%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP298-1 : 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 15.98s 3.28s
% Output : CNFRefutation 15.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 30
% Syntax : Number of formulae : 219 ( 94 unt; 11 def)
% Number of atoms : 722 ( 385 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 360 ( 148 ~; 212 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 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 : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 77 !; 0 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c8 = inverse(sk_c2)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c8 = inverse(sk_c3)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f13]) ).
fof(f21,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f23]) ).
fof(f37,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f39]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = inverse(sk_c3)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c7 = multiply(sk_c4,sk_c5)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f63]) ).
fof(f67,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(X4,sk_c6) != sk_c7
| inverse(X3) != X4
| multiply(X3,X4) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| inverse(X2) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
! [X2,X3,X0,X1,X4] :
( sk_c7 != multiply(X4,sk_c6)
| inverse(X3) != X4
| sk_c7 != multiply(X3,X4)
| sk_c8 != multiply(X2,sk_c7)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,sk_c6)
| sk_c8 != inverse(X1)
| sk_c7 != multiply(X1,sk_c8)
| sk_c7 != multiply(sk_c6,sk_c8)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8)
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(reorient_equations,[],[f69]) ).
fof(f71,plain,
! [X2,X3,X0,X1] :
( sk_c7 != multiply(inverse(X3),sk_c6)
| sk_c7 != multiply(X3,inverse(X3))
| sk_c8 != multiply(X2,sk_c7)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,sk_c6)
| sk_c8 != inverse(X1)
| sk_c7 != multiply(X1,sk_c8)
| sk_c7 != multiply(sk_c6,sk_c8)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8)
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(equality_resolution,[],[f70]) ).
tcf(c_85,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_86,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_88,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_90,negated_conjecture,
( ( multiply(sk_c8,sk_c6) = sk_c7 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_92,negated_conjecture,
( ( multiply(sk_c3,sk_c7) = sk_c8 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_96,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c7 )
| ( multiply(sk_c2,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c2,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c2) = sk_c8 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_114,negated_conjecture,
( ( multiply(sk_c6,sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_116,negated_conjecture,
( ( multiply(sk_c3,sk_c7) = sk_c8 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_117,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c7 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_119,negated_conjecture,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_120,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c8 )
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c6,sk_c8) != sk_c7 )
| ( multiply(sk_c8,sk_c6) != sk_c7 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( multiply(X2,sk_c8) != sk_c7 )
| ( multiply(X1,sk_c7) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 )
| ( multiply(inverse(X3),sk_c6) != sk_c7 )
| ( multiply(X3,inverse(X3)) != sk_c7 ) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_433,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_120]) ).
tcf(c_434,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_120]) ).
tcf(c_435,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( multiply(inverse(X0),sk_c6) != sk_c7 )
| ( multiply(X0,inverse(X0)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_120]) ).
tcf(c_436,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c6,sk_c8) != sk_c7 )
| ( multiply(sk_c8,sk_c6) != sk_c7 )
| ( multiply(sk_c8,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_120]) ).
tcf(c_437,definition,
iPr_def_13 = multiply(sk_c8,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_438,definition,
iPr_def_14 = multiply(sk_c8,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_439,definition,
iPr_def_15 = multiply(sk_c6,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_440,definition,
iPr_def_16 = multiply(sk_c5,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_442,definition,
iPr_def_18 = multiply(sk_c4,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_443,definition,
iPr_def_19 = multiply(sk_c3,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_444,definition,
iPr_def_20 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_445,definition,
iPr_def_21 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_446,definition,
iPr_def_22 = multiply(sk_c2,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_447,definition,
iPr_def_23 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_448,definition,
iPr_def_24 = multiply(sk_c1,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_449,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c7 )
| ( iPr_def_14 != sk_c7 )
| ( iPr_def_13 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_436,c_439,c_438,c_437]) ).
tcf(c_450,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( multiply(inverse(X0),sk_c6) != sk_c7 )
| ( multiply(X0,inverse(X0)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_435]) ).
tcf(c_452,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_434]) ).
tcf(c_453,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_433]) ).
tcf(c_454,negated_conjecture,
( ( iPr_def_16 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_119,c_440]) ).
tcf(c_456,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_117,c_442]) ).
