%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP315-1 : 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 : n018.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 01:32:49 PM UTC 2026
% Result : Unsatisfiable 1.12s 1.75s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 30
% Syntax : Number of formulae : 236 ( 88 unt; 9 def)
% Number of atoms : 750 ( 413 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 372 ( 148 ~; 224 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 73 ( 0 sgn 73 !; 0 ?; 59 :)
% 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_c6,sk_c7) = sk_c5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c6 = inverse(sk_c4)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c6 = inverse(sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c7 = inverse(sk_c3)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c6 = inverse(sk_c4)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c6 = inverse(sk_c4)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(X3,sk_c5) != sk_c6
| inverse(X3) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c5
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( sk_c6 != multiply(X3,sk_c5)
| sk_c6 != inverse(X3)
| sk_c7 != multiply(X2,sk_c6)
| sk_c7 != inverse(X2)
| sk_c6 != inverse(X1)
| sk_c5 != multiply(X1,sk_c6)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7)
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(reorient_equations,[],[f38]) ).
tcf(c_70,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_71,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_73,negated_conjecture,
multiply(sk_c6,sk_c7) = sk_c5,
inference(cnf_transformation,[],[f5]) ).
tcf(c_74,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_75,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_76,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_77,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_78,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_79,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_80,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_81,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_82,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_83,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_84,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_85,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_86,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_90,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c7 )
| ( inverse(X2) != sk_c6 )
| ( inverse(X1) != sk_c6 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(X3,sk_c6) != sk_c7 )
| ( multiply(X2,sk_c6) != sk_c5 )
| ( multiply(X1,sk_c5) != sk_c6 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c7 )
| ( inverse(X2) != sk_c6 )
| ( inverse(X1) != sk_c6 )
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 )
| ( multiply(X1,sk_c5) != sk_c6 )
| ( multiply(X2,sk_c6) != sk_c5 )
| ( multiply(X3,sk_c6) != sk_c7 ) ),
inference(global_subsumption_just,[status(thm)],[c_90,c_73,c_90]) ).
tcf(c_96,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c7 )
| ( inverse(X2) != sk_c6 )
| ( inverse(X1) != sk_c6 )
| ( inverse(X0) != sk_c7 )
| ( multiply(X3,sk_c6) != sk_c7 )
| ( multiply(X2,sk_c6) != sk_c5 )
| ( multiply(X1,sk_c5) != sk_c6 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(renaming,[status(thm)],[c_95]) ).
tcf(c_268,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_96]) ).
tcf(c_269,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_96]) ).
tcf(c_270,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_96]) ).
tcf(c_271,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_96]) ).
tcf(c_272,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_96]) ).
tcf(c_273,definition,
iPr_def_14 = multiply(sk_c4,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_274,definition,
iPr_def_15 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_275,definition,
iPr_def_16 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_276,definition,
iPr_def_17 = multiply(sk_c3,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_277,definition,
iPr_def_18 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_278,definition,
iPr_def_19 = multiply(sk_c2,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_279,definition,
iPr_def_20 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_280,definition,
iPr_def_21 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_281,definition,
iPr_def_22 = multiply(sk_c6,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_282,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_272]) ).
tcf(c_283,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_271]) ).
tcf(c_284,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_270]) ).
tcf(c_285,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_269]) ).
tcf(c_286,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_268]) ).
tcf(c_287,negated_conjecture,
( ( iPr_def_15 = sk_c6 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89,c_274,c_273]) ).
tcf(c_288,negated_conjecture,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_88,c_275]) ).
tcf(c_289,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_87,c_276]) ).
tcf(c_290,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_86,c_277]) ).
tcf(c_291,negated_conjecture,
( ( iPr_def_19 = sk_c5 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_85,c_278]) ).
tcf(c_292,negated_conjecture,
( ( iPr_def_19 = sk_c5 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_293,negated_conjecture,
( ( iPr_def_19 = sk_c5 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_294,negated_conjecture,
( ( iPr_def_19 = sk_c5 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_295,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_81,c_279]) ).
