%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP367-1 : 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 : n015.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 20.61s 3.80s
% Output : CNFRefutation 8.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 40
% Syntax : Number of formulae : 272 ( 108 unt; 11 def)
% Number of atoms : 846 ( 493 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 376 ( 129 ~; 247 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 97 ( 0 sgn 97 !; 0 ?; 77 :)
% 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_c7,sk_c8) = sk_c6
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c8 = inverse(sk_c4)
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c7 = inverse(sk_c5)
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c2) ),
inference(reorient_equations,[],[f15]) ).
fof(f21,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = inverse(sk_c5)
| sk_c7 = multiply(sk_c8,sk_c2) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c7 = multiply(sk_c8,sk_c2) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| sk_c2 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f25]) ).
fof(f31,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c5)
| sk_c2 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c2 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f35]) ).
fof(f41,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = inverse(sk_c5)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f43]) ).
fof(f47,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c7 = inverse(sk_c5)
| sk_c8 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c8 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = inverse(sk_c4)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c7 = inverse(sk_c5)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c8
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( sk_c7 != multiply(X4,sk_c6)
| sk_c7 != inverse(X4)
| sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3)
| sk_c6 != multiply(sk_c7,sk_c8)
| sk_c6 != inverse(X2)
| sk_c8 != multiply(X2,sk_c6)
| sk_c8 != inverse(X1)
| multiply(X1,sk_c8) != X0
| sk_c7 != multiply(sk_c8,X0)
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X1,X4] :
( sk_c7 != multiply(X4,sk_c6)
| sk_c7 != inverse(X4)
| sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3)
| sk_c6 != multiply(sk_c7,sk_c8)
| sk_c6 != inverse(X2)
| sk_c8 != multiply(X2,sk_c6)
| sk_c8 != inverse(X1)
| sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(equality_resolution,[],[f66]) ).
tcf(c_83,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_84,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_86,negated_conjecture,
( ( multiply(sk_c7,sk_c8) = sk_c6 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_88,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_90,negated_conjecture,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_91,negated_conjecture,
( ( multiply(sk_c7,sk_c8) = sk_c6 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_95,negated_conjecture,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_96,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c2 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c1,sk_c8) = sk_c2 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_100,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c2 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c3,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_108,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c8 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( inverse(sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c7 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c8 )
| ( inverse(X0) != sk_c6 )
| ( multiply(sk_c7,sk_c8) != sk_c6 )
| ( multiply(sk_c6,sk_c8) != sk_c7 )
| ( multiply(X3,sk_c6) != sk_c7 )
| ( multiply(X1,sk_c7) != sk_c8 )
| ( multiply(X0,sk_c6) != sk_c8 )
| ( multiply(sk_c8,multiply(X2,sk_c8)) != sk_c7 ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_409,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_116]) ).
tcf(c_410,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_116]) ).
tcf(c_411,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_116]) ).
tcf(c_412,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_116]) ).
tcf(c_413,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c7,sk_c8) != sk_c6 )
| ( multiply(sk_c6,sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_414,definition,
iPr_def_14 = multiply(sk_c6,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_415,definition,
iPr_def_15 = multiply(sk_c7,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_416,definition,
iPr_def_16 = multiply(sk_c5,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_417,definition,
iPr_def_17 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_418,definition,
iPr_def_18 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_419,definition,
iPr_def_19 = multiply(sk_c4,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_420,definition,
iPr_def_20 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_421,definition,
iPr_def_21 = multiply(sk_c3,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_422,definition,
iPr_def_22 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_423,definition,
iPr_def_23 = multiply(sk_c1,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_424,definition,
iPr_def_24 = multiply(sk_c8,sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_425,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c6 )
| ( iPr_def_14 != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_413,c_415,c_414]) ).
tcf(c_426,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_412]) ).
tcf(c_427,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_411]) ).
tcf(c_428,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_410]) ).
tcf(c_429,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_409]) ).
tcf(c_430,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_115,c_417,c_416]) ).
tcf(c_431,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_114,c_418]) ).
tcf(c_432,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_113,c_419]) ).
tcf(c_433,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_112,c_420]) ).
tcf(c_434,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_435,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_110,c_421]) ).
tcf(c_436,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_437,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_438,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_440,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_105,c_422]) ).
tcf(c_441,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_444,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_445,negated_conjecture,
( ( iPr_def_23 = sk_c2 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_100,c_423]) ).
