%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP277-1 : 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 : n009.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 01:32:42 PM UTC 2026
% Result : Unsatisfiable 10.34s 2.62s
% Output : CNFRefutation 10.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 31
% Syntax : Number of formulae : 258 ( 119 unt; 10 def)
% Number of atoms : 774 ( 425 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 281 ( 89 ~; 192 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 2 avg)
% Maximal term depth : 5 ( 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 : 83 ( 0 sgn 83 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c7 = inverse(sk_c2)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c6 = multiply(sk_c3,sk_c4)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( inverse(sk_c3) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c4 = inverse(sk_c3)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f14]) ).
fof(f22,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c6 = multiply(sk_c3,sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c4 = inverse(sk_c3)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f24]) ).
fof(f28,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c7 = inverse(sk_c2)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c6 = multiply(sk_c3,sk_c4)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c3) = sk_c4
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c4 = inverse(sk_c3)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f44]) ).
fof(f52,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(X3,sk_c7) != sk_c6
| inverse(X2) != X3
| multiply(X2,X3) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( sk_c6 != multiply(X3,sk_c7)
| inverse(X2) != X3
| sk_c6 != multiply(X2,X3)
| sk_c7 != multiply(X1,sk_c6)
| sk_c7 != inverse(X1)
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c7 != multiply(sk_c5,sk_c6)
| sk_c6 != multiply(sk_c7,sk_c5)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,plain,
! [X2,X0,X1] :
( sk_c6 != multiply(inverse(X2),sk_c7)
| sk_c6 != multiply(X2,inverse(X2))
| sk_c7 != multiply(X1,sk_c6)
| sk_c7 != inverse(X1)
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c7 != multiply(sk_c5,sk_c6)
| sk_c6 != multiply(sk_c7,sk_c5)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7) ),
inference(equality_resolution,[],[f53]) ).
tcf(c_77,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_78,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_80,negated_conjecture,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_81,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_82,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_83,negated_conjecture,
( ( multiply(sk_c3,sk_c4) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_84,negated_conjecture,
( ( inverse(sk_c3) = sk_c4 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_85,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c3) = sk_c4 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_92,negated_conjecture,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_94,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_95,negated_conjecture,
( ( multiply(sk_c3,sk_c4) = sk_c6 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c3) = sk_c4 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_97,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c6 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_100,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_104,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X1) != sk_c7 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c5,sk_c6) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c5) != sk_c6 )
| ( multiply(X1,sk_c6) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 )
| ( multiply(inverse(X2),sk_c7) != sk_c6 )
| ( multiply(X2,inverse(X2)) != sk_c6 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_345,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_104]) ).
tcf(c_346,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_104]) ).
tcf(c_347,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( multiply(inverse(X0),sk_c7) != sk_c6 )
| ( multiply(X0,inverse(X0)) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_104]) ).
tcf(c_348,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c5,sk_c6) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c5) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_104]) ).
tcf(c_349,definition,
iPr_def_13 = multiply(sk_c7,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_350,definition,
iPr_def_14 = multiply(sk_c6,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_351,definition,
iPr_def_15 = multiply(sk_c5,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_352,definition,
iPr_def_16 = multiply(sk_c4,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_353,definition,
iPr_def_17 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_354,definition,
iPr_def_18 = multiply(sk_c3,sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_355,definition,
iPr_def_19 = multiply(sk_c2,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_356,definition,
iPr_def_20 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_357,definition,
iPr_def_21 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_358,definition,
iPr_def_22 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_359,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c7 )
| ( iPr_def_14 != sk_c5 )
| ( iPr_def_13 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_348,c_351,c_350,c_349]) ).
tcf(c_360,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( multiply(inverse(X0),sk_c7) != sk_c6 )
| ( multiply(X0,inverse(X0)) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_347]) ).
tcf(c_361,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_346]) ).
tcf(c_362,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_345]) ).
tcf(c_366,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_100,c_355]) ).
tcf(c_367,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_99,c_356]) ).
tcf(c_368,negated_conjecture,
( ( iPr_def_15 = sk_c7 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_369,negated_conjecture,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_370,negated_conjecture,
( ( iPr_def_17 = sk_c4 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_371,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_372,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_373,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_374,negated_conjecture,
( ( iPr_def_14 = sk_c5 )
| ( iPr_def_13 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_376,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_17 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_377,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_381,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_85,c_358]) ).
