption_just,[status(thm)],[c_1081,c_1085,c_1081,c_3378,c_3604]) ).
tcf(c_6369,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_6367,c_1085,c_3539,c_3655,c_6367]) ).
tcf(c_6373,plain,
( iPr_def_12
| iPr_def_11
| ( iPr_def_18 = iPr_def_22 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2558,c_6369]) ).
tcf(c_6375,plain,
( iPr_def_12
| iPr_def_11
| ( iPr_def_20 = iPr_def_22 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1729,c_6369]) ).
tcf(c_6377,plain,
( iPr_def_12
| iPr_def_11
| ( sk_c7 != iPr_def_13 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_329,c_6369]) ).
tcf(c_6429,plain,
( iPr_def_12
| iPr_def_11
| ( sk_c7 = iPr_def_16 )
| ( iPr_def_13 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_348,c_6377]) ).
tcf(c_6571,plain,
( iPr_def_12
| iPr_def_11
| ( iPr_def_13 != iPr_def_20 ) ),
inference(global_subsumption_just,[status(thm)],[c_6429,c_3830,c_6377]) ).
tcf(c_6609,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_13,sk_c6) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_2094,c_2117]) ).
tcf(c_6615,plain,
( ( identity = iPr_def_20 )
| ( sk_c7 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_6609,c_751]) ).
tcf(c_6688,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_13,sk_c6) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_2094,c_2118]) ).
tcf(c_6694,plain,
( ( identity = iPr_def_20 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_6688,c_751]) ).
tcf(c_6719,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(iPr_def_13,sk_c6) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_2094,c_2119]) ).
tcf(c_6725,plain,
( ( identity = iPr_def_20 )
| ( sk_c7 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_6719,c_751]) ).
tcf(c_6875,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(iPr_def_13,iPr_def_18) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_2419,c_2122]) ).
tcf(c_6876,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(iPr_def_13,iPr_def_18) = sk_c4 ) ),
inference(superposition,[status(thm)],[c_2433,c_2122]) ).
tcf(c_8061,plain,
( ( identity = iPr_def_20 )
| ( multiply(sk_c5,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_6694,c_322]) ).
tcf(c_8169,plain,
( ( iPr_def_13 = iPr_def_16 )
| ( identity = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_6725,c_6615]) ).
tcf(c_8170,plain,
( iPr_def_12
| iPr_def_11
| ( identity = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_6725,c_6377]) ).
tcf(c_8199,plain,
( ( identity = iPr_def_20 )
| ( multiply(sk_c3,iPr_def_13) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_6725,c_323]) ).
tcf(c_8994,plain,
( ( identity = iPr_def_20 )
| ( multiply(iPr_def_14,iPr_def_17) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_8199,c_1463]) ).
tcf(c_9000,plain,
multiply(sk_c5,iPr_def_15) = identity,
inference(superposition,[status(thm)],[c_5115,c_75]) ).
tcf(c_9005,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_15,X0)) = X0,
inference(superposition,[status(thm)],[c_5115,c_5025]) ).
tcf(c_9013,plain,
( ( identity = iPr_def_20 )
| ( identity = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_8061,c_9000]) ).
tcf(c_9014,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( identity = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_1477,c_9000]) ).
tcf(c_9016,plain,
( ( identity = iPr_def_16 )
| ( sk_c7 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_689,c_9000]) ).
tcf(c_9117,plain,
multiply(sk_c5,sk_c8) = iPr_def_16,
inference(superposition,[status(thm)],[c_2152,c_9005]) ).
tcf(c_9342,plain,
! [X0: $i] :
( ( identity = iPr_def_16 )
| ( multiply(iPr_def_20,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_9013,c_74]) ).
tcf(c_9762,plain,
( ( identity = iPr_def_16 )
| ( multiply(iPr_def_20,sk_c4) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_9016,c_324]) ).
tcf(c_9763,plain,
( ( identity = iPr_def_16 )
| ( multiply(sk_c3,iPr_def_20) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_9016,c_323]) ).
tcf(c_10916,plain,
( ( identity = iPr_def_16 )
| ( sk_c4 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_9762,c_9342]) ).
tcf(c_10930,plain,
( ( identity = iPr_def_16 )
| ( multiply(iPr_def_14,iPr_def_17) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_9763,c_1463]) ).
