%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP292-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:32:45 PM UTC 2026
% Result : Unsatisfiable 1.42s 1.73s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 31
% Syntax : Number of formulae : 259 ( 76 unt; 9 def)
% Number of atoms : 869 ( 451 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 408 ( 133 ~; 275 |; 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 : 14 ( 12 usr; 13 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 57 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c6 = multiply(sk_c3,sk_c4)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c3) = sk_c4
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c4 = inverse(sk_c3)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c6 = multiply(sk_c3,sk_c4)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c3) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c4 = inverse(sk_c3)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = multiply(sk_c3,sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c4 = inverse(sk_c3)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f31,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c6 = multiply(sk_c3,sk_c4)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c3) = sk_c4
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c4 = inverse(sk_c3)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f35]) ).
fof(f39,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c6
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c6 = multiply(sk_c3,sk_c4)
| sk_c5 = inverse(sk_c2) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c3) = sk_c4
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c4 = inverse(sk_c3)
| sk_c5 = inverse(sk_c2) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c5 = inverse(sk_c2) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(X3,sk_c5) != sk_c6
| inverse(X2) != X3
| multiply(X2,X3) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(X1) != sk_c5
| multiply(X1,sk_c5) != sk_c6
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( sk_c6 != multiply(X3,sk_c5)
| inverse(X2) != X3
| sk_c6 != multiply(X2,X3)
| sk_c7 != multiply(sk_c5,sk_c6)
| sk_c5 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7)
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(reorient_equations,[],[f45]) ).
fof(f47,plain,
! [X2,X0,X1] :
( sk_c6 != multiply(inverse(X2),sk_c5)
| sk_c6 != multiply(X2,inverse(X2))
| sk_c7 != multiply(sk_c5,sk_c6)
| sk_c5 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7)
| multiply(sk_c7,sk_c6) != sk_c5 ),
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,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_77,negated_conjecture,
( ( multiply(sk_c3,sk_c4) = sk_c6 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_78,negated_conjecture,
( ( inverse(sk_c3) = sk_c4 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_79,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_80,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_81,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_82,negated_conjecture,
( ( inverse(sk_c3) = sk_c4 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_83,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_84,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_85,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_86,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c3) = sk_c4 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_89,negated_conjecture,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( multiply(sk_c3,sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c3) = sk_c4 )
| ( multiply(sk_c2,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_91,negated_conjecture,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c2) = sk_c5 )
| ( multiply(sk_c3,sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c2) = sk_c5 )
| ( inverse(sk_c3) = sk_c4 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c2) = sk_c5 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_96,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X2) != sk_c5 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c5,sk_c6) != sk_c7 )
| ( multiply(sk_c7,sk_c6) != sk_c5 )
| ( multiply(X2,sk_c5) != sk_c6 )
| ( multiply(X0,sk_c7) != sk_c6 )
| ( multiply(inverse(X1),sk_c5) != sk_c6 )
| ( multiply(X1,inverse(X1)) != sk_c6 ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_301,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( 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_c5 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_96]) ).
tcf(c_303,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( multiply(inverse(X0),sk_c5) != sk_c6 )
| ( multiply(X0,inverse(X0)) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_96]) ).
tcf(c_304,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c5,sk_c6) != sk_c7 )
| ( multiply(sk_c7,sk_c6) != sk_c5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_96]) ).
tcf(c_305,definition,
iPr_def_13 = multiply(sk_c7,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_306,definition,
iPr_def_14 = multiply(sk_c5,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_307,definition,
iPr_def_15 = multiply(sk_c4,sk_c5),
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 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_310,definition,
iPr_def_18 = multiply(sk_c3,sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_311,definition,
iPr_def_19 = multiply(sk_c2,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_312,definition,
iPr_def_20 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_313,definition,
iPr_def_21 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_314,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_14 != sk_c7 )
| ( iPr_def_13 != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_304,c_306,c_305]) ).