tcf(c_446,negated_conjecture,
( ( iPr_def_23 = sk_c2 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_449,negated_conjecture,
( ( iPr_def_23 = sk_c2 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_450,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_95,c_424]) ).
tcf(c_451,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_454,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_455,negated_conjecture,
( ( iPr_def_16 = sk_c7 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_456,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_457,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_458,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_459,negated_conjecture,
( ( iPr_def_15 = sk_c6 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_460,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_461,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_699,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c8 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_435,c_436]) ).
tcf(c_707,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_17,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_434,c_414]) ).
tcf(c_710,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(iPr_def_17,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_431,c_414]) ).
tcf(c_711,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_17,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_430,c_414]) ).
tcf(c_725,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(iPr_def_18,sk_c8) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_436,c_415]) ).
tcf(c_821,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c8 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_441,c_440]) ).
tcf(c_904,plain,
! [X0: $i,X1: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_461]) ).
tcf(c_930,plain,
! [X0: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != sk_c7 )
| ( X0 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_904]) ).
tcf(c_931,plain,
sk_c7 = sk_c7,
inference(instantiation,[status(thm)],[c_460]) ).
tcf(c_939,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c7 )
| ( sk_c7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_461]) ).
tcf(c_941,plain,
( ( sk_c7 = iPr_def_16 )
| ( iPr_def_16 != sk_c7 )
| ( sk_c7 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_930]) ).
tcf(c_942,plain,
( ( sk_c7 = iPr_def_18 )
| ( iPr_def_18 != sk_c7 )
| ( sk_c7 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_930]) ).
tcf(c_977,plain,
multiply(iPr_def_20,sk_c4) = identity,
inference(superposition,[status(thm)],[c_420,c_84]) ).
tcf(c_978,plain,
multiply(iPr_def_18,sk_c5) = identity,
inference(superposition,[status(thm)],[c_418,c_84]) ).
tcf(c_979,plain,
multiply(iPr_def_22,sk_c1) = identity,
inference(superposition,[status(thm)],[c_422,c_84]) ).
tcf(c_980,plain,
multiply(iPr_def_17,sk_c3) = identity,
inference(superposition,[status(thm)],[c_417,c_84]) ).
tcf(c_987,plain,
! [X0: $i] :
( ( X0 = sk_c7 )
| ( sk_c7 != iPr_def_18 )
| ( X0 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_939]) ).
tcf(c_989,plain,
! [X0: $i] :
( ( X0 = sk_c7 )
| ( sk_c7 != iPr_def_16 )
| ( X0 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_939]) ).
tcf(c_1132,plain,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_18 != iPr_def_18 )
| ( sk_c7 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_987]) ).
tcf(c_1133,plain,
iPr_def_18 = iPr_def_18,
inference(instantiation,[status(thm)],[c_460]) ).
tcf(c_1138,plain,
( ( iPr_def_16 = sk_c7 )
| ( iPr_def_16 != iPr_def_16 )
| ( sk_c7 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_989]) ).
tcf(c_1139,plain,
iPr_def_16 = iPr_def_16,
inference(instantiation,[status(thm)],[c_460]) ).
tcf(c_1329,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_14 = X0 )
| ( iPr_def_14 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_461]) ).
tcf(c_1349,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c7 = iPr_def_18 )
| ( sk_c8 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_457,c_451]) ).
tcf(c_1350,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c7 = iPr_def_16 )
| ( sk_c8 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_457,c_450]) ).
tcf(c_1399,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_16 = X0 )
| ( iPr_def_16 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_461]) ).
tcf(c_1632,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( iPr_def_16 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_821,c_699]) ).
tcf(c_1634,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_821,c_423]) ).
tcf(c_2130,plain,
! [X0: $i] :
( ( iPr_def_14 = X0 )
| ( iPr_def_14 != sk_c7 )
| ( X0 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_1329]) ).
tcf(c_2657,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_17,iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_821,c_707]) ).
tcf(c_2730,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( iPr_def_24 != sk_c7 )
| ( iPr_def_14 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_2130]) ).
tcf(c_2734,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c8,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_414,c_85]) ).
tcf(c_2735,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_415,c_85]) ).
tcf(c_2736,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c7,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_419,c_85]) ).
tcf(c_2738,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c2,X0)) = multiply(iPr_def_24,X0),
inference(superposition,[status(thm)],[c_424,c_85]) ).