tcf(c_296,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_297,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_298,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_299,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_77,c_280]) ).
tcf(c_300,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_301,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_302,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_303,negated_conjecture,
iPr_def_22 = sk_c5,
inference(demodulation,[status(thm)],[c_73,c_281]) ).
tcf(c_484,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( sk_c6 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_291,c_303]) ).
tcf(c_501,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( sk_c6 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_292,c_303]) ).
tcf(c_517,plain,
multiply(sk_c4,iPr_def_22) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_273,c_303]) ).
tcf(c_548,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( sk_c7 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_293,c_303]) ).
tcf(c_560,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( sk_c7 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_294,c_303]) ).
tcf(c_586,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_295,c_280]) ).
tcf(c_613,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_296,c_280]) ).
tcf(c_640,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_297,c_280]) ).
tcf(c_674,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_298,c_280]) ).
tcf(c_699,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(sk_c2,iPr_def_21) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_299,c_278]) ).
tcf(c_757,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_21) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_300,c_278]) ).
tcf(c_781,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( multiply(iPr_def_16,sk_c7) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_501,c_281]) ).
tcf(c_837,plain,
multiply(iPr_def_18,sk_c3) = identity,
inference(superposition,[status(thm)],[c_277,c_71]) ).
tcf(c_838,plain,
multiply(iPr_def_16,sk_c4) = identity,
inference(superposition,[status(thm)],[c_275,c_71]) ).
tcf(c_839,plain,
multiply(iPr_def_20,sk_c1) = identity,
inference(superposition,[status(thm)],[c_279,c_71]) ).
tcf(c_840,plain,
multiply(iPr_def_15,sk_c2) = identity,
inference(superposition,[status(thm)],[c_274,c_71]) ).
tcf(c_851,plain,
( ( sk_c6 = iPr_def_21 )
| ( multiply(sk_c6,iPr_def_17) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_301,c_281]) ).
tcf(c_901,plain,
( ( sk_c6 = iPr_def_21 )
| ( multiply(sk_c6,iPr_def_18) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_302,c_281]) ).
tcf(c_907,plain,
( ( sk_c6 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_18) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_302,c_280]) ).
tcf(c_936,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_281,c_72]) ).
tcf(c_939,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c6,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_278,c_72]) ).
tcf(c_941,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_71,c_72]) ).
tcf(c_943,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_22,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_517,c_72]) ).
tcf(c_963,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_837,c_72]) ).
tcf(c_964,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_963,c_70]) ).
tcf(c_968,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_838,c_72]) ).
tcf(c_969,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_968,c_70]) ).
tcf(c_978,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_839,c_72]) ).
tcf(c_979,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_978,c_70]) ).
tcf(c_981,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_840,c_72]) ).
tcf(c_982,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_981,c_70]) ).
tcf(c_993,plain,
( ~ iPr_def_13
| ( sk_c6 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_71,c_283]) ).
tcf(c_1123,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_17 )
| ( inverse(sk_c3) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_276,c_284]) ).
tcf(c_1125,plain,
( ~ iPr_def_12
| ( sk_c6 != sk_c7 )
| ( inverse(identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_70,c_284]) ).
tcf(c_1141,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_18 )
| ( sk_c7 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_1123,c_277]) ).
tcf(c_1233,plain,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,iPr_def_22) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_285,c_303]) ).
tcf(c_1246,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_14 )
| ( inverse(sk_c4) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_517,c_1233]) ).
tcf(c_1247,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_16 )
| ( sk_c6 != iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_1246,c_275]) ).
tcf(c_1270,plain,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_286,c_303]) ).
tcf(c_1282,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_22 )
| ( inverse(identity) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_70,c_1270]) ).
tcf(c_1678,plain,
multiply(iPr_def_18,iPr_def_17) = sk_c6,
inference(superposition,[status(thm)],[c_276,c_964]) ).
