%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP390-1 : 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 : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:33:38 PM UTC 2026
% Result : Unsatisfiable 7.14s 1.63s
% Output : CNFRefutation 7.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 32
% Syntax : Number of formulae : 234 ( 89 unt; 12 def)
% Number of atoms : 760 ( 414 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 387 ( 143 ~; 244 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 84 !; 0 ?; 61 :)
% 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_c4,sk_c9) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c8 = multiply(sk_c4,sk_c9)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c9 = inverse(sk_c4)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c7 = multiply(sk_c5,sk_c8)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c8 = inverse(sk_c5)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f11]) ).
fof(f17,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = multiply(sk_c4,sk_c9)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f17]) ).
fof(f25,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c9 = inverse(sk_c6)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c9 = multiply(sk_c6,sk_c8)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c8 = multiply(sk_c4,sk_c9)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f29]) ).
fof(f37,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c9 = inverse(sk_c6)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c9 = multiply(sk_c6,sk_c8)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = multiply(sk_c4,sk_c9)
| sk_c8 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c9 = inverse(sk_c4)
| sk_c8 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f43]) ).
fof(f53,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c8 = multiply(sk_c4,sk_c9)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c9 = inverse(sk_c4)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f55]) ).
fof(f77,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(X5,sk_c8) != sk_c9
| inverse(X5) != sk_c9
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != X2
| multiply(X1,X2) != sk_c8
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9
| inverse(sk_c8) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk_c9 != multiply(X5,sk_c8)
| sk_c9 != inverse(X5)
| sk_c8 != inverse(X4)
| sk_c7 != multiply(X4,sk_c8)
| sk_c9 != inverse(X3)
| sk_c8 != multiply(X3,sk_c9)
| sk_c8 != multiply(X2,sk_c7)
| inverse(X1) != X2
| multiply(X1,X2) != sk_c8
| sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c9
| inverse(sk_c8) != sk_c7 ),
inference(reorient_equations,[],[f77]) ).
fof(f79,plain,
! [X3,X0,X1,X4,X5] :
( sk_c9 != multiply(X5,sk_c8)
| sk_c9 != inverse(X5)
| sk_c8 != inverse(X4)
| sk_c7 != multiply(X4,sk_c8)
| sk_c9 != inverse(X3)
| sk_c8 != multiply(X3,sk_c9)
| sk_c8 != multiply(inverse(X1),sk_c7)
| sk_c8 != multiply(X1,inverse(X1))
| sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c9
| inverse(sk_c8) != sk_c7 ),
inference(equality_resolution,[],[f78]) ).
tcf(c_89,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_90,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c4,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c4) = sk_c9 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c5,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c4,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( inverse(sk_c6) = sk_c9 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c6,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_104,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c9 )
| ( multiply(sk_c4,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_109,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c9 )
| ( multiply(sk_c6,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c2,sk_c3) = sk_c8 )
| ( multiply(sk_c4,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c4) = sk_c9 )
| ( multiply(sk_c2,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_116,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c4,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_117,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( inverse(sk_c4) = sk_c9 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_128,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( inverse(sk_c8) != sk_c7 )
| ( inverse(X4) != sk_c9 )
| ( inverse(X3) != sk_c8 )
| ( inverse(X2) != sk_c9 )
| ( inverse(X0) != sk_c9 )
| ( multiply(X4,sk_c8) != sk_c9 )
| ( multiply(X3,sk_c8) != sk_c7 )
| ( multiply(X2,sk_c9) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c9 )
| ( multiply(inverse(X1),sk_c7) != sk_c8 )
| ( multiply(X1,inverse(X1)) != sk_c8 ) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_473,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_128]) ).
tcf(c_474,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_128]) ).
tcf(c_475,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_128]) ).
tcf(c_476,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( multiply(inverse(X0),sk_c7) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_128]) ).
tcf(c_477,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_128]) ).
