%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP370-1 : 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 01:33:25 PM UTC 2026
% Result : Unsatisfiable 4.75s 2.19s
% Output : CNFRefutation 10.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 40
% Syntax : Number of formulae : 294 ( 76 unt; 11 def)
% Number of atoms : 991 ( 525 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 521 ( 183 ~; 338 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 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 : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 78 !; 0 ?; 51 :)
% 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_c3,sk_c9) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c9 = inverse(sk_c3)
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c7 = inverse(sk_c4)
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c7 = multiply(sk_c9,sk_c6)
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c6 = multiply(sk_c5,sk_c9)
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c9 = inverse(sk_c5)
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| sk_c8 = multiply(sk_c1,sk_c2) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c9 = inverse(sk_c3)
| sk_c8 = multiply(sk_c1,sk_c2) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = multiply(sk_c1,sk_c2) ),
inference(reorient_equations,[],[f23]) ).
fof(f29,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c6 = multiply(sk_c5,sk_c9)
| sk_c8 = multiply(sk_c1,sk_c2) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c9 = inverse(sk_c5)
| sk_c8 = multiply(sk_c1,sk_c2) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c9 = inverse(sk_c3)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = inverse(sk_c4)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c9,sk_c6)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f41]) ).
fof(f47,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f47]) ).
fof(f51,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c7 = inverse(sk_c4)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c7 = multiply(sk_c9,sk_c6)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c6 = multiply(sk_c5,sk_c9)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c9 = inverse(sk_c5)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( inverse(X5) != sk_c9
| multiply(X5,sk_c9) != X4
| multiply(sk_c9,X4) != sk_c7
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk_c9 != inverse(X5)
| multiply(X5,sk_c9) != X4
| sk_c7 != multiply(sk_c9,X4)
| sk_c7 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(X2,sk_c9)
| sk_c8 != multiply(X1,sk_c7)
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c9 ),
inference(reorient_equations,[],[f61]) ).
fof(f63,plain,
! [X2,X3,X0,X4,X5] :
( sk_c9 != inverse(X5)
| multiply(X5,sk_c9) != X4
| sk_c7 != multiply(sk_c9,X4)
| sk_c7 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(X2,sk_c9)
| sk_c8 != multiply(inverse(X0),sk_c7)
| sk_c8 != multiply(X0,inverse(X0))
| multiply(sk_c7,sk_c8) != sk_c9 ),
inference(equality_resolution,[],[f62]) ).
fof(f64,plain,
! [X2,X3,X0,X5] :
( sk_c9 != inverse(X5)
| sk_c7 != multiply(sk_c9,multiply(X5,sk_c9))
| sk_c7 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(X2,sk_c9)
| sk_c8 != multiply(inverse(X0),sk_c7)
| sk_c8 != multiply(X0,inverse(X0))
| multiply(sk_c7,sk_c8) != sk_c9 ),
inference(equality_resolution,[],[f63]) ).
tcf(c_81,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_82,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_84,negated_conjecture,
( ( multiply(sk_c3,sk_c9) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_85,negated_conjecture,
( ( inverse(sk_c3) = sk_c9 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_86,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_88,negated_conjecture,
( ( multiply(sk_c9,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_89,negated_conjecture,
( ( multiply(sk_c5,sk_c9) = sk_c6 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c5) = sk_c9 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_91,negated_conjecture,
( ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c3) = sk_c9 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_93,negated_conjecture,
( ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_96,negated_conjecture,
( ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( multiply(sk_c5,sk_c9) = sk_c6 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c5) = sk_c9 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( inverse(sk_c3) = sk_c9 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( inverse(sk_c4) = sk_c7 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c9,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_105,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_107,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_109,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c9,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c5,sk_c9) = sk_c6 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c5) = sk_c9 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_112,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c9 )
| ( inverse(X1) != sk_c7 )
| ( inverse(X0) != sk_c9 )
| ( multiply(sk_c7,sk_c8) != sk_c9 )
| ( multiply(X3,sk_c9) != sk_c8 )
| ( multiply(X1,sk_c7) != sk_c8 )
| ( multiply(inverse(X2),sk_c7) != sk_c8 )
| ( multiply(X2,inverse(X2)) != sk_c8 )
| ( multiply(sk_c9,multiply(X0,sk_c9)) != sk_c7 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_385,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_112]) ).
