%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP334-1 : 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 01:33:03 PM UTC 2026
% Result : Unsatisfiable 7.01s 1.75s
% Output : CNFRefutation 7.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 23
% Syntax : Number of formulae : 227 ( 45 unt; 0 def)
% Number of atoms : 515 ( 443 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 477 ( 189 ~; 288 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 72 !; 0 ?; 55 :)
% 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_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c5 = inverse(sk_c6)
| sk_c7 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f6]) ).
fof(f10,negated_conjecture,
( multiply(sk_c6,sk_c4) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c5 = multiply(sk_c6,sk_c4)
| sk_c7 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c4 = multiply(sk_c3,sk_c6)
| sk_c7 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c6 = inverse(sk_c3)
| sk_c7 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c6) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c5 = inverse(sk_c6)
| sk_c6 = inverse(sk_c1) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c5 = inverse(sk_c7)
| sk_c6 = inverse(sk_c1) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c6,sk_c4) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c5 = multiply(sk_c6,sk_c4)
| sk_c6 = inverse(sk_c1) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c4
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c4 = multiply(sk_c3,sk_c6)
| sk_c6 = inverse(sk_c1) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c6 = inverse(sk_c3)
| sk_c6 = inverse(sk_c1) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c5 = inverse(sk_c6)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c5 = inverse(sk_c7)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c6,sk_c4) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c5 = multiply(sk_c6,sk_c4)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c4
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c4 = multiply(sk_c3,sk_c6)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f32]) ).
fof(f36,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c5 = inverse(sk_c6)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c5 = inverse(sk_c7)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( multiply(sk_c6,sk_c4) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c5 = multiply(sk_c6,sk_c4)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c4
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c4 = multiply(sk_c3,sk_c6)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f42]) ).
fof(f46,negated_conjecture,
! [X2,X3,X0,X1] :
( inverse(X3) != sk_c6
| multiply(X3,sk_c6) != X2
| multiply(sk_c6,X2) != sk_c5
| inverse(sk_c7) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(X1,sk_c5) != sk_c6
| inverse(X1) != sk_c6
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( sk_c6 != inverse(X3)
| multiply(X3,sk_c6) != X2
| sk_c5 != multiply(sk_c6,X2)
| sk_c5 != inverse(sk_c7)
| sk_c5 != inverse(sk_c6)
| sk_c6 != multiply(X1,sk_c5)
| sk_c6 != inverse(X1)
| inverse(X0) != sk_c6
| sk_c7 != multiply(X0,sk_c6)
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(reorient_equations,[],[f46]) ).
fof(f48,plain,
! [X3,X0,X1] :
( sk_c6 != inverse(X3)
| sk_c5 != multiply(sk_c6,multiply(X3,sk_c6))
| sk_c5 != inverse(sk_c7)
| sk_c5 != inverse(sk_c6)
| sk_c6 != multiply(X1,sk_c5)
| sk_c6 != inverse(X1)
| inverse(X0) != sk_c6
| sk_c7 != multiply(X0,sk_c6)
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(equality_resolution,[],[f47]) ).
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_c6,sk_c7) = sk_c5,
inference(cnf_transformation,[],[f5]) ).
tcf(c_78,negated_conjecture,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_80,negated_conjecture,
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ( multiply(sk_c6,sk_c4) = sk_c5 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_81,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c4 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_82,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_83,negated_conjecture,
( ( inverse(sk_c1) = sk_c6 )
| ( inverse(sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_84,negated_conjecture,
( ( inverse(sk_c1) = sk_c6 )
| ( inverse(sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_85,negated_conjecture,
( ( inverse(sk_c1) = sk_c6 )
| ( multiply(sk_c6,sk_c4) = sk_c5 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_86,negated_conjecture,
( ( inverse(sk_c1) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c4 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( inverse(sk_c1) = sk_c6 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c6,sk_c4) = sk_c5 ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c4 ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(sk_c2,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c2,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_95,negated_conjecture,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( multiply(sk_c6,sk_c4) = sk_c5 ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_96,negated_conjecture,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c4 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_98,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(sk_c7) != sk_c5 )
| ( inverse(sk_c6) != sk_c5 )
| ( inverse(X2) != sk_c6 )
| ( inverse(X1) != sk_c6 )
| ( inverse(X0) != sk_c6 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(X1,sk_c5) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c7 )
| ( multiply(sk_c6,multiply(X2,sk_c6)) != sk_c5 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(sk_c7) != sk_c5 )
| ( inverse(sk_c6) != sk_c5 )
| ( inverse(X2) != sk_c6 )
| ( inverse(X1) != sk_c6 )
| ( inverse(X0) != sk_c6 )
| ( multiply(sk_c6,multiply(X2,sk_c6)) != sk_c5 )
| ( multiply(X0,sk_c6) != sk_c7 )
| ( multiply(X1,sk_c5) != sk_c6 ) ),
inference(global_subsumption_just,[status(thm)],[c_98,c_77,c_98]) ).