tcf(c_382,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_17 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_383,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_384,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_385,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_386,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_635,plain,
( ( sk_c6 = iPr_def_13 )
| ( multiply(sk_c5,iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_369,c_351]) ).
tcf(c_658,plain,
( ( sk_c6 = iPr_def_13 )
| ( multiply(sk_c3,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_370,c_354]) ).
tcf(c_672,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c6 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_371,c_369]) ).
tcf(c_799,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c3,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_376,c_354]) ).
tcf(c_862,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c2,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_377,c_355]) ).
tcf(c_866,plain,
( ( sk_c6 = iPr_def_13 )
| ( multiply(sk_c2,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_371,c_355]) ).
tcf(c_900,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_367,c_358]) ).
tcf(c_909,plain,
multiply(iPr_def_20,sk_c2) = identity,
inference(superposition,[status(thm)],[c_356,c_78]) ).
tcf(c_910,plain,
multiply(iPr_def_17,sk_c3) = identity,
inference(superposition,[status(thm)],[c_353,c_78]) ).
tcf(c_911,plain,
multiply(iPr_def_21,sk_c1) = identity,
inference(superposition,[status(thm)],[c_357,c_78]) ).
tcf(c_1051,plain,
( ( sk_c6 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_382,c_354]) ).
tcf(c_1069,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_383,c_355]) ).
tcf(c_1139,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_384,c_355]) ).
tcf(c_1143,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( sk_c7 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_384,c_372]) ).
tcf(c_1206,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_385,c_355]) ).
tcf(c_1209,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_385,c_373]) ).
tcf(c_1279,plain,
( ( sk_c6 = iPr_def_22 )
| ( multiply(sk_c7,iPr_def_14) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_386,c_349]) ).
tcf(c_1302,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_19 )
| ( inverse(sk_c2) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_355,c_361]) ).
tcf(c_1303,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_15 )
| ( inverse(sk_c5) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_351,c_361]) ).
tcf(c_1324,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_20 )
| ( sk_c7 != iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_1302,c_356]) ).
tcf(c_1466,plain,
( ~ iPr_def_10
| ( sk_c6 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_78,c_362]) ).
tcf(c_1719,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c7,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_358,c_79]) ).
tcf(c_1720,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_350,c_79]) ).
tcf(c_1721,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c6,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_355,c_79]) ).
tcf(c_1723,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c7,X0)) = multiply(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_352,c_79]) ).
tcf(c_1724,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c5,X0)) = multiply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_349,c_79]) ).
tcf(c_1725,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c6,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_351,c_79]) ).
tcf(c_1727,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_78,c_79]) ).
tcf(c_1729,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_909,c_79]) ).
tcf(c_1730,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_910,c_79]) ).
tcf(c_1731,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_911,c_79]) ).
tcf(c_1735,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1731,c_77]) ).
tcf(c_1736,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1730,c_77]) ).
tcf(c_1737,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1729,c_77]) ).
tcf(c_1865,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_13 = iPr_def_22 )
| ( sk_c6 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_672,c_383]) ).
tcf(c_1866,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_13 = iPr_def_22 )
| ( sk_c6 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_672,c_381]) ).
tcf(c_2113,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_13 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1209,c_1143]) ).
tcf(c_2122,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( multiply(sk_c6,iPr_def_20) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1209,c_350]) ).
tcf(c_2158,plain,
multiply(iPr_def_21,iPr_def_22) = sk_c7,
inference(superposition,[status(thm)],[c_358,c_1735]) ).
tcf(c_2170,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(iPr_def_22,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_2158,c_79]) ).
tcf(c_2511,plain,
multiply(iPr_def_20,iPr_def_19) = sk_c6,
inference(superposition,[status(thm)],[c_355,c_1737]) ).
tcf(c_2516,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_19,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_2511,c_79]) ).
tcf(c_2734,plain,
( ( sk_c6 = iPr_def_13 )
| ( multiply(iPr_def_14,iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_374,c_635]) ).
tcf(c_3622,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_862,c_1737]) ).
tcf(c_3623,plain,
( ( sk_c6 = iPr_def_18 )
| ( sk_c7 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_3622,c_2511]) ).
