%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP253-1 : 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 : n013.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 01:32:28 PM UTC 2026
% Result : Unsatisfiable 7.11s 1.71s
% Output : CNFRefutation 7.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 33
% Syntax : Number of formulae : 255 ( 65 unt; 9 def)
% Number of atoms : 858 ( 457 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 404 ( 135 ~; 269 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 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 : 14 ( 12 usr; 13 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 71 !; 0 ?; 57 :)
% 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_c4,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c7 = inverse(sk_c4)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c6 = inverse(sk_c5)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c7 = inverse(sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c6 = inverse(sk_c5)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = inverse(sk_c4)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = inverse(sk_c5)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = inverse(sk_c4)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = inverse(sk_c5)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c4)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c6 = inverse(sk_c5)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c3,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| sk_c6 = multiply(sk_c3,sk_c5) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c3,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = inverse(sk_c4)
| sk_c6 = multiply(sk_c3,sk_c5) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c3,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c6 = inverse(sk_c5)
| sk_c6 = multiply(sk_c3,sk_c5) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
! [X2,X3,X0,X1] :
( inverse(sk_c5) != sk_c6
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c5
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
! [X2,X3,X0,X1] :
( sk_c6 != inverse(sk_c5)
| sk_c7 != inverse(X3)
| sk_c6 != multiply(X3,sk_c7)
| sk_c6 != multiply(X2,sk_c5)
| sk_c6 != inverse(X2)
| sk_c6 != inverse(X1)
| sk_c5 != multiply(X1,sk_c6)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
tcf(c_71,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_72,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_74,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_75,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_76,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_77,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_78,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_79,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_80,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( multiply(sk_c4,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_81,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_82,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_83,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c4,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_84,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c4) = sk_c7 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_85,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_86,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c4,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( inverse(sk_c4) = sk_c7 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( inverse(sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_89,negated_conjecture,
( ( multiply(sk_c3,sk_c5) = sk_c6 )
| ( multiply(sk_c4,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c3,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c3,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_92,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(sk_c5) != sk_c6 )
| ( inverse(X3) != sk_c6 )
| ( inverse(X2) != sk_c6 )
| ( inverse(X1) != sk_c7 )
| ( inverse(X0) != sk_c7 )
| ( multiply(X3,sk_c6) != sk_c5 )
| ( multiply(X2,sk_c5) != sk_c6 )
| ( multiply(X1,sk_c7) != sk_c6 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_285,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_92]) ).
tcf(c_286,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_92]) ).
tcf(c_287,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_92]) ).
tcf(c_288,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c5) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_92]) ).
tcf(c_289,definition,
iPr_def_13 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_290,definition,
iPr_def_14 = multiply(sk_c3,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_291,definition,
iPr_def_15 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_292,definition,
iPr_def_16 = multiply(sk_c4,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_293,definition,
iPr_def_17 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_294,definition,
iPr_def_18 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_295,definition,
iPr_def_19 = multiply(sk_c2,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_296,definition,
iPr_def_20 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_297,definition,
iPr_def_21 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_298,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_13 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_288,c_289]) ).
tcf(c_300,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_287]) ).
tcf(c_301,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_286]) ).
tcf(c_302,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_285]) ).
tcf(c_303,negated_conjecture,
( ( iPr_def_14 = sk_c6 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_91,c_290]) ).
tcf(c_304,negated_conjecture,
( ( iPr_def_15 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_90,c_291]) ).
tcf(c_305,negated_conjecture,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89,c_292]) ).
tcf(c_306,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_88,c_293]) ).
tcf(c_307,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_308,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_309,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_85,c_294]) ).
tcf(c_310,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_311,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_312,negated_conjecture,
( ( iPr_def_19 = sk_c5 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_82,c_295]) ).
tcf(c_313,negated_conjecture,
( ( iPr_def_19 = sk_c5 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_314,negated_conjecture,
( ( iPr_def_19 = sk_c5 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_315,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_79,c_296]) ).
tcf(c_316,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_317,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_318,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_76,c_297]) ).
tcf(c_319,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_320,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_321,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_322,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_511,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c6 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_306,c_303]) ).
tcf(c_535,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c6 = iPr_def_16 )
| ( iPr_def_13 != iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_308,c_298]) ).
