%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP301-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:32:46 PM UTC 2026
% Result : Unsatisfiable 10.76s 2.74s
% Output : CNFRefutation 10.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 40
% Syntax : Number of formulae : 303 ( 110 unt; 11 def)
% Number of atoms : 932 ( 520 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 433 ( 159 ~; 274 |; 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 : 72 ( 0 sgn 72 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c7 = inverse(sk_c3)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c6 = inverse(sk_c4)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f13]) ).
fof(f19,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = inverse(sk_c4)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f29,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c6 = inverse(sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = inverse(sk_c3)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = inverse(sk_c4)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f43]) ).
fof(f47,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = inverse(sk_c3)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = inverse(sk_c4)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c6 = inverse(sk_c4)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(X3,sk_c5) != sk_c6
| inverse(X3) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c5
| inverse(sk_c7) != sk_c5
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( sk_c6 != multiply(X3,sk_c5)
| sk_c6 != inverse(X3)
| sk_c7 != multiply(X2,sk_c6)
| sk_c7 != inverse(X2)
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c6 != inverse(X1)
| sk_c5 != multiply(X1,sk_c6)
| sk_c5 != inverse(sk_c7)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7)
| multiply(sk_c7,sk_c6) != 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_c7) = sk_c5 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_88,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_90,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_93,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_95,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_108,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(sk_c7) != sk_c5 )
| ( inverse(X3) != sk_c6 )
| ( inverse(X2) != sk_c6 )
| ( inverse(X1) != sk_c7 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c6) != sk_c5 )
| ( multiply(X3,sk_c6) != sk_c5 )
| ( multiply(X2,sk_c5) != sk_c6 )
| ( multiply(X1,sk_c6) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_413,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != 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_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
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_c7) != sk_c6 ) ),
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_c7) != sk_c5 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c6) != sk_c5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_418,definition,
iPr_def_14 = multiply(sk_c7,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_419,definition,
iPr_def_15 = multiply(sk_c6,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_420,definition,
iPr_def_16 = inverse(sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_421,definition,
iPr_def_17 = multiply(sk_c4,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_422,definition,
iPr_def_18 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_423,definition,
iPr_def_19 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_424,definition,
iPr_def_20 = multiply(sk_c3,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_425,definition,
iPr_def_21 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_426,definition,
iPr_def_22 = multiply(sk_c2,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_427,definition,
iPr_def_23 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_428,definition,
iPr_def_24 = multiply(sk_c1,sk_c7),
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_c5 )
| ( 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_c7) != sk_c6 ) ),
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_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_414]) ).
tcf(c_433,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != 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_c6 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_114,c_423]) ).
tcf(c_436,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_113,c_424]) ).
tcf(c_437,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_112,c_425]) ).
tcf(c_438,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_15 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_439,negated_conjecture,
( ( iPr_def_22 = sk_c5 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_110,c_426]) ).
tcf(c_440,negated_conjecture,
( ( iPr_def_22 = sk_c5 )
| ( iPr_def_19 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_441,negated_conjecture,
( ( iPr_def_22 = sk_c5 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_442,negated_conjecture,
( ( iPr_def_22 = sk_c5 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_444,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_445,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_446,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_447,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_448,negated_conjecture,
( ( iPr_def_16 = sk_c5 )
| ( iPr_def_15 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_449,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_100,c_427]) ).
tcf(c_450,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_19 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_451,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_454,negated_conjecture,
( ( iPr_def_24 = sk_c6 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_95,c_428]) ).
tcf(c_455,negated_conjecture,
( ( iPr_def_24 = sk_c6 )
| ( iPr_def_19 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_456,negated_conjecture,
( ( iPr_def_24 = sk_c6 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_459,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_460,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( 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_c7 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_463,negated_conjecture,
( ( iPr_def_15 = sk_c5 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_780,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c4,iPr_def_22) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_442,c_421]) ).
tcf(c_947,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_23,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_449,c_418]) ).
tcf(c_1001,plain,
multiply(iPr_def_21,sk_c3) = identity,
inference(superposition,[status(thm)],[c_425,c_84]) ).
tcf(c_1002,plain,
multiply(iPr_def_19,sk_c4) = identity,
inference(superposition,[status(thm)],[c_423,c_84]) ).
tcf(c_1003,plain,
multiply(iPr_def_23,sk_c1) = identity,
inference(superposition,[status(thm)],[c_427,c_84]) ).
tcf(c_1004,plain,
multiply(iPr_def_16,sk_c7) = identity,
inference(superposition,[status(thm)],[c_420,c_84]) ).
tcf(c_1005,plain,
multiply(iPr_def_18,sk_c2) = identity,
inference(superposition,[status(thm)],[c_422,c_84]) ).
tcf(c_1018,plain,
( ( sk_c6 = iPr_def_19 )
| ( multiply(iPr_def_23,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_450,c_418]) ).