tcf(c_315,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( multiply(inverse(X0),sk_c5) != sk_c6 )
| ( multiply(X0,inverse(X0)) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_303]) ).
tcf(c_316,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c5 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_302]) ).
tcf(c_317,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_301]) ).
tcf(c_318,negated_conjecture,
( ( iPr_def_16 = sk_c5 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_95,c_308,c_307]) ).
tcf(c_319,negated_conjecture,
( ( iPr_def_17 = sk_c4 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_94,c_309]) ).
tcf(c_320,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_93,c_310]) ).
tcf(c_322,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_91,c_311]) ).
tcf(c_323,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_17 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_324,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_326,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_87,c_312]) ).
tcf(c_327,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_17 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_328,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_329,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_330,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_83,c_313]) ).
tcf(c_331,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_17 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_332,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_333,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_334,negated_conjecture,
( ( iPr_def_15 = sk_c6 )
| ( iPr_def_13 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_335,negated_conjecture,
( ( iPr_def_17 = sk_c4 )
| ( iPr_def_13 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_336,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_13 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_337,negated_conjecture,
( ( iPr_def_14 = sk_c7 )
| ( iPr_def_13 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_540,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_16,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_320,c_306]) ).
tcf(c_541,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_16,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_318,c_306]) ).
tcf(c_564,plain,
( ( sk_c6 = iPr_def_19 )
| ( multiply(sk_c3,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_323,c_310]) ).
tcf(c_565,plain,
( ( sk_c5 = iPr_def_16 )
| ( multiply(sk_c3,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_319,c_310]) ).
tcf(c_570,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(sk_c2,iPr_def_16) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_320,c_311]) ).
tcf(c_571,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c2,iPr_def_16) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_318,c_311]) ).
tcf(c_582,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_20,sk_c6) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_326,c_305]) ).
tcf(c_597,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c3,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_327,c_310]) ).
tcf(c_609,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_20,sk_c6) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_328,c_305]) ).
tcf(c_660,plain,
( ( sk_c6 = iPr_def_21 )
| ( multiply(sk_c3,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_331,c_310]) ).
tcf(c_723,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_326,c_313]) ).
tcf(c_741,plain,
multiply(iPr_def_17,sk_c3) = identity,
inference(superposition,[status(thm)],[c_309,c_74]) ).
tcf(c_742,plain,
multiply(iPr_def_20,sk_c1) = identity,
inference(superposition,[status(thm)],[c_312,c_74]) ).
tcf(c_743,plain,
multiply(iPr_def_16,sk_c2) = identity,
inference(superposition,[status(thm)],[c_308,c_74]) ).
tcf(c_788,plain,
( ( sk_c5 = iPr_def_13 )
| ( multiply(sk_c3,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_335,c_310]) ).
tcf(c_864,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c6 = iPr_def_18 )
| ( sk_c7 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_336,c_314]) ).
tcf(c_865,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c6 = iPr_def_15 )
| ( sk_c7 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_334,c_314]) ).
tcf(c_898,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_15 )
| ( inverse(sk_c4) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_307,c_316]) ).
tcf(c_899,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_19 )
| ( inverse(sk_c2) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_311,c_316]) ).
tcf(c_909,plain,
( ~ iPr_def_11
| ( sk_c5 != iPr_def_16 )
| ( sk_c6 != iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_899,c_308]) ).
tcf(c_970,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_21 )
| ( inverse(sk_c1) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_313,c_317]) ).
tcf(c_972,plain,
( ~ iPr_def_10
| ( sk_c6 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_74,c_317]) ).
tcf(c_983,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_21 )
| ( sk_c7 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_970,c_312]) ).
tcf(c_1321,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_74,c_75]) ).
tcf(c_1324,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_741,c_75]) ).
tcf(c_1325,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_742,c_75]) ).
tcf(c_1326,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_743,c_75]) ).