tcf(c_556,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c6 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_309,c_306]) ).
tcf(c_575,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_307,c_292]) ).
tcf(c_576,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(sk_c4,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_304,c_292]) ).
tcf(c_581,plain,
( ( sk_c6 = iPr_def_13 )
| ( multiply(sk_c2,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_309,c_295]) ).
tcf(c_582,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_308,c_295]) ).
tcf(c_583,plain,
( ( sk_c6 = iPr_def_13 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_306,c_295]) ).
tcf(c_584,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(sk_c2,iPr_def_16) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_305,c_295]) ).
tcf(c_600,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(sk_c4,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_310,c_292]) ).
tcf(c_611,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_311,c_295]) ).
tcf(c_612,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c6 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_311,c_308]) ).
tcf(c_636,plain,
( ( sk_c6 = iPr_def_13 )
| ( multiply(sk_c3,iPr_def_19) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_312,c_290]) ).
tcf(c_637,plain,
( ( sk_c6 = iPr_def_13 )
| ( inverse(iPr_def_19) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_312,c_289]) ).
tcf(c_646,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c3,iPr_def_19) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_313,c_290]) ).
tcf(c_656,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c3,iPr_def_19) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_314,c_290]) ).
tcf(c_662,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = sk_c6 )
| ( sk_c6 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_322]) ).
tcf(c_686,plain,
! [X0: $i] : inverse(X0) = inverse(X0),
inference(instantiation,[status(thm)],[c_321]) ).
tcf(c_689,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_322]) ).
tcf(c_699,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_20) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_316,c_292]) ).
tcf(c_720,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != inverse(X1) )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_689]) ).
tcf(c_730,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c4,iPr_def_20) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_317,c_292]) ).
tcf(c_755,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_13 )
| ( iPr_def_13 != inverse(sk_c5) )
| ( inverse(X0) != inverse(sk_c5) ) ),
inference(instantiation,[status(thm)],[c_720]) ).
tcf(c_767,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_316,c_297]) ).
tcf(c_768,plain,
( ( sk_c6 = iPr_def_13 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_315,c_297]) ).
tcf(c_784,plain,
multiply(iPr_def_15,sk_c4) = identity,
inference(superposition,[status(thm)],[c_291,c_72]) ).
tcf(c_785,plain,
multiply(iPr_def_13,sk_c5) = identity,
inference(superposition,[status(thm)],[c_289,c_72]) ).
tcf(c_786,plain,
multiply(iPr_def_20,sk_c1) = identity,
inference(superposition,[status(thm)],[c_296,c_72]) ).
tcf(c_787,plain,
multiply(iPr_def_18,sk_c2) = identity,
inference(superposition,[status(thm)],[c_294,c_72]) ).
tcf(c_788,plain,
multiply(iPr_def_17,sk_c3) = identity,
inference(superposition,[status(thm)],[c_293,c_72]) ).
tcf(c_801,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( sk_c6 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_318,c_309]) ).
tcf(c_805,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( sk_c6 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_318,c_303]) ).
tcf(c_832,plain,
! [X0: $i] :
( ( inverse(X0) = sk_c6 )
| ( sk_c6 != iPr_def_13 )
| ( inverse(X0) != iPr_def_13 ) ),
inference(instantiation,[status(thm)],[c_662]) ).
tcf(c_847,plain,
( ( sk_c6 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_15) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_319,c_297]) ).
tcf(c_881,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_21) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_320,c_295]) ).
tcf(c_886,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( sk_c6 = iPr_def_16 )
| ( sk_c6 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_320,c_303]) ).
tcf(c_930,plain,
( ~ iPr_def_12
| ( sk_c5 != iPr_def_19 )
| ( inverse(sk_c2) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_295,c_300]) ).
tcf(c_944,plain,
( ~ iPr_def_12
| ( sk_c5 != iPr_def_19 )
| ( sk_c6 != iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_930,c_294]) ).
tcf(c_1007,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_21 )
| ( inverse(sk_c1) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_297,c_301]) ).
tcf(c_1008,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_16 )
| ( inverse(sk_c4) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_292,c_301]) ).
tcf(c_1021,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_16 )
| ( sk_c7 != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_1008,c_291]) ).
