%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP234-1 : 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 : n005.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 01:32:04 PM UTC 2026
% Result : Unsatisfiable 1.38s 1.75s
% Output : CNFRefutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 35
% Syntax : Number of formulae : 307 ( 78 unt; 9 def)
% Number of atoms : 1081 ( 555 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 553 ( 204 ~; 349 |; 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 : 15 ( 13 usr; 14 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn 85 !; 0 ?; 65 :)
% 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,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c7 = inverse(sk_c3)
| inverse(sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| inverse(sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| inverse(sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c5 = multiply(sk_c4,sk_c7)
| inverse(sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c7 = inverse(sk_c4)
| inverse(sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,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_7) ).
fof(f18,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c5 = multiply(sk_c4,sk_c7)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = inverse(sk_c4)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c5 = multiply(sk_c4,sk_c7)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c4)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c5 = multiply(sk_c4,sk_c7)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = inverse(sk_c4)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(X4) != sk_c7
| multiply(X4,sk_c7) != X3
| multiply(sk_c7,X3) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| multiply(X0,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
! [X2,X3,X0,X1,X4] :
( sk_c7 != inverse(X4)
| multiply(X4,sk_c7) != X3
| sk_c6 != multiply(sk_c7,X3)
| sk_c7 != multiply(X2,sk_c6)
| sk_c7 != inverse(X2)
| sk_c7 != inverse(X1)
| sk_c6 != multiply(X1,sk_c7)
| sk_c6 != multiply(X0,sk_c7)
| inverse(sk_c7) != sk_c6 ),
inference(reorient_equations,[],[f45]) ).
fof(f47,plain,
! [X2,X0,X1,X4] :
( sk_c7 != inverse(X4)
| sk_c6 != multiply(sk_c7,multiply(X4,sk_c7))
| sk_c7 != multiply(X2,sk_c6)
| sk_c7 != inverse(X2)
| sk_c7 != inverse(X1)
| sk_c6 != multiply(X1,sk_c7)
| sk_c6 != multiply(X0,sk_c7)
| inverse(sk_c7) != sk_c6 ),
inference(equality_resolution,[],[f46]) ).
tcf(c_73,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_74,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_76,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_77,negated_conjecture,
( ( inverse(sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_78,negated_conjecture,
( ( inverse(sk_c7) = sk_c6 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_79,negated_conjecture,
( ( inverse(sk_c7) = sk_c6 )
| ( multiply(sk_c4,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_80,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( inverse(sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_81,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_82,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_83,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_84,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c4,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_85,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_86,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c2,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_87,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_88,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c6 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_89,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c6 )
| ( multiply(sk_c4,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c2,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c4) = sk_c7 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_96,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(sk_c7) != sk_c6 )
| ( inverse(X2) != sk_c7 )
| ( inverse(X1) != sk_c7 )
| ( inverse(X0) != sk_c7 )
| ( multiply(X3,sk_c7) != sk_c6 )
| ( multiply(X2,sk_c7) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c7 )
| ( multiply(sk_c7,multiply(X1,sk_c7)) != sk_c6 ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_301,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_96]) ).
tcf(c_302,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_96]) ).
tcf(c_303,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_96]) ).
tcf(c_304,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_96]) ).
tcf(c_305,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_96]) ).
tcf(c_306,definition,
iPr_def_14 = inverse(sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_307,definition,
iPr_def_15 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_308,definition,
iPr_def_16 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_309,definition,
iPr_def_17 = multiply(sk_c4,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_310,definition,
iPr_def_18 = multiply(sk_c7,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_311,definition,
iPr_def_19 = multiply(sk_c3,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_312,definition,
iPr_def_20 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_313,definition,
iPr_def_21 = multiply(sk_c2,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_314,definition,
iPr_def_22 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_315,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_14 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_305,c_306]) ).
tcf(c_316,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_304]) ).
tcf(c_317,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_303]) ).
tcf(c_318,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_302]) ).