tcf(c_104,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(sk_c7) != sk_c5 )
| ( inverse(sk_c6) != sk_c5 )
| ( inverse(X2) != sk_c6 )
| ( inverse(X1) != sk_c6 )
| ( inverse(X0) != sk_c6 )
| ( multiply(X2,sk_c5) != sk_c6 )
| ( multiply(X1,sk_c6) != sk_c7 )
| ( multiply(sk_c6,multiply(X0,sk_c6)) != sk_c5 ) ),
inference(renaming,[status(thm)],[c_103]) ).
tcf(c_214,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_104]) ).
tcf(c_215,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_104]) ).
tcf(c_216,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c6 )
| ( multiply(sk_c6,multiply(X0,sk_c6)) != sk_c5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_104]) ).
tcf(c_217,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c7) != sk_c5 )
| ( inverse(sk_c6) != sk_c5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_104]) ).
tcf(c_219,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_363,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_75,c_76]) ).
tcf(c_368,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_363,c_74]) ).
tcf(c_410,plain,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(sk_c6,sk_c1) = identity ) ),
inference(superposition,[status(thm)],[c_83,c_75]) ).
tcf(c_415,plain,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c6,sk_c1) = identity ) ),
inference(superposition,[status(thm)],[c_84,c_75]) ).
tcf(c_545,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,sk_c6) = X2 )
| ( X2 != X1 )
| ( multiply(X0,sk_c6) != X1 ) ),
inference(instantiation,[status(thm)],[c_219]) ).
tcf(c_548,plain,
! [X0: $i] :
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(sk_c6,multiply(sk_c1,X0)) = multiply(identity,X0) ) ),
inference(superposition,[status(thm)],[c_410,c_76]) ).
tcf(c_552,plain,
! [X0: $i] :
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(sk_c6,multiply(sk_c1,X0)) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_548,c_74]) ).
tcf(c_584,plain,
( ( inverse(sk_c3) = sk_c6 )
| ~ iPr_def_10
| ( inverse(sk_c1) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_82,c_214]) ).
tcf(c_585,plain,
( ( multiply(sk_c3,sk_c6) = sk_c4 )
| ~ iPr_def_10
| ( inverse(sk_c1) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_81,c_214]) ).
tcf(c_586,plain,
( ( multiply(sk_c6,sk_c4) = sk_c5 )
| ~ iPr_def_10
| ( inverse(sk_c1) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_80,c_214]) ).
tcf(c_588,plain,
( ( inverse(sk_c6) = sk_c5 )
| ~ iPr_def_10
| ( inverse(sk_c1) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_78,c_214]) ).
tcf(c_597,plain,
( ( inverse(sk_c6) = sk_c5 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_588,c_83,c_588]) ).
tcf(c_605,plain,
( ( inverse(sk_c3) = sk_c6 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_584,c_87,c_584]) ).
tcf(c_616,plain,
( ( multiply(sk_c3,sk_c6) = sk_c4 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_585,c_86,c_585]) ).
tcf(c_666,plain,
( ( multiply(sk_c3,sk_c6) = sk_c4 )
| ~ iPr_def_11
| ( inverse(sk_c2) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_96,c_215]) ).
tcf(c_667,plain,
( ( multiply(sk_c6,sk_c4) = sk_c5 )
| ~ iPr_def_11
| ( inverse(sk_c2) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_95,c_215]) ).
tcf(c_668,plain,
( ( inverse(sk_c7) = sk_c5 )
| ~ iPr_def_11
| ( inverse(sk_c2) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_94,c_215]) ).
tcf(c_680,plain,
( ( inverse(sk_c7) = sk_c5 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_668,c_89,c_668]) ).