tcf(c_386,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( multiply(inverse(X0),sk_c7) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_112]) ).
tcf(c_387,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_112]) ).
tcf(c_388,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c9 )
| ( multiply(sk_c9,multiply(X0,sk_c9)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_112]) ).
tcf(c_389,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c7,sk_c8) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_112]) ).
tcf(c_390,definition,
iPr_def_14 = multiply(sk_c7,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_391,definition,
iPr_def_15 = multiply(sk_c2,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_392,definition,
iPr_def_16 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_393,definition,
iPr_def_17 = multiply(sk_c5,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_394,definition,
iPr_def_18 = multiply(sk_c9,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_395,definition,
iPr_def_19 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_396,definition,
iPr_def_20 = multiply(sk_c4,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_397,definition,
iPr_def_21 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_398,definition,
iPr_def_22 = multiply(sk_c3,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_399,definition,
iPr_def_23 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_400,definition,
iPr_def_24 = multiply(sk_c1,sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_401,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_14 != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_389,c_390]) ).
tcf(c_402,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c9 )
| ( multiply(sk_c9,multiply(X0,sk_c9)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_388]) ).
tcf(c_403,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_387]) ).
tcf(c_404,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( multiply(inverse(X0),sk_c7) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_386]) ).
tcf(c_405,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_385]) ).
tcf(c_406,negated_conjecture,
( ( iPr_def_16 = sk_c9 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_111,c_392,c_391]) ).
tcf(c_407,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_110,c_393]) ).
tcf(c_408,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_109,c_394]) ).
tcf(c_409,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_108,c_395]) ).
tcf(c_410,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_107,c_396]) ).
tcf(c_412,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_105,c_398]) ).
tcf(c_415,negated_conjecture,
( ( iPr_def_23 = sk_c2 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_416,negated_conjecture,
( ( iPr_def_23 = sk_c2 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_417,negated_conjecture,
( ( iPr_def_23 = sk_c2 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_418,negated_conjecture,
( ( iPr_def_23 = sk_c2 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_419,negated_conjecture,
( ( iPr_def_23 = sk_c2 )
| ( iPr_def_22 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_420,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_97,c_400]) ).
tcf(c_421,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_424,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_425,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_426,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_22 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_427,negated_conjecture,
( ( iPr_def_16 = sk_c9 )
| ( iPr_def_14 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_428,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_14 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_429,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_14 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_430,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_14 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_431,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_14 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_432,negated_conjecture,
( ( iPr_def_21 = sk_c9 )
| ( iPr_def_14 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_433,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_14 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_434,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_435,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_679,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_19,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_409,c_390]) ).
tcf(c_707,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_16,sk_c6) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_406,c_394]) ).
tcf(c_762,plain,
( ( sk_c8 = iPr_def_24 )
| ( multiply(iPr_def_16,sk_c6) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_420,c_394]) ).
tcf(c_779,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_409,c_396]) ).
tcf(c_794,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_419,c_400]) ).
tcf(c_795,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_418,c_400]) ).
tcf(c_796,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_417,c_400]) ).
tcf(c_797,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_416,c_400]) ).
tcf(c_798,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_415,c_400]) ).
tcf(c_812,plain,
multiply(iPr_def_21,sk_c3) = identity,
inference(superposition,[status(thm)],[c_397,c_82]) ).
tcf(c_813,plain,
multiply(iPr_def_19,sk_c4) = identity,
inference(superposition,[status(thm)],[c_395,c_82]) ).
tcf(c_814,plain,
multiply(iPr_def_16,sk_c5) = identity,
inference(superposition,[status(thm)],[c_392,c_82]) ).