tcf(c_1025,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_21 )
| ( sk_c7 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_1007,c_296]) ).
tcf(c_1093,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_14 )
| ( inverse(sk_c3) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_290,c_302]) ).
tcf(c_1106,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_17 )
| ( sk_c6 != iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_1093,c_293]) ).
tcf(c_1174,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_14 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_511,c_298]) ).
tcf(c_1289,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_17 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_556,c_298]) ).
tcf(c_1431,plain,
( ( inverse(sk_c5) = iPr_def_13 )
| ( iPr_def_13 != inverse(sk_c5) )
| ( inverse(sk_c5) != inverse(sk_c5) ) ),
inference(instantiation,[status(thm)],[c_755]) ).
tcf(c_1432,plain,
inverse(sk_c5) = inverse(sk_c5),
inference(instantiation,[status(thm)],[c_686]) ).
tcf(c_1554,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_72,c_73]) ).
tcf(c_1556,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_784,c_73]) ).
tcf(c_1557,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_785,c_73]) ).
tcf(c_1558,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_786,c_73]) ).
tcf(c_1559,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_787,c_73]) ).
tcf(c_1564,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1559,c_71]) ).
tcf(c_1565,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1558,c_71]) ).
tcf(c_1566,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1557,c_71]) ).
tcf(c_1567,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1556,c_71]) ).
tcf(c_1614,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_788,c_73]) ).
tcf(c_1615,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1614,c_71]) ).
tcf(c_1754,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_18 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_801,c_298]) ).
tcf(c_1918,plain,
( ( inverse(sk_c5) = sk_c6 )
| ( sk_c6 != iPr_def_13 )
| ( inverse(sk_c5) != iPr_def_13 ) ),
inference(instantiation,[status(thm)],[c_832]) ).
tcf(c_1985,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( iPr_def_13 = iPr_def_17 )
| ( sk_c6 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_805,c_308]) ).
tcf(c_2441,plain,
multiply(iPr_def_18,iPr_def_19) = sk_c6,
inference(superposition,[status(thm)],[c_295,c_1564]) ).
tcf(c_2451,plain,
multiply(iPr_def_20,iPr_def_21) = sk_c7,
inference(superposition,[status(thm)],[c_297,c_1565]) ).
tcf(c_2499,plain,
multiply(iPr_def_15,iPr_def_16) = sk_c7,
inference(superposition,[status(thm)],[c_292,c_1567]) ).
tcf(c_2514,plain,
multiply(iPr_def_17,iPr_def_14) = sk_c5,
inference(superposition,[status(thm)],[c_290,c_1615]) ).
tcf(c_2558,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_18,iPr_def_19) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_582,c_1564]) ).
tcf(c_2559,plain,
( ( sk_c6 = iPr_def_17 )
| ( sk_c6 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_2558,c_2441]) ).
tcf(c_2570,plain,
( ( sk_c6 = iPr_def_13 )
| ( multiply(iPr_def_18,iPr_def_19) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_583,c_1564]) ).
tcf(c_2571,plain,
( ( sk_c6 = iPr_def_17 )
| ( sk_c6 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_2570,c_2441]) ).
tcf(c_2582,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(iPr_def_18,iPr_def_19) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_584,c_1564]) ).
tcf(c_2583,plain,
( ( sk_c6 = iPr_def_16 )
| ( sk_c6 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_2582,c_2441]) ).
tcf(c_2606,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_15,iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_600,c_1567]) ).
tcf(c_2607,plain,
( ( sk_c6 = iPr_def_18 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_2606,c_2499]) ).
tcf(c_2618,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_18,iPr_def_19) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_611,c_1564]) ).
tcf(c_2619,plain,
( ( sk_c6 = iPr_def_18 )
| ( sk_c6 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_2618,c_2441]) ).
tcf(c_2625,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_14,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2514,c_73]) ).
tcf(c_2632,plain,
( ( sk_c6 = iPr_def_13 )
| ( multiply(iPr_def_17,iPr_def_14) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_636,c_1615]) ).
tcf(c_2633,plain,
( ( sk_c5 = iPr_def_19 )
| ( sk_c6 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_2632,c_2514]) ).