tcf(c_749,plain,
( ( inverse(sk_c3) = sk_c6 )
| ~ iPr_def_12
| ( inverse(sk_c1) != sk_c6 )
| ( multiply(sk_c6,sk_c7) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_82,c_216]) ).
tcf(c_750,plain,
( ( multiply(sk_c3,sk_c6) = sk_c4 )
| ~ iPr_def_12
| ( inverse(sk_c1) != sk_c6 )
| ( multiply(sk_c6,sk_c7) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_81,c_216]) ).
tcf(c_751,plain,
( ( multiply(sk_c6,sk_c4) = sk_c5 )
| ~ iPr_def_12
| ( inverse(sk_c1) != sk_c6 )
| ( multiply(sk_c6,sk_c7) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_80,c_216]) ).
tcf(c_755,plain,
( ( inverse(sk_c1) = sk_c6 )
| ~ iPr_def_12
| ( inverse(sk_c3) != sk_c6 )
| ( multiply(sk_c6,sk_c4) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_86,c_216]) ).
tcf(c_757,plain,
( ~ iPr_def_12
| ( inverse(inverse(sk_c6)) != sk_c6 )
| ( multiply(sk_c6,identity) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_75,c_216]) ).
tcf(c_765,plain,
( ( inverse(sk_c1) = sk_c6 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_755,c_87,c_85,c_755]) ).
tcf(c_789,plain,
( ( multiply(sk_c6,sk_c4) = sk_c5 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_751,c_77,c_87,c_85,c_755,c_751]) ).
tcf(c_793,plain,
( ( multiply(sk_c3,sk_c6) = sk_c4 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_750,c_77,c_765,c_750]) ).
tcf(c_842,plain,
multiply(inverse(sk_c6),sk_c5) = sk_c7,
inference(superposition,[status(thm)],[c_77,c_368]) ).
tcf(c_843,plain,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(inverse(sk_c1),sk_c7) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_82,c_368]) ).
tcf(c_844,plain,
( ( multiply(sk_c3,sk_c6) = sk_c4 )
| ( multiply(inverse(sk_c1),sk_c7) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_81,c_368]) ).
tcf(c_845,plain,
( ( multiply(sk_c6,sk_c4) = sk_c5 )
| ( multiply(inverse(sk_c1),sk_c7) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_80,c_368]) ).
tcf(c_853,plain,
( ( multiply(sk_c3,sk_c6) = sk_c4 )
| ( multiply(inverse(sk_c2),sk_c6) = sk_c5 ) ),
inference(superposition,[status(thm)],[c_96,c_368]) ).
tcf(c_854,plain,
( ( multiply(sk_c6,sk_c4) = sk_c5 )
| ( multiply(inverse(sk_c2),sk_c6) = sk_c5 ) ),
inference(superposition,[status(thm)],[c_95,c_368]) ).
tcf(c_855,plain,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(inverse(sk_c2),sk_c6) = sk_c5 ) ),
inference(superposition,[status(thm)],[c_94,c_368]) ).
tcf(c_856,plain,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(inverse(sk_c2),sk_c6) = sk_c5 ) ),
inference(superposition,[status(thm)],[c_93,c_368]) ).
tcf(c_858,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_75,c_368]) ).
tcf(c_859,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[status(thm)],[c_76,c_368]) ).
tcf(c_862,plain,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(inverse(sk_c6),identity) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_415,c_368]) ).
tcf(c_863,plain,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(inverse(sk_c6),identity) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_410,c_368]) ).
tcf(c_865,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_368,c_368]) ).
tcf(c_976,plain,
! [X0: $i] :
( ( multiply(sk_c3,sk_c6) = X0 )
| ( X0 != sk_c4 )
| ( multiply(sk_c3,sk_c6) != sk_c4 ) ),
inference(instantiation,[status(thm)],[c_545]) ).
tcf(c_1038,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_75,c_76]) ).
tcf(c_1041,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1038,c_74]) ).
tcf(c_1169,plain,
( ( inverse(sk_c6) = sk_c5 )
| ~ iPr_def_10
| ( inverse(sk_c1) != sk_c6 ) ),
inference(resolution,[status(thm)],[c_214,c_78]) ).
tcf(c_1210,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( sk_c7 != sk_c4 )
| ( multiply(sk_c3,sk_c6) != sk_c4 ) ),
inference(instantiation,[status(thm)],[c_976]) ).