tcf(c_815,plain,
multiply(iPr_def_23,sk_c1) = identity,
inference(superposition,[status(thm)],[c_399,c_82]) ).
tcf(c_834,plain,
! [X0: $i] :
( ( iPr_def_14 = sk_c9 )
| ( iPr_def_14 != X0 )
| ( sk_c9 != X0 ) ),
inference(instantiation,[status(thm)],[c_435]) ).
tcf(c_935,plain,
( ( sk_c9 = iPr_def_14 )
| ( multiply(iPr_def_16,sk_c6) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_427,c_394]) ).
tcf(c_1005,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c9 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_430,c_429]) ).
tcf(c_1164,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_390,c_83]) ).
tcf(c_1172,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_82,c_83]) ).
tcf(c_1174,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_812,c_83]) ).
tcf(c_1175,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_813,c_83]) ).
tcf(c_1176,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_814,c_83]) ).
tcf(c_1177,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_815,c_83]) ).
tcf(c_1179,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1177,c_81]) ).
tcf(c_1180,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1176,c_81]) ).
tcf(c_1181,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1175,c_81]) ).
tcf(c_1182,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1174,c_81]) ).
tcf(c_1224,plain,
iPr_def_14 = iPr_def_14,
inference(instantiation,[status(thm)],[c_434]) ).
tcf(c_1383,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c9 = iPr_def_14 )
| ( iPr_def_14 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_432,c_401]) ).
tcf(c_1458,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_22 )
| ( inverse(sk_c3) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_398,c_403]) ).
tcf(c_1461,plain,
( ~ iPr_def_12
| ( sk_c8 != identity )
| ( inverse(inverse(sk_c9)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_82,c_403]) ).
tcf(c_1478,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_21 )
| ( sk_c8 != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_1458,c_397]) ).
tcf(c_1582,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_20 )
| ( inverse(sk_c4) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_396,c_405]) ).
tcf(c_1585,plain,
( ~ iPr_def_10
| ( sk_c8 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_82,c_405]) ).
tcf(c_1599,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_20 )
| ( sk_c7 != iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_1582,c_395]) ).
tcf(c_1650,plain,
( ( iPr_def_14 = sk_c9 )
| ( iPr_def_14 != iPr_def_14 )
| ( sk_c9 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_834]) ).
tcf(c_1701,plain,
( ~ iPr_def_13
| ( inverse(inverse(sk_c9)) != sk_c9 )
| ( multiply(sk_c9,identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_82,c_402]) ).
tcf(c_1864,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_18 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1005,c_401]) ).
tcf(c_2054,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_410,c_679]) ).
tcf(c_2109,plain,
multiply(iPr_def_16,iPr_def_17) = sk_c9,
inference(superposition,[status(thm)],[c_393,c_1180]) ).
tcf(c_2122,plain,
multiply(iPr_def_19,iPr_def_20) = sk_c7,
inference(superposition,[status(thm)],[c_396,c_1181]) ).
tcf(c_2139,plain,
multiply(iPr_def_21,iPr_def_22) = sk_c9,
inference(superposition,[status(thm)],[c_398,c_1182]) ).
tcf(c_2489,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_407,c_707]) ).
tcf(c_2491,plain,
( ( sk_c9 = iPr_def_18 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_2489,c_2109]) ).
tcf(c_2942,plain,
( ( sk_c8 = iPr_def_24 )
| ( multiply(iPr_def_16,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_421,c_762]) ).
tcf(c_2946,plain,
( ( sk_c9 = iPr_def_18 )
| ( sk_c8 = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_2942,c_2109]) ).
tcf(c_3010,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_15 )
| ( iPr_def_14 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_2491,c_401]) ).
tcf(c_3137,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_24 )
| ( iPr_def_14 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_2946,c_401]) ).
tcf(c_4209,plain,
( ( sk_c9 = iPr_def_14 )
| ( multiply(iPr_def_16,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_428,c_935]) ).