tcf(c_1331,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1326,c_73]) ).
tcf(c_1332,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1325,c_73]) ).
tcf(c_1333,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1324,c_73]) ).
tcf(c_1396,plain,
multiply(iPr_def_16,iPr_def_19) = sk_c5,
inference(superposition,[status(thm)],[c_311,c_1331]) ).
tcf(c_1403,plain,
multiply(iPr_def_20,iPr_def_21) = sk_c7,
inference(superposition,[status(thm)],[c_313,c_1332]) ).
tcf(c_1615,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_16,iPr_def_19) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_324,c_540]) ).
tcf(c_1618,plain,
( ( sk_c5 = iPr_def_14 )
| ( sk_c6 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_1615,c_1396]) ).
tcf(c_1636,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c2,iPr_def_16) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_318,c_311]) ).
tcf(c_1652,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_19) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_322,c_541]) ).
tcf(c_1654,plain,
( ( sk_c5 = iPr_def_14 )
| ( sk_c6 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_1652,c_1396]) ).
tcf(c_1828,plain,
( ( iPr_def_13 = iPr_def_14 )
| ( sk_c6 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1618,c_336]) ).
tcf(c_1893,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_20,sk_c6) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_328,c_305]) ).
tcf(c_1926,plain,
( ( iPr_def_13 = iPr_def_14 )
| ( sk_c6 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1654,c_334]) ).
tcf(c_2332,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_330,c_582]) ).
tcf(c_2336,plain,
( ( sk_c6 = iPr_def_15 )
| ( sk_c7 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_2332,c_1403]) ).
tcf(c_2660,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_332,c_609]) ).
tcf(c_2665,plain,
( ( sk_c6 = iPr_def_18 )
| ( sk_c7 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_2660,c_1403]) ).
tcf(c_2892,plain,
multiply(iPr_def_20,sk_c1) = identity,
inference(superposition,[status(thm)],[c_312,c_74]) ).
tcf(c_2893,plain,
multiply(iPr_def_16,sk_c2) = identity,
inference(superposition,[status(thm)],[c_308,c_74]) ).
tcf(c_4634,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c6 = iPr_def_18 )
| ( iPr_def_13 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_2665,c_864]) ).
tcf(c_4637,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c6 = iPr_def_21 )
| ( sk_c6 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_333,c_864]) ).
tcf(c_4744,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c6 = iPr_def_18 ) ),
inference(global_subsumption_just,[status(thm)],[c_4637,c_1828,c_4634]) ).
tcf(c_4774,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c6 = iPr_def_15 )
| ( iPr_def_13 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_2336,c_865]) ).
tcf(c_4776,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c6 = iPr_def_21 )
| ( sk_c6 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_333,c_865]) ).
tcf(c_4814,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c6 = iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_4776,c_1926,c_4774]) ).
tcf(c_6764,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1321,c_73]) ).
tcf(c_6771,plain,
multiply(inverse(sk_c4),iPr_def_15) = sk_c5,
inference(superposition,[status(thm)],[c_307,c_6764]) ).
tcf(c_6775,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_74,c_6764]) ).
tcf(c_6867,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_1333,c_6764]) ).
tcf(c_6868,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_1332,c_6764]) ).
tcf(c_6869,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_1331,c_6764]) ).
tcf(c_6919,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_6764,c_6764]) ).
tcf(c_7296,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_2892,c_75]) ).
tcf(c_7297,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_2893,c_75]) ).
tcf(c_7302,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_7297,c_73]) ).
tcf(c_7303,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_7296,c_73]) ).
tcf(c_7371,plain,
multiply(iPr_def_16,iPr_def_19) = sk_c5,
inference(superposition,[status(thm)],[c_311,c_7302]) ).
tcf(c_7384,plain,
multiply(iPr_def_20,iPr_def_21) = sk_c7,
inference(superposition,[status(thm)],[c_313,c_7303]) ).