tcf(c_1211,plain,
( ~ iPr_def_10
| ( inverse(sk_c3) != sk_c6 )
| ( multiply(sk_c3,sk_c6) != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_214]) ).
tcf(c_1559,plain,
( ( inverse(sk_c6) = sk_c5 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_1169,c_597]) ).
tcf(c_1608,plain,
! [X0: $i] :
( ( multiply(sk_c6,sk_c7) = X0 )
| ( X0 != sk_c5 ) ),
inference(resolution,[status(thm)],[c_219,c_77]) ).
tcf(c_1609,plain,
( ( multiply(sk_c6,sk_c7) = sk_c6 )
| ( sk_c6 != sk_c5 ) ),
inference(instantiation,[status(thm)],[c_1608]) ).
tcf(c_1618,plain,
! [X0: $i] :
( ( inverse(sk_c6) = X0 )
| ~ iPr_def_10
| ( X0 != sk_c5 ) ),
inference(resolution,[status(thm)],[c_219,c_1559]) ).
tcf(c_1619,plain,
( ( inverse(sk_c6) = sk_c6 )
| ~ iPr_def_10
| ( sk_c6 != sk_c5 ) ),
inference(instantiation,[status(thm)],[c_1618]) ).
tcf(c_1654,plain,
( ~ iPr_def_11
| ( sk_c6 != sk_c7 )
| ( inverse(inverse(sk_c6)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_842,c_215]) ).
tcf(c_1661,plain,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_87,c_843]) ).
tcf(c_1668,plain,
( ( sk_c6 = sk_c5 )
| ( inverse(sk_c3) = sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_1661,c_77]) ).
tcf(c_1701,plain,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c4 )
| ( multiply(sk_c6,sk_c7) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_84,c_844]) ).
tcf(c_1702,plain,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c4 )
| ( multiply(sk_c6,sk_c7) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_83,c_844]) ).
tcf(c_1718,plain,
( ( multiply(sk_c6,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c4 ) ),
inference(global_subsumption_just,[status(thm)],[c_1701,c_91,c_86,c_217,c_585,c_666,c_793,c_1702,c_1701]) ).
tcf(c_1719,plain,
( ( multiply(sk_c3,sk_c6) = sk_c4 )
| ( multiply(sk_c6,sk_c7) = sk_c6 ) ),
inference(renaming,[status(thm)],[c_1718]) ).
tcf(c_1722,plain,
( ( sk_c6 = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c4 ) ),
inference(light_normalisation,[status(thm)],[c_1719,c_77]) ).
tcf(c_1747,plain,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c6,sk_c4) = sk_c5 )
| ( multiply(sk_c6,sk_c7) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_84,c_845]) ).
tcf(c_1748,plain,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(sk_c6,sk_c4) = sk_c5 )
| ( multiply(sk_c6,sk_c7) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_83,c_845]) ).
tcf(c_1764,plain,
( ( multiply(sk_c6,sk_c7) = sk_c6 )
| ( multiply(sk_c6,sk_c4) = sk_c5 ) ),
inference(global_subsumption_just,[status(thm)],[c_1747,c_90,c_85,c_217,c_586,c_667,c_789,c_1748,c_1747]) ).
tcf(c_1765,plain,
( ( multiply(sk_c6,sk_c4) = sk_c5 )
| ( multiply(sk_c6,sk_c7) = sk_c6 ) ),
inference(renaming,[status(thm)],[c_1764]) ).
tcf(c_1768,plain,
( ( sk_c6 = sk_c5 )
| ( multiply(sk_c6,sk_c4) = sk_c5 ) ),
inference(light_normalisation,[status(thm)],[c_1765,c_77]) ).
tcf(c_1906,plain,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c4 )
| ( multiply(sk_c6,sk_c6) = sk_c5 ) ),
inference(superposition,[status(thm)],[c_89,c_853]) ).
tcf(c_1907,plain,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c4 )
| ( multiply(sk_c6,sk_c6) = sk_c5 ) ),
inference(superposition,[status(thm)],[c_88,c_853]) ).
tcf(c_1922,plain,
( ( multiply(sk_c6,sk_c6) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c4 ) ),
inference(global_subsumption_just,[status(thm)],[c_1906,c_91,c_86,c_217,c_585,c_666,c_793,c_1907,c_1906]) ).