tcf(c_4214,plain,
( ( sk_c9 = iPr_def_18 )
| ( sk_c9 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_4209,c_2109]) ).
tcf(c_4486,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c9 = iPr_def_14 )
| ( iPr_def_14 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_4214,c_401]) ).
tcf(c_5464,plain,
( ( sk_c8 = iPr_def_15 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_2054,c_2122]) ).
tcf(c_5509,plain,
( ( iPr_def_14 = iPr_def_18 )
| ( sk_c8 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_5464,c_408]) ).
tcf(c_7300,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1172,c_81]) ).
tcf(c_7312,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_81,c_7300]) ).
tcf(c_7313,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_82,c_7300]) ).
tcf(c_7393,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_1182,c_7300]) ).
tcf(c_7394,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_1181,c_7300]) ).
tcf(c_7396,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_1179,c_7300]) ).
tcf(c_7415,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_7300,c_7300]) ).
tcf(c_8133,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_7313,c_7415]) ).
tcf(c_8156,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_8133,c_7312]) ).
tcf(c_8503,plain,
multiply(sk_c3,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_7393,c_82]) ).
tcf(c_9410,plain,
multiply(sk_c4,iPr_def_19) = identity,
inference(superposition,[status(thm)],[c_7394,c_82]) ).
tcf(c_9432,plain,
( ( identity = iPr_def_20 )
| ( sk_c8 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_779,c_9410]) ).
tcf(c_11262,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_14 != iPr_def_21 ) ),
inference(global_subsumption_just,[status(thm)],[c_1383,c_401,c_1224,c_1383,c_1650]) ).
tcf(c_11371,plain,
multiply(sk_c1,iPr_def_23) = identity,
inference(superposition,[status(thm)],[c_7396,c_82]) ).
tcf(c_11391,plain,
( ( identity = iPr_def_24 )
| ( sk_c7 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_798,c_11371]) ).
tcf(c_11392,plain,
( ( identity = iPr_def_24 )
| ( sk_c7 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_797,c_11371]) ).
tcf(c_11393,plain,
( ( identity = iPr_def_24 )
| ( sk_c8 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_796,c_11371]) ).
tcf(c_11394,plain,
( ( identity = iPr_def_24 )
| ( sk_c9 = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_795,c_11371]) ).
tcf(c_11395,plain,
( ( identity = iPr_def_24 )
| ( sk_c8 = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_794,c_11371]) ).
tcf(c_12207,plain,
( ( identity = iPr_def_24 )
| ( multiply(sk_c4,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_11392,c_396]) ).
tcf(c_12209,plain,
( ( identity = iPr_def_24 )
| ( multiply(iPr_def_19,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_11392,c_390]) ).
tcf(c_12217,plain,
( ( identity = iPr_def_24 )
| ( identity = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_12207,c_9410]) ).
tcf(c_12963,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_14 != iPr_def_18 ) ),
inference(global_subsumption_just,[status(thm)],[c_3137,c_401,c_1224,c_1650,c_4486]) ).
tcf(c_16087,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_7415,c_82]) ).
tcf(c_16092,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_7415,c_7300]) ).
tcf(c_16093,plain,
! [X0: $i] : multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_7415,c_8133]) ).
tcf(c_16094,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_16093,c_8133]) ).
tcf(c_16107,plain,
! [X0: $i] :
( ~ iPr_def_11
| ( sk_c8 != identity )
| ( multiply(inverse(X0),sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_404,c_16087]) ).
tcf(c_16111,plain,
( ~ iPr_def_10
| ( sk_c8 != identity ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1585,c_16094]) ).
tcf(c_16112,plain,
( ~ iPr_def_12
| ( sk_c8 != identity ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1461,c_16094]) ).
tcf(c_16498,plain,
multiply(iPr_def_14,inverse(sk_c8)) = multiply(sk_c7,identity),
inference(superposition,[status(thm)],[c_16087,c_1164]) ).
tcf(c_17036,plain,
( ( identity = iPr_def_24 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_11393,c_12209]) ).