tcf(c_319,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_301]) ).
tcf(c_320,negated_conjecture,
( ( iPr_def_16 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_95,c_308,c_307]) ).
tcf(c_321,negated_conjecture,
( ( iPr_def_17 = sk_c5 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_94,c_309]) ).
tcf(c_322,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_93,c_310]) ).
tcf(c_323,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_92,c_311]) ).
tcf(c_324,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_91,c_312]) ).
tcf(c_325,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_90,c_313]) ).
tcf(c_326,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_327,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_328,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_329,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_330,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_85,c_314]) ).
tcf(c_331,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_332,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_333,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_334,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_335,negated_conjecture,
( ( iPr_def_15 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_336,negated_conjecture,
( ( iPr_def_17 = sk_c5 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_337,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_338,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_339,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_340,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_341,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_580,plain,
( ( sk_c6 = iPr_def_21 )
| ( multiply(sk_c7,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_326,c_310]) ).
tcf(c_592,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(sk_c3,iPr_def_21) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_327,c_311]) ).
tcf(c_593,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c3,iPr_def_21) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_325,c_311]) ).
tcf(c_594,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c3,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_322,c_311]) ).
tcf(c_601,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_324,c_313]) ).
tcf(c_602,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_19) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_323,c_313]) ).
tcf(c_615,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c3,iPr_def_21) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_328,c_311]) ).
tcf(c_627,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c3,iPr_def_21) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_329,c_311]) ).
tcf(c_684,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( sk_c6 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_332,c_327]) ).
tcf(c_694,plain,
! [X0: $i] :
( ( iPr_def_14 = sk_c6 )
| ( iPr_def_14 != X0 )
| ( sk_c6 != X0 ) ),
inference(instantiation,[status(thm)],[c_341]) ).
tcf(c_722,plain,
! [X0: $i,X1: $i] :
( ( sk_c6 = X0 )
| ( sk_c6 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_341]) ).
tcf(c_723,plain,
! [X0: $i] :
( ( sk_c6 = X0 )
| ( sk_c6 != sk_c6 )
| ( X0 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_722]) ).
tcf(c_724,plain,
sk_c6 = sk_c6,
inference(instantiation,[status(thm)],[c_340]) ).
tcf(c_732,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c6 )
| ( sk_c6 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_341]) ).
tcf(c_734,plain,
( ( sk_c6 = iPr_def_18 )
| ( iPr_def_18 != sk_c6 )
| ( sk_c6 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_723]) ).
tcf(c_773,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c6 = iPr_def_18 )
| ( sk_c7 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_335,c_332]) ).
tcf(c_778,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( sk_c6 = iPr_def_18 )
| ( sk_c7 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_335,c_327]) ).
tcf(c_779,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( sk_c7 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_335,c_325]) ).
tcf(c_833,plain,
multiply(iPr_def_14,sk_c7) = identity,
inference(superposition,[status(thm)],[c_306,c_74]) ).
tcf(c_834,plain,
multiply(iPr_def_20,sk_c3) = identity,
inference(superposition,[status(thm)],[c_312,c_74]) ).
tcf(c_835,plain,
multiply(iPr_def_15,sk_c4) = identity,
inference(superposition,[status(thm)],[c_307,c_74]) ).
tcf(c_836,plain,
multiply(iPr_def_16,sk_c2) = identity,
inference(superposition,[status(thm)],[c_308,c_74]) ).
tcf(c_849,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(sk_c7,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_336,c_310]) ).
tcf(c_872,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(sk_c3,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_337,c_311]) ).
tcf(c_940,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( sk_c7 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_338,c_328]) ).
tcf(c_987,plain,
iPr_def_14 = iPr_def_14,
inference(instantiation,[status(thm)],[c_340]) ).
tcf(c_988,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_14 = X0 )
| ( iPr_def_14 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_341]) ).
tcf(c_1014,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_339,c_334]) ).
tcf(c_1018,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_339,c_329]) ).