tcf(c_478,definition,
iPr_def_14 = inverse(sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_479,definition,
iPr_def_15 = multiply(sk_c6,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_480,definition,
iPr_def_16 = multiply(sk_c3,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_481,definition,
iPr_def_17 = inverse(sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_482,definition,
iPr_def_18 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_483,definition,
iPr_def_19 = multiply(sk_c5,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_484,definition,
iPr_def_20 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_485,definition,
iPr_def_21 = multiply(sk_c4,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_486,definition,
iPr_def_22 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_487,definition,
iPr_def_23 = multiply(sk_c2,sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_488,definition,
iPr_def_24 = multiply(sk_c1,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_489,definition,
iPr_def_25 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_490,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_14 != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_477,c_478]) ).
tcf(c_491,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( multiply(inverse(X0),sk_c7) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_476]) ).
tcf(c_493,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_475]) ).
tcf(c_494,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_474]) ).
tcf(c_495,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_473]) ).
tcf(c_506,negated_conjecture,
( ( iPr_def_22 = sk_c3 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_507,negated_conjecture,
( ( iPr_def_22 = sk_c3 )
| ( iPr_def_21 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_512,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_513,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_21 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_514,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_109,c_488]) ).
tcf(c_515,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_519,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_21 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_520,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_103,c_489]) ).
tcf(c_521,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_525,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_21 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_528,negated_conjecture,
( ( iPr_def_18 = sk_c8 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_529,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_530,negated_conjecture,
( ( iPr_def_20 = sk_c9 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_531,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_532,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_533,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_861,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(iPr_def_22,sk_c7) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_507,c_480]) ).
tcf(c_944,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_507,c_487]) ).
tcf(c_945,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_506,c_487]) ).
tcf(c_971,plain,
multiply(iPr_def_14,sk_c8) = identity,
inference(superposition,[status(thm)],[c_478,c_90]) ).
tcf(c_972,plain,
multiply(iPr_def_20,sk_c4) = identity,
inference(superposition,[status(thm)],[c_484,c_90]) ).
tcf(c_973,plain,
multiply(iPr_def_18,sk_c5) = identity,
inference(superposition,[status(thm)],[c_482,c_90]) ).
tcf(c_975,plain,
multiply(iPr_def_25,sk_c1) = identity,
inference(superposition,[status(thm)],[c_489,c_90]) ).
tcf(c_976,plain,
multiply(iPr_def_22,sk_c2) = identity,
inference(superposition,[status(thm)],[c_486,c_90]) ).
tcf(c_986,plain,
! [X0: $i] :
( ( iPr_def_14 = sk_c7 )
| ( iPr_def_14 != X0 )
| ( sk_c7 != X0 ) ),
inference(instantiation,[status(thm)],[c_533]) ).
tcf(c_989,plain,
! [X0: $i,X1: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_533]) ).
tcf(c_998,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(sk_c4,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_512,c_485]) ).
tcf(c_1009,plain,
! [X0: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != sk_c7 )
| ( X0 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_989]) ).
tcf(c_1010,plain,
sk_c7 = sk_c7,
inference(instantiation,[status(thm)],[c_532]) ).
tcf(c_1020,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_513,c_488]) ).
tcf(c_1049,plain,
( ( sk_c7 = iPr_def_19 )
| ( iPr_def_19 != sk_c7 )
| ( sk_c7 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_1009]) ).
tcf(c_1062,plain,
( ( sk_c9 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_514,c_485]) ).
tcf(c_1088,plain,
( ( iPr_def_14 = sk_c7 )
| ( iPr_def_14 != iPr_def_19 )
| ( sk_c7 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_986]) ).
tcf(c_1113,plain,
( ( sk_c9 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_515,c_485]) ).
tcf(c_1269,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(sk_c4,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_519,c_485]) ).
tcf(c_1325,plain,
( ( sk_c9 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_25) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_520,c_485]) ).