tcf(c_17083,plain,
( ( identity = iPr_def_24 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_17036,c_2122]) ).
tcf(c_17135,plain,
( ( sk_c8 = iPr_def_22 )
| ~ iPr_def_10
| ( identity != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_426,c_16111]) ).
tcf(c_17136,plain,
( ( sk_c8 = iPr_def_20 )
| ~ iPr_def_10
| ( identity != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_424,c_16111]) ).
tcf(c_17138,plain,
( ( sk_c8 = iPr_def_15 )
| ~ iPr_def_10
| ( identity != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_410,c_16111]) ).
tcf(c_17486,plain,
( ( sk_c8 = iPr_def_22 )
| ~ iPr_def_12
| ( identity != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_426,c_16112]) ).
tcf(c_17487,plain,
( ( sk_c8 = iPr_def_20 )
| ~ iPr_def_12
| ( identity != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_424,c_16112]) ).
tcf(c_17489,plain,
( ( sk_c8 = iPr_def_15 )
| ~ iPr_def_12
| ( identity != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_410,c_16112]) ).
tcf(c_17784,plain,
( ( iPr_def_14 = iPr_def_18 )
| ( identity = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_17083,c_11391]) ).
tcf(c_17986,plain,
( ( sk_c8 = iPr_def_22 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_17135,c_11395,c_17135]) ).
tcf(c_17997,plain,
( ( sk_c8 = iPr_def_20 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_17136,c_11393,c_17136]) ).
tcf(c_18024,plain,
( ( sk_c8 = iPr_def_22 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_17486,c_11395,c_17486]) ).
tcf(c_18041,plain,
( ( sk_c8 = iPr_def_20 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_17487,c_1478,c_11395,c_11394,c_17487,c_17486]) ).
tcf(c_18309,plain,
( ~ iPr_def_13
| ( sk_c7 != sk_c9 )
| ( inverse(inverse(sk_c9)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_16092,c_402]) ).
tcf(c_18343,plain,
( ~ iPr_def_13
| ( sk_c7 != sk_c9 ) ),
inference(ground_joinability,[status(thm)],[c_18309,c_16094]) ).
tcf(c_19510,plain,
( ~ iPr_def_11
| ( sk_c8 != identity ) ),
inference(superposition,[status(thm)],[c_82,c_16107]) ).
tcf(c_19634,plain,
( ( identity = iPr_def_24 )
| ~ iPr_def_11
| ( identity != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_11393,c_19510]) ).
tcf(c_19670,plain,
( ( sk_c8 = iPr_def_22 )
| ~ iPr_def_11
| ( identity != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_426,c_19510]) ).
tcf(c_19671,plain,
( ( sk_c8 = iPr_def_20 )
| ~ iPr_def_11
| ( identity != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_424,c_19510]) ).
tcf(c_19672,plain,
( ( sk_c8 = iPr_def_15 )
| ~ iPr_def_11
| ( identity != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_412,c_19510]) ).
tcf(c_19673,plain,
( ( sk_c8 = iPr_def_15 )
| ~ iPr_def_11
| ( identity != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_410,c_19510]) ).
tcf(c_19949,plain,
( ( identity = iPr_def_24 )
| ~ iPr_def_13
| ( sk_c9 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_17083,c_18343]) ).
tcf(c_19951,plain,
( ( identity = iPr_def_24 )
| ~ iPr_def_13
| ( sk_c9 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_11391,c_18343]) ).
tcf(c_19959,plain,
( ( sk_c9 = iPr_def_14 )
| ~ iPr_def_13
| ( sk_c9 != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_430,c_18343]) ).
tcf(c_19960,plain,
( ( sk_c9 = iPr_def_14 )
| ~ iPr_def_13
| ( sk_c9 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_429,c_18343]) ).
tcf(c_19964,plain,
( ( sk_c8 = iPr_def_15 )
| ~ iPr_def_13
| ( sk_c9 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_408,c_18343]) ).