tcf(c_2644,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_17,iPr_def_14) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_646,c_1615]) ).
tcf(c_2645,plain,
( ( sk_c5 = iPr_def_19 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_2644,c_2514]) ).
tcf(c_2678,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_17,iPr_def_14) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_656,c_1615]) ).
tcf(c_2679,plain,
( ( sk_c5 = iPr_def_19 )
| ( sk_c6 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_2678,c_2514]) ).
tcf(c_2764,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_15,iPr_def_16) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_699,c_1567]) ).
tcf(c_2765,plain,
( ( sk_c7 = iPr_def_20 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_2764,c_2499]) ).
tcf(c_2776,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_15,iPr_def_16) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_730,c_1567]) ).
tcf(c_2777,plain,
( ( sk_c6 = iPr_def_16 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_2776,c_2499]) ).
tcf(c_2900,plain,
( ( sk_c6 = iPr_def_21 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_847,c_1565]) ).
tcf(c_2901,plain,
( ( sk_c6 = iPr_def_21 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_2900,c_2451]) ).
tcf(c_3088,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_18,iPr_def_19) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_881,c_1564]) ).
tcf(c_3089,plain,
( ( sk_c6 = iPr_def_21 )
| ( sk_c6 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_3088,c_2441]) ).
tcf(c_3135,plain,
( ( iPr_def_13 != iPr_def_17 )
| ( sk_c6 = iPr_def_16 ) ),
inference(global_subsumption_just,[status(thm)],[c_535,c_535,c_944,c_1025,c_1106,c_2559,c_2583,c_2619,c_2679,c_2777,c_3089]) ).
tcf(c_3136,plain,
( ( sk_c6 = iPr_def_16 )
| ( iPr_def_13 != iPr_def_17 ) ),
inference(renaming,[status(thm)],[c_3135]) ).
tcf(c_3685,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( sk_c6 = iPr_def_16 ) ),
inference(global_subsumption_just,[status(thm)],[c_886,c_1985,c_3136]) ).
tcf(c_4128,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1554,c_71]) ).
tcf(c_4141,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_71,c_4128]) ).
tcf(c_4142,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_72,c_4128]) ).
tcf(c_4194,plain,
! [X0: $i] : multiply(inverse(iPr_def_15),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_1567,c_4128]) ).
tcf(c_4195,plain,
! [X0: $i] : multiply(inverse(iPr_def_13),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_1566,c_4128]) ).
tcf(c_4196,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_1565,c_4128]) ).
tcf(c_4197,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_1564,c_4128]) ).
tcf(c_4198,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_1615,c_4128]) ).
tcf(c_4210,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_4128,c_4128]) ).
tcf(c_4402,plain,
( ~ iPr_def_10
| ( inverse(sk_c5) != sk_c6 )
| ( multiply(sk_c5,sk_c5) != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_302]) ).
tcf(c_4439,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_4142,c_4210]) ).
tcf(c_4453,plain,
multiply(sk_c5,identity) = multiply(iPr_def_17,iPr_def_14),
inference(superposition,[status(thm)],[c_4439,c_2625]) ).
tcf(c_4460,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_4439,c_4141]) ).
tcf(c_4498,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_4460,c_72]) ).
tcf(c_4546,plain,
( ( sk_c6 = iPr_def_16 )
| ~ iPr_def_12
| ( sk_c5 != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_311,c_944]) ).
tcf(c_4547,plain,
( ( sk_c6 = iPr_def_13 )
| ~ iPr_def_12
| ( sk_c5 != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_309,c_944]) ).
tcf(c_4548,plain,
( ( sk_c6 = iPr_def_16 )
| ~ iPr_def_12
| ( iPr_def_17 != iPr_def_18 )
| ( sk_c5 != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_308,c_944]) ).
tcf(c_4649,plain,
( ( sk_c6 = iPr_def_16 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_4546,c_612,c_2679,c_4548]) ).
tcf(c_4698,plain,
( ( sk_c6 = iPr_def_13 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_4547,c_2633,c_4547]) ).
tcf(c_4728,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_16 ) ),
inference(global_subsumption_just,[status(thm)],[c_1021,c_1025,c_1021,c_2765,c_2901]) ).