tcf(c_3751,plain,
( ( sk_c6 = iPr_def_13 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_866,c_1737]) ).
tcf(c_3752,plain,
( ( sk_c6 = iPr_def_18 )
| ( sk_c6 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_3751,c_2511]) ).
tcf(c_3815,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_900,c_1735]) ).
tcf(c_3816,plain,
( ( sk_c7 = iPr_def_20 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_3815,c_2158]) ).
tcf(c_4390,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1069,c_1737]) ).
tcf(c_4391,plain,
( ( sk_c6 = iPr_def_22 )
| ( sk_c6 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_4390,c_2511]) ).
tcf(c_4473,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1139,c_1737]) ).
tcf(c_4474,plain,
( ( sk_c6 = iPr_def_22 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_4473,c_2511]) ).
tcf(c_4754,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1206,c_1737]) ).
tcf(c_4755,plain,
( ( sk_c6 = iPr_def_22 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_4754,c_2511]) ).
tcf(c_5600,plain,
multiply(sk_c2,iPr_def_14) = multiply(iPr_def_19,sk_c7),
inference(superposition,[status(thm)],[c_350,c_1721]) ).
tcf(c_5844,plain,
multiply(sk_c4,iPr_def_13) = multiply(iPr_def_16,sk_c5),
inference(superposition,[status(thm)],[c_349,c_1723]) ).
tcf(c_6145,plain,
multiply(sk_c5,iPr_def_14) = multiply(iPr_def_15,sk_c7),
inference(superposition,[status(thm)],[c_350,c_1725]) ).
tcf(c_6226,plain,
( ( sk_c6 = iPr_def_22 )
| ( multiply(iPr_def_14,iPr_def_14) = multiply(iPr_def_15,sk_c7) ) ),
inference(superposition,[status(thm)],[c_386,c_6145]) ).
tcf(c_6819,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1727,c_77]) ).
tcf(c_6824,plain,
multiply(inverse(sk_c6),iPr_def_14) = sk_c7,
inference(superposition,[status(thm)],[c_350,c_6819]) ).
tcf(c_6828,plain,
multiply(inverse(sk_c7),iPr_def_13) = sk_c5,
inference(superposition,[status(thm)],[c_349,c_6819]) ).
tcf(c_6829,plain,
multiply(inverse(sk_c5),iPr_def_15) = sk_c6,
inference(superposition,[status(thm)],[c_351,c_6819]) ).
tcf(c_6830,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_77,c_6819]) ).
tcf(c_6831,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_78,c_6819]) ).
tcf(c_6832,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[status(thm)],[c_79,c_6819]) ).
tcf(c_6936,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_1737,c_6819]) ).
tcf(c_6937,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_1736,c_6819]) ).
tcf(c_6938,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_1735,c_6819]) ).
tcf(c_6969,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_6819,c_6819]) ).
tcf(c_7613,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_6831,c_6969]) ).
tcf(c_7622,plain,
multiply(sk_c7,identity) = multiply(iPr_def_21,iPr_def_22),
inference(superposition,[status(thm)],[c_7613,c_2170]) ).
tcf(c_7624,plain,
multiply(sk_c6,sk_c7) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_7613,c_1720]) ).
tcf(c_7635,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_7613,c_6830]) ).
tcf(c_7643,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_7624,c_350]) ).
tcf(c_7667,plain,
( ( sk_c7 = iPr_def_15 )
| ~ iPr_def_11
| ( sk_c7 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_366,c_1324]) ).
tcf(c_7706,plain,
( ( sk_c7 = iPr_def_15 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_7667,c_3816,c_7667]) ).
tcf(c_8202,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_13 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1866,c_1865]) ).
tcf(c_8855,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_6936,c_6819]) ).
tcf(c_9017,plain,
( ( sk_c6 = iPr_def_22 )
| ( multiply(inverse(iPr_def_15),multiply(iPr_def_14,iPr_def_14)) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_6226,c_6819]) ).
tcf(c_9318,plain,
multiply(sk_c2,sk_c6) = iPr_def_19,
inference(superposition,[status(thm)],[c_2511,c_8855]) ).
tcf(c_9381,plain,
multiply(sk_c3,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_6937,c_78]) ).