tcf(c_7749,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_6775,c_6919]) ).
tcf(c_7810,plain,
( ( sk_c6 = iPr_def_18 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_320,c_909]) ).
tcf(c_7811,plain,
( ( sk_c6 = iPr_def_15 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_318,c_909]) ).
tcf(c_7874,plain,
( ( sk_c6 = iPr_def_18 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_324,c_7810]) ).
tcf(c_7884,plain,
( iPr_def_12
| iPr_def_10
| ( sk_c6 = iPr_def_18 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_4744,c_7874]) ).
tcf(c_7911,plain,
( ( sk_c6 = iPr_def_15 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_322,c_7811]) ).
tcf(c_7920,plain,
( iPr_def_12
| iPr_def_10
| ( sk_c6 = iPr_def_15 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_4814,c_7911]) ).
tcf(c_7921,plain,
( ~ iPr_def_11
| ( inverse(sk_c4) != sk_c5 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_898,c_7911]) ).
tcf(c_8003,plain,
( ( sk_c6 = iPr_def_18 )
| ~ iPr_def_10
| ( sk_c6 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_328,c_983]) ).
tcf(c_8004,plain,
( ( sk_c6 = iPr_def_15 )
| ~ iPr_def_10
| ( sk_c6 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_326,c_983]) ).
tcf(c_8068,plain,
multiply(sk_c3,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_6867,c_74]) ).
tcf(c_8082,plain,
( ( identity = iPr_def_18 )
| ( sk_c5 = iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_788,c_8068]) ).
tcf(c_8083,plain,
( ( identity = iPr_def_18 )
| ( sk_c6 = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_660,c_8068]) ).
tcf(c_8084,plain,
( ( identity = iPr_def_18 )
| ( sk_c7 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_597,c_8068]) ).
tcf(c_8085,plain,
( ( identity = iPr_def_18 )
| ( sk_c5 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_565,c_8068]) ).
tcf(c_8086,plain,
( ( identity = iPr_def_18 )
| ( sk_c6 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_564,c_8068]) ).
tcf(c_8144,plain,
( ( sk_c6 = iPr_def_18 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_332,c_8003]) ).
tcf(c_8160,plain,
( iPr_def_12
| ( sk_c6 = iPr_def_18 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_7884,c_8144]) ).
tcf(c_8193,plain,
( ( sk_c6 = iPr_def_15 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_330,c_8004]) ).
tcf(c_8209,plain,
( iPr_def_12
| ( sk_c6 = iPr_def_15 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_7920,c_8193]) ).
tcf(c_8271,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( identity = iPr_def_18 )
| ( sk_c7 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_8082,c_314]) ).
tcf(c_8549,plain,
( iPr_def_12
| ( identity = iPr_def_18 )
| ( sk_c7 != iPr_def_14 ) ),
inference(global_subsumption_just,[status(thm)],[c_8271,c_909,c_983,c_8086,c_8085,c_8084,c_8083,c_8271]) ).
tcf(c_8729,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c7,iPr_def_21) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_8083,c_305]) ).
tcf(c_8901,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_8084,c_313]) ).
tcf(c_9059,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( identity = iPr_def_18 )
| ( iPr_def_13 != iPr_def_16 )
| ( sk_c7 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_8085,c_314]) ).
tcf(c_9064,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_16,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_8085,c_306]) ).
tcf(c_9420,plain,
multiply(sk_c1,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_6868,c_74]) ).
tcf(c_9437,plain,
( ( identity = iPr_def_21 )
| ( sk_c6 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_723,c_9420]) ).
tcf(c_10227,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_8084,c_8729]) ).
tcf(c_10248,plain,
( ( identity = iPr_def_18 )
| ( sk_c7 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_10227,c_1403]) ).
tcf(c_10317,plain,
( iPr_def_12
| ( identity = iPr_def_18 )
| ( iPr_def_13 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_10248,c_8549]) ).