tcf(c_2742,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_2745,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_977,c_85]) ).
tcf(c_2746,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_978,c_85]) ).
tcf(c_2747,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_979,c_85]) ).
tcf(c_2748,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_980,c_85]) ).
tcf(c_2754,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2748,c_83]) ).
tcf(c_2755,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2747,c_83]) ).
tcf(c_2756,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2746,c_83]) ).
tcf(c_2757,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2745,c_83]) ).
tcf(c_2869,plain,
multiply(iPr_def_17,iPr_def_21) = sk_c6,
inference(superposition,[status(thm)],[c_421,c_2754]) ).
tcf(c_2907,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_21,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_2869,c_85]) ).
tcf(c_2909,plain,
multiply(iPr_def_22,iPr_def_23) = sk_c8,
inference(superposition,[status(thm)],[c_423,c_2755]) ).
tcf(c_2912,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(iPr_def_23,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2909,c_85]) ).
tcf(c_3042,plain,
! [X0: $i] :
( ( iPr_def_16 = X0 )
| ( iPr_def_16 != sk_c7 )
| ( X0 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_1399]) ).
tcf(c_3056,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c7 = iPr_def_18 )
| ( multiply(iPr_def_17,iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_821,c_710]) ).
tcf(c_3111,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_17,iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_821,c_711]) ).
tcf(c_3447,plain,
multiply(iPr_def_18,iPr_def_16) = sk_c6,
inference(superposition,[status(thm)],[c_416,c_2756]) ).
tcf(c_3465,plain,
multiply(iPr_def_20,iPr_def_19) = sk_c7,
inference(superposition,[status(thm)],[c_419,c_2757]) ).
tcf(c_3468,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_19,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_3465,c_85]) ).
tcf(c_7500,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_18 != sk_c7 )
| ( iPr_def_16 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_3042]) ).
tcf(c_10071,plain,
multiply(sk_c4,iPr_def_15) = multiply(iPr_def_19,sk_c8),
inference(superposition,[status(thm)],[c_415,c_2736]) ).
tcf(c_10156,plain,
multiply(iPr_def_20,multiply(iPr_def_19,sk_c8)) = iPr_def_15,
inference(superposition,[status(thm)],[c_10071,c_2757]) ).
tcf(c_10476,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c7 = iPr_def_18 ) ),
inference(global_subsumption_just,[status(thm)],[c_1349,c_451,c_456,c_931,c_942,c_2730]) ).
tcf(c_10618,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c7 = iPr_def_16 ) ),
inference(global_subsumption_just,[status(thm)],[c_1350,c_450,c_455,c_931,c_941,c_2730]) ).
tcf(c_10644,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_10618,c_10476]) ).
tcf(c_14303,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(iPr_def_17,iPr_def_22) = iPr_def_14 ) ),
inference(global_subsumption_just,[status(thm)],[c_2657,c_1132,c_1133,c_1138,c_1139,c_3056,c_3111,c_7500]) ).
tcf(c_14311,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(iPr_def_17,iPr_def_21) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1632,c_14303]) ).
tcf(c_14313,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c6 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_14311,c_2869]) ).
tcf(c_15506,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2742,c_83]) ).
tcf(c_15511,plain,
multiply(inverse(sk_c6),iPr_def_14) = sk_c8,
inference(superposition,[status(thm)],[c_414,c_15506]) ).
tcf(c_15512,plain,
multiply(inverse(sk_c7),iPr_def_15) = sk_c8,
inference(superposition,[status(thm)],[c_415,c_15506]) ).
tcf(c_15518,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_83,c_15506]) ).
tcf(c_15519,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_84,c_15506]) ).
tcf(c_15520,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[status(thm)],[c_85,c_15506]) ).
tcf(c_15682,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2757,c_15506]) ).
tcf(c_15683,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2756,c_15506]) ).
tcf(c_15684,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2755,c_15506]) ).
tcf(c_15685,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_2754,c_15506]) ).
tcf(c_15779,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_15506,c_15506]) ).
tcf(c_17181,plain,
( ~ iPr_def_11
| ( sk_c6 != sk_c8 )
| ( inverse(inverse(identity)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_15518,c_428]) ).
tcf(c_17334,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_15519,c_15779]) ).
tcf(c_17340,plain,
multiply(sk_c7,sk_c8) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_17334,c_2735]) ).