tcf(c_9395,plain,
( ( identity = iPr_def_18 )
| ( sk_c6 = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_1051,c_9381]) ).
tcf(c_9396,plain,
( ( identity = iPr_def_18 )
| ( sk_c7 = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_799,c_9381]) ).
tcf(c_9398,plain,
( ( identity = iPr_def_18 )
| ( sk_c6 = iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_658,c_9381]) ).
tcf(c_9449,plain,
( ~ iPr_def_11
| ( inverse(sk_c5) != sk_c7 ) ),
inference(global_subsumption_just,[status(thm)],[c_1303,c_1303,c_7706]) ).
tcf(c_9455,plain,
( ( sk_c6 = iPr_def_22 )
| ~ iPr_def_11
| ( inverse(iPr_def_14) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_386,c_9449]) ).
tcf(c_9499,plain,
( ( sk_c6 = iPr_def_22 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_9455,c_1324,c_4474,c_4755]) ).
tcf(c_9570,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_22,sk_c7) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_9395,c_350]) ).
tcf(c_9702,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_9396,c_358]) ).
tcf(c_10142,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( identity = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_9398,c_9395]) ).
tcf(c_10730,plain,
multiply(sk_c1,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_6938,c_78]) ).
tcf(c_10733,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_6938,c_6819]) ).
tcf(c_10734,plain,
multiply(sk_c1,identity) = inverse(iPr_def_21),
inference(superposition,[status(thm)],[c_6938,c_7613]) ).
tcf(c_10749,plain,
( ( identity = iPr_def_22 )
| ( identity = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_9702,c_10730]) ).
tcf(c_11070,plain,
! [X0: $i] :
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_22,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_10749,c_77]) ).
tcf(c_11620,plain,
inverse(iPr_def_21) = sk_c1,
inference(demodulation,[status(thm)],[c_10734,c_7613]) ).
tcf(c_11639,plain,
multiply(sk_c1,sk_c7) = iPr_def_22,
inference(superposition,[status(thm)],[c_2158,c_10733]) ).
tcf(c_12720,plain,
( ( identity = iPr_def_18 )
| ( sk_c7 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_11070,c_9570]) ).
tcf(c_15505,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_6969,c_78]) ).
tcf(c_15508,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_6969,c_6819]) ).
tcf(c_15509,plain,
! [X0: $i] : multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_6969,c_7613]) ).
tcf(c_15510,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_15509,c_7613]) ).
tcf(c_15524,plain,
! [X0: $i] :
( ~ iPr_def_12
| ( sk_c6 != identity )
| ( multiply(inverse(X0),sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_360,c_15505]) ).
tcf(c_15528,plain,
( ~ iPr_def_10
| ( sk_c6 != identity ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1466,c_15510]) ).
tcf(c_15584,plain,
( ~ iPr_def_12
| ( sk_c6 != identity ) ),
inference(superposition,[status(thm)],[c_78,c_15524]) ).
tcf(c_15871,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c_15505,c_79]) ).
tcf(c_15875,plain,
multiply(sk_c7,inverse(iPr_def_22)) = multiply(iPr_def_21,identity),
inference(superposition,[status(thm)],[c_15505,c_2170]) ).
tcf(c_15879,plain,
multiply(iPr_def_16,inverse(sk_c7)) = multiply(sk_c4,identity),
inference(superposition,[status(thm)],[c_15505,c_1723]) ).
tcf(c_15880,plain,
multiply(iPr_def_14,inverse(sk_c7)) = multiply(sk_c6,identity),
inference(superposition,[status(thm)],[c_15505,c_1720]) ).
tcf(c_15881,plain,
multiply(iPr_def_22,inverse(sk_c7)) = multiply(sk_c1,identity),
inference(superposition,[status(thm)],[c_15505,c_1719]) ).
tcf(c_15884,plain,
multiply(sk_c6,inverse(iPr_def_19)) = multiply(iPr_def_20,identity),
inference(superposition,[status(thm)],[c_15505,c_2516]) ).
tcf(c_15886,plain,
multiply(iPr_def_15,inverse(sk_c6)) = multiply(sk_c5,identity),
inference(superposition,[status(thm)],[c_15505,c_1725]) ).