tcf(c_1061,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_339,c_315]) ).
tcf(c_1062,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_338,c_315]) ).
tcf(c_1064,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_335,c_315]) ).
tcf(c_1123,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_314,c_319]) ).
tcf(c_1124,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_313,c_319]) ).
tcf(c_1179,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_17 )
| ( inverse(sk_c4) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_309,c_317]) ).
tcf(c_1181,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_21 )
| ( inverse(sk_c2) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_313,c_317]) ).
tcf(c_1182,plain,
( ~ iPr_def_12
| ( sk_c7 != sk_c6 )
| ( inverse(identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_73,c_317]) ).
tcf(c_1184,plain,
( ~ iPr_def_12
| ( sk_c6 != identity )
| ( inverse(iPr_def_14) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_833,c_317]) ).
tcf(c_1194,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_21 )
| ( sk_c7 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_1181,c_308]) ).
tcf(c_1201,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_17 )
| ( sk_c7 != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_1179,c_307]) ).
tcf(c_1243,plain,
( ~ iPr_def_11
| ( sk_c7 != sk_c6 )
| ( inverse(identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_73,c_318]) ).
tcf(c_1244,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( inverse(inverse(sk_c6)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_74,c_318]) ).
tcf(c_1340,plain,
! [X0: $i] :
( ( X0 = sk_c6 )
| ( sk_c6 != iPr_def_21 )
| ( X0 != iPr_def_21 ) ),
inference(instantiation,[status(thm)],[c_732]) ).
tcf(c_1370,plain,
( ( iPr_def_14 = sk_c6 )
| ( iPr_def_14 != iPr_def_22 )
| ( sk_c6 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_694]) ).
tcf(c_1371,plain,
! [X0: $i] :
( ( X0 = sk_c6 )
| ( sk_c6 != iPr_def_22 )
| ( X0 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_732]) ).
tcf(c_1410,plain,
( ~ iPr_def_13
| ( inverse(sk_c4) != sk_c7 )
| ( multiply(sk_c7,iPr_def_17) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_309,c_316]) ).
tcf(c_1415,plain,
( ~ iPr_def_13
| ( inverse(iPr_def_14) != sk_c7 )
| ( multiply(sk_c7,identity) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_833,c_316]) ).
tcf(c_1432,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_15 )
| ( multiply(sk_c7,iPr_def_17) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_1410,c_307]) ).
tcf(c_1453,plain,
( ( iPr_def_14 = sk_c6 )
| ( iPr_def_14 != iPr_def_14 )
| ( sk_c6 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_694]) ).
tcf(c_1584,plain,
( ( sk_c7 = iPr_def_20 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_334,c_1123]) ).
tcf(c_1585,plain,
( ( sk_c7 = iPr_def_19 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_333,c_1123]) ).
tcf(c_1586,plain,
( ( sk_c6 = iPr_def_18 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_332,c_1123]) ).
tcf(c_1587,plain,
( ( sk_c7 = iPr_def_15 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_330,c_1123]) ).
tcf(c_1632,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_74,c_75]) ).
tcf(c_1634,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c7,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_833,c_75]) ).
tcf(c_1635,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_834,c_75]) ).
tcf(c_1636,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_835,c_75]) ).
tcf(c_1637,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_836,c_75]) ).
tcf(c_1640,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_10
| ( multiply(X0,multiply(X1,sk_c7)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_75,c_319]) ).
tcf(c_1643,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1637,c_73]) ).
tcf(c_1644,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1636,c_73]) ).
tcf(c_1645,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1635,c_73]) ).
tcf(c_1646,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c7,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1634,c_73]) ).
tcf(c_1678,plain,
! [X0: $i] :
( ( iPr_def_14 = X0 )
| ( iPr_def_14 != sk_c6 )
| ( X0 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_988]) ).
tcf(c_2556,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( iPr_def_21 != sk_c6 )
| ( iPr_def_14 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_1678]) ).