tcf(c_10484,plain,
multiply(sk_c2,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_6869,c_74]) ).
tcf(c_10499,plain,
( ( identity = iPr_def_19 )
| ( sk_c6 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_571,c_10484]) ).
tcf(c_10500,plain,
( ( identity = iPr_def_19 )
| ( sk_c6 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_570,c_10484]) ).
tcf(c_10889,plain,
( ( identity = iPr_def_21 )
| ( identity = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_8901,c_9420]) ).
tcf(c_11250,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_16,iPr_def_19) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_8086,c_9064]) ).
tcf(c_11276,plain,
( ( identity = iPr_def_18 )
| ( sk_c5 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_11250,c_1396]) ).
tcf(c_11348,plain,
( ( iPr_def_13 = iPr_def_14 )
| ( identity = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_11276,c_8082]) ).
tcf(c_11768,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_19) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_1636,c_7302]) ).
tcf(c_11769,plain,
( ( sk_c5 = iPr_def_16 )
| ( sk_c6 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_11768,c_7371]) ).
tcf(c_13572,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_332,c_1893]) ).
tcf(c_13577,plain,
( ( sk_c6 = iPr_def_18 )
| ( sk_c7 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_13572,c_7384]) ).
tcf(c_14349,plain,
( iPr_def_12
| ( identity = iPr_def_18 ) ),
inference(global_subsumption_just,[status(thm)],[c_9059,c_10317,c_11348]) ).
tcf(c_15421,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_6919,c_74]) ).
tcf(c_15425,plain,
! [X0: $i] : multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_6919,c_7749]) ).
tcf(c_15426,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_15425,c_7749]) ).
tcf(c_15439,plain,
! [X0: $i] :
( ~ iPr_def_12
| ( sk_c6 != identity )
| ( multiply(inverse(X0),sk_c5) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_315,c_15421]) ).
tcf(c_15443,plain,
( ~ iPr_def_10
| ( sk_c6 != identity ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_972,c_15426]) ).
tcf(c_15527,plain,
( ~ iPr_def_12
| ( sk_c6 != identity ) ),
inference(superposition,[status(thm)],[c_74,c_15439]) ).
tcf(c_15985,plain,
( ( identity = iPr_def_21 )
| ~ iPr_def_12
| ( identity != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_9437,c_15527]) ).
tcf(c_15987,plain,
( ( identity = iPr_def_18 )
| ~ iPr_def_12
| ( identity != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_8083,c_15527]) ).
tcf(c_16002,plain,
( ( sk_c6 = iPr_def_18 )
| ~ iPr_def_12
| ( identity != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_332,c_15527]) ).
tcf(c_16004,plain,
( ( sk_c6 = iPr_def_18 )
| ~ iPr_def_12
| ( identity != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_324,c_15527]) ).
tcf(c_16005,plain,
( ( sk_c6 = iPr_def_15 )
| ~ iPr_def_12
| ( identity != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_322,c_15527]) ).
tcf(c_16097,plain,
sk_c6 = iPr_def_18,
inference(global_subsumption_just,[status(thm)],[c_13577,c_8160,c_10500,c_16004]) ).
tcf(c_16137,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( sk_c7 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_333,c_16097]) ).
tcf(c_16247,plain,
sk_c6 = iPr_def_15,
inference(global_subsumption_just,[status(thm)],[c_11769,c_8209,c_10499,c_16005]) ).
tcf(c_16249,plain,
iPr_def_15 = iPr_def_18,
inference(demodulation,[status(thm)],[c_16097,c_16247]) ).
tcf(c_17450,plain,
sk_c6 = iPr_def_18,
inference(global_subsumption_just,[status(thm)],[c_16002,c_16097]) ).
tcf(c_17452,plain,
( ~ iPr_def_10
| ( identity != iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_15443,c_17450]) ).