tcf(c_15887,plain,
multiply(iPr_def_19,inverse(sk_c6)) = multiply(sk_c2,identity),
inference(superposition,[status(thm)],[c_15505,c_1721]) ).
tcf(c_15896,plain,
multiply(iPr_def_13,inverse(sk_c5)) = multiply(sk_c7,identity),
inference(superposition,[status(thm)],[c_15505,c_1724]) ).
tcf(c_15897,plain,
multiply(iPr_def_20,identity) = inverse(sk_c2),
inference(superposition,[status(thm)],[c_15505,c_1737]) ).
tcf(c_16298,plain,
multiply(sk_c6,sk_c7) = iPr_def_14,
inference(superposition,[status(thm)],[c_6824,c_15508]) ).
tcf(c_16300,plain,
multiply(sk_c7,sk_c5) = iPr_def_13,
inference(superposition,[status(thm)],[c_6828,c_15508]) ).
tcf(c_16301,plain,
multiply(sk_c5,sk_c6) = iPr_def_15,
inference(superposition,[status(thm)],[c_6829,c_15508]) ).
tcf(c_17101,plain,
multiply(iPr_def_22,inverse(multiply(sk_c1,sk_c7))) = identity,
inference(superposition,[status(thm)],[c_15871,c_1719]) ).
tcf(c_17103,plain,
multiply(iPr_def_14,inverse(multiply(sk_c6,sk_c7))) = identity,
inference(superposition,[status(thm)],[c_15871,c_1720]) ).
tcf(c_17107,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(X0,inverse(multiply(sk_c6,X0)))) = multiply(sk_c5,identity),
inference(superposition,[status(thm)],[c_15871,c_1725]) ).
tcf(c_17109,plain,
multiply(iPr_def_19,inverse(multiply(sk_c2,sk_c6))) = identity,
inference(superposition,[status(thm)],[c_15871,c_1721]) ).
tcf(c_17121,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(X0,inverse(multiply(sk_c5,X0)))) = multiply(sk_c7,identity),
inference(superposition,[status(thm)],[c_15871,c_1724]) ).
tcf(c_17140,plain,
! [X0: $i] : multiply(X0,inverse(multiply(iPr_def_20,X0))) = multiply(sk_c2,identity),
inference(superposition,[status(thm)],[c_15871,c_8855]) ).
tcf(c_17170,plain,
multiply(iPr_def_19,inverse(iPr_def_19)) = identity,
inference(light_normalisation,[status(thm)],[c_17109,c_9318]) ).
tcf(c_17171,plain,
multiply(iPr_def_14,inverse(iPr_def_14)) = identity,
inference(light_normalisation,[status(thm)],[c_17103,c_16298]) ).
tcf(c_17172,plain,
multiply(iPr_def_22,inverse(iPr_def_22)) = identity,
inference(light_normalisation,[status(thm)],[c_17101,c_11639]) ).
tcf(c_17191,plain,
! [X0: $i] : multiply(X0,inverse(multiply(iPr_def_20,X0))) = multiply(iPr_def_19,inverse(sk_c6)),
inference(light_normalisation,[status(thm)],[c_17140,c_15887]) ).
tcf(c_17212,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(X0,inverse(multiply(sk_c5,X0)))) = multiply(iPr_def_13,inverse(sk_c5)),
inference(light_normalisation,[status(thm)],[c_17121,c_15896]) ).
tcf(c_17223,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(X0,inverse(multiply(sk_c6,X0)))) = multiply(iPr_def_15,inverse(sk_c6)),
inference(light_normalisation,[status(thm)],[c_17107,c_15886]) ).
tcf(c_19817,plain,
multiply(sk_c7,inverse(iPr_def_22)) = iPr_def_21,
inference(demodulation,[status(thm)],[c_15875,c_7613]) ).
tcf(c_19844,plain,
multiply(inverse(sk_c7),iPr_def_21) = inverse(iPr_def_22),
inference(superposition,[status(thm)],[c_19817,c_6819]) ).
tcf(c_19851,plain,
multiply(iPr_def_22,inverse(iPr_def_22)) = multiply(sk_c1,iPr_def_21),
inference(superposition,[status(thm)],[c_19817,c_1719]) ).
