%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP345-1 : 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 : n018.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 01:33:18 PM UTC 2026
% Result : Unsatisfiable 14.30s 12.85s
% Output : CNFRefutation 14.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 41
% Syntax : Number of formulae : 291 ( 113 unt; 11 def)
% Number of atoms : 881 ( 495 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 377 ( 129 ~; 248 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 65 !; 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_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c7 = multiply(sk_c6,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c6 = multiply(sk_c3,sk_c7)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c7 = inverse(sk_c3)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c5 = inverse(sk_c6)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f11]) ).
fof(f17,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = multiply(sk_c6,sk_c5)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = multiply(sk_c3,sk_c7)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c6) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c5 = inverse(sk_c6)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f23]) ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = inverse(sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = multiply(sk_c6,sk_c5)
| sk_c7 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c6 = multiply(sk_c3,sk_c7)
| sk_c7 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c5 = inverse(sk_c6)
| sk_c7 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f35]) ).
fof(f39,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c6 = inverse(sk_c4)
| sk_c7 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c6,sk_c5)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = multiply(sk_c3,sk_c7)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c5 = inverse(sk_c6)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = inverse(sk_c4)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c7 = multiply(sk_c6,sk_c5)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c6 = multiply(sk_c3,sk_c7)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c5 = inverse(sk_c6)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c6 = inverse(sk_c4)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1] :
( inverse(X3) != sk_c6
| multiply(X3,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(X1,sk_c5) != sk_c6
| inverse(X1) != sk_c6
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( sk_c6 != inverse(X3)
| sk_c5 != multiply(X3,sk_c6)
| sk_c5 != inverse(sk_c6)
| sk_c7 != inverse(X2)
| sk_c6 != multiply(X2,sk_c7)
| sk_c7 != multiply(sk_c6,sk_c5)
| sk_c6 != multiply(X1,sk_c5)
| sk_c6 != inverse(X1)
| sk_c7 != multiply(X0,sk_c6)
| inverse(X0) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(reorient_equations,[],[f65]) ).
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_c6,sk_c5) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_87,negated_conjecture,
( ( multiply(sk_c3,sk_c7) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_99,negated_conjecture,
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ( multiply(sk_c3,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c3,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_106,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c4,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_111,negated_conjecture,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( multiply(sk_c3,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c2,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(sk_c2,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_114,negated_conjecture,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( multiply(sk_c4,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c2,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(sk_c6) != sk_c5 )
| ( inverse(X3) != sk_c6 )
| ( inverse(X2) != sk_c7 )
| ( inverse(X1) != sk_c6 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c6,sk_c5) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(X3,sk_c6) != sk_c5 )
| ( multiply(X2,sk_c7) != sk_c6 )
| ( multiply(X1,sk_c5) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_413,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_116]) ).
tcf(c_414,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_116]) ).
tcf(c_415,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_116]) ).
tcf(c_416,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_116]) ).
tcf(c_417,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c6) != sk_c5 )
| ( multiply(sk_c6,sk_c5) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_418,definition,
iPr_def_14 = multiply(sk_c6,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_419,definition,
iPr_def_15 = multiply(sk_c6,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_420,definition,
iPr_def_16 = inverse(sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_421,definition,
iPr_def_17 = multiply(sk_c2,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_422,definition,
iPr_def_18 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_423,definition,
iPr_def_19 = multiply(sk_c4,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_424,definition,
iPr_def_20 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_425,definition,
iPr_def_21 = multiply(sk_c3,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_426,definition,
iPr_def_22 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_427,definition,
iPr_def_23 = multiply(sk_c1,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_428,definition,
iPr_def_24 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_429,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_16 != sk_c5 )
| ( iPr_def_15 != sk_c7 )
| ( iPr_def_14 != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_417,c_420,c_419,c_418]) ).
tcf(c_430,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_416]) ).
tcf(c_431,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_415]) ).
tcf(c_432,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_414]) ).
tcf(c_433,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_413]) ).
tcf(c_434,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_115,c_422,c_421]) ).
tcf(c_435,negated_conjecture,
( ( iPr_def_19 = sk_c5 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_114,c_423]) ).
tcf(c_436,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_113]) ).
tcf(c_437,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_112,c_424]) ).