tcf(c_17453,plain,
( ~ iPr_def_12
| ( identity != iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_15527,c_17450]) ).
tcf(c_17518,plain,
( ( iPr_def_18 = iPr_def_21 )
| ( identity = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_8083,c_17450]) ).
tcf(c_17641,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c5 = iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_334,c_17450]) ).
tcf(c_17648,plain,
multiply(sk_c5,iPr_def_18) = iPr_def_14,
inference(demodulation,[status(thm)],[c_306,c_17450]) ).
tcf(c_17649,plain,
multiply(sk_c7,iPr_def_18) = iPr_def_13,
inference(demodulation,[status(thm)],[c_305,c_17450]) ).
tcf(c_17913,plain,
iPr_def_15 = iPr_def_18,
inference(global_subsumption_just,[status(thm)],[c_17641,c_16249]) ).
tcf(c_17924,plain,
( iPr_def_12
| ( identity = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_14349,c_17913]) ).
tcf(c_17953,plain,
( ( identity = iPr_def_21 )
| ( identity = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_10889,c_17913]) ).
tcf(c_18186,plain,
identity = iPr_def_15,
inference(global_subsumption_just,[status(thm)],[c_17924,c_15987,c_17453,c_17924,c_17953]) ).
tcf(c_18196,plain,
multiply(sk_c1,iPr_def_20) = iPr_def_15,
inference(demodulation,[status(thm)],[c_9420,c_18186]) ).
tcf(c_18199,plain,
! [X0: $i] : multiply(X0,iPr_def_15) = X0,
inference(demodulation,[status(thm)],[c_7749,c_18186]) ).
tcf(c_18225,plain,
inverse(sk_c4) = sk_c5,
inference(demodulation,[status(thm)],[c_6771,c_18199]) ).
tcf(c_18226,plain,
~ iPr_def_11,
inference(backward_subsumption_resolution,[status(thm)],[c_7921,c_18225]) ).
tcf(c_18227,plain,
( iPr_def_12
| iPr_def_10
| ( sk_c5 != iPr_def_13 )
| ( sk_c7 != iPr_def_14 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_314,c_18226]) ).
tcf(c_18300,plain,
( iPr_def_12
| ( sk_c7 != iPr_def_14 )
| ( sk_c5 != iPr_def_13 ) ),
inference(global_subsumption_just,[status(thm)],[c_18227,c_14349,c_15987,c_15985,c_17453,c_17452,c_17924,c_17953,c_18227]) ).
tcf(c_18301,plain,
( iPr_def_12
| ( sk_c5 != iPr_def_13 )
| ( sk_c7 != iPr_def_14 ) ),
inference(renaming,[status(thm)],[c_18300]) ).
tcf(c_18302,plain,
( ( sk_c7 != iPr_def_14 )
| ( sk_c5 != iPr_def_13 ) ),
inference(global_subsumption_just,[status(thm)],[c_18301,c_14349,c_15987,c_15985,c_17453,c_17452,c_17924,c_17953,c_18227]) ).
tcf(c_18303,plain,
( ( sk_c5 != iPr_def_13 )
| ( sk_c7 != iPr_def_14 ) ),
inference(renaming,[status(thm)],[c_18302]) ).
tcf(c_18314,plain,
( ( sk_c7 = iPr_def_14 )
| ( iPr_def_14 != iPr_def_20 )
| ( sk_c5 != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_329,c_18303]) ).
tcf(c_18342,plain,
multiply(sk_c5,iPr_def_15) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_17648,c_17913]) ).
tcf(c_18343,plain,
sk_c5 = iPr_def_14,
inference(demodulation,[status(thm)],[c_18342,c_18199]) ).
tcf(c_18360,plain,
( ( iPr_def_13 = iPr_def_14 )
| ( sk_c7 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_337,c_18343]) ).
tcf(c_18391,plain,
multiply(sk_c7,iPr_def_15) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_17649,c_17913]) ).