tcf(c_457,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_116,c_443]) ).
tcf(c_458,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_115,c_444]) ).
tcf(c_459,negated_conjecture,
( ( iPr_def_15 = sk_c7 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_460,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_113,c_445]) ).
tcf(c_468,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_21 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_469,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_22 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_476,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_21 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_477,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_22 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_481,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_482,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_483,negated_conjecture,
( ( iPr_def_14 = sk_c7 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_484,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_485,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_712,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c7 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_454,c_456]) ).
tcf(c_991,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(iPr_def_23,sk_c7) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_468,c_437]) ).
tcf(c_1022,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(sk_c8,iPr_def_22) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_469,c_437]) ).
tcf(c_1076,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(sk_c3,iPr_def_22) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_469,c_443]) ).
tcf(c_1125,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(sk_c2,iPr_def_23) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_468,c_446]) ).
tcf(c_1155,plain,
multiply(iPr_def_21,sk_c2) = identity,
inference(superposition,[status(thm)],[c_445,c_86]) ).
tcf(c_1156,plain,
multiply(iPr_def_20,sk_c3) = identity,
inference(superposition,[status(thm)],[c_444,c_86]) ).
tcf(c_1158,plain,
multiply(iPr_def_23,sk_c1) = identity,
inference(superposition,[status(thm)],[c_447,c_86]) ).
tcf(c_1620,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(sk_c3,iPr_def_24) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_476,c_443]) ).
tcf(c_1720,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_24) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_477,c_443]) ).
tcf(c_1725,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(sk_c8,iPr_def_24) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_477,c_437]) ).
tcf(c_1974,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(iPr_def_13,sk_c8) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_484,c_439]) ).
tcf(c_2140,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_22 )
| ( inverse(sk_c2) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_446,c_452]) ).
tcf(c_2141,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_24 )
| ( inverse(sk_c1) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_448,c_452]) ).
tcf(c_2154,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_24 )
| ( sk_c8 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_2141,c_447]) ).
tcf(c_2158,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_22 )
| ( sk_c8 != iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_2140,c_445]) ).
tcf(c_2220,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_19 )
| ( inverse(sk_c3) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_443,c_453]) ).
tcf(c_2223,plain,
! [X0: $i] :
( ( iPr_def_16 = iPr_def_18 )
| ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,iPr_def_15) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_712,c_453]) ).
tcf(c_2238,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_20 )
| ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,iPr_def_15) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_458,c_453]) ).
tcf(c_2239,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_19 )
| ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,iPr_def_15) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_457,c_453]) ).
tcf(c_2245,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_20 )
| ( sk_c8 != iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_2220,c_444]) ).
tcf(c_2914,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c6,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_438,c_87]) ).
tcf(c_2918,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c8,X0)) = multiply(iPr_def_24,X0),
inference(superposition,[status(thm)],[c_448,c_87]) ).
tcf(c_2919,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c8,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_439,c_87]) ).
tcf(c_2921,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_86,c_87]) ).
tcf(c_2923,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1155,c_87]) ).
tcf(c_2924,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1156,c_87]) ).
tcf(c_2926,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1158,c_87]) ).
tcf(c_2931,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2926,c_85]) ).
tcf(c_2933,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2924,c_85]) ).
tcf(c_2934,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2923,c_85]) ).
tcf(c_4100,plain,
multiply(iPr_def_23,iPr_def_24) = sk_c8,
inference(superposition,[status(thm)],[c_448,c_2931]) ).
tcf(c_4124,plain,
multiply(iPr_def_20,iPr_def_19) = sk_c7,
inference(superposition,[status(thm)],[c_443,c_2933]) ).
tcf(c_4127,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_19,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_4124,c_87]) ).
tcf(c_4129,plain,
multiply(iPr_def_21,iPr_def_22) = sk_c8,
inference(superposition,[status(thm)],[c_446,c_2934]) ).
tcf(c_4141,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(iPr_def_22,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_4129,c_87]) ).
tcf(c_5401,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_476,c_991]) ).
tcf(c_5420,plain,
( ( sk_c8 = iPr_def_21 )
| ( sk_c8 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_5401,c_4100]) ).
tcf(c_5606,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1076,c_2933]) ).