tcf(c_2557,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( iPr_def_22 != sk_c6 )
| ( iPr_def_14 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_1678]) ).
tcf(c_2587,plain,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_21 != iPr_def_21 )
| ( sk_c6 != iPr_def_21 ) ),
inference(instantiation,[status(thm)],[c_1340]) ).
tcf(c_2588,plain,
iPr_def_21 = iPr_def_21,
inference(instantiation,[status(thm)],[c_340]) ).
tcf(c_2688,plain,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_22 != iPr_def_22 )
| ( sk_c6 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_1371]) ).
tcf(c_2689,plain,
iPr_def_22 = iPr_def_22,
inference(instantiation,[status(thm)],[c_340]) ).
tcf(c_2929,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( inverse(iPr_def_20) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1014,c_306]) ).
tcf(c_3010,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1018,c_940]) ).
tcf(c_3013,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1018,c_779]) ).
tcf(c_3027,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( inverse(iPr_def_20) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1018,c_306]) ).
tcf(c_3074,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( sk_c7 = iPr_def_20 ) ),
inference(global_subsumption_just,[status(thm)],[c_1061,c_1061,c_1584]) ).
tcf(c_3108,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( sk_c7 = iPr_def_19 ) ),
inference(global_subsumption_just,[status(thm)],[c_1062,c_1062,c_1585]) ).
tcf(c_3118,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( sk_c7 = iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_1064,c_1064,c_1587]) ).
tcf(c_3128,plain,
multiply(iPr_def_16,iPr_def_21) = sk_c7,
inference(superposition,[status(thm)],[c_313,c_1643]) ).
tcf(c_3131,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_21,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_3128,c_75]) ).
tcf(c_3287,plain,
multiply(iPr_def_15,iPr_def_17) = sk_c7,
inference(superposition,[status(thm)],[c_309,c_1644]) ).
tcf(c_3303,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(iPr_def_17,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_3287,c_75]) ).
tcf(c_3323,plain,
multiply(iPr_def_20,iPr_def_19) = sk_c6,
inference(superposition,[status(thm)],[c_311,c_1645]) ).
tcf(c_3328,plain,
multiply(iPr_def_14,iPr_def_18) = sk_c5,
inference(superposition,[status(thm)],[c_310,c_1646]) ).
tcf(c_3344,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_14,multiply(iPr_def_16,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_320,c_1646]) ).
tcf(c_3474,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_18,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_3328,c_75]) ).
tcf(c_3658,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_592,c_1645]) ).
tcf(c_3659,plain,
( ( sk_c6 = iPr_def_21 )
| ( sk_c6 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_3658,c_3323]) ).
tcf(c_3699,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_593,c_1645]) ).
tcf(c_3700,plain,
( ( sk_c6 = iPr_def_21 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_3699,c_3323]) ).
tcf(c_3711,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_594,c_1645]) ).
tcf(c_3712,plain,
( ( sk_c6 = iPr_def_18 )
| ( sk_c7 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_3711,c_3323]) ).
tcf(c_3723,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_601,c_1643]) ).
tcf(c_3724,plain,
( ( sk_c7 = iPr_def_20 )
| ( sk_c7 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_3723,c_3128]) ).
tcf(c_3735,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_602,c_1643]) ).
tcf(c_3736,plain,
( ( sk_c7 = iPr_def_19 )
| ( sk_c7 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_3735,c_3128]) ).
tcf(c_3816,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_615,c_1645]) ).
tcf(c_3817,plain,
( ( sk_c6 = iPr_def_21 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_3816,c_3323]) ).
tcf(c_3829,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_627,c_1645]) ).
tcf(c_3830,plain,
( ( sk_c6 = iPr_def_21 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_3829,c_3323]) ).
tcf(c_4091,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_16,iPr_def_14) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_3010,c_3128]) ).
tcf(c_4109,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( multiply(iPr_def_16,iPr_def_14) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_3013,c_3128]) ).