tcf(c_438,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_111,c_425]) ).
tcf(c_439,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_440,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_109,c_426]) ).
tcf(c_441,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_19 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_442,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_443,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_444,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_21 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_445,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_446,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_103,c_427]) ).
tcf(c_448,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_449,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_450,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_21 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_451,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_452,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_97,c_428]) ).
tcf(c_454,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_455,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_456,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_21 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_457,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_460,negated_conjecture,
( ( iPr_def_16 = sk_c5 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_461,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_462,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_463,negated_conjecture,
( ( iPr_def_15 = sk_c7 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_793,plain,
( ( sk_c6 = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_16) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_442,c_421]) ).
tcf(c_795,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( sk_c6 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_442,c_441]) ).
tcf(c_808,plain,
( ( sk_c6 = iPr_def_22 )
| ( multiply(sk_c6,iPr_def_20) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_443,c_418]) ).
tcf(c_961,plain,
( ( sk_c6 = iPr_def_21 )
| ( multiply(sk_c4,iPr_def_22) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_444,c_423]) ).
tcf(c_962,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(sk_c4,iPr_def_22) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_440,c_423]) ).
tcf(c_976,plain,
( ( sk_c6 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_443,c_425]) ).
tcf(c_1022,plain,
multiply(iPr_def_20,sk_c3) = identity,
inference(superposition,[status(thm)],[c_424,c_84]) ).
tcf(c_1023,plain,
multiply(iPr_def_16,sk_c6) = identity,
inference(superposition,[status(thm)],[c_420,c_84]) ).
tcf(c_1024,plain,
multiply(iPr_def_18,sk_c4) = identity,
inference(superposition,[status(thm)],[c_422,c_84]) ).
tcf(c_1025,plain,
multiply(iPr_def_24,sk_c1) = identity,
inference(superposition,[status(thm)],[c_428,c_84]) ).
tcf(c_1026,plain,
multiply(iPr_def_22,sk_c2) = identity,
inference(superposition,[status(thm)],[c_426,c_84]) ).
tcf(c_1152,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(sk_c3,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_452,c_425]) ).
tcf(c_1276,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c3,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_455,c_425]) ).
tcf(c_1277,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_455,c_449]) ).
tcf(c_1337,plain,
( ( sk_c6 = iPr_def_21 )
| ( multiply(sk_c3,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_456,c_425]) ).
tcf(c_1392,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c3,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_457,c_425]) ).
tcf(c_2118,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_23 )
| ( inverse(sk_c1) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_427,c_430]) ).
tcf(c_2135,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_24 )
| ( sk_c7 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_2118,c_428]) ).
tcf(c_2204,plain,
( ~ iPr_def_12
| ( sk_c5 != identity )
| ( inverse(iPr_def_16) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_1023,c_431]) ).
tcf(c_2292,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_17 )
| ( inverse(sk_c2) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_421,c_432]) ).
tcf(c_2312,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_22 )
| ( sk_c6 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_2292,c_426]) ).
tcf(c_2467,plain,
( ~ iPr_def_10
| ( sk_c6 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_84,c_433]) ).
tcf(c_2807,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( inverse(iPr_def_22) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_795,c_420]) ).
tcf(c_3041,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c6,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_423,c_85]) ).
tcf(c_3042,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c6,X0)) = multiply(iPr_def_23,X0),
inference(superposition,[status(thm)],[c_427,c_85]) ).
tcf(c_3045,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_3047,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1022,c_85]) ).
tcf(c_3048,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c6,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1023,c_85]) ).
tcf(c_3049,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1024,c_85]) ).
tcf(c_3050,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1025,c_85]) ).
tcf(c_3051,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1026,c_85]) ).
tcf(c_3057,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3051,c_83]) ).
tcf(c_3058,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3050,c_83]) ).
tcf(c_3059,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3049,c_83]) ).
tcf(c_3060,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c6,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3048,c_83]) ).
tcf(c_3061,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3047,c_83]) ).
tcf(c_3342,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( multiply(sk_c6,iPr_def_20) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1277,c_418]) ).
tcf(c_4147,plain,
multiply(iPr_def_22,iPr_def_17) = sk_c5,
inference(superposition,[status(thm)],[c_421,c_3057]) ).