tcf(c_5607,plain,
( ( sk_c7 = iPr_def_22 )
| ( sk_c8 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_5606,c_4124]) ).
tcf(c_5710,plain,
( ( sk_c8 = iPr_def_23 )
| ( sk_c8 = iPr_def_13 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_5420,c_1022]) ).
tcf(c_5740,plain,
( ( sk_c8 = iPr_def_13 )
| ( multiply(iPr_def_21,sk_c7) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_5420,c_437]) ).
tcf(c_5791,plain,
( ( sk_c8 = iPr_def_23 )
| ( sk_c8 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_5710,c_4129]) ).
tcf(c_6209,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1125,c_2934]) ).
tcf(c_6210,plain,
( ( sk_c8 = iPr_def_23 )
| ( sk_c8 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_6209,c_4129]) ).
tcf(c_7562,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1620,c_2933]) ).
tcf(c_7563,plain,
( ( sk_c7 = iPr_def_24 )
| ( sk_c8 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_7562,c_4124]) ).
tcf(c_7632,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1720,c_2933]) ).
tcf(c_7633,plain,
( ( sk_c7 = iPr_def_24 )
| ( sk_c7 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_7632,c_4124]) ).
tcf(c_7652,plain,
( ( sk_c7 = iPr_def_22 )
| ( sk_c8 = iPr_def_13 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_5791,c_1725]) ).
tcf(c_7737,plain,
( ( sk_c7 = iPr_def_22 )
| ( sk_c8 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_7652,c_4100]) ).
tcf(c_8978,plain,
( ( sk_c8 = iPr_def_21 )
| ~ iPr_def_11
| ( sk_c7 != iPr_def_15 )
| ( inverse(iPr_def_13) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_1974,c_452]) ).
tcf(c_14740,plain,
multiply(sk_c8,iPr_def_15) = multiply(iPr_def_14,sk_c8),
inference(superposition,[status(thm)],[c_439,c_2914]) ).
tcf(c_16726,plain,
multiply(sk_c1,iPr_def_13) = multiply(iPr_def_24,sk_c7),
inference(superposition,[status(thm)],[c_437,c_2918]) ).
tcf(c_16727,plain,
multiply(sk_c1,iPr_def_14) = multiply(iPr_def_24,sk_c6),
inference(superposition,[status(thm)],[c_438,c_2918]) ).
tcf(c_17897,plain,
multiply(sk_c6,iPr_def_14) = multiply(iPr_def_15,sk_c6),
inference(superposition,[status(thm)],[c_438,c_2919]) ).
tcf(c_18946,plain,
multiply(sk_c8,multiply(iPr_def_15,sk_c6)) = multiply(iPr_def_14,iPr_def_14),
inference(superposition,[status(thm)],[c_17897,c_2914]) ).
tcf(c_30800,plain,
( ( sk_c8 = iPr_def_13 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_7737,c_5740]) ).
tcf(c_30855,plain,
sk_c8 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_30800,c_4129]) ).
tcf(c_30859,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(iPr_def_22,X0)) = multiply(iPr_def_13,X0),
inference(demodulation,[status(thm)],[c_4141,c_30855]) ).
tcf(c_30863,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_13,X0)) = multiply(iPr_def_24,X0),
inference(demodulation,[status(thm)],[c_2918,c_30855]) ).
tcf(c_30865,plain,
multiply(iPr_def_13,iPr_def_15) = multiply(iPr_def_14,iPr_def_13),
inference(demodulation,[status(thm)],[c_14740,c_30855]) ).
tcf(c_30866,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(sk_c6,X0)) = multiply(iPr_def_14,X0),
inference(demodulation,[status(thm)],[c_2914,c_30855]) ).
tcf(c_30961,plain,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != iPr_def_13 )
| ( multiply(X0,sk_c7) != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_453,c_30855]) ).
tcf(c_30969,plain,
multiply(sk_c1,iPr_def_13) = iPr_def_24,
inference(demodulation,[status(thm)],[c_448,c_30855]) ).
tcf(c_30979,plain,
multiply(sk_c6,iPr_def_13) = iPr_def_15,
inference(demodulation,[status(thm)],[c_439,c_30855]) ).