tcf(c_18392,plain,
sk_c7 = iPr_def_13,
inference(demodulation,[status(thm)],[c_18391,c_18199]) ).
tcf(c_18401,plain,
multiply(iPr_def_20,iPr_def_21) = iPr_def_13,
inference(demodulation,[status(thm)],[c_1403,c_18392]) ).
tcf(c_18432,plain,
iPr_def_13 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_18360,c_18392]) ).
tcf(c_18436,plain,
sk_c5 = iPr_def_13,
inference(demodulation,[status(thm)],[c_18343,c_18432]) ).
tcf(c_18451,plain,
iPr_def_14 != iPr_def_20,
inference(global_subsumption_just,[status(thm)],[c_18314,c_14349,c_15987,c_15985,c_17453,c_17452,c_17924,c_17953,c_18227,c_18314,c_18436]) ).
tcf(c_18453,plain,
iPr_def_13 != iPr_def_20,
inference(light_normalisation,[status(thm)],[c_18451,c_18432]) ).
tcf(c_18491,plain,
iPr_def_18 = iPr_def_21,
inference(global_subsumption_just,[status(thm)],[c_17518,c_16137,c_18303,c_18436]) ).
tcf(c_18493,plain,
iPr_def_15 = iPr_def_21,
inference(light_normalisation,[status(thm)],[c_18491,c_17913]) ).
tcf(c_18519,plain,
multiply(iPr_def_20,iPr_def_15) = iPr_def_20,
inference(superposition,[status(thm)],[c_18196,c_1332]) ).
tcf(c_18594,plain,
iPr_def_13 = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_18401,c_18493,c_18519]) ).
tcf(c_18595,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_18594,c_18453]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP292-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 14:22:37 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.42/1.73 % SZS status Started for theBenchmark.p
% 1.42/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.42/1.73
% 1.42/1.73 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.42/1.73
% 1.42/1.73 % ------ iProver source info
% 1.42/1.73
% 1.42/1.73 % git: date: 2026-07-19 20:42:38 +0200
% 1.42/1.73 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.42/1.73 % git: non_committed_changes: false
% 1.42/1.73
% 1.42/1.73 % ------ Parsing...% successful
% 1.42/1.73
% 1.42/1.73
% 1.42/1.73 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.42/1.73
% 1.42/1.73 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.42/1.73
% 1.42/1.73 % ------ Preprocessing... gs_s sp: 3 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.42/1.73
% 1.42/1.73 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.42/1.73 % ------ Proving...
% 1.42/1.73 % ------ Problem Properties
% 1.42/1.73
% 1.42/1.73 %
% 1.42/1.73 % clauses 36
% 1.42/1.73 % conjectures 24
% 1.42/1.73 % EPR 21
% 1.42/1.73 % Horn 15
% 1.42/1.73 % unary 12
% 1.42/1.73 % binary 20
% 1.42/1.73 % lits 66
% 1.42/1.73 % lits eq 60
% 1.42/1.73 % fd_pure 0
% 1.42/1.73 % fd_pseudo 0
% 1.42/1.73 % fd_cond 0
% 1.42/1.73 % fd_pseudo_cond 0
% 1.42/1.73 % AC symbols 0
% 1.42/1.73
% 1.42/1.73 % ------ Schedule dynamic 5 is on
% 1.42/1.73
% 1.42/1.73 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.42/1.73
% 1.42/1.73
% 1.42/1.73 % ------
% 1.42/1.73 % Current options:
% 1.42/1.73 % ------
% 1.42/1.73
% 1.42/1.73
% 1.42/1.73 %
% 1.42/1.73
% 1.42/1.73 % ------ Proving...
% 1.42/1.73 %
% 1.42/1.73
% 1.42/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.42/1.73
% 1.42/1.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.42/1.73
% 1.42/1.73
%------------------------------------------------------------------------------