tcf(c_4165,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(iPr_def_17,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_4147,c_85]) ).
tcf(c_4169,plain,
multiply(iPr_def_24,iPr_def_23) = sk_c6,
inference(superposition,[status(thm)],[c_427,c_3058]) ).
tcf(c_4172,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(iPr_def_23,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_4169,c_85]) ).
tcf(c_4207,plain,
multiply(iPr_def_18,iPr_def_19) = sk_c6,
inference(superposition,[status(thm)],[c_423,c_3059]) ).
tcf(c_4219,plain,
multiply(iPr_def_16,iPr_def_14) = sk_c7,
inference(superposition,[status(thm)],[c_418,c_3060]) ).
tcf(c_4220,plain,
multiply(iPr_def_16,iPr_def_15) = sk_c5,
inference(superposition,[status(thm)],[c_419,c_3060]) ).
tcf(c_4735,plain,
multiply(iPr_def_20,iPr_def_21) = sk_c7,
inference(superposition,[status(thm)],[c_425,c_3061]) ).
tcf(c_5729,plain,
( ( sk_c6 = iPr_def_21 )
| ( multiply(iPr_def_18,iPr_def_19) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_961,c_3059]) ).
tcf(c_5730,plain,
( ( sk_c6 = iPr_def_22 )
| ( sk_c6 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_5729,c_4207]) ).
tcf(c_5749,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_18,iPr_def_19) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_962,c_3059]) ).
tcf(c_5750,plain,
( ( sk_c6 = iPr_def_22 )
| ( sk_c6 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_5749,c_4207]) ).
tcf(c_6532,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1152,c_3061]) ).
tcf(c_6533,plain,
( ( sk_c7 = iPr_def_24 )
| ( sk_c6 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_6532,c_4735]) ).
tcf(c_6899,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1276,c_3061]) ).
tcf(c_6900,plain,
( ( sk_c7 = iPr_def_24 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_6899,c_4735]) ).
tcf(c_7001,plain,
( ( sk_c6 = iPr_def_21 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1337,c_3061]) ).
tcf(c_7002,plain,
( ( sk_c7 = iPr_def_24 )
| ( sk_c6 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_7001,c_4735]) ).
tcf(c_7084,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1392,c_3061]) ).
tcf(c_7085,plain,
( ( sk_c7 = iPr_def_24 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_7084,c_4735]) ).
tcf(c_9395,plain,
multiply(sk_c4,iPr_def_14) = multiply(iPr_def_19,sk_c7),
inference(superposition,[status(thm)],[c_418,c_3041]) ).
tcf(c_9396,plain,
multiply(sk_c4,iPr_def_15) = multiply(iPr_def_19,sk_c5),
inference(superposition,[status(thm)],[c_419,c_3041]) ).
tcf(c_9627,plain,
multiply(sk_c1,iPr_def_14) = multiply(iPr_def_23,sk_c7),
inference(superposition,[status(thm)],[c_418,c_3042]) ).
tcf(c_9628,plain,
multiply(sk_c1,iPr_def_15) = multiply(iPr_def_23,sk_c5),
inference(superposition,[status(thm)],[c_419,c_3042]) ).
tcf(c_11126,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_3045,c_83]) ).
tcf(c_11144,plain,
multiply(inverse(sk_c6),iPr_def_14) = sk_c7,
inference(superposition,[status(thm)],[c_418,c_11126]) ).
tcf(c_11149,plain,
multiply(inverse(sk_c2),iPr_def_17) = sk_c5,
inference(superposition,[status(thm)],[c_421,c_11126]) ).
tcf(c_11151,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_84,c_11126]) ).
tcf(c_11164,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( multiply(inverse(sk_c6),iPr_def_14) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_3342,c_11126]) ).
tcf(c_11165,plain,
( ( sk_c6 = iPr_def_22 )
| ( multiply(inverse(sk_c6),iPr_def_14) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_808,c_11126]) ).
tcf(c_11193,plain,
( ( sk_c6 = iPr_def_22 )
| ( multiply(inverse(sk_c2),iPr_def_17) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_793,c_11126]) ).
tcf(c_11286,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_3061,c_11126]) ).
tcf(c_11287,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_3060,c_11126]) ).