tcf(c_30980,plain,
multiply(iPr_def_13,sk_c6) = iPr_def_14,
inference(demodulation,[status(thm)],[c_438,c_30855]) ).
tcf(c_30981,plain,
multiply(iPr_def_13,sk_c7) = iPr_def_13,
inference(demodulation,[status(thm)],[c_437,c_30855]) ).
tcf(c_31009,plain,
multiply(iPr_def_24,sk_c7) = iPr_def_24,
inference(demodulation,[status(thm)],[c_16726,c_30969]) ).
tcf(c_32581,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2921,c_85]) ).
tcf(c_32590,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_86,c_32581]) ).
tcf(c_32591,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[status(thm)],[c_87,c_32581]) ).
tcf(c_32655,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2934,c_32581]) ).
tcf(c_32658,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2931,c_32581]) ).
tcf(c_32680,plain,
multiply(inverse(sk_c6),iPr_def_15) = iPr_def_13,
inference(superposition,[status(thm)],[c_30979,c_32581]) ).
tcf(c_32681,plain,
multiply(inverse(iPr_def_13),iPr_def_14) = sk_c6,
inference(superposition,[status(thm)],[c_30980,c_32581]) ).
tcf(c_32682,plain,
multiply(inverse(iPr_def_13),iPr_def_13) = sk_c7,
inference(superposition,[status(thm)],[c_30981,c_32581]) ).
tcf(c_32694,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_32581,c_32581]) ).
tcf(c_32852,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_32590,c_32694]) ).
tcf(c_33590,plain,
! [X0: $i] : multiply(inverse(iPr_def_13),multiply(iPr_def_14,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_32681,c_87]) ).
tcf(c_33592,plain,
sk_c7 = identity,
inference(demodulation,[status(thm)],[c_32682,c_86]) ).
tcf(c_33615,plain,
multiply(iPr_def_24,identity) = iPr_def_24,
inference(demodulation,[status(thm)],[c_31009,c_33592]) ).
tcf(c_33626,plain,
multiply(iPr_def_13,identity) = iPr_def_13,
inference(demodulation,[status(thm)],[c_30981,c_33592]) ).
tcf(c_33641,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_19,X0)) = multiply(identity,X0),
inference(demodulation,[status(thm)],[c_4127,c_33592]) ).
tcf(c_33683,plain,
! [X0: $i] :
( ~ iPr_def_12
| ( multiply(inverse(X0),sk_c6) != identity )
| ( multiply(X0,inverse(X0)) != identity ) ),
inference(demodulation,[status(thm)],[c_450,c_33592]) ).
tcf(c_33684,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( identity != iPr_def_15 )
| ( identity != iPr_def_14 )
| ( sk_c6 != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_449,c_33592]) ).
tcf(c_33808,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_19,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_33641,c_85]) ).
tcf(c_35412,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_33808,c_32581]) ).
tcf(c_35459,plain,
multiply(sk_c2,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_32655,c_86]) ).
tcf(c_35460,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_32655,c_32581]) ).
tcf(c_35461,plain,
multiply(sk_c2,identity) = inverse(iPr_def_21),
inference(superposition,[status(thm)],[c_32655,c_32852]) ).
tcf(c_35470,plain,
multiply(iPr_def_21,identity) = iPr_def_21,
inference(superposition,[status(thm)],[c_35459,c_2934]) ).
tcf(c_35473,plain,
inverse(iPr_def_21) = sk_c2,
inference(demodulation,[status(thm)],[c_35461,c_32852]) ).
tcf(c_35477,plain,
multiply(sk_c2,identity) = sk_c2,
inference(superposition,[status(thm)],[c_1155,c_35460]) ).
tcf(c_35722,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_23,X0)) = X0,
inference(superposition,[status(thm)],[c_32658,c_32581]) ).
tcf(c_35723,plain,
multiply(sk_c1,identity) = inverse(iPr_def_23),
inference(superposition,[status(thm)],[c_32658,c_32852]) ).
tcf(c_36043,plain,
inverse(iPr_def_23) = sk_c1,
inference(demodulation,[status(thm)],[c_35723,c_32852]) ).
tcf(c_36086,plain,
multiply(sk_c1,identity) = sk_c1,
inference(superposition,[status(thm)],[c_1158,c_35722]) ).