tcf(c_1367,plain,
( ( sk_c7 = iPr_def_14 )
| ( iPr_def_14 != sk_c7 )
| ( sk_c7 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_1009]) ).
tcf(c_1389,plain,
( ( sk_c9 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_25) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_521,c_485]) ).
tcf(c_1597,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(sk_c4,iPr_def_25) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_525,c_485]) ).
tcf(c_1755,plain,
( ( iPr_def_14 = iPr_def_19 )
| ( sk_c7 = iPr_def_14 )
| ( sk_c8 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_529,c_528]) ).
tcf(c_1833,plain,
( ( iPr_def_14 = iPr_def_19 )
| ( sk_c7 = iPr_def_14 )
| ( sk_c8 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_531,c_529]) ).
tcf(c_1837,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(sk_c3,iPr_def_14) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_531,c_480]) ).
tcf(c_1892,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c9 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_530,c_490]) ).
tcf(c_1893,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_14 )
| ( iPr_def_14 != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_529,c_490]) ).
tcf(c_1894,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_528,c_490]) ).
tcf(c_2004,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_15 )
| ( inverse(sk_c6) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_479,c_493]) ).
tcf(c_2005,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_24 )
| ( inverse(sk_c1) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_488,c_493]) ).
tcf(c_2019,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_25 )
| ( sk_c9 != iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_2005,c_489]) ).
tcf(c_2023,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_17 )
| ( sk_c9 != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_2004,c_481]) ).
tcf(c_2091,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_19 )
| ( inverse(sk_c5) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_483,c_494]) ).
tcf(c_2096,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( inverse(iPr_def_14) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_971,c_494]) ).
tcf(c_2115,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_19 )
| ( sk_c8 != iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_2091,c_482]) ).
tcf(c_2220,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c8,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_483,c_91]) ).
tcf(c_2223,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c3,X0)) = multiply(iPr_def_23,X0),
inference(superposition,[status(thm)],[c_487,c_91]) ).
tcf(c_2226,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_90,c_91]) ).
tcf(c_2228,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c8,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_971,c_91]) ).
tcf(c_2229,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_972,c_91]) ).
tcf(c_2230,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_973,c_91]) ).
tcf(c_2232,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_975,c_91]) ).
tcf(c_2233,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_976,c_91]) ).
tcf(c_2237,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2233,c_89]) ).
tcf(c_2238,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2232,c_89]) ).
tcf(c_2240,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2230,c_89]) ).
tcf(c_2241,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2229,c_89]) ).
tcf(c_2242,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c8,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2228,c_89]) ).
tcf(c_2885,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_21 )
| ( inverse(sk_c4) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_485,c_495]) ).
tcf(c_2887,plain,
( ~ iPr_def_10
| ( sk_c8 != identity )
| ( inverse(inverse(sk_c9)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_90,c_495]) ).
tcf(c_2909,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_20 )
| ( sk_c8 != iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_2885,c_484]) ).
tcf(c_3062,plain,
( ~ iPr_def_13
| ( inverse(identity) != sk_c8 )
| ( multiply(inverse(identity),sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_89,c_491]) ).
tcf(c_4062,plain,
multiply(iPr_def_18,iPr_def_19) = sk_c8,
inference(superposition,[status(thm)],[c_483,c_2240]) ).
tcf(c_4067,plain,
multiply(iPr_def_20,iPr_def_21) = sk_c9,
inference(superposition,[status(thm)],[c_485,c_2241]) ).
tcf(c_4070,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_21,X0)) = multiply(sk_c9,X0),
inference(superposition,[status(thm)],[c_4067,c_91]) ).
tcf(c_4359,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(iPr_def_22,iPr_def_14) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_531,c_861]) ).
tcf(c_5306,plain,
( ( sk_c9 = iPr_def_15 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1062,c_2241]) ).