tcf(c_11288,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_3059,c_11126]) ).
tcf(c_11289,plain,
! [X0: $i] : multiply(inverse(iPr_def_24),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_3058,c_11126]) ).
tcf(c_11290,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_3057,c_11126]) ).
tcf(c_11328,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_11126,c_11126]) ).
tcf(c_11866,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_11151,c_11328]) ).
tcf(c_11882,plain,
multiply(sk_c1,sk_c6) = multiply(iPr_def_23,identity),
inference(superposition,[status(thm)],[c_11866,c_3042]) ).
tcf(c_11885,plain,
multiply(sk_c6,identity) = multiply(iPr_def_24,iPr_def_23),
inference(superposition,[status(thm)],[c_11866,c_4172]) ).
tcf(c_11886,plain,
multiply(sk_c5,identity) = multiply(iPr_def_22,iPr_def_17),
inference(superposition,[status(thm)],[c_11866,c_4165]) ).
tcf(c_11892,plain,
multiply(sk_c5,identity) = sk_c5,
inference(light_normalisation,[status(thm)],[c_11886,c_4147]) ).
tcf(c_11895,plain,
multiply(iPr_def_23,identity) = iPr_def_23,
inference(light_normalisation,[status(thm)],[c_11882,c_427]) ).
tcf(c_11967,plain,
( ( sk_c7 = iPr_def_15 )
| ~ iPr_def_13
| ( sk_c7 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_451,c_2135]) ).
tcf(c_11968,plain,
( ( sk_c6 = iPr_def_21 )
| ~ iPr_def_13
| ( sk_c7 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_450,c_2135]) ).
tcf(c_11969,plain,
( ( sk_c7 = iPr_def_20 )
| ~ iPr_def_13
| ( sk_c7 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_449,c_2135]) ).
tcf(c_11970,plain,
( ( sk_c6 = iPr_def_18 )
| ~ iPr_def_13
| ( sk_c7 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_446,c_2135]) ).
tcf(c_12047,plain,
( ( sk_c7 = iPr_def_15 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_11967,c_7085,c_11967]) ).
tcf(c_12053,plain,
( ( sk_c6 = iPr_def_21 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_11968,c_7002,c_11968]) ).
tcf(c_12059,plain,
( ( sk_c7 = iPr_def_20 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_11969,c_6900,c_11969]) ).
tcf(c_12065,plain,
( ( sk_c6 = iPr_def_18 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_11970,c_6533,c_11970]) ).
tcf(c_12933,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_20)) != sk_c7 )
| ( multiply(sk_c3,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_11286,c_430]) ).
tcf(c_12934,plain,
multiply(sk_c3,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_11286,c_84]) ).
tcf(c_12937,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_20)) != sk_c7 )
| ( multiply(sk_c3,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_11286,c_433]) ).
tcf(c_12939,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_11286,c_11126]) ).
tcf(c_12940,plain,
multiply(sk_c3,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_11286,c_11866]) ).
tcf(c_12944,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_21 )
| ( inverse(inverse(iPr_def_20)) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_12937,c_425]) ).
tcf(c_12956,plain,
( ( identity = iPr_def_21 )
| ( sk_c6 = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_976,c_12934]) ).
tcf(c_13514,plain,
( ( identity = iPr_def_21 )
| ( inverse(iPr_def_22) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_12956,c_420]) ).
tcf(c_13687,plain,
inverse(iPr_def_20) = sk_c3,
inference(demodulation,[status(thm)],[c_12940,c_11866]) ).
tcf(c_13691,plain,
multiply(sk_c3,identity) = sk_c3,
inference(superposition,[status(thm)],[c_1022,c_12939]) ).
tcf(c_13692,plain,
multiply(sk_c3,sk_c7) = iPr_def_21,
inference(superposition,[status(thm)],[c_4735,c_12939]) ).
tcf(c_15983,plain,
multiply(sk_c6,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_11287,c_84]) ).
tcf(c_15988,plain,
! [X0: $i] : multiply(sk_c6,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_11287,c_11126]) ).
tcf(c_15989,plain,
multiply(sk_c6,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_11287,c_11866]) ).