tcf(c_17341,plain,
multiply(sk_c6,sk_c8) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_17334,c_2734]) ).
tcf(c_17346,plain,
multiply(sk_c7,identity) = multiply(iPr_def_20,iPr_def_19),
inference(superposition,[status(thm)],[c_17334,c_3468]) ).
tcf(c_17351,plain,
multiply(sk_c8,sk_c2) = multiply(iPr_def_24,identity),
inference(superposition,[status(thm)],[c_17334,c_2738]) ).
tcf(c_17352,plain,
multiply(sk_c8,identity) = multiply(iPr_def_22,iPr_def_23),
inference(superposition,[status(thm)],[c_17334,c_2912]) ).
tcf(c_17353,plain,
multiply(sk_c6,identity) = multiply(iPr_def_17,iPr_def_21),
inference(superposition,[status(thm)],[c_17334,c_2907]) ).
tcf(c_17358,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_17334,c_15518]) ).
tcf(c_17359,plain,
multiply(sk_c6,identity) = sk_c6,
inference(light_normalisation,[status(thm)],[c_17353,c_2869]) ).
tcf(c_17360,plain,
multiply(sk_c8,identity) = sk_c8,
inference(light_normalisation,[status(thm)],[c_17352,c_2909]) ).
tcf(c_17361,plain,
multiply(iPr_def_24,identity) = iPr_def_24,
inference(light_normalisation,[status(thm)],[c_17351,c_424]) ).
tcf(c_17366,plain,
multiply(sk_c7,identity) = sk_c7,
inference(light_normalisation,[status(thm)],[c_17346,c_3465]) ).
tcf(c_17367,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_17341,c_414]) ).
tcf(c_17368,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_17340,c_415]) ).
tcf(c_17592,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_17358,c_84]) ).
tcf(c_19466,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_20)) != sk_c8 )
| ( multiply(sk_c8,multiply(sk_c4,sk_c8)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_15682,c_426]) ).
tcf(c_19467,plain,
multiply(sk_c4,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_15682,c_84]) ).
tcf(c_19473,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_15682,c_15506]) ).
tcf(c_19474,plain,
multiply(sk_c4,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_15682,c_17334]) ).
tcf(c_19544,plain,
inverse(iPr_def_20) = sk_c4,
inference(demodulation,[status(thm)],[c_19474,c_17334]) ).
tcf(c_19561,plain,
multiply(sk_c4,sk_c7) = iPr_def_19,
inference(superposition,[status(thm)],[c_3465,c_19473]) ).
tcf(c_19692,plain,
multiply(sk_c5,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_15683,c_84]) ).
tcf(c_19698,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_15683,c_15506]) ).
tcf(c_19699,plain,
multiply(sk_c5,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_15683,c_17334]) ).
tcf(c_19738,plain,
inverse(iPr_def_18) = sk_c5,
inference(demodulation,[status(thm)],[c_19699,c_17334]) ).
tcf(c_20177,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c6)),multiply(X0,iPr_def_14)) = sk_c8,
inference(superposition,[status(thm)],[c_414,c_15520]) ).
tcf(c_20199,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_21 )
| ( multiply(inverse(multiply(X0,iPr_def_18)),multiply(X0,iPr_def_15)) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_725,c_15520]) ).
tcf(c_20269,plain,
! [X0: $i] : multiply(inverse(multiply(X0,iPr_def_17)),multiply(X0,identity)) = sk_c3,
inference(superposition,[status(thm)],[c_980,c_15520]) ).
tcf(c_20379,plain,
! [X0: $i] : multiply(inverse(multiply(X0,iPr_def_18)),multiply(X0,sk_c6)) = iPr_def_16,
inference(superposition,[status(thm)],[c_3447,c_15520]) ).
tcf(c_20455,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c4)),multiply(X0,identity)) = iPr_def_20,
inference(superposition,[status(thm)],[c_19467,c_15520]) ).
tcf(c_20457,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c5)),multiply(X0,identity)) = iPr_def_18,
inference(superposition,[status(thm)],[c_19692,c_15520]) ).
tcf(c_20469,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c5)),X0) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_20457,c_17334]) ).
tcf(c_20470,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c4)),X0) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_20455,c_17334]) ).