tcf(c_4730,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_4728,c_1025,c_2777,c_3089,c_4728]) ).
tcf(c_4734,plain,
( iPr_def_12
| iPr_def_10
| ( iPr_def_18 = iPr_def_21 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1754,c_4730]) ).
tcf(c_4736,plain,
( iPr_def_12
| iPr_def_10
| ( iPr_def_17 = iPr_def_18 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1289,c_4730]) ).
tcf(c_4737,plain,
( iPr_def_12
| iPr_def_10
| ( iPr_def_14 = iPr_def_17 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1174,c_4730]) ).
tcf(c_4738,plain,
( iPr_def_12
| iPr_def_10
| ( sk_c6 != iPr_def_13 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_298,c_4730]) ).
tcf(c_4822,plain,
( ( sk_c6 = iPr_def_16 )
| ~ iPr_def_10
| ( iPr_def_14 != iPr_def_21 )
| ( sk_c6 != iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_320,c_1106]) ).
tcf(c_4829,plain,
( ( sk_c6 = iPr_def_13 )
| ~ iPr_def_10
| ( sk_c6 != iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_303,c_1106]) ).
tcf(c_4953,plain,
( ( sk_c6 = iPr_def_13 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_4829,c_2571,c_4829]) ).
tcf(c_5029,plain,
multiply(sk_c4,iPr_def_15) = identity,
inference(superposition,[status(thm)],[c_4194,c_72]) ).
tcf(c_5034,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_15,X0)) = X0,
inference(superposition,[status(thm)],[c_4194,c_4128]) ).
tcf(c_5044,plain,
( ( identity = iPr_def_16 )
| ( sk_c6 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_576,c_5029]) ).
tcf(c_5045,plain,
( ( identity = iPr_def_16 )
| ( sk_c6 = iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_575,c_5029]) ).
tcf(c_5479,plain,
( ( identity = iPr_def_16 )
| ~ iPr_def_10
| ( sk_c6 != iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_5044,c_1106]) ).
tcf(c_5799,plain,
multiply(sk_c4,sk_c7) = iPr_def_16,
inference(superposition,[status(thm)],[c_2499,c_5034]) ).
tcf(c_6314,plain,
multiply(sk_c5,iPr_def_13) = identity,
inference(superposition,[status(thm)],[c_4195,c_72]) ).
tcf(c_6317,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_13)) != sk_c6 )
| ( multiply(sk_c5,sk_c5) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_4195,c_302]) ).
tcf(c_6318,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_13)) != sk_c6 )
| ( multiply(sk_c5,sk_c6) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_4195,c_300]) ).
tcf(c_6320,plain,
multiply(sk_c5,identity) = inverse(iPr_def_13),
inference(superposition,[status(thm)],[c_4195,c_4439]) ).
tcf(c_6375,plain,
inverse(iPr_def_13) = sk_c5,
inference(demodulation,[status(thm)],[c_6320,c_4439]) ).
tcf(c_6727,plain,
multiply(sk_c1,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_4196,c_72]) ).
tcf(c_6740,plain,
( ( identity = iPr_def_21 )
| ( sk_c6 = iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_768,c_6727]) ).
tcf(c_6741,plain,
( ( identity = iPr_def_21 )
| ( sk_c7 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_767,c_6727]) ).
tcf(c_6959,plain,
( iPr_def_12
| iPr_def_10
| ( identity = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_6740,c_4738]) ).
tcf(c_7046,plain,
( ( identity = iPr_def_21 )
| ( multiply(sk_c4,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_6741,c_292]) ).
tcf(c_7047,plain,
( ( identity = iPr_def_21 )
| ( identity = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_7046,c_5029]) ).
tcf(c_7230,plain,
! [X0: $i] :
( ( identity = iPr_def_16 )
| ( multiply(iPr_def_21,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_7047,c_71]) ).
tcf(c_7363,plain,
multiply(sk_c2,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_4197,c_72]) ).
tcf(c_7384,plain,
( ( identity = iPr_def_19 )
| ( sk_c6 = iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_581,c_7363]) ).
tcf(c_7437,plain,
( ( sk_c6 = iPr_def_16 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_4822,c_2559,c_3685,c_4822]) ).