tcf(c_1708,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_17,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_1678,c_72]) ).
tcf(c_1717,plain,
multiply(iPr_def_16,iPr_def_14) = iPr_def_22,
inference(superposition,[status(thm)],[c_517,c_969]) ).
tcf(c_1728,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_14,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_1717,c_72]) ).
tcf(c_1737,plain,
multiply(iPr_def_20,iPr_def_21) = sk_c7,
inference(superposition,[status(thm)],[c_280,c_979]) ).
tcf(c_1771,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_21,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_1737,c_72]) ).
tcf(c_1866,plain,
multiply(iPr_def_15,iPr_def_19) = sk_c6,
inference(superposition,[status(thm)],[c_278,c_982]) ).
tcf(c_1885,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(iPr_def_19,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_1866,c_72]) ).
tcf(c_2011,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(iPr_def_15,iPr_def_19) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_699,c_982]) ).
tcf(c_2012,plain,
( ( sk_c6 = iPr_def_21 )
| ( sk_c6 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_2011,c_1866]) ).
tcf(c_2035,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_15,iPr_def_19) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_757,c_982]) ).
tcf(c_2036,plain,
( ( sk_c6 = iPr_def_21 )
| ( sk_c6 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_2035,c_1866]) ).
tcf(c_2919,plain,
( ( sk_c6 = iPr_def_21 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_907,c_979]) ).
tcf(c_2920,plain,
( ( sk_c7 = iPr_def_18 )
| ( sk_c6 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_2919,c_1737]) ).
tcf(c_3329,plain,
multiply(sk_c2,iPr_def_22) = multiply(iPr_def_19,sk_c7),
inference(superposition,[status(thm)],[c_281,c_939]) ).
tcf(c_4107,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_941,c_70]) ).
tcf(c_4112,plain,
multiply(inverse(sk_c6),iPr_def_22) = sk_c7,
inference(superposition,[status(thm)],[c_281,c_4107]) ).
tcf(c_4116,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_70,c_4107]) ).
tcf(c_4117,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_71,c_4107]) ).
tcf(c_4161,plain,
( ( sk_c6 = iPr_def_21 )
| ( multiply(inverse(sk_c6),iPr_def_22) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_901,c_4107]) ).
tcf(c_4165,plain,
( ( sk_c6 = iPr_def_21 )
| ( multiply(inverse(sk_c6),iPr_def_22) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_851,c_4107]) ).
tcf(c_4177,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_964,c_4107]) ).
tcf(c_4178,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_969,c_4107]) ).
tcf(c_4179,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_979,c_4107]) ).
tcf(c_4180,plain,
! [X0: $i] : multiply(inverse(iPr_def_15),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_982,c_4107]) ).
tcf(c_4202,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_4107,c_4107]) ).
tcf(c_4498,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_4117,c_4202]) ).
tcf(c_4506,plain,
multiply(sk_c4,iPr_def_22) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_4498,c_943]) ).
tcf(c_4508,plain,
multiply(sk_c6,sk_c7) = multiply(iPr_def_22,identity),
inference(superposition,[status(thm)],[c_4498,c_936]) ).
tcf(c_4509,plain,
multiply(sk_c7,identity) = multiply(iPr_def_20,iPr_def_21),
inference(superposition,[status(thm)],[c_4498,c_1771]) ).
tcf(c_4510,plain,
multiply(sk_c6,identity) = multiply(iPr_def_18,iPr_def_17),
inference(superposition,[status(thm)],[c_4498,c_1708]) ).
tcf(c_4513,plain,
multiply(sk_c6,identity) = multiply(iPr_def_15,iPr_def_19),
inference(superposition,[status(thm)],[c_4498,c_1885]) ).
tcf(c_4514,plain,
multiply(iPr_def_16,iPr_def_14) = multiply(iPr_def_22,identity),
inference(superposition,[status(thm)],[c_4498,c_1728]) ).