tcf(c_23087,plain,
multiply(inverse(inverse(sk_c7)),inverse(iPr_def_22)) = iPr_def_21,
inference(superposition,[status(thm)],[c_19844,c_6819]) ).
tcf(c_23088,plain,
! [X0: $i] : multiply(inverse(sk_c7),multiply(iPr_def_21,X0)) = multiply(inverse(iPr_def_22),X0),
inference(superposition,[status(thm)],[c_19844,c_79]) ).
tcf(c_23135,plain,
multiply(iPr_def_16,inverse(sk_c7)) = sk_c4,
inference(demodulation,[status(thm)],[c_15879,c_7613]) ).
tcf(c_23154,plain,
multiply(inverse(iPr_def_16),sk_c4) = inverse(sk_c7),
inference(superposition,[status(thm)],[c_23135,c_6819]) ).
tcf(c_23615,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),multiply(sk_c4,X0)) = multiply(inverse(sk_c7),X0),
inference(superposition,[status(thm)],[c_23154,c_79]) ).
tcf(c_23626,plain,
multiply(iPr_def_14,inverse(sk_c7)) = sk_c6,
inference(demodulation,[status(thm)],[c_15880,c_7613]) ).
tcf(c_23627,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_14,inverse(iPr_def_14)) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_12720,c_23626]) ).
tcf(c_23893,plain,
multiply(inverse(sk_c7),identity) = multiply(inverse(iPr_def_22),sk_c1),
inference(superposition,[status(thm)],[c_911,c_23088]) ).
tcf(c_24111,plain,
multiply(inverse(iPr_def_16),multiply(iPr_def_16,sk_c5)) = multiply(inverse(sk_c7),iPr_def_13),
inference(superposition,[status(thm)],[c_5844,c_23615]) ).
tcf(c_24112,plain,
multiply(inverse(sk_c7),identity) = multiply(inverse(iPr_def_16),sk_c4),
inference(superposition,[status(thm)],[c_7613,c_23615]) ).
tcf(c_24126,plain,
multiply(inverse(sk_c7),identity) = inverse(sk_c7),
inference(light_normalisation,[status(thm)],[c_24112,c_23154,c_23893]) ).
tcf(c_24127,plain,
multiply(inverse(iPr_def_16),multiply(iPr_def_16,sk_c5)) = sk_c5,
inference(light_normalisation,[status(thm)],[c_24111,c_6828]) ).
tcf(c_24467,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c7)),multiply(X0,iPr_def_13)) = sk_c5,
inference(superposition,[status(thm)],[c_16300,c_6832]) ).
tcf(c_24481,plain,
! [X0: $i] :
( ( sk_c6 = iPr_def_22 )
| ( multiply(inverse(multiply(X0,sk_c7)),multiply(X0,iPr_def_13)) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1279,c_6832]) ).
tcf(c_24632,plain,
! [X0: $i] :
( ( sk_c6 = iPr_def_13 )
| ( multiply(inverse(multiply(X0,iPr_def_14)),multiply(X0,iPr_def_15)) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_2734,c_6832]) ).
tcf(c_24686,plain,
! [X0: $i] : multiply(inverse(multiply(X0,inverse(sk_c7))),multiply(X0,sk_c5)) = iPr_def_13,
inference(superposition,[status(thm)],[c_6828,c_6832]) ).
tcf(c_27760,plain,
multiply(iPr_def_22,inverse(sk_c7)) = sk_c1,
inference(demodulation,[status(thm)],[c_15881,c_7613]) ).
tcf(c_27776,plain,
( ( iPr_def_13 = iPr_def_22 )
| ( multiply(iPr_def_22,inverse(iPr_def_19)) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_1143,c_27760]) ).
tcf(c_27890,plain,
multiply(sk_c6,inverse(iPr_def_19)) = iPr_def_20,
inference(demodulation,[status(thm)],[c_15884,c_7613]) ).
tcf(c_27918,plain,
multiply(inverse(sk_c6),iPr_def_20) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_27890,c_6819]) ).
tcf(c_27922,plain,
multiply(iPr_def_19,inverse(iPr_def_19)) = multiply(sk_c2,iPr_def_20),
inference(superposition,[status(thm)],[c_27890,c_1721]) ).