tcf(c_16057,plain,
multiply(sk_c1,identity) = multiply(iPr_def_23,iPr_def_16),
inference(superposition,[status(thm)],[c_15983,c_3042]) ).
tcf(c_16058,plain,
multiply(sk_c4,identity) = multiply(iPr_def_19,iPr_def_16),
inference(superposition,[status(thm)],[c_15983,c_3041]) ).
tcf(c_16125,plain,
inverse(iPr_def_16) = sk_c6,
inference(demodulation,[status(thm)],[c_15989,c_11866]) ).
tcf(c_17057,plain,
multiply(sk_c6,sk_c7) = iPr_def_14,
inference(superposition,[status(thm)],[c_4219,c_15988]) ).
tcf(c_17058,plain,
multiply(sk_c6,sk_c5) = iPr_def_15,
inference(superposition,[status(thm)],[c_4220,c_15988]) ).
tcf(c_18395,plain,
multiply(iPr_def_23,iPr_def_16) = sk_c1,
inference(demodulation,[status(thm)],[c_16057,c_11866]) ).
tcf(c_18396,plain,
multiply(inverse(iPr_def_23),sk_c1) = iPr_def_16,
inference(superposition,[status(thm)],[c_18395,c_11126]) ).
tcf(c_18401,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),multiply(sk_c1,X0)) = multiply(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_18396,c_85]) ).
tcf(c_18403,plain,
multiply(iPr_def_19,iPr_def_16) = sk_c4,
inference(demodulation,[status(thm)],[c_16058,c_11866]) ).
tcf(c_18404,plain,
multiply(inverse(iPr_def_19),sk_c4) = iPr_def_16,
inference(superposition,[status(thm)],[c_18403,c_11126]) ).
tcf(c_18409,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),multiply(sk_c4,X0)) = multiply(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_18404,c_85]) ).
tcf(c_20594,plain,
( ~ iPr_def_12
| ( sk_c5 != identity ) ),
inference(ground_joinability,[status(thm)],[c_2204,c_16125]) ).
tcf(c_20902,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_18)) != sk_c6 )
| ( multiply(sk_c4,sk_c6) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_11288,c_431]) ).
tcf(c_20904,plain,
multiply(sk_c4,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_11288,c_84]) ).
tcf(c_20908,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_18)) != sk_c6 )
| ( multiply(sk_c4,sk_c5) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_11288,c_432]) ).
tcf(c_20909,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_11288,c_11126]) ).
tcf(c_20910,plain,
multiply(sk_c4,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_11288,c_11866]) ).
tcf(c_20923,plain,
( ~ iPr_def_12
| ( sk_c5 != iPr_def_19 )
| ( inverse(inverse(iPr_def_18)) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_20902,c_423]) ).
tcf(c_20980,plain,
inverse(iPr_def_18) = sk_c4,
inference(demodulation,[status(thm)],[c_20910,c_11866]) ).
tcf(c_20997,plain,
multiply(sk_c4,sk_c6) = iPr_def_19,
inference(superposition,[status(thm)],[c_4207,c_20909]) ).
tcf(c_21919,plain,
( ( sk_c7 = iPr_def_20 )
| ~ iPr_def_10
| ( sk_c6 != identity )
| ( inverse(inverse(iPr_def_23)) != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_449,c_2467]) ).
tcf(c_22233,plain,
multiply(sk_c1,iPr_def_24) = identity,
inference(superposition,[status(thm)],[c_11289,c_84]) ).
tcf(c_22238,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_24,X0)) = X0,
inference(superposition,[status(thm)],[c_11289,c_11126]) ).
tcf(c_22239,plain,
multiply(sk_c1,identity) = inverse(iPr_def_24),
inference(superposition,[status(thm)],[c_11289,c_11866]) ).
tcf(c_22416,plain,
inverse(iPr_def_24) = sk_c1,
inference(demodulation,[status(thm)],[c_22239,c_11866]) ).
tcf(c_22476,plain,
multiply(sk_c1,identity) = sk_c1,
inference(superposition,[status(thm)],[c_1025,c_22238]) ).
tcf(c_22477,plain,
multiply(sk_c1,sk_c6) = iPr_def_23,
inference(superposition,[status(thm)],[c_4169,c_22238]) ).