tcf(c_5307,plain,
( ( sk_c9 = iPr_def_24 )
| ( sk_c9 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_5306,c_4067]) ).
tcf(c_5318,plain,
( ( sk_c9 = iPr_def_17 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1113,c_2241]) ).
tcf(c_5319,plain,
( ( sk_c9 = iPr_def_24 )
| ( sk_c9 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_5318,c_4067]) ).
tcf(c_5384,plain,
( ( sk_c9 = iPr_def_15 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1325,c_2241]) ).
tcf(c_5385,plain,
( ( sk_c9 = iPr_def_25 )
| ( sk_c9 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_5384,c_4067]) ).
tcf(c_5400,plain,
( ( sk_c9 = iPr_def_17 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1389,c_2241]) ).
tcf(c_5401,plain,
( ( sk_c9 = iPr_def_25 )
| ( sk_c9 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_5400,c_4067]) ).
tcf(c_6322,plain,
multiply(sk_c2,iPr_def_16) = multiply(iPr_def_23,sk_c7),
inference(superposition,[status(thm)],[c_480,c_2223]) ).
tcf(c_6328,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(sk_c2,iPr_def_16) = multiply(iPr_def_23,iPr_def_14) ) ),
inference(superposition,[status(thm)],[c_1837,c_2223]) ).
tcf(c_7211,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2226,c_89]) ).
tcf(c_7231,plain,
multiply(inverse(sk_c4),iPr_def_21) = sk_c9,
inference(superposition,[status(thm)],[c_485,c_7211]) ).
tcf(c_7237,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_89,c_7211]) ).
tcf(c_7238,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_90,c_7211]) ).
tcf(c_7308,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(inverse(sk_c4),iPr_def_21) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1269,c_7211]) ).
tcf(c_7313,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(inverse(sk_c4),iPr_def_21) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1597,c_7211]) ).
tcf(c_7346,plain,
! [X0: $i] : multiply(inverse(iPr_def_14),X0) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2242,c_7211]) ).
tcf(c_7347,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2241,c_7211]) ).
tcf(c_7348,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2240,c_7211]) ).
tcf(c_7350,plain,
! [X0: $i] : multiply(inverse(iPr_def_25),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2238,c_7211]) ).
tcf(c_7351,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2237,c_7211]) ).
tcf(c_7372,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_7211,c_7211]) ).
tcf(c_7761,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_7238,c_7372]) ).
tcf(c_7769,plain,
multiply(sk_c9,identity) = multiply(iPr_def_20,iPr_def_21),
inference(superposition,[status(thm)],[c_7761,c_4070]) ).
tcf(c_7779,plain,
multiply(sk_c2,sk_c3) = multiply(iPr_def_23,identity),
inference(superposition,[status(thm)],[c_7761,c_2223]) ).
tcf(c_7786,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_7761,c_7237]) ).
tcf(c_7788,plain,
multiply(iPr_def_23,identity) = iPr_def_23,
inference(light_normalisation,[status(thm)],[c_7779,c_487]) ).
tcf(c_7797,plain,
multiply(sk_c9,identity) = sk_c9,
inference(light_normalisation,[status(thm)],[c_7769,c_4067]) ).
tcf(c_7814,plain,
( ( sk_c8 = iPr_def_18 )
| ( sk_c7 = iPr_def_14 ) ),
inference(global_subsumption_just,[status(thm)],[c_1755,c_529,c_1010,c_1049,c_1088,c_1367,c_1755]) ).
tcf(c_7815,plain,
( ( sk_c7 = iPr_def_14 )
| ( sk_c8 = iPr_def_18 ) ),
inference(renaming,[status(thm)],[c_7814]) ).
tcf(c_7918,plain,
( ( sk_c8 = iPr_def_21 )
| ( sk_c7 = iPr_def_14 ) ),
inference(global_subsumption_just,[status(thm)],[c_1833,c_529,c_1010,c_1049,c_1088,c_1367,c_1833]) ).