tcf(c_5356,plain,
! [X0: $i] :
( ~ iPr_def_10
| ( multiply(X0,iPr_def_17) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_309,c_1640]) ).
tcf(c_5357,plain,
! [X0: $i] :
( ~ iPr_def_10
| ( multiply(X0,iPr_def_22) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_314,c_1640]) ).
tcf(c_5702,plain,
( ( sk_c6 = iPr_def_21 )
| ~ iPr_def_10
| ( sk_c6 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_580,c_5356]) ).
tcf(c_5766,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_5357,c_1124,c_1586,c_5702]) ).
tcf(c_5768,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( sk_c6 != iPr_def_14 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_315,c_5766]) ).
tcf(c_5791,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( sk_c6 = iPr_def_14 )
| ( iPr_def_14 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_337,c_5768]) ).
tcf(c_6154,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c6 = iPr_def_18 ) ),
inference(global_subsumption_just,[status(thm)],[c_773,c_332,c_337,c_724,c_734,c_2557]) ).
tcf(c_6205,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_6154,c_311]) ).
tcf(c_6236,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( sk_c6 = iPr_def_18 ) ),
inference(global_subsumption_just,[status(thm)],[c_778,c_327,c_337,c_724,c_734,c_2556]) ).
tcf(c_6287,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( multiply(sk_c3,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_6236,c_311]) ).
tcf(c_6410,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1632,c_73]) ).
tcf(c_6428,plain,
multiply(inverse(sk_c3),iPr_def_19) = sk_c6,
inference(superposition,[status(thm)],[c_311,c_6410]) ).
tcf(c_6433,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_73,c_6410]) ).
tcf(c_6434,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_74,c_6410]) ).
tcf(c_6451,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(inverse(sk_c3),iPr_def_19) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_593,c_6410]) ).
tcf(c_6452,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(inverse(sk_c3),iPr_def_19) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_592,c_6410]) ).
tcf(c_6487,plain,
! [X0: $i] : multiply(inverse(iPr_def_14),X0) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_1646,c_6410]) ).
tcf(c_6488,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_1645,c_6410]) ).
tcf(c_6489,plain,
! [X0: $i] : multiply(inverse(iPr_def_15),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_1644,c_6410]) ).
tcf(c_6490,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_1643,c_6410]) ).
tcf(c_6504,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_6410,c_6410]) ).
tcf(c_6790,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_6434,c_6504]) ).
tcf(c_6807,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_6790,c_6433]) ).
tcf(c_6993,plain,
multiply(sk_c7,iPr_def_14) = identity,
inference(superposition,[status(thm)],[c_6487,c_74]) ).
tcf(c_6996,plain,
( ~ iPr_def_11
| ( multiply(sk_c7,sk_c6) != sk_c7 )
| ( inverse(inverse(iPr_def_14)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_6487,c_318]) ).
tcf(c_6997,plain,
! [X0: $i] : multiply(sk_c7,multiply(iPr_def_14,X0)) = X0,
inference(superposition,[status(thm)],[c_6487,c_6410]) ).
tcf(c_6998,plain,
multiply(sk_c7,identity) = inverse(iPr_def_14),
inference(superposition,[status(thm)],[c_6487,c_6790]) ).
tcf(c_7096,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(superposition,[status(thm)],[c_6993,c_1646]) ).
tcf(c_7178,plain,
inverse(iPr_def_14) = sk_c7,
inference(demodulation,[status(thm)],[c_6998,c_6790]) ).
tcf(c_7198,plain,
multiply(sk_c7,identity) = sk_c7,
inference(superposition,[status(thm)],[c_833,c_6997]) ).
tcf(c_7204,plain,
multiply(sk_c7,sk_c5) = iPr_def_18,
inference(superposition,[status(thm)],[c_3328,c_6997]) ).
tcf(c_7209,plain,
( ~ iPr_def_13
| ( sk_c7 != sk_c6 )
| ( inverse(iPr_def_14) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_6997,c_316]) ).