tcf(c_22891,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_22)) != sk_c6 )
| ( multiply(sk_c2,sk_c6) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_11290,c_431]) ).
tcf(c_22893,plain,
multiply(sk_c2,iPr_def_22) = identity,
inference(superposition,[status(thm)],[c_11290,c_84]) ).
tcf(c_22898,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_22,X0)) = X0,
inference(superposition,[status(thm)],[c_11290,c_11126]) ).
tcf(c_22899,plain,
multiply(sk_c2,identity) = inverse(iPr_def_22),
inference(superposition,[status(thm)],[c_11290,c_11866]) ).
tcf(c_22994,plain,
multiply(iPr_def_22,identity) = iPr_def_22,
inference(superposition,[status(thm)],[c_22893,c_3057]) ).
tcf(c_23005,plain,
inverse(iPr_def_22) = sk_c2,
inference(demodulation,[status(thm)],[c_22899,c_11866]) ).
tcf(c_23008,plain,
( ( identity = iPr_def_21 )
| ( sk_c2 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_13514,c_23005]) ).
tcf(c_23010,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( sk_c2 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_2807,c_23005]) ).
tcf(c_23385,plain,
multiply(sk_c2,sk_c5) = iPr_def_17,
inference(superposition,[status(thm)],[c_4147,c_22898]) ).
tcf(c_23640,plain,
( ( identity = iPr_def_21 )
| ( multiply(iPr_def_16,sk_c5) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_23008,c_421]) ).
tcf(c_24048,plain,
( ( identity = iPr_def_21 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_17 )
| ( inverse(iPr_def_16) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_23640,c_432]) ).
tcf(c_24053,plain,
( ( identity = iPr_def_21 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_17 ) ),
inference(ground_joinability,[status(thm)],[c_24048,c_16125]) ).
tcf(c_24077,plain,
multiply(inverse(iPr_def_23),multiply(iPr_def_23,sk_c7)) = multiply(iPr_def_16,iPr_def_14),
inference(superposition,[status(thm)],[c_9627,c_18401]) ).
tcf(c_24079,plain,
multiply(inverse(iPr_def_23),sk_c1) = multiply(iPr_def_16,identity),
inference(superposition,[status(thm)],[c_11866,c_18401]) ).
tcf(c_24080,plain,
multiply(inverse(iPr_def_23),identity) = multiply(iPr_def_16,iPr_def_24),
inference(superposition,[status(thm)],[c_22233,c_18401]) ).
tcf(c_24087,plain,
multiply(inverse(iPr_def_23),multiply(iPr_def_23,sk_c7)) = sk_c7,
inference(light_normalisation,[status(thm)],[c_24077,c_4219]) ).
tcf(c_24186,plain,
multiply(inverse(iPr_def_19),iPr_def_19) = multiply(iPr_def_16,sk_c6),
inference(superposition,[status(thm)],[c_20997,c_18409]) ).
tcf(c_24206,plain,
multiply(inverse(iPr_def_19),multiply(iPr_def_19,sk_c7)) = multiply(iPr_def_16,iPr_def_14),
inference(superposition,[status(thm)],[c_9395,c_18409]) ).
tcf(c_24207,plain,
multiply(inverse(iPr_def_19),multiply(iPr_def_19,sk_c5)) = multiply(iPr_def_16,iPr_def_15),
inference(superposition,[status(thm)],[c_9396,c_18409]) ).
tcf(c_24208,plain,
multiply(inverse(iPr_def_19),sk_c4) = multiply(iPr_def_16,identity),
inference(superposition,[status(thm)],[c_11866,c_18409]) ).
tcf(c_24214,plain,
multiply(inverse(iPr_def_19),iPr_def_19) = identity,
inference(light_normalisation,[status(thm)],[c_24186,c_1023]) ).
tcf(c_24215,plain,
multiply(inverse(iPr_def_19),multiply(iPr_def_19,sk_c5)) = sk_c5,
inference(light_normalisation,[status(thm)],[c_24207,c_4220]) ).
tcf(c_24216,plain,
multiply(inverse(iPr_def_19),multiply(iPr_def_19,sk_c7)) = sk_c7,
inference(light_normalisation,[status(thm)],[c_24206,c_4219]) ).