tcf(c_1923,plain,
( ( multiply(sk_c3,sk_c6) = sk_c4 )
| ( multiply(sk_c6,sk_c6) = sk_c5 ) ),
inference(renaming,[status(thm)],[c_1922]) ).
tcf(c_1944,plain,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c6,sk_c4) = sk_c5 )
| ( multiply(sk_c6,sk_c6) = sk_c5 ) ),
inference(superposition,[status(thm)],[c_89,c_854]) ).
tcf(c_1945,plain,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(sk_c6,sk_c4) = sk_c5 )
| ( multiply(sk_c6,sk_c6) = sk_c5 ) ),
inference(superposition,[status(thm)],[c_88,c_854]) ).
tcf(c_1960,plain,
( ( multiply(sk_c6,sk_c6) = sk_c5 )
| ( multiply(sk_c6,sk_c4) = sk_c5 ) ),
inference(global_subsumption_just,[status(thm)],[c_1944,c_90,c_85,c_217,c_586,c_667,c_789,c_1945,c_1944]) ).
tcf(c_1961,plain,
( ( multiply(sk_c6,sk_c4) = sk_c5 )
| ( multiply(sk_c6,sk_c6) = sk_c5 ) ),
inference(renaming,[status(thm)],[c_1960]) ).
tcf(c_1987,plain,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c6,sk_c6) = sk_c5 ) ),
inference(superposition,[status(thm)],[c_89,c_855]) ).
tcf(c_2023,plain,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(sk_c6,sk_c6) = sk_c5 ) ),
inference(superposition,[status(thm)],[c_88,c_856]) ).
tcf(c_2165,plain,
( ( sk_c6 = sk_c5 )
| ~ iPr_def_10
| ( sk_c7 != sk_c4 )
| ( inverse(sk_c3) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_1722,c_214]) ).
tcf(c_2166,plain,
( ( sk_c6 = sk_c5 )
| ( multiply(inverse(sk_c3),sk_c4) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_1722,c_368]) ).
tcf(c_2174,plain,
( ( sk_c7 != sk_c4 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_2165,c_605,c_616,c_1210,c_1211]) ).
tcf(c_2175,plain,
( ~ iPr_def_10
| ( sk_c7 != sk_c4 ) ),
inference(renaming,[status(thm)],[c_2174]) ).
tcf(c_2234,plain,
( ( sk_c6 = sk_c5 )
| ( multiply(inverse(sk_c6),sk_c5) = sk_c4 ) ),
inference(superposition,[status(thm)],[c_1768,c_368]) ).
tcf(c_2240,plain,
( ( sk_c7 = sk_c4 )
| ( sk_c6 = sk_c5 ) ),
inference(light_normalisation,[status(thm)],[c_2234,c_842]) ).
tcf(c_2776,plain,
( ( multiply(sk_c3,sk_c6) = sk_c4 )
| ( multiply(inverse(sk_c6),sk_c5) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_1923,c_368]) ).
tcf(c_2787,plain,
( ( sk_c6 = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c4 ) ),
inference(light_normalisation,[status(thm)],[c_2776,c_842]) ).
tcf(c_2834,plain,
( ( multiply(sk_c6,sk_c6) = sk_c5 )
| ( multiply(inverse(sk_c6),sk_c5) = sk_c4 ) ),
inference(superposition,[status(thm)],[c_1961,c_368]) ).
tcf(c_2843,plain,
( ( sk_c7 = sk_c4 )
| ( multiply(sk_c6,sk_c6) = sk_c5 ) ),
inference(light_normalisation,[status(thm)],[c_2834,c_842]) ).
tcf(c_2882,plain,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(inverse(sk_c6),sk_c5) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_1987,c_368]) ).
tcf(c_2893,plain,
( ( sk_c6 = sk_c7 )
| ( inverse(sk_c7) = sk_c5 ) ),
inference(light_normalisation,[status(thm)],[c_2882,c_842]) ).
tcf(c_2931,plain,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(inverse(sk_c6),sk_c5) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_2023,c_368]) ).
tcf(c_2942,plain,
( ( sk_c6 = sk_c7 )
| ( inverse(sk_c6) = sk_c5 ) ),
inference(light_normalisation,[status(thm)],[c_2931,c_842]) ).
tcf(c_2975,plain,
( ( inverse(sk_c7) = sk_c5 )
| ~ iPr_def_11
| ( inverse(sk_c2) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_94,c_215]) ).