tcf(c_20020,plain,
multiply(iPr_def_14,inverse(sk_c8)) = sk_c7,
inference(demodulation,[status(thm)],[c_16498,c_8133]) ).
tcf(c_20058,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(iPr_def_14,inverse(iPr_def_24)) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_426,c_20020]) ).
tcf(c_20059,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_14,inverse(iPr_def_24)) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_424,c_20020]) ).
tcf(c_20196,plain,
( ( sk_c8 = iPr_def_22 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_19670,c_1478,c_1599,c_4214,c_11395,c_11394,c_11393,c_11392,c_12217,c_12963,c_17784,c_19670,c_19634,c_19951,c_19949]) ).
tcf(c_20205,plain,
( ( sk_c8 = iPr_def_20 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_19671,c_1478,c_1599,c_4214,c_11395,c_11394,c_11393,c_11392,c_12217,c_12963,c_17784,c_19671,c_19634,c_19951,c_19949]) ).
tcf(c_20225,plain,
sk_c8 = iPr_def_15,
inference(global_subsumption_just,[status(thm)],[c_19672,c_2491,c_3010,c_5509,c_9432,c_17138,c_17489,c_19673,c_19964]) ).
tcf(c_20227,plain,
( ( iPr_def_15 = iPr_def_20 )
| ~ iPr_def_11 ),
inference(demodulation,[status(thm)],[c_20205,c_20225]) ).
tcf(c_20228,plain,
( ( iPr_def_15 = iPr_def_22 )
| ~ iPr_def_11 ),
inference(demodulation,[status(thm)],[c_20196,c_20225]) ).
tcf(c_20230,plain,
( ~ iPr_def_11
| ( identity != iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_19510,c_20225]) ).
tcf(c_20239,plain,
( ( iPr_def_15 = iPr_def_20 )
| ~ iPr_def_12 ),
inference(demodulation,[status(thm)],[c_18041,c_20225]) ).
tcf(c_20240,plain,
( ( iPr_def_15 = iPr_def_22 )
| ~ iPr_def_12 ),
inference(demodulation,[status(thm)],[c_18024,c_20225]) ).
tcf(c_20242,plain,
( ( iPr_def_15 = iPr_def_20 )
| ~ iPr_def_10 ),
inference(demodulation,[status(thm)],[c_17997,c_20225]) ).
tcf(c_20243,plain,
( ( iPr_def_15 = iPr_def_22 )
| ~ iPr_def_10 ),
inference(demodulation,[status(thm)],[c_17986,c_20225]) ).
tcf(c_20244,plain,
( ~ iPr_def_12
| ( identity != iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_16112,c_20225]) ).
tcf(c_20245,plain,
( ~ iPr_def_10
| ( identity != iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_16111,c_20225]) ).
tcf(c_20283,plain,
( ( iPr_def_15 = iPr_def_22 )
| ( identity = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_11395,c_20225]) ).
tcf(c_20379,plain,
( ( iPr_def_15 = iPr_def_22 )
| ( sk_c9 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_433,c_20225]) ).
tcf(c_20380,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( sk_c9 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_431,c_20225]) ).
tcf(c_20382,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( sk_c9 = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_425,c_20225]) ).
tcf(c_20390,plain,
multiply(sk_c7,iPr_def_15) = iPr_def_14,
inference(demodulation,[status(thm)],[c_390,c_20225]) ).
tcf(c_20559,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_20379,c_401]) ).
tcf(c_20560,plain,
( ( iPr_def_15 = iPr_def_22 )
| ( iPr_def_14 = iPr_def_21 )
| ( sk_c9 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_20379,c_432]) ).
tcf(c_20637,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_20380,c_401]) ).
tcf(c_20638,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_21 )
| ( sk_c9 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_20380,c_432]) ).
tcf(c_21158,plain,
( iPr_def_13
| ( iPr_def_15 = iPr_def_22 ) ),
inference(global_subsumption_just,[status(thm)],[c_20559,c_20243,c_20240,c_20228,c_20559]) ).