tcf(c_24478,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( multiply(iPr_def_16,sk_c5) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_23010,c_421]) ).
tcf(c_24804,plain,
( ( iPr_def_16 = iPr_def_19 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_17 )
| ( inverse(iPr_def_16) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_24478,c_432]) ).
tcf(c_24809,plain,
( ( iPr_def_16 = iPr_def_19 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_17 ) ),
inference(ground_joinability,[status(thm)],[c_24804,c_16125]) ).
tcf(c_29208,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_24809,c_24216,c_24215,c_24214,c_24208,c_24207,c_24206,c_24186,c_24087,c_24080,c_24079,c_24053,c_23385,c_23005,c_22994,c_22891,c_22893,c_22477,c_22476,c_22416,c_22233,c_21919,c_20997,c_20980,c_20923,c_20908,c_20904,c_20594,c_18404,c_18403,c_17058,c_17057,c_16125,c_15989,c_15983,c_13692,c_13691,c_13687,c_12944,c_12933,c_12934,c_12065,c_12059,c_12053,c_12047,c_11895,c_11892,c_11886,c_11885,c_11193,c_11165,c_11164,c_11149,c_11144,c_9628,c_9627,c_9396,c_9395,c_5750,c_5730,c_2312,c_463,c_462,c_461,c_460,c_457,c_456,c_455,c_454,c_451,c_450,c_448,c_445,c_442,c_439,c_438,c_437,c_436,c_435,c_434,c_429,c_428,c_426,c_424,c_422,c_420]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP345-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/10.37 % Computer : n018.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.37 % CPULimit : 300
% 0.10/10.37 % WCLimit : 300
% 0.10/10.37 % DateTime : Wed Sep 23 14:34:13 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/10.42 Running first-order theorem proving
% 0.13/10.42 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
% 0.13/10.43
% 0.13/10.43 % ======== iProver multi-core TPTP/SMT =========
% 0.13/10.43
% 0.13/10.43 % Detected problem language: tptp
% 0.13/10.44 % Proving...
% 14.30/12.85 % SZS status Started for theBenchmark.p
% 14.30/12.85 % SZS status Unsatisfiable for theBenchmark.p
% 14.30/12.85
% 14.30/12.85 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 14.30/12.85
% 14.30/12.85 % ------ iProver source info
% 14.30/12.85
% 14.30/12.85 % git: date: 2026-07-19 20:42:38 +0200
% 14.30/12.85 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 14.30/12.85 % git: non_committed_changes: false
% 14.30/12.85
% 14.30/12.85 % ------ Parsing...% successful
% 14.30/12.85
% 14.30/12.85
% 14.30/12.85 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 14.30/12.85
% 14.30/12.85 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 14.30/12.85
% 14.30/12.85 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 14.30/12.85
% 14.30/12.85 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 14.30/12.85 % ------ Proving...
% 14.30/12.85 % ------ Problem Properties
% 14.30/12.85
% 14.30/12.85 %
% 14.30/12.85 % clauses 49
% 14.30/12.85 % conjectures 35
% 14.30/12.85 % EPR 31
% 14.30/12.85 % Horn 18
% 14.30/12.85 % unary 14
% 14.30/12.85 % binary 30
% 14.30/12.85 % lits 93
% 14.30/12.85 % lits eq 85
% 14.30/12.85 % fd_pure 0
% 14.30/12.85 % fd_pseudo 0
% 14.30/12.85 % fd_cond 0
% 14.30/12.85 % fd_pseudo_cond 0
% 14.30/12.85 % AC symbols 0
% 14.30/12.85
% 14.30/12.85 % ------ Schedule dynamic 5 is on
% 14.30/12.85
% 14.30/12.85 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 14.30/12.85
% 14.30/12.85
% 14.30/12.85 % ------
% 14.30/12.85 % Current options:
% 14.30/12.85 % ------
% 14.30/12.85
% 14.30/12.85
% 14.30/12.85 %
% 14.30/12.85
% 14.30/12.85 % ------ Proving...
% 14.30/12.85 %
% 14.30/12.85
% 14.30/12.85 % SZS status Unsatisfiable for theBenchmark.p
% 14.30/12.85
% 14.30/12.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 14.30/12.86
% 14.30/12.86
%------------------------------------------------------------------------------