tcf(c_2979,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_11
| ( inverse(multiply(X0,X1)) != sk_c6 )
| ( multiply(X0,multiply(X1,sk_c5)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_76,c_215]) ).
tcf(c_2987,plain,
( ( inverse(sk_c7) = sk_c5 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_2975,c_680]) ).
tcf(c_4275,plain,
multiply(inverse(sk_c6),sk_c5) = sk_c7,
inference(superposition,[status(thm)],[c_77,c_1041]) ).
tcf(c_4276,plain,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(inverse(sk_c1),sk_c7) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_82,c_1041]) ).
tcf(c_4549,plain,
( ( sk_c6 = sk_c5 )
| ( multiply(sk_c6,sk_c4) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_1668,c_2166]) ).
tcf(c_4571,plain,
( ( sk_c6 = sk_c5 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_2240,c_2175]) ).
tcf(c_4841,plain,
( ( sk_c6 = sk_c7 )
| ~ iPr_def_12
| ( inverse(sk_c3) != sk_c6 )
| ( multiply(sk_c6,sk_c4) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_2787,c_216]) ).
tcf(c_4854,plain,
( ( sk_c6 = sk_c7 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_4841,c_77,c_87,c_85,c_755,c_749,c_751,c_4841]) ).
tcf(c_4895,plain,
( ( sk_c7 = sk_c4 )
| ~ iPr_def_10
| ( sk_c7 != sk_c5 )
| ( inverse(sk_c6) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_2843,c_214]) ).
tcf(c_4896,plain,
( ( sk_c7 = sk_c4 )
| ( multiply(inverse(sk_c6),sk_c5) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_2843,c_368]) ).
tcf(c_4909,plain,
( ( sk_c7 = sk_c4 )
| ( sk_c6 = sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_4896,c_842]) ).
tcf(c_4926,plain,
( ( sk_c7 != sk_c5 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_4895,c_1619,c_2175,c_4571,c_4895]) ).
tcf(c_4927,plain,
( ~ iPr_def_10
| ( sk_c7 != sk_c5 ) ),
inference(renaming,[status(thm)],[c_4926]) ).
tcf(c_6180,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_858,c_865]) ).
tcf(c_6930,plain,
sk_c6 = sk_c5,
inference(superposition,[status(thm)],[c_4549,c_1768]) ).
tcf(c_7138,plain,
( ( sk_c7 = sk_c4 )
| ( sk_c7 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_4909,c_6930]) ).
tcf(c_7153,plain,
( ( sk_c7 = sk_c5 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_7138,c_2175]) ).
tcf(c_7159,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_7153,c_4927,c_7153]) ).
tcf(c_7225,plain,
( iPr_def_12
| iPr_def_11
| ( inverse(sk_c7) != sk_c5 )
| ( inverse(sk_c6) != sk_c5 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_217,c_7159]) ).
tcf(c_7237,plain,
( iPr_def_12
| iPr_def_11
| ( inverse(sk_c5) != sk_c5 )
| ( inverse(sk_c7) != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_7225,c_6930]) ).
tcf(c_7614,plain,
! [X0: $i] :
( ( inverse(sk_c5) = sk_c5 )
| ( multiply(sk_c5,multiply(sk_c1,X0)) = X0 ) ),
inference(demodulation,[status(thm)],[c_552,c_6930]) ).
tcf(c_7642,plain,
( ( inverse(sk_c5) = sk_c5 )
| ( multiply(sk_c5,sk_c1) = identity ) ),
inference(superposition,[status(thm)],[c_6180,c_7614]) ).
tcf(c_8237,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c6)),multiply(X0,sk_c5)) = sk_c7,
inference(superposition,[status(thm)],[c_77,c_859]) ).
tcf(c_8247,plain,
! [X0: $i] :
( ( inverse(sk_c1) = sk_c6 )
| ( multiply(inverse(multiply(X0,sk_c6)),multiply(X0,sk_c5)) = sk_c4 ) ),
inference(superposition,[status(thm)],[c_85,c_859]) ).
tcf(c_8363,plain,
sk_c7 = identity,
inference(demodulation,[status(thm)],[c_8237,c_75,c_6930]) ).
tcf(c_8574,plain,
( ( sk_c4 = identity )
| ( inverse(sk_c1) = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_8247,c_75,c_6930]) ).