tcf(c_28441,plain,
multiply(iPr_def_15,inverse(sk_c6)) = sk_c5,
inference(demodulation,[status(thm)],[c_15886,c_7613]) ).
tcf(c_28469,plain,
multiply(inverse(iPr_def_15),sk_c5) = inverse(sk_c6),
inference(superposition,[status(thm)],[c_28441,c_6819]) ).
tcf(c_28533,plain,
( ( sk_c6 = iPr_def_22 )
| ( multiply(inverse(iPr_def_15),iPr_def_14) = inverse(sk_c6) ) ),
inference(superposition,[status(thm)],[c_386,c_28469]) ).
tcf(c_28553,plain,
multiply(iPr_def_19,inverse(sk_c6)) = sk_c2,
inference(demodulation,[status(thm)],[c_15887,c_7613]) ).
tcf(c_31006,plain,
multiply(iPr_def_13,inverse(sk_c5)) = sk_c7,
inference(demodulation,[status(thm)],[c_15896,c_7613]) ).
tcf(c_31011,plain,
multiply(inverse(iPr_def_13),sk_c7) = inverse(sk_c5),
inference(superposition,[status(thm)],[c_31006,c_6819]) ).
tcf(c_31474,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_31011,c_31006,c_28553,c_28533,c_28441,c_27922,c_27918,c_27890,c_27776,c_24686,c_24632,c_24481,c_24467,c_24127,c_24126,c_24111,c_23627,c_23087,c_19851,c_19817,c_17223,c_17212,c_17191,c_17172,c_17171,c_17170,c_17140,c_17121,c_17107,c_16301,c_16298,c_15897,c_15884,c_15875,c_15584,c_15528,c_15505,c_11639,c_11620,c_10142,c_9499,c_9449,c_9318,c_9017,c_8202,c_7643,c_7622,c_7635,c_5600,c_4755,c_4474,c_4391,c_3752,c_3623,c_2122,c_2113,c_1279,c_368,c_359]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP277-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 14:20:44 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 10.34/2.62 % SZS status Started for theBenchmark.p
% 10.34/2.62 % SZS status Unsatisfiable for theBenchmark.p
% 10.34/2.62
% 10.34/2.62 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.34/2.62
% 10.34/2.62 % ------ iProver source info
% 10.34/2.62
% 10.34/2.62 % git: date: 2026-07-19 20:42:38 +0200
% 10.34/2.62 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.34/2.62 % git: non_committed_changes: false
% 10.34/2.62
% 10.34/2.62 % ------ Parsing...% successful
% 10.34/2.62
% 10.34/2.62
% 10.34/2.62 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.34/2.62
% 10.34/2.62 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.34/2.62
% 10.34/2.62 % ------ Preprocessing... gs_s sp: 3 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.34/2.62
% 10.34/2.62 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.34/2.62 % ------ Proving...
% 10.34/2.62 % ------ Problem Properties
% 10.34/2.62
% 10.34/2.62 %
% 10.34/2.62 % clauses 41
% 10.34/2.62 % conjectures 28
% 10.34/2.62 % EPR 25
% 10.34/2.62 % Horn 16
% 10.34/2.62 % unary 13
% 10.34/2.62 % binary 24
% 10.34/2.62 % lits 76
% 10.34/2.62 % lits eq 70
% 10.34/2.62 % fd_pure 0
% 10.34/2.62 % fd_pseudo 0
% 10.34/2.62 % fd_cond 0
% 10.34/2.62 % fd_pseudo_cond 0
% 10.34/2.62 % AC symbols 0
% 10.34/2.62
% 10.34/2.62 % ------ Schedule dynamic 5 is on
% 10.34/2.62
% 10.34/2.62 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.34/2.62
% 10.34/2.62
% 10.34/2.62 % ------
% 10.34/2.62 % Current options:
% 10.34/2.62 % ------
% 10.34/2.62
% 10.34/2.62
% 10.34/2.62 %
% 10.34/2.62
% 10.34/2.62 % ------ Proving...
% 10.34/2.62 %
% 10.34/2.62
% 10.34/2.62 % SZS status Unsatisfiable for theBenchmark.p
% 10.34/2.62
% 10.34/2.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.34/2.63
% 10.34/2.63
%------------------------------------------------------------------------------