tcf(c_7919,plain,
( ( sk_c7 = iPr_def_14 )
| ( sk_c8 = iPr_def_21 ) ),
inference(renaming,[status(thm)],[c_7918]) ).
tcf(c_7949,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_25 ) ),
inference(global_subsumption_just,[status(thm)],[c_2019,c_2023,c_2019,c_5307,c_5319]) ).
tcf(c_7951,plain,
~ iPr_def_12,
inference(global_subsumption_just,[status(thm)],[c_7949,c_2023,c_5385,c_5401,c_7949]) ).
tcf(c_7955,plain,
( iPr_def_13
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_18 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1894,c_7951]) ).
tcf(c_7956,plain,
( iPr_def_13
| iPr_def_11
| iPr_def_10
| ( sk_c9 = iPr_def_20 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1892,c_7951]) ).
tcf(c_7958,plain,
( iPr_def_13
| iPr_def_11
| iPr_def_10
| ( sk_c7 != iPr_def_14 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_490,c_7951]) ).
tcf(c_8022,plain,
( iPr_def_13
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_14 )
| ( iPr_def_14 != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_529,c_7958]) ).
tcf(c_8329,plain,
multiply(sk_c8,iPr_def_14) = identity,
inference(superposition,[status(thm)],[c_7346,c_90]) ).
tcf(c_8332,plain,
! [X0: $i] : multiply(sk_c8,multiply(iPr_def_14,X0)) = X0,
inference(superposition,[status(thm)],[c_7346,c_7211]) ).
tcf(c_8333,plain,
multiply(sk_c8,identity) = inverse(iPr_def_14),
inference(superposition,[status(thm)],[c_7346,c_7761]) ).
tcf(c_8377,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(iPr_def_23,iPr_def_14) = identity ) ),
inference(superposition,[status(thm)],[c_513,c_8329]) ).
tcf(c_8385,plain,
multiply(sk_c5,identity) = multiply(iPr_def_19,iPr_def_14),
inference(superposition,[status(thm)],[c_8329,c_2220]) ).
tcf(c_8449,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_21 )
| ( multiply(iPr_def_23,multiply(iPr_def_14,X0)) = multiply(identity,X0) ) ),
inference(superposition,[status(thm)],[c_8377,c_91]) ).
tcf(c_8455,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_21 )
| ( multiply(iPr_def_23,multiply(iPr_def_14,X0)) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_8449,c_89]) ).
tcf(c_8588,plain,
inverse(iPr_def_14) = sk_c8,
inference(demodulation,[status(thm)],[c_8333,c_7761]) ).
tcf(c_9257,plain,
multiply(iPr_def_19,iPr_def_14) = sk_c5,
inference(demodulation,[status(thm)],[c_8385,c_7761]) ).
tcf(c_9258,plain,
multiply(inverse(iPr_def_19),sk_c5) = iPr_def_14,
inference(superposition,[status(thm)],[c_9257,c_7211]) ).
tcf(c_9263,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),multiply(sk_c5,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_9258,c_91]) ).
tcf(c_9384,plain,
multiply(inverse(iPr_def_19),iPr_def_19) = multiply(iPr_def_14,sk_c8),
inference(superposition,[status(thm)],[c_483,c_9263]) ).
tcf(c_9403,plain,
multiply(inverse(iPr_def_19),iPr_def_19) = identity,
inference(light_normalisation,[status(thm)],[c_9384,c_971]) ).
tcf(c_9649,plain,
multiply(sk_c4,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_7347,c_90]) ).
tcf(c_9652,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_7347,c_7211]) ).
tcf(c_9712,plain,
multiply(iPr_def_20,identity) = iPr_def_20,
inference(superposition,[status(thm)],[c_9649,c_2241]) ).
tcf(c_10077,plain,
multiply(sk_c4,sk_c9) = iPr_def_21,
inference(superposition,[status(thm)],[c_4067,c_9652]) ).