tcf(c_10289,plain,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_87,c_4276]) ).
tcf(c_10294,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(global_subsumption_just,[status(thm)],[c_10289,c_1609,c_6930]) ).
tcf(c_10296,plain,
sk_c6 = sk_c5,
inference(light_normalisation,[status(thm)],[c_10294,c_77]) ).
tcf(c_11374,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm)],[c_10296,c_4275]) ).
tcf(c_11390,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c5) != sk_c5 )
| ( inverse(sk_c7) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_10296,c_217]) ).
tcf(c_11401,plain,
sk_c7 = identity,
inference(demodulation,[status(thm)],[c_11374,c_75]) ).
tcf(c_11437,plain,
( iPr_def_12
| iPr_def_11
| ( inverse(sk_c7) != sk_c5 )
| ( inverse(sk_c5) != sk_c5 ) ),
inference(global_subsumption_just,[status(thm)],[c_11390,c_7159,c_11390]) ).
tcf(c_11438,plain,
( iPr_def_12
| iPr_def_11
| ( inverse(sk_c5) != sk_c5 )
| ( inverse(sk_c7) != sk_c5 ) ),
inference(renaming,[status(thm)],[c_11437]) ).
tcf(c_11651,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_11
| ( inverse(multiply(X0,X1)) != sk_c5 )
| ( multiply(X0,multiply(X1,sk_c5)) != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_2979,c_10296]) ).
tcf(c_11656,plain,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(multiply(inverse(X0),X0)) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_1041,c_11651]) ).
tcf(c_11681,plain,
( ~ iPr_def_11
| ( inverse(identity) != sk_c5 ) ),
inference(light_normalisation,[status(thm)],[c_11656,c_75]) ).
tcf(c_11682,plain,
( ~ iPr_def_11
| ( inverse(sk_c7) != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_11681,c_11401]) ).
tcf(c_11685,plain,
~ iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_11682,c_2987]) ).
tcf(c_11716,plain,
( iPr_def_12
| ( inverse(sk_c5) != sk_c5 )
| ( inverse(sk_c7) != sk_c5 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_11438,c_11685]) ).
tcf(c_12884,plain,
( ( sk_c6 = sk_c7 )
| ( inverse(sk_c5) = sk_c5 ) ),
inference(superposition,[status(thm)],[c_6930,c_2942]) ).
tcf(c_12910,plain,
( ~ iPr_def_11
| ( sk_c6 != sk_c7 )
| ( inverse(inverse(sk_c5)) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_6930,c_1654]) ).
tcf(c_12921,plain,
( ~ iPr_def_12
| ( inverse(inverse(sk_c5)) != sk_c5 )
| ( multiply(sk_c6,identity) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_6930,c_757]) ).
tcf(c_12940,plain,
sk_c6 = sk_c7,
inference(global_subsumption_just,[status(thm)],[c_12884,c_4854,c_2893,c_11716,c_12884]) ).
tcf(c_12942,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm)],[c_12940,c_6930]) ).
tcf(c_13024,plain,
( ~ iPr_def_11
| ( inverse(inverse(sk_c5)) != sk_c5 ) ),
inference(global_subsumption_just,[status(thm)],[c_12910,c_4854,c_2893,c_11716,c_12884,c_12910]) ).
tcf(c_13064,plain,
( ~ iPr_def_12
| ( inverse(inverse(sk_c5)) != sk_c5 )
| ( multiply(sk_c5,identity) != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_12921,c_6930]) ).
tcf(c_13068,plain,
( ~ iPr_def_12
| ( inverse(inverse(sk_c5)) != sk_c5 ) ),
inference(ground_joinability,[status(thm)],[c_13064,c_6180]) ).
tcf(c_13176,plain,
( iPr_def_12
| iPr_def_11
| ( inverse(sk_c5) != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_7237,c_12942]) ).
tcf(c_13971,plain,
! [X0: $i] : multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_865,c_6180]) ).
tcf(c_13975,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_13971,c_6180]) ).
tcf(c_14020,plain,
~ iPr_def_11,
inference(backward_subsumption_resolution,[status(thm)],[c_13024,c_13975]) ).
tcf(c_14021,plain,
~ iPr_def_12,
inference(backward_subsumption_resolution,[status(thm)],[c_13068,c_13975]) ).