tcf(c_21160,plain,
( iPr_def_13
| ( iPr_def_15 = iPr_def_20 ) ),
inference(global_subsumption_just,[status(thm)],[c_20637,c_20242,c_20239,c_20227,c_20637]) ).
tcf(c_21256,plain,
identity = iPr_def_24,
inference(global_subsumption_just,[status(thm)],[c_20283,c_1478,c_1599,c_4214,c_11395,c_11394,c_11393,c_11392,c_12217,c_12963,c_17784,c_19634,c_19951,c_19949]) ).
tcf(c_21304,plain,
multiply(sk_c3,iPr_def_21) = iPr_def_24,
inference(demodulation,[status(thm)],[c_8503,c_21256]) ).
tcf(c_21305,plain,
inverse(iPr_def_24) = iPr_def_24,
inference(demodulation,[status(thm)],[c_8156,c_21256]) ).
tcf(c_21306,plain,
! [X0: $i] : multiply(X0,iPr_def_24) = X0,
inference(demodulation,[status(thm)],[c_8133,c_21256]) ).
tcf(c_21461,plain,
( ( sk_c9 = iPr_def_14 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_19959,c_4214,c_19960]) ).
tcf(c_21496,plain,
( ( iPr_def_15 = iPr_def_22 )
| ( multiply(iPr_def_14,iPr_def_24) = sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_20058,c_20225,c_21305]) ).
tcf(c_21497,plain,
( ( iPr_def_15 = iPr_def_22 )
| ( sk_c7 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_21496,c_21306]) ).
tcf(c_21514,plain,
( ( iPr_def_15 = iPr_def_22 )
| ~ iPr_def_13
| ( sk_c9 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_21497,c_18343]) ).
tcf(c_21685,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( multiply(iPr_def_14,iPr_def_24) = sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_20059,c_20225,c_21305]) ).
tcf(c_21686,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( sk_c7 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_21685,c_21306]) ).
tcf(c_21703,plain,
( ( iPr_def_15 = iPr_def_20 )
| ~ iPr_def_13
| ( sk_c9 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_21686,c_18343]) ).
tcf(c_21744,plain,
iPr_def_15 = iPr_def_22,
inference(global_subsumption_just,[status(thm)],[c_20560,c_20379,c_21158,c_21514]) ).
tcf(c_21767,plain,
multiply(iPr_def_21,iPr_def_15) = sk_c9,
inference(demodulation,[status(thm)],[c_2139,c_21744]) ).
tcf(c_21768,plain,
multiply(sk_c3,sk_c9) = iPr_def_15,
inference(demodulation,[status(thm)],[c_398,c_21744]) ).
tcf(c_21794,plain,
iPr_def_15 = iPr_def_20,
inference(global_subsumption_just,[status(thm)],[c_20638,c_20380,c_21160,c_21703]) ).
tcf(c_21808,plain,
multiply(iPr_def_19,iPr_def_15) = sk_c7,
inference(demodulation,[status(thm)],[c_2122,c_21794]) ).
tcf(c_21823,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( multiply(sk_c3,iPr_def_21) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_20382,c_21768]) ).
tcf(c_21842,plain,
iPr_def_15 = iPr_def_24,
inference(light_normalisation,[status(thm)],[c_21823,c_21304]) ).
tcf(c_21850,plain,
! [X0: $i] : multiply(X0,iPr_def_15) = X0,
inference(demodulation,[status(thm)],[c_21306,c_21842]) ).
tcf(c_21858,plain,
identity = iPr_def_15,
inference(demodulation,[status(thm)],[c_21256,c_21842]) ).
tcf(c_21859,plain,
sk_c7 = iPr_def_14,
inference(demodulation,[status(thm)],[c_20390,c_21850]) ).
tcf(c_21860,plain,
sk_c9 = iPr_def_21,
inference(demodulation,[status(thm)],[c_21767,c_21850]) ).