tcf(c_20471,plain,
! [X0: $i] : multiply(inverse(multiply(X0,iPr_def_17)),X0) = sk_c3,
inference(light_normalisation,[status(thm)],[c_20269,c_17334]) ).
tcf(c_27387,plain,
multiply(inverse(multiply(inverse(iPr_def_14),sk_c6)),identity) = sk_c8,
inference(superposition,[status(thm)],[c_84,c_20177]) ).
tcf(c_27487,plain,
multiply(sk_c5,sk_c6) = iPr_def_16,
inference(superposition,[status(thm)],[c_3447,c_19698]) ).
tcf(c_27655,plain,
multiply(sk_c1,iPr_def_22) = identity,
inference(superposition,[status(thm)],[c_15684,c_84]) ).
tcf(c_27686,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( identity = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_1634,c_27655]) ).
tcf(c_28861,plain,
inverse(multiply(inverse(iPr_def_14),sk_c6)) = sk_c8,
inference(demodulation,[status(thm)],[c_27387,c_17334]) ).
tcf(c_28885,plain,
multiply(sk_c8,multiply(inverse(iPr_def_14),sk_c6)) = identity,
inference(superposition,[status(thm)],[c_28861,c_84]) ).
tcf(c_28887,plain,
multiply(sk_c8,multiply(inverse(iPr_def_14),iPr_def_14)) = sk_c8,
inference(superposition,[status(thm)],[c_28861,c_20177]) ).
tcf(c_28955,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(sk_c8,multiply(inverse(iPr_def_14),iPr_def_14)) = identity ) ),
inference(superposition,[status(thm)],[c_14313,c_28885]) ).
tcf(c_28980,plain,
multiply(iPr_def_15,multiply(inverse(iPr_def_14),sk_c6)) = multiply(sk_c7,identity),
inference(superposition,[status(thm)],[c_28885,c_2735]) ).
tcf(c_28981,plain,
multiply(iPr_def_14,multiply(inverse(iPr_def_14),sk_c6)) = multiply(sk_c6,identity),
inference(superposition,[status(thm)],[c_28885,c_2734]) ).
tcf(c_28983,plain,
multiply(inverse(sk_c8),identity) = multiply(inverse(iPr_def_14),sk_c6),
inference(superposition,[status(thm)],[c_28885,c_15506]) ).
tcf(c_29014,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c8 = identity ) ),
inference(light_normalisation,[status(thm)],[c_28955,c_28887]) ).
tcf(c_30187,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( identity = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_29014,c_699]) ).
tcf(c_30188,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(identity,sk_c2) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_29014,c_424]) ).
tcf(c_33283,plain,
( ( iPr_def_21 = iPr_def_23 )
| ( iPr_def_16 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_30187,c_27686]) ).
tcf(c_40093,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_17)) != sk_c8 )
| ( multiply(sk_c8,multiply(sk_c3,sk_c8)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_15685,c_426]) ).
tcf(c_40094,plain,
multiply(sk_c3,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_15685,c_84]) ).
tcf(c_40100,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_17)) != sk_c8 )
| ( multiply(sk_c3,sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_15685,c_429]) ).
tcf(c_40102,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_17)) != sk_c6 )
| ( multiply(sk_c3,sk_c6) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_15685,c_428]) ).
tcf(c_40105,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_15685,c_15506]) ).
tcf(c_40106,plain,
multiply(sk_c3,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_15685,c_17334]) ).
tcf(c_40114,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_21 )
| ( inverse(inverse(iPr_def_17)) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_40102,c_421]) ).
tcf(c_42414,plain,
inverse(iPr_def_17) = sk_c3,
inference(demodulation,[status(thm)],[c_40106,c_17334]) ).
tcf(c_42434,plain,
multiply(sk_c3,sk_c6) = iPr_def_21,
inference(superposition,[status(thm)],[c_2869,c_40105]) ).
tcf(c_45200,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c2 = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_30188,c_83]) ).
tcf(c_45243,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( iPr_def_16 = iPr_def_18 )
| ( sk_c6 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_45200,c_449]) ).
tcf(c_45246,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( iPr_def_16 = iPr_def_18 )
| ( sk_c7 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_45200,c_446]) ).
tcf(c_45248,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( iPr_def_16 = iPr_def_18 )
| ( sk_c7 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_45200,c_445]) ).
tcf(c_45410,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( iPr_def_16 = iPr_def_18 ) ),
inference(global_subsumption_just,[status(thm)],[c_45243,c_1132,c_1133,c_1138,c_1139,c_7500,c_45248,c_45246]) ).