tcf(c_10294,plain,
( iPr_def_13
| iPr_def_11
| iPr_def_10
| ( iPr_def_14 != iPr_def_19 ) ),
inference(global_subsumption_just,[status(thm)],[c_8022,c_1893,c_7951,c_7958]) ).
tcf(c_10581,plain,
multiply(sk_c5,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_7348,c_90]) ).
tcf(c_10584,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_7348,c_7211]) ).
tcf(c_10633,plain,
multiply(inverse(iPr_def_19),identity) = multiply(iPr_def_14,iPr_def_18),
inference(superposition,[status(thm)],[c_10581,c_9263]) ).
tcf(c_11047,plain,
multiply(sk_c5,sk_c8) = iPr_def_19,
inference(superposition,[status(thm)],[c_4062,c_10584]) ).
tcf(c_11521,plain,
( ~ iPr_def_11
| ( sk_c7 != identity ) ),
inference(ground_joinability,[status(thm)],[c_2096,c_8588]) ).
tcf(c_11535,plain,
( ( sk_c7 = iPr_def_14 )
| ~ iPr_def_11
| ( identity != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_529,c_11521]) ).
tcf(c_11627,plain,
( ( sk_c7 = iPr_def_14 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_11535,c_529,c_1010,c_1049,c_1367,c_2115,c_7815]) ).
tcf(c_12002,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_25,X0)) = X0,
inference(superposition,[status(thm)],[c_7350,c_7211]) ).
tcf(c_12003,plain,
multiply(sk_c1,identity) = inverse(iPr_def_25),
inference(superposition,[status(thm)],[c_7350,c_7761]) ).
tcf(c_12609,plain,
inverse(iPr_def_25) = sk_c1,
inference(demodulation,[status(thm)],[c_12003,c_7761]) ).
tcf(c_12633,plain,
multiply(sk_c1,identity) = sk_c1,
inference(superposition,[status(thm)],[c_975,c_12002]) ).
tcf(c_12809,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(iPr_def_23,identity) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_971,c_8455]) ).
tcf(c_13006,plain,
multiply(sk_c2,iPr_def_22) = identity,
inference(superposition,[status(thm)],[c_7351,c_90]) ).
tcf(c_13009,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_22,X0)) = X0,
inference(superposition,[status(thm)],[c_7351,c_7211]) ).
tcf(c_13024,plain,
( ( identity = iPr_def_23 )
| ( sk_c9 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_945,c_13006]) ).
tcf(c_13025,plain,
( ( identity = iPr_def_23 )
| ( sk_c8 = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_944,c_13006]) ).
tcf(c_13920,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(sk_c2,iPr_def_16) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_861,c_13009]) ).
tcf(c_13929,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(sk_c2,iPr_def_16) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_4359,c_13009]) ).
tcf(c_13959,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(iPr_def_23,sk_c7) = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_13929,c_6322]) ).
tcf(c_13977,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(iPr_def_23,sk_c7) = sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_13920,c_6322]) ).
tcf(c_14087,plain,
( ( identity = iPr_def_23 )
| ( multiply(sk_c4,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_13024,c_485]) ).
tcf(c_15432,plain,
multiply(iPr_def_14,iPr_def_18) = inverse(iPr_def_19),
inference(demodulation,[status(thm)],[c_10633,c_7761]) ).
tcf(c_15443,plain,
multiply(sk_c8,inverse(iPr_def_19)) = iPr_def_18,
inference(superposition,[status(thm)],[c_15432,c_8332]) ).
tcf(c_15477,plain,
multiply(iPr_def_19,inverse(iPr_def_19)) = multiply(sk_c5,iPr_def_18),
inference(superposition,[status(thm)],[c_15443,c_2220]) ).
tcf(c_15480,plain,
multiply(iPr_def_19,inverse(iPr_def_19)) = identity,
inference(light_normalisation,[status(thm)],[c_15477,c_10581]) ).