tcf(c_7250,plain,
( ~ iPr_def_13
| ( sk_c7 != sk_c6 ) ),
inference(ground_joinability,[status(thm)],[c_7209,c_7178]) ).
tcf(c_7413,plain,
( ( sk_c6 = iPr_def_18 )
| ~ iPr_def_13
| ( sk_c7 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_327,c_7250]) ).
tcf(c_8527,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_14,sk_c7) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_3128,c_3344]) ).
tcf(c_8533,plain,
( ( identity = iPr_def_21 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_8527,c_833]) ).
tcf(c_8548,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( iPr_def_14 != iPr_def_18 ) ),
inference(global_subsumption_just,[status(thm)],[c_5791,c_5768,c_5791]) ).
tcf(c_9099,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_20)) != sk_c7 )
| ( multiply(sk_c7,multiply(sk_c3,sk_c7)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_6488,c_316]) ).
tcf(c_9101,plain,
multiply(sk_c3,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_6488,c_74]) ).
tcf(c_9104,plain,
( ~ iPr_def_11
| ( multiply(sk_c3,sk_c6) != sk_c7 )
| ( inverse(inverse(iPr_def_20)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_6488,c_318]) ).
tcf(c_9105,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_6488,c_6410]) ).
tcf(c_9106,plain,
multiply(sk_c3,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_6488,c_6790]) ).
tcf(c_9150,plain,
inverse(iPr_def_20) = sk_c3,
inference(demodulation,[status(thm)],[c_9106,c_6790]) ).
tcf(c_9152,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( sk_c3 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_3027,c_9150]) ).
tcf(c_9153,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c3 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_2929,c_9150]) ).
tcf(c_9923,plain,
multiply(sk_c7,identity) = multiply(iPr_def_16,iPr_def_21),
inference(superposition,[status(thm)],[c_6790,c_3131]) ).
tcf(c_9959,plain,
multiply(sk_c7,identity) = multiply(iPr_def_15,iPr_def_17),
inference(superposition,[status(thm)],[c_6790,c_3303]) ).
tcf(c_9974,plain,
multiply(sk_c3,sk_c6) = iPr_def_19,
inference(superposition,[status(thm)],[c_3323,c_9105]) ).
tcf(c_10217,plain,
( ~ iPr_def_12
| ( sk_c7 != identity )
| ( sk_c7 != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_1182,c_6807]) ).
tcf(c_10361,plain,
( ~ iPr_def_12
| ( sk_c6 != identity ) ),
inference(ground_joinability,[status(thm)],[c_1184,c_7178]) ).
tcf(c_10384,plain,
( ( sk_c7 = iPr_def_20 )
| ~ iPr_def_12
| ( identity != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_339,c_10361]) ).
tcf(c_10385,plain,
( ( sk_c7 = iPr_def_19 )
| ~ iPr_def_12
| ( identity != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_338,c_10361]) ).
tcf(c_10387,plain,
( ( sk_c7 = iPr_def_15 )
| ~ iPr_def_12
| ( identity != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_335,c_10361]) ).
tcf(c_10390,plain,
( ( sk_c6 = iPr_def_18 )
| ~ iPr_def_12
| ( identity != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_332,c_10361]) ).
tcf(c_10395,plain,
( ( sk_c7 = iPr_def_15 )
| ~ iPr_def_12
| ( identity != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_325,c_10361]) ).
tcf(c_10531,plain,
multiply(sk_c5,identity) = multiply(iPr_def_14,iPr_def_18),
inference(superposition,[status(thm)],[c_6790,c_3474]) ).
tcf(c_10538,plain,
multiply(sk_c5,identity) = sk_c5,
inference(light_normalisation,[status(thm)],[c_10531,c_3328]) ).
tcf(c_10545,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(iPr_def_14,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_9153,c_6205]) ).