tcf(c_37594,plain,
multiply(iPr_def_19,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_35412,c_86]) ).
tcf(c_37596,plain,
multiply(iPr_def_19,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_35412,c_32852]) ).
tcf(c_37605,plain,
inverse(iPr_def_20) = iPr_def_19,
inference(demodulation,[status(thm)],[c_37596,c_32852]) ).
tcf(c_37988,plain,
! [X0: $i] :
( ~ iPr_def_10
| ( X0 != iPr_def_13 )
| ( inverse(X0) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_30961,c_32852,c_33592]) ).
tcf(c_38002,plain,
( ~ iPr_def_10
| ( iPr_def_13 != iPr_def_23 )
| ( sk_c1 != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_36043,c_37988]) ).
tcf(c_41601,plain,
( ( sk_c8 = iPr_def_21 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_8978,c_2158,c_2154,c_5607,c_6210,c_7563,c_7633]) ).
tcf(c_41603,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_41601,c_2158,c_2154,c_5607,c_7633,c_41601]) ).
tcf(c_41895,plain,
multiply(iPr_def_13,multiply(iPr_def_15,sk_c6)) = multiply(iPr_def_14,iPr_def_14),
inference(light_normalisation,[status(thm)],[c_18946,c_30855]) ).
tcf(c_41910,plain,
multiply(inverse(iPr_def_13),multiply(iPr_def_14,iPr_def_14)) = multiply(iPr_def_15,sk_c6),
inference(superposition,[status(thm)],[c_41895,c_32581]) ).
tcf(c_42326,plain,
( ~ iPr_def_12
| ( multiply(iPr_def_23,sk_c1) != identity )
| ( multiply(inverse(iPr_def_23),sk_c6) != identity ) ),
inference(superposition,[status(thm)],[c_36043,c_33683]) ).
tcf(c_42340,plain,
( ~ iPr_def_12
| ( multiply(iPr_def_21,sk_c2) != identity )
| ( multiply(inverse(iPr_def_21),sk_c6) != identity ) ),
inference(superposition,[status(thm)],[c_35473,c_33683]) ).
tcf(c_42384,plain,
( ~ iPr_def_12
| ( multiply(inverse(iPr_def_21),sk_c6) != identity ) ),
inference(ground_joinability,[status(thm)],[c_42340,c_1155]) ).
tcf(c_42385,plain,
( ~ iPr_def_12
| ( multiply(sk_c2,sk_c6) != identity ) ),
inference(light_normalisation,[status(thm)],[c_42384,c_35473]) ).
tcf(c_42396,plain,
( ~ iPr_def_12
| ( multiply(inverse(iPr_def_23),sk_c6) != identity ) ),
inference(ground_joinability,[status(thm)],[c_42326,c_1158]) ).
tcf(c_42397,plain,
( ~ iPr_def_12
| ( multiply(sk_c1,sk_c6) != identity ) ),
inference(light_normalisation,[status(thm)],[c_42396,c_36043]) ).
tcf(c_43015,plain,
( iPr_def_12
| ( sk_c6 != iPr_def_13 )
| ( identity != iPr_def_14 )
| ( identity != iPr_def_15 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_33684,c_33684,c_41603]) ).
tcf(c_43016,plain,
( iPr_def_12
| iPr_def_10
| ( identity != iPr_def_15 )
| ( identity != iPr_def_14 )
| ( sk_c6 != iPr_def_13 ) ),
inference(renaming,[status(thm)],[c_43015]) ).
tcf(c_43894,plain,
! [X0: $i] :
( ( multiply(X0,iPr_def_15) != sk_c8 )
| ( inverse(X0) != sk_c8 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_2223,c_2245,c_2239,c_2238]) ).
tcf(c_43895,plain,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,iPr_def_15) != sk_c8 ) ),
inference(renaming,[status(thm)],[c_43894]) ).
tcf(c_43896,plain,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != iPr_def_13 )
| ( multiply(X0,iPr_def_15) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_43895,c_30855]) ).
tcf(c_43947,plain,
( ~ iPr_def_10
| ( inverse(inverse(sk_c6)) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_32680,c_43896]) ).