tcf(c_15584,plain,
( ~ iPr_def_13
| ( sk_c8 != identity )
| ( multiply(inverse(iPr_def_19),sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_15480,c_491]) ).
tcf(c_15827,plain,
( ( sk_c7 = iPr_def_14 )
| ~ iPr_def_13
| ( sk_c8 != identity )
| ( multiply(inverse(iPr_def_19),iPr_def_19) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_529,c_15584]) ).
tcf(c_16729,plain,
( ~ iPr_def_13
| ( sk_c8 != identity )
| ( multiply(identity,sk_c7) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_3062,c_7786]) ).
tcf(c_16730,plain,
( ~ iPr_def_13
| ( sk_c8 != identity )
| ( sk_c8 != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_16729,c_89]) ).
tcf(c_17382,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_16730,c_15827,c_15480,c_15477,c_14087,c_13977,c_13959,c_13025,c_12809,c_12633,c_12609,c_11627,c_11521,c_11047,c_10294,c_10077,c_9712,c_9649,c_9403,c_8377,c_7958,c_7956,c_7955,c_7919,c_7797,c_7788,c_7769,c_7786,c_7313,c_7308,c_7231,c_6328,c_6322,c_2909,c_2887,c_1020,c_998,c_478]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP390-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 14:38:51 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.39 Running first-order theorem proving
% 0.11/0.39 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
% 0.11/0.39
% 0.11/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.39
% 0.11/0.40 % Detected problem language: tptp
% 0.11/0.41 % Proving...
% 7.14/1.63 % SZS status Started for theBenchmark.p
% 7.14/1.63 % SZS status Unsatisfiable for theBenchmark.p
% 7.14/1.63
% 7.14/1.63 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.14/1.63
% 7.14/1.63 % ------ iProver source info
% 7.14/1.63
% 7.14/1.63 % git: date: 2026-07-19 20:42:38 +0200
% 7.14/1.63 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.14/1.63 % git: non_committed_changes: false
% 7.14/1.63
% 7.14/1.63 % ------ Parsing...% successful
% 7.14/1.63
% 7.14/1.63
% 7.14/1.63 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.14/1.63
% 7.14/1.63 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 7.14/1.63
% 7.14/1.63 % ------ Preprocessing... gs_s sp: 5 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.14/1.63
% 7.14/1.63 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 7.14/1.63 % ------ Proving...
% 7.14/1.63 % ------ Problem Properties
% 7.14/1.63
% 7.14/1.63 %
% 7.14/1.63 % clauses 56
% 7.14/1.63 % conjectures 41
% 7.14/1.63 % EPR 37
% 7.14/1.63 % Horn 19
% 7.14/1.63 % unary 15
% 7.14/1.63 % binary 36
% 7.14/1.63 % lits 104
% 7.14/1.63 % lits eq 96
% 7.14/1.63 % fd_pure 0
% 7.14/1.63 % fd_pseudo 0
% 7.14/1.63 % fd_cond 0
% 7.14/1.63 % fd_pseudo_cond 0
% 7.14/1.63 % AC symbols 0
% 7.14/1.63
% 7.14/1.63 % ------ Schedule dynamic 5 is on
% 7.14/1.63
% 7.14/1.63 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.14/1.63
% 7.14/1.63
% 7.14/1.63 % ------
% 7.14/1.63 % Current options:
% 7.14/1.63 % ------
% 7.14/1.63
% 7.14/1.63
% 7.14/1.63 %
% 7.14/1.63
% 7.14/1.63 % ------ Proving...
% 7.14/1.63 %
% 7.14/1.63
% 7.14/1.63 % SZS status Unsatisfiable for theBenchmark.p
% 7.14/1.63
% 7.14/1.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.14/1.63
% 7.14/1.63
%------------------------------------------------------------------------------