tcf(c_10551,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c5 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_10545,c_3328]) ).
tcf(c_10564,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( multiply(iPr_def_14,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_9152,c_6287]) ).
tcf(c_10569,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( sk_c5 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_10564,c_3328]) ).
tcf(c_10679,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_22 )
| ( sk_c6 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_10551,c_336]) ).
tcf(c_10680,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_22 )
| ( sk_c6 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_10551,c_331]) ).
tcf(c_10803,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_21 )
| ( sk_c6 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_10569,c_336]) ).
tcf(c_10804,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_21 )
| ( sk_c6 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_10569,c_331]) ).
tcf(c_10806,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_21 )
| ( sk_c6 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_10569,c_326]) ).
tcf(c_10872,plain,
( ( sk_c7 = iPr_def_20 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_10384,c_1194,c_3724,c_3830]) ).
tcf(c_10878,plain,
( iPr_def_13
| iPr_def_11
| ( sk_c7 = iPr_def_20 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3074,c_10872]) ).
tcf(c_10882,plain,
( ( sk_c7 = iPr_def_19 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_10385,c_1194,c_3736,c_3817]) ).
tcf(c_10888,plain,
( iPr_def_13
| iPr_def_11
| ( sk_c7 = iPr_def_19 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3108,c_10882]) ).
tcf(c_10898,plain,
( ( sk_c7 = iPr_def_15 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_10387,c_8533,c_10395]) ).
tcf(c_10904,plain,
( iPr_def_13
| iPr_def_11
| ( sk_c7 = iPr_def_15 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3118,c_10898]) ).
tcf(c_10912,plain,
( ( sk_c6 = iPr_def_18 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_10390,c_1194,c_3659,c_3712]) ).
tcf(c_11386,plain,
multiply(sk_c4,iPr_def_15) = identity,
inference(superposition,[status(thm)],[c_6489,c_74]) ).
tcf(c_11390,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_15,X0)) = X0,
inference(superposition,[status(thm)],[c_6489,c_6410]) ).
tcf(c_11505,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_22 ) ),
inference(global_subsumption_just,[status(thm)],[c_10679,c_987,c_1453,c_2557,c_2688,c_2689,c_10680,c_10679]) ).
tcf(c_11743,plain,
multiply(sk_c4,sk_c7) = iPr_def_17,
inference(superposition,[status(thm)],[c_3287,c_11390]) ).
tcf(c_11850,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_21 ) ),
inference(global_subsumption_just,[status(thm)],[c_10803,c_1370,c_2556,c_2587,c_2588,c_10806,c_10804,c_11505]) ).
tcf(c_11864,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( multiply(iPr_def_16,iPr_def_14) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_11850,c_3128]) ).
tcf(c_12756,plain,
( ~ iPr_def_12
| ( multiply(sk_c2,sk_c7) != sk_c6 )
| ( inverse(inverse(iPr_def_16)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_6490,c_317]) ).
tcf(c_12757,plain,
multiply(sk_c2,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_6490,c_74]) ).
tcf(c_12760,plain,
( ~ iPr_def_11
| ( multiply(sk_c2,sk_c6) != sk_c7 )
| ( inverse(inverse(iPr_def_16)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_6490,c_318]) ).
tcf(c_12761,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_6490,c_6410]) ).
tcf(c_12762,plain,
multiply(sk_c2,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_6490,c_6790]) ).
tcf(c_12770,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_21 )
| ( inverse(inverse(iPr_def_16)) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_12756,c_313]) ).
tcf(c_12819,plain,
inverse(iPr_def_16) = sk_c2,
inference(demodulation,[status(thm)],[c_12762,c_6790]) ).
tcf(c_12836,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( sk_c7 != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_1243,c_6807]) ).
tcf(c_13211,plain,
multiply(sk_c2,sk_c7) = iPr_def_21,
inference(superposition,[status(thm)],[c_3128,c_12761]) ).