tcf(c_7698,plain,
( iPr_def_12
| iPr_def_10
| ( identity = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_7384,c_4738]) ).
tcf(c_7838,plain,
( ( identity = iPr_def_16 )
| ~ iPr_def_10
| ( sk_c6 != sk_c5 )
| ( inverse(iPr_def_21) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_7230,c_302]) ).
tcf(c_8219,plain,
( ~ iPr_def_10
| ( multiply(sk_c5,sk_c5) != sk_c6 ) ),
inference(global_subsumption_just,[status(thm)],[c_6317,c_289,c_1431,c_1432,c_1918,c_4402,c_4953]) ).
tcf(c_8246,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_13 )
| ( multiply(sk_c5,sk_c6) != sk_c5 ) ),
inference(light_normalisation,[status(thm)],[c_6318,c_289,c_6375]) ).
tcf(c_8250,plain,
( ~ iPr_def_12
| ( multiply(sk_c5,sk_c6) != sk_c5 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8246,c_4698]) ).
tcf(c_8261,plain,
( ( sk_c7 = iPr_def_15 )
| ~ iPr_def_12
| ( multiply(iPr_def_19,sk_c6) != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_313,c_8250]) ).
tcf(c_8434,plain,
( ( sk_c7 = iPr_def_15 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_8261,c_944,c_2607,c_2645]) ).
tcf(c_10062,plain,
multiply(sk_c3,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_4198,c_72]) ).
tcf(c_10086,plain,
multiply(iPr_def_17,identity) = iPr_def_17,
inference(superposition,[status(thm)],[c_10062,c_1615]) ).
tcf(c_11709,plain,
( ( identity = iPr_def_16 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_7838,c_5045,c_5479]) ).
tcf(c_11826,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_11709,c_10086,c_8434,c_8250,c_8246,c_8219,c_7698,c_7437,c_6959,c_6375,c_6320,c_6314,c_5799,c_5029,c_4953,c_4738,c_4737,c_4736,c_4734,c_4698,c_4649,c_4453,c_4460,c_4498,c_1106,c_637,c_305,c_304,c_303]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP253-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 14:16:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 7.11/1.71 % SZS status Started for theBenchmark.p
% 7.11/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 7.11/1.71
% 7.11/1.71 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.11/1.71
% 7.11/1.71 % ------ iProver source info
% 7.11/1.71
% 7.11/1.71 % git: date: 2026-07-19 20:42:38 +0200
% 7.11/1.71 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.11/1.71 % git: non_committed_changes: false
% 7.11/1.71
% 7.11/1.71 % ------ Parsing...% successful
% 7.11/1.71
% 7.11/1.71
% 7.11/1.71 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.11/1.71
% 7.11/1.71 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 7.11/1.71
% 7.11/1.71 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.11/1.71
% 7.11/1.71 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 7.11/1.71 % ------ Proving...
% 7.11/1.71 % ------ Problem Properties
% 7.11/1.71
% 7.11/1.71 %
% 7.11/1.71 % clauses 34
% 7.11/1.71 % conjectures 22
% 7.11/1.71 % EPR 19
% 7.11/1.71 % Horn 15
% 7.11/1.71 % unary 12
% 7.11/1.71 % binary 18
% 7.11/1.71 % lits 61
% 7.11/1.71 % lits eq 55
% 7.11/1.71 % fd_pure 0
% 7.11/1.71 % fd_pseudo 0
% 7.11/1.71 % fd_cond 0
% 7.11/1.71 % fd_pseudo_cond 0
% 7.11/1.71 % AC symbols 0
% 7.11/1.71
% 7.11/1.71 % ------ Schedule dynamic 5 is on
% 7.11/1.71
% 7.11/1.71 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.11/1.71
% 7.11/1.71
% 7.11/1.71 % ------
% 7.11/1.71 % Current options:
% 7.11/1.71 % ------
% 7.11/1.71
% 7.11/1.71
% 7.11/1.71 %
% 7.11/1.71
% 7.11/1.71 % ------ Proving...
% 7.11/1.71 %
% 7.11/1.71
% 7.11/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 7.11/1.71
% 7.11/1.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.11/1.71
% 7.11/1.71
%------------------------------------------------------------------------------