tcf(c_14044,plain,
sk_c5 = identity,
inference(demodulation,[status(thm)],[c_8363,c_12942]) ).
tcf(c_14045,plain,
! [X0: $i] : multiply(X0,sk_c5) = X0,
inference(superposition,[status(thm)],[c_14044,c_6180]) ).
tcf(c_14056,plain,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(inverse(sk_c6),sk_c5) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_14044,c_863]) ).
tcf(c_14057,plain,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(inverse(sk_c6),sk_c5) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_14044,c_862]) ).
tcf(c_14059,plain,
! [X0: $i] : multiply(sk_c5,X0) = X0,
inference(superposition,[status(thm)],[c_14044,c_74]) ).
tcf(c_14065,plain,
multiply(inverse(sk_c6),sk_c5) = sk_c1,
inference(global_subsumption_just,[status(thm)],[c_14056,c_217,c_7159,c_14020,c_14021,c_14057,c_14056]) ).
tcf(c_14067,plain,
inverse(sk_c6) = sk_c1,
inference(demodulation,[status(thm)],[c_14065,c_14045]) ).
tcf(c_14068,plain,
inverse(sk_c5) = sk_c1,
inference(light_normalisation,[status(thm)],[c_14067,c_6930]) ).
tcf(c_14096,plain,
( ( sk_c5 = sk_c4 )
| ( inverse(sk_c1) = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_8574,c_14044]) ).
tcf(c_14117,plain,
( ( sk_c5 = sk_c4 )
| ( multiply(sk_c5,sk_c1) = identity ) ),
inference(superposition,[status(thm)],[c_14096,c_75]) ).
tcf(c_14118,plain,
multiply(sk_c5,sk_c1) = identity,
inference(global_subsumption_just,[status(thm)],[c_14117,c_7642,c_13176,c_14020,c_14021]) ).
tcf(c_14120,plain,
multiply(sk_c5,sk_c1) = sk_c5,
inference(light_normalisation,[status(thm)],[c_14118,c_14044]) ).
tcf(c_14121,plain,
sk_c5 = sk_c1,
inference(demodulation,[status(thm)],[c_14120,c_14059]) ).
tcf(c_14217,plain,
inverse(sk_c5) = sk_c5,
inference(demodulation,[status(thm)],[c_14068,c_14121]) ).
tcf(c_14218,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_14217,c_14021,c_14020,c_13176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP334-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n018.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 14:32:02 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 7.01/1.75 % SZS status Started for theBenchmark.p
% 7.01/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 7.01/1.75
% 7.01/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.01/1.75
% 7.01/1.75 % ------ iProver source info
% 7.01/1.75
% 7.01/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 7.01/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.01/1.75 % git: non_committed_changes: false
% 7.01/1.75
% 7.01/1.75 % ------ Parsing...% successful
% 7.01/1.75
% 7.01/1.75
% 7.01/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.01/1.75
% 7.01/1.75 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 7.01/1.75
% 7.01/1.75 % ------ Preprocessing... gs_s sp: 3 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.01/1.75
% 7.01/1.75 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 7.01/1.75 % ------ Proving...
% 7.01/1.75 % ------ Problem Properties
% 7.01/1.75
% 7.01/1.75 %
% 7.01/1.75 % clauses 28
% 7.01/1.75 % conjectures 25
% 7.01/1.75 % EPR 0
% 7.01/1.75 % Horn 7
% 7.01/1.75 % unary 4
% 7.01/1.75 % binary 20
% 7.01/1.75 % lits 58
% 7.01/1.75 % lits eq 52
% 7.01/1.75 % fd_pure 0
% 7.01/1.75 % fd_pseudo 0
% 7.01/1.75 % fd_cond 0
% 7.01/1.75 % fd_pseudo_cond 0
% 7.01/1.75 % AC symbols 0
% 7.01/1.75
% 7.01/1.75 % ------ Input Options Time Limit: Unbounded
% 7.01/1.75
% 7.01/1.75
% 7.01/1.75 % ------
% 7.01/1.75 % Current options:
% 7.01/1.75 % ------
% 7.01/1.75
% 7.01/1.75
% 7.01/1.75 %
% 7.01/1.75
% 7.01/1.75 % ------ Proving...
% 7.01/1.75 %
% 7.01/1.75
% 7.01/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 7.01/1.75
% 7.01/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.01/1.76
% 7.01/1.76
%------------------------------------------------------------------------------