tcf(c_21866,plain,
( ( iPr_def_14 = iPr_def_21 )
| ~ iPr_def_13 ),
inference(demodulation,[status(thm)],[c_21461,c_21860]) ).
tcf(c_21896,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( sk_c7 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_430,c_21860]) ).
tcf(c_21948,plain,
multiply(iPr_def_19,iPr_def_15) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_21808,c_21859]) ).
tcf(c_21949,plain,
iPr_def_14 = iPr_def_19,
inference(demodulation,[status(thm)],[c_21948,c_21850]) ).
tcf(c_21955,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_14 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_1864,c_21949]) ).
tcf(c_21970,plain,
iPr_def_14 = iPr_def_21,
inference(global_subsumption_just,[status(thm)],[c_21896,c_12963,c_20245,c_20244,c_20230,c_21858,c_21866,c_21955]) ).
tcf(c_21972,plain,
sk_c9 = iPr_def_14,
inference(demodulation,[status(thm)],[c_21860,c_21970]) ).
tcf(c_22057,plain,
( ( multiply(sk_c9,identity) != sk_c7 )
| ( inverse(inverse(sk_c9)) != sk_c9 ) ),
inference(global_subsumption_just,[status(thm)],[c_1701,c_1701,c_11262,c_20245,c_20244,c_20230,c_21858,c_21970]) ).
tcf(c_22058,plain,
( ( inverse(inverse(sk_c9)) != sk_c9 )
| ( multiply(sk_c9,identity) != sk_c7 ) ),
inference(renaming,[status(thm)],[c_22057]) ).
tcf(c_22059,plain,
$false,
inference(ground_joinability,[status(thm)],[c_22058,c_16094,c_21850,c_21858,c_21859,c_21972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP370-1 : 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 14:35:44 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.42
% 0.14/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.42
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 4.75/2.19 % SZS status Started for theBenchmark.p
% 4.75/2.19 % SZS status Unsatisfiable for theBenchmark.p
% 4.75/2.19
% 4.75/2.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.75/2.19
% 4.75/2.19 % ------ iProver source info
% 4.75/2.19
% 4.75/2.19 % git: date: 2026-07-19 20:42:38 +0200
% 4.75/2.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.75/2.19 % git: non_committed_changes: false
% 4.75/2.19
% 4.75/2.19 % ------ Parsing...% successful
% 4.75/2.19
% 4.75/2.19
% 4.75/2.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.75/2.19
% 4.75/2.19 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.75/2.19
% 4.75/2.19 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.75/2.19
% 4.75/2.19 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.75/2.19 % ------ Proving...
% 4.75/2.19 % ------ Problem Properties
% 4.75/2.19
% 4.75/2.19 %
% 4.75/2.19 % clauses 47
% 4.75/2.19 % conjectures 33
% 4.75/2.19 % EPR 29
% 4.75/2.19 % Horn 18
% 4.75/2.19 % unary 14
% 4.75/2.19 % binary 28
% 4.75/2.19 % lits 87
% 4.75/2.19 % lits eq 79
% 4.75/2.19 % fd_pure 0
% 4.75/2.19 % fd_pseudo 0
% 4.75/2.19 % fd_cond 0
% 4.75/2.19 % fd_pseudo_cond 0
% 4.75/2.19 % AC symbols 0
% 4.75/2.19
% 4.75/2.19 % ------ Schedule dynamic 5 is on
% 4.75/2.19
% 4.75/2.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.75/2.19
% 4.75/2.19
% 4.75/2.19 % ------
% 4.75/2.19 % Current options:
% 4.75/2.19 % ------
% 4.75/2.19
% 4.75/2.19
% 4.75/2.19 %
% 4.75/2.19
% 4.75/2.19 % ------ Proving...
% 4.75/2.19 %
% 4.75/2.19
% 4.75/2.19 % SZS status Unsatisfiable for theBenchmark.p
% 4.75/2.19
% 4.75/2.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.26/2.20
% 10.26/2.20
%------------------------------------------------------------------------------