tcf(c_13384,plain,
( ( iPr_def_14 = iPr_def_22 )
| ~ iPr_def_11
| ( sk_c7 != identity )
| ( inverse(inverse(iPr_def_18)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_6154,c_1244]) ).
tcf(c_13398,plain,
( ( iPr_def_21 = iPr_def_22 )
| ~ iPr_def_11
| ( sk_c7 != identity )
| ( inverse(inverse(iPr_def_18)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_684,c_1244]) ).
tcf(c_14364,plain,
( ~ iPr_def_13
| ( multiply(sk_c7,identity) != sk_c6 ) ),
inference(ground_joinability,[status(thm)],[c_1415,c_7178]) ).
tcf(c_17467,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_14 )
| ( multiply(sk_c7,sk_c6) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_6996,c_306,c_7178]) ).
tcf(c_17527,plain,
( ( sk_c7 = iPr_def_15 )
| ~ iPr_def_11
| ( sk_c7 != iPr_def_14 )
| ( multiply(sk_c7,iPr_def_21) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_325,c_17467]) ).
tcf(c_19189,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_17527,c_14364,c_13398,c_13384,c_13211,c_12836,c_12819,c_12770,c_12760,c_12757,c_11864,c_11743,c_11386,c_10912,c_10904,c_10898,c_10888,c_10878,c_10538,c_10531,c_10217,c_9974,c_9959,c_9923,c_9150,c_9104,c_9099,c_9101,c_8548,c_7413,c_7204,c_7198,c_7178,c_7096,c_6993,c_6807,c_6452,c_6451,c_6428,c_5768,c_4109,c_4091,c_3700,c_1432,c_1201,c_872,c_849,c_833,c_580,c_339,c_338,c_337,c_336,c_335,c_326,c_324,c_323,c_322,c_321,c_320,c_312,c_308,c_306]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP234-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n005.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Wed Sep 23 14:13:02 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.43 % Proving...
% 1.38/1.75 % SZS status Started for theBenchmark.p
% 1.38/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 1.38/1.75
% 1.38/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.38/1.75
% 1.38/1.75 % ------ iProver source info
% 1.38/1.75
% 1.38/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 1.38/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.38/1.75 % git: non_committed_changes: false
% 1.38/1.75
% 1.38/1.75 % ------ Parsing...% successful
% 1.38/1.75
% 1.38/1.75
% 1.38/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.38/1.75
% 1.38/1.75 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.38/1.75
% 1.38/1.75 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.38/1.75
% 1.38/1.75 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.38/1.75 % ------ Proving...
% 1.38/1.75 % ------ Problem Properties
% 1.38/1.75
% 1.38/1.75 %
% 1.38/1.75 % clauses 37
% 1.38/1.75 % conjectures 25
% 1.38/1.75 % EPR 21
% 1.38/1.75 % Horn 16
% 1.38/1.75 % unary 12
% 1.38/1.75 % binary 21
% 1.38/1.75 % lits 68
% 1.38/1.75 % lits eq 60
% 1.38/1.76 % fd_pure 0
% 1.38/1.76 % fd_pseudo 0
% 1.38/1.76 % fd_cond 0
% 1.38/1.76 % fd_pseudo_cond 0
% 1.38/1.76 % AC symbols 0
% 1.38/1.76
% 1.38/1.76 % ------ Schedule dynamic 5 is on
% 1.38/1.76
% 1.38/1.76 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.38/1.76
% 1.38/1.76
% 1.38/1.76 % ------
% 1.38/1.76 % Current options:
% 1.38/1.76 % ------
% 1.38/1.76
% 1.38/1.76
% 1.38/1.76 %
% 1.38/1.76
% 1.38/1.76 % ------ Proving...
% 1.38/1.76 %
% 1.38/1.76
% 1.38/1.76 % SZS status Unsatisfiable for theBenchmark.p
% 1.38/1.76
% 1.38/1.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.38/1.76
% 1.38/1.76
%------------------------------------------------------------------------------