tcf(c_45866,plain,
multiply(inverse(iPr_def_13),multiply(iPr_def_13,iPr_def_15)) = multiply(sk_c6,iPr_def_13),
inference(superposition,[status(thm)],[c_30865,c_33590]) ).
tcf(c_45869,plain,
multiply(inverse(iPr_def_13),iPr_def_14) = multiply(sk_c6,identity),
inference(superposition,[status(thm)],[c_32852,c_33590]) ).
tcf(c_45876,plain,
multiply(sk_c6,identity) = sk_c6,
inference(light_normalisation,[status(thm)],[c_45869,c_32681]) ).
tcf(c_45877,plain,
multiply(inverse(iPr_def_13),multiply(iPr_def_13,iPr_def_15)) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_45866,c_30979]) ).
tcf(c_47293,plain,
multiply(iPr_def_13,identity) = multiply(iPr_def_21,iPr_def_22),
inference(superposition,[status(thm)],[c_32852,c_30859]) ).
tcf(c_48040,plain,
multiply(sk_c1,iPr_def_13) = multiply(iPr_def_24,identity),
inference(superposition,[status(thm)],[c_32852,c_30863]) ).
tcf(c_48134,plain,
multiply(iPr_def_13,sk_c6) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_32852,c_30866]) ).
tcf(c_48147,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_48134,c_30980]) ).
tcf(c_49162,plain,
multiply(inverse(multiply(iPr_def_13,iPr_def_15)),multiply(iPr_def_14,iPr_def_14)) = sk_c6,
inference(superposition,[status(thm)],[c_41895,c_32591]) ).
tcf(c_53466,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_49162,c_48147,c_48134,c_48040,c_47293,c_45877,c_45876,c_45869,c_45866,c_43947,c_43016,c_42397,c_42385,c_41910,c_38002,c_37605,c_37594,c_36086,c_36043,c_35477,c_35473,c_35470,c_33626,c_33615,c_33592,c_32682,c_30855,c_16727,c_485,c_483,c_482,c_481,c_477,c_469,c_460,c_459,c_458,c_457,c_445]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP298-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 14:23:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 15.98/3.28 % SZS status Started for theBenchmark.p
% 15.98/3.28 % SZS status Unsatisfiable for theBenchmark.p
% 15.98/3.28
% 15.98/3.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 15.98/3.28
% 15.98/3.28 % ------ iProver source info
% 15.98/3.28
% 15.98/3.28 % git: date: 2026-07-19 20:42:38 +0200
% 15.98/3.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 15.98/3.28 % git: non_committed_changes: false
% 15.98/3.28
% 15.98/3.28 % ------ Parsing...% successful
% 15.98/3.28
% 15.98/3.28
% 15.98/3.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 15.98/3.28
% 15.98/3.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 15.98/3.28
% 15.98/3.28 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 15.98/3.28
% 15.98/3.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 15.98/3.28 % ------ Proving...
% 15.98/3.28 % ------ Problem Properties
% 15.98/3.28
% 15.98/3.28 %
% 15.98/3.28 % clauses 51
% 15.98/3.28 % conjectures 36
% 15.98/3.28 % EPR 33
% 15.98/3.28 % Horn 18
% 15.98/3.28 % unary 15
% 15.98/3.28 % binary 32
% 15.98/3.28 % lits 94
% 15.98/3.28 % lits eq 88
% 15.98/3.28 % fd_pure 0
% 15.98/3.28 % fd_pseudo 0
% 15.98/3.28 % fd_cond 0
% 15.98/3.28 % fd_pseudo_cond 0
% 15.98/3.28 % AC symbols 0
% 15.98/3.28
% 15.98/3.28 % ------ Schedule dynamic 5 is on
% 15.98/3.28
% 15.98/3.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 15.98/3.28
% 15.98/3.28
% 15.98/3.28 % ------
% 15.98/3.28 % Current options:
% 15.98/3.28 % ------
% 15.98/3.28
% 15.98/3.28
% 15.98/3.28 %
% 15.98/3.28
% 15.98/3.28 % ------ Proving...
% 15.98/3.28 %
% 15.98/3.28
% 15.98/3.28 % SZS status Unsatisfiable for theBenchmark.p
% 15.98/3.28
% 15.98/3.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.98/3.28
% 15.98/3.28
%------------------------------------------------------------------------------