tcf(c_45452,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_45410,c_10644]) ).
tcf(c_45974,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_45452,c_33283]) ).
tcf(c_47334,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_18 )
| ( inverse(inverse(multiply(sk_c6,sk_c5))) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_20469,c_427]) ).
tcf(c_47487,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_20 )
| ( inverse(inverse(multiply(sk_c7,sk_c4))) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_20470,c_429]) ).
tcf(c_49241,plain,
( ~ iPr_def_12
| ( sk_c7 != sk_c3 )
| ( inverse(inverse(multiply(sk_c6,iPr_def_17))) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_20471,c_427]) ).
tcf(c_49246,plain,
multiply(inverse(sk_c3),inverse(multiply(sk_c5,iPr_def_17))) = iPr_def_18,
inference(superposition,[status(thm)],[c_20471,c_20469]) ).
tcf(c_49249,plain,
multiply(iPr_def_17,inverse(multiply(sk_c5,iPr_def_17))) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_49246,c_417]) ).
tcf(c_49533,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_49249,c_49241,c_47487,c_47334,c_45974,c_42434,c_42414,c_40114,c_40100,c_40093,c_40094,c_28983,c_28981,c_28980,c_28885,c_27487,c_20379,c_20199,c_19738,c_19561,c_19544,c_19466,c_19474,c_19467,c_17368,c_17367,c_17366,c_17361,c_17360,c_17359,c_17352,c_17351,c_17346,c_17341,c_17340,c_17358,c_17181,c_15512,c_15511,c_10156,c_17592,c_980,c_977,c_459,c_458,c_457,c_456,c_455,c_454,c_450,c_449,c_445,c_444,c_440,c_438,c_437,c_434,c_433,c_432,c_431,c_430,c_425,c_420,c_417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP367-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 % Computer : n015.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Wed Sep 23 14:38:40 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 0.13/0.44
% 0.13/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.44
% 0.13/0.44 % Detected problem language: tptp
% 0.13/0.46 % Proving...
% 20.61/3.80 % SZS status Started for theBenchmark.p
% 20.61/3.80 % SZS status Unsatisfiable for theBenchmark.p
% 20.61/3.80
% 20.61/3.80 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 20.61/3.80
% 20.61/3.80 % ------ iProver source info
% 20.61/3.80
% 20.61/3.80 % git: date: 2026-07-19 20:42:38 +0200
% 20.61/3.80 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 20.61/3.80 % git: non_committed_changes: false
% 20.61/3.80
% 20.61/3.80 % ------ Parsing...% successful
% 20.61/3.80
% 20.61/3.80
% 20.61/3.80 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 20.61/3.80
% 20.61/3.80 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 20.61/3.80
% 20.61/3.80 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 20.61/3.80
% 20.61/3.80 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 20.61/3.80 % ------ Proving...
% 20.61/3.80 % ------ Problem Properties
% 20.61/3.80
% 20.61/3.80 %
% 20.61/3.80 % clauses 49
% 20.61/3.80 % conjectures 35
% 20.61/3.80 % EPR 31
% 20.61/3.80 % Horn 18
% 20.61/3.80 % unary 14
% 20.61/3.80 % binary 30
% 20.61/3.80 % lits 92
% 20.61/3.80 % lits eq 84
% 20.61/3.80 % fd_pure 0
% 20.61/3.80 % fd_pseudo 0
% 20.61/3.80 % fd_cond 0
% 20.61/3.80 % fd_pseudo_cond 0
% 20.61/3.80 % AC symbols 0
% 20.61/3.80
% 20.61/3.80 % ------ Schedule dynamic 5 is on
% 20.61/3.80
% 20.61/3.80 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 20.61/3.80
% 20.61/3.80
% 20.61/3.80 % ------
% 20.61/3.80 % Current options:
% 20.61/3.80 % ------
% 20.61/3.80
% 20.61/3.80
% 20.61/3.80 %
% 20.61/3.80
% 20.61/3.80 % ------ Proving...
% 20.61/3.80 %
% 20.61/3.80
% 20.61/3.80 % SZS status Unsatisfiable for theBenchmark.p
% 20.61/3.80
% 20.61/3.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.81/3.81
% 8.81/3.81
%------------------------------------------------------------------------------