tcf(c_4519,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_4498,c_4116]) ).
tcf(c_4520,plain,
multiply(iPr_def_22,identity) = iPr_def_22,
inference(light_normalisation,[status(thm)],[c_4514,c_1717]) ).
tcf(c_4521,plain,
multiply(sk_c6,identity) = sk_c6,
inference(light_normalisation,[status(thm)],[c_4513,c_1866]) ).
tcf(c_4525,plain,
multiply(sk_c7,identity) = sk_c7,
inference(light_normalisation,[status(thm)],[c_4509,c_1737]) ).
tcf(c_4528,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_4506,c_517]) ).
tcf(c_4740,plain,
( ~ iPr_def_12
| ( sk_c7 != identity )
| ( sk_c6 != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_1125,c_4519]) ).
tcf(c_5233,plain,
( ( sk_c6 = iPr_def_21 )
| ~ iPr_def_12
| ( sk_c7 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_301,c_1141]) ).
tcf(c_5239,plain,
( ( iPr_def_19 = iPr_def_22 )
| ~ iPr_def_12
| ( sk_c7 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_548,c_1141]) ).
tcf(c_5275,plain,
( ( sk_c6 = iPr_def_21 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_5233,c_2920,c_5233]) ).
tcf(c_5288,plain,
( ( iPr_def_19 = iPr_def_22 )
| ~ iPr_def_12 ),
inference(forward_subsumption_resolution,[status(thm)],[c_5239,c_560]) ).
tcf(c_5384,plain,
( ( iPr_def_19 = iPr_def_22 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_484,c_1247]) ).
tcf(c_5502,plain,
( ( iPr_def_19 = iPr_def_22 )
| ~ iPr_def_11 ),
inference(forward_subsumption_resolution,[status(thm)],[c_5384,c_501]) ).
tcf(c_5579,plain,
multiply(sk_c3,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_4177,c_71]) ).
tcf(c_5584,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_4177,c_4107]) ).
tcf(c_5586,plain,
multiply(sk_c3,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_4177,c_4498]) ).
tcf(c_5616,plain,
inverse(iPr_def_18) = sk_c3,
inference(demodulation,[status(thm)],[c_5586,c_4498]) ).
tcf(c_5893,plain,
multiply(sk_c3,sk_c6) = iPr_def_17,
inference(superposition,[status(thm)],[c_1678,c_5584]) ).
tcf(c_5922,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_16)) != sk_c7 )
| ( multiply(sk_c4,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_4178,c_283]) ).
tcf(c_5923,plain,
multiply(sk_c4,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_4178,c_71]) ).
tcf(c_5926,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_16)) != sk_c6 )
| ( multiply(sk_c4,sk_c6) != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_4178,c_1270]) ).
tcf(c_5928,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_4178,c_4107]) ).
tcf(c_5929,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_16)) != sk_c6 )
| ( multiply(sk_c4,iPr_def_22) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_4178,c_1233]) ).
tcf(c_5930,plain,
multiply(sk_c4,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_4178,c_4498]) ).
tcf(c_6247,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_22 )
| ( sk_c6 != identity ) ),
inference(light_normalisation,[status(thm)],[c_1282,c_4519]) ).
tcf(c_6268,plain,
( ( iPr_def_19 = iPr_def_22 )
| ~ iPr_def_10
| ( iPr_def_14 != iPr_def_22 )
| ( sk_c6 != identity ) ),
inference(superposition,[status(thm)],[c_484,c_6247]) ).
tcf(c_6324,plain,
inverse(iPr_def_16) = sk_c4,
inference(demodulation,[status(thm)],[c_5930,c_4498]) ).
tcf(c_6328,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( multiply(sk_c4,iPr_def_22) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_781,c_5928]) ).
tcf(c_6356,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_6328,c_517]) ).
tcf(c_8097,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_20)) != sk_c7 )
| ( multiply(sk_c1,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_4179,c_283]) ).