tcf(c_10976,plain,
( ( identity = iPr_def_16 )
| ( multiply(sk_c7,iPr_def_18) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_10916,c_324]) ).
tcf(c_10978,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( identity = iPr_def_16 )
| ( sk_c8 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_10916,c_338]) ).
tcf(c_11058,plain,
multiply(sk_c6,iPr_def_13) = identity,
inference(superposition,[status(thm)],[c_5116,c_75]) ).
tcf(c_11062,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_13)) != sk_c7 )
| ( multiply(sk_c7,multiply(sk_c6,sk_c7)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_5116,c_330]) ).
tcf(c_11064,plain,
multiply(sk_c6,identity) = inverse(iPr_def_13),
inference(superposition,[status(thm)],[c_5116,c_5717]) ).
tcf(c_11124,plain,
inverse(iPr_def_13) = sk_c6,
inference(demodulation,[status(thm)],[c_11064,c_5717]) ).
tcf(c_11126,plain,
( ~ iPr_def_11
| ( sk_c6 != sk_c6 )
| ( sk_c7 != identity ) ),
inference(demodulation,[status(thm)],[c_1002,c_11124]) ).
tcf(c_11127,plain,
( ~ iPr_def_11
| ( sk_c7 != identity ) ),
inference(equality_resolution_simp,[status(thm)],[c_11126]) ).
tcf(c_11236,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( identity = iPr_def_16 )
| ( multiply(sk_c5,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_10978,c_322]) ).
tcf(c_11237,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( identity = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_11236,c_9000]) ).
tcf(c_11960,plain,
( ( identity = iPr_def_16 )
| ~ iPr_def_11
| ( identity != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_9016,c_11127]) ).
tcf(c_12209,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_11960,c_11237,c_11127,c_11124,c_11062,c_11064,c_11058,c_10976,c_10930,c_9117,c_9014,c_9013,c_9000,c_8994,c_8170,c_8169,c_6876,c_6875,c_6571,c_6377,c_6375,c_6373,c_5920,c_5751,c_5750,c_5742,c_5741,c_5748,c_5126,c_5088,c_5078,c_5075,c_5062,c_5041,c_5040,c_5039,c_3988,c_5918,c_1170,c_568,c_336,c_335,c_334,c_325,c_320,c_319]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP267-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n006.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Wed Sep 23 14:18:46 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 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
% 0.14/5.42
% 0.14/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.42
% 0.14/5.42 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 1.17/6.29 % SZS status Started for theBenchmark.p
% 1.17/6.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.17/6.29
% 1.17/6.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.17/6.29
% 1.17/6.29 % ------ iProver source info
% 1.17/6.29
% 1.17/6.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.17/6.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.17/6.29 % git: non_committed_changes: false
% 1.17/6.29
% 1.17/6.29 % ------ Parsing...% successful
% 1.17/6.29
% 1.17/6.29
% 1.17/6.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.17/6.29
% 1.17/6.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.17/6.29
% 1.17/6.29 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.17/6.29
% 1.17/6.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.17/6.29 % ------ Proving...
% 1.17/6.29 % ------ Problem Properties
% 1.17/6.29
% 1.17/6.29 %
% 1.17/6.29 % clauses 38
% 1.17/6.29 % conjectures 25
% 1.17/6.29 % EPR 22
% 1.17/6.29 % Horn 16
% 1.17/6.29 % unary 13
% 1.17/6.29 % binary 21
% 1.17/6.29 % lits 68
% 1.17/6.29 % lits eq 62
% 1.17/6.29 % fd_pure 0
% 1.17/6.29 % fd_pseudo 0
% 1.17/6.29 % fd_cond 0
% 1.17/6.29 % fd_pseudo_cond 0
% 1.17/6.29 % AC symbols 0
% 1.17/6.29
% 1.17/6.29 % ------ Schedule dynamic 5 is on
% 1.17/6.29
% 1.17/6.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.17/6.29
% 1.17/6.29
% 1.17/6.29 % ------
% 1.17/6.29 % Current options:
% 1.17/6.29 % ------
% 1.17/6.29
% 1.17/6.29
% 1.17/6.29 %
% 1.17/6.29
% 1.17/6.29 % ------ Proving...
% 1.17/6.29 %
% 1.17/6.29
% 1.17/6.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.17/6.29
% 1.17/6.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.39/6.30
% 4.39/6.30
%------------------------------------------------------------------------------