tcf(c_8098,plain,
multiply(sk_c1,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_4179,c_71]) ).
tcf(c_8103,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_4179,c_4107]) ).
tcf(c_8104,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_20)) != sk_c6 )
| ( multiply(sk_c1,iPr_def_22) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_4179,c_1233]) ).
tcf(c_8105,plain,
multiply(sk_c1,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_4179,c_4498]) ).
tcf(c_8115,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_21 )
| ( inverse(inverse(iPr_def_20)) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_8097,c_280]) ).
tcf(c_8119,plain,
( ( identity = iPr_def_21 )
| ( sk_c7 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_674,c_8098]) ).
tcf(c_8120,plain,
( ( identity = iPr_def_21 )
| ( sk_c7 = iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_640,c_8098]) ).
tcf(c_8121,plain,
( ( identity = iPr_def_21 )
| ( sk_c6 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_613,c_8098]) ).
tcf(c_8122,plain,
( ( identity = iPr_def_21 )
| ( sk_c6 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_586,c_8098]) ).
tcf(c_8142,plain,
multiply(iPr_def_20,identity) = iPr_def_20,
inference(superposition,[status(thm)],[c_8098,c_979]) ).
tcf(c_8145,plain,
inverse(iPr_def_20) = sk_c1,
inference(demodulation,[status(thm)],[c_8105,c_4498]) ).
tcf(c_8150,plain,
multiply(sk_c1,sk_c7) = iPr_def_21,
inference(superposition,[status(thm)],[c_1737,c_8103]) ).
tcf(c_8359,plain,
( ( identity = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_18) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_8119,c_280]) ).
tcf(c_8593,plain,
( ( identity = iPr_def_21 )
| ( multiply(sk_c6,iPr_def_17) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_8120,c_281]) ).
tcf(c_8739,plain,
( ( identity = iPr_def_21 )
| ~ iPr_def_11
| ( iPr_def_14 != iPr_def_16 )
| ( sk_c6 != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_8121,c_1247]) ).
tcf(c_8743,plain,
( ( identity = iPr_def_21 )
| ( multiply(inverse(iPr_def_16),iPr_def_22) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_8121,c_4112]) ).
tcf(c_8778,plain,
( ( identity = iPr_def_21 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_8743,c_517,c_6324]) ).
tcf(c_8998,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( identity = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_8122,c_8121]) ).
tcf(c_9038,plain,
( ( identity = iPr_def_21 )
| ( multiply(iPr_def_14,sk_c7) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_8122,c_281]) ).
tcf(c_9042,plain,
( ( identity = iPr_def_21 )
| ( multiply(sk_c3,iPr_def_14) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_8122,c_276]) ).
tcf(c_9353,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( identity = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_8778,c_8120]) ).
tcf(c_9354,plain,
( ( iPr_def_14 = iPr_def_18 )
| ( identity = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_8778,c_8119]) ).
tcf(c_9360,plain,
( ( identity = iPr_def_21 )
| ~ iPr_def_12
| ( iPr_def_14 != iPr_def_17 )
| ( sk_c7 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_8778,c_1141]) ).
tcf(c_10062,plain,
multiply(sk_c2,iPr_def_15) = identity,
inference(superposition,[status(thm)],[c_4180,c_71]) ).
tcf(c_10065,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_15)) != sk_c6 )
| ( multiply(sk_c2,sk_c6) != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_4180,c_1270]) ).
tcf(c_10067,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_15,X0)) = X0,
inference(superposition,[status(thm)],[c_4180,c_4107]) ).
tcf(c_10069,plain,
multiply(sk_c2,identity) = inverse(iPr_def_15),
inference(superposition,[status(thm)],[c_4180,c_4498]) ).
tcf(c_10078,plain,
( ~ iPr_def_10
| ( iPr_def_19 != iPr_def_22 )
| ( inverse(inverse(iPr_def_15)) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_10065,c_278]) ).
tcf(c_11047,plain,
inverse(iPr_def_15) = sk_c2,
inference(demodulation,[status(thm)],[c_10069,c_4498]) ).
tcf(c_11081,plain,
multiply(sk_c2,identity) = sk_c2,
inference(superposition,[status(thm)],[c_840,c_10067]) ).
tcf(c_11082,plain,
multiply(sk_c2,sk_c6) = iPr_def_19,
inference(superposition,[status(thm)],[c_1866,c_10067]) ).
tcf(c_11962,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_16 )
| ( multiply(sk_c4,sk_c7) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_5922,c_275,c_6324]) ).
tcf(c_11986,plain,
( ( sk_c6 = iPr_def_21 )
| ~ iPr_def_13
| ( sk_c7 != iPr_def_16 )
| ( multiply(sk_c4,iPr_def_17) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_301,c_11962]) ).
tcf(c_12696,plain,
( ( identity = iPr_def_21 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_8359,c_979]) ).
tcf(c_12725,plain,
( ( identity = iPr_def_21 )
| ( multiply(inverse(sk_c6),iPr_def_22) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_8593,c_4107]) ).
tcf(c_13329,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_12725,c_12696,c_11986,c_11082,c_11081,c_11047,c_10078,c_10062,c_9360,c_9354,c_9353,c_9038,c_9042,c_8998,c_8739,c_8150,c_8145,c_8142,c_8122,c_8121,c_8119,c_8115,c_8104,c_6356,c_6324,c_6268,c_5929,c_5926,c_5923,c_5893,c_5616,c_5579,c_5502,c_5288,c_5275,c_4740,c_4528,c_4525,c_4521,c_4520,c_4514,c_4510,c_4509,c_4508,c_4506,c_4519,c_4165,c_4161,c_4112,c_3329,c_2036,c_2012,c_1141,c_993,c_290,c_289,c_288,c_287,c_279,c_277,c_275,c_274,c_282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP315-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 14:29:18 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 1.12/1.75 % SZS status Started for theBenchmark.p
% 1.12/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 1.12/1.75
% 1.12/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.12/1.75
% 1.12/1.75 % ------ iProver source info
% 1.12/1.75
% 1.12/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 1.12/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.12/1.75 % git: non_committed_changes: false
% 1.12/1.75
% 1.12/1.75 % ------ Parsing...% successful
% 1.12/1.75
% 1.12/1.75
% 1.12/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.12/1.75
% 1.12/1.75 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.12/1.75
% 1.12/1.75 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.12/1.75
% 1.12/1.75 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.12/1.75 % ------ Proving...
% 1.12/1.75 % ------ Problem Properties
% 1.12/1.75
% 1.12/1.75 %
% 1.12/1.75 % clauses 34
% 1.12/1.75 % conjectures 22
% 1.12/1.75 % EPR 18
% 1.12/1.75 % Horn 17
% 1.12/1.75 % unary 13
% 1.12/1.75 % binary 16
% 1.12/1.75 % lits 61
% 1.12/1.75 % lits eq 53
% 1.12/1.75 % fd_pure 0
% 1.12/1.75 % fd_pseudo 0
% 1.12/1.75 % fd_cond 0
% 1.12/1.75 % fd_pseudo_cond 0
% 1.12/1.75 % AC symbols 0
% 1.12/1.75
% 1.12/1.75 % ------ Schedule dynamic 5 is on
% 1.12/1.75
% 1.12/1.75 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.12/1.75
% 1.12/1.75
% 1.12/1.75 % ------
% 1.12/1.75 % Current options:
% 1.12/1.75 % ------
% 1.12/1.75
% 1.12/1.75
% 1.12/1.75 %
% 1.12/1.75
% 1.12/1.75 % ------ Proving...
% 1.12/1.75 %
% 1.12/1.75
% 1.12/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 1.12/1.75
% 1.12/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.12/1.76
% 1.12/1.76
%------------------------------------------------------------------------------