tcf(c_1237,plain,
( ( iPr_def_18 = iPr_def_24 )
| ( sk_c6 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_454,c_434]) ).
tcf(c_1537,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c6 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_459,c_439]) ).
tcf(c_1608,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c6 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_460,c_440]) ).
tcf(c_1801,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c7 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_462,c_442]) ).
tcf(c_2104,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_24 )
| ( inverse(sk_c1) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_428,c_430]) ).
tcf(c_2107,plain,
( ~ iPr_def_13
| ( sk_c6 != identity )
| ( inverse(iPr_def_16) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_1004,c_430]) ).
tcf(c_2122,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_24 )
| ( sk_c7 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_2104,c_427]) ).
tcf(c_2206,plain,
( ~ iPr_def_12
| ( sk_c6 != sk_c5 )
| ( inverse(identity) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_83,c_431]) ).
tcf(c_2435,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_17 )
| ( inverse(sk_c4) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_421,c_433]) ).
tcf(c_2436,plain,
( ~ iPr_def_10
| ( sk_c6 != sk_c5 )
| ( inverse(identity) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_83,c_433]) ).
tcf(c_2437,plain,
( ~ iPr_def_10
| ( sk_c6 != identity )
| ( inverse(inverse(sk_c5)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_84,c_433]) ).
tcf(c_2459,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_19 )
| ( sk_c6 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_2435,c_423]) ).
tcf(c_2635,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c6 = iPr_def_17 )
| ( sk_c5 != iPr_def_16 )
| ( sk_c5 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_459,c_429]) ).
tcf(c_3139,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c6,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_418,c_85]) ).
tcf(c_3140,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_419,c_85]) ).
tcf(c_3141,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c6,X0)) = multiply(iPr_def_20,X0),
inference(superposition,[status(thm)],[c_424,c_85]) ).
tcf(c_3143,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c7,X0)) = multiply(iPr_def_24,X0),
inference(superposition,[status(thm)],[c_428,c_85]) ).
tcf(c_3144,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c6,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_426,c_85]) ).
tcf(c_3146,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_3148,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1001,c_85]) ).
tcf(c_3149,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1002,c_85]) ).
tcf(c_3150,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1003,c_85]) ).
tcf(c_3151,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c7,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1004,c_85]) ).
tcf(c_3152,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1005,c_85]) ).
tcf(c_3158,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3152,c_83]) ).
tcf(c_3159,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c7,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3151,c_83]) ).
tcf(c_3160,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3150,c_83]) ).
tcf(c_3161,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3149,c_83]) ).
tcf(c_3162,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3148,c_83]) ).
tcf(c_3293,plain,
( ( iPr_def_18 = iPr_def_24 )
| ( iPr_def_17 = iPr_def_19 )
| ( sk_c6 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1237,c_435]) ).
tcf(c_3697,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1608,c_1537]) ).
tcf(c_4018,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(iPr_def_21,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1801,c_418]) ).
tcf(c_4139,plain,
multiply(iPr_def_18,iPr_def_22) = sk_c6,
inference(superposition,[status(thm)],[c_426,c_3158]) ).
tcf(c_4170,plain,
multiply(iPr_def_16,iPr_def_14) = sk_c6,
inference(superposition,[status(thm)],[c_418,c_3159]) ).
tcf(c_4258,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_14,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_4170,c_85]) ).
tcf(c_4274,plain,
multiply(iPr_def_23,iPr_def_24) = sk_c7,
inference(superposition,[status(thm)],[c_428,c_3160]) ).
tcf(c_4277,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(iPr_def_24,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_4274,c_85]) ).
tcf(c_4595,plain,
multiply(iPr_def_19,iPr_def_17) = sk_c5,
inference(superposition,[status(thm)],[c_421,c_3161]) ).
tcf(c_4598,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(iPr_def_17,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_4595,c_85]) ).
tcf(c_4627,plain,
multiply(iPr_def_21,iPr_def_20) = sk_c6,
inference(superposition,[status(thm)],[c_424,c_3162]) ).
tcf(c_4630,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(iPr_def_20,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_4627,c_85]) ).
tcf(c_4726,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( multiply(iPr_def_18,iPr_def_14) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_3697,c_4139]) ).
tcf(c_5360,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_454,c_947]) ).
tcf(c_5366,plain,
( ( sk_c6 = iPr_def_17 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_5360,c_4274]) ).
tcf(c_5445,plain,
! [X0: $i] :
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_16,multiply(iPr_def_14,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_5366,c_3159]) ).
tcf(c_5457,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_16,iPr_def_14) = identity ) ),
inference(superposition,[status(thm)],[c_5366,c_1004]) ).
tcf(c_5459,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(sk_c1,iPr_def_14) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_5366,c_428]) ).
tcf(c_5476,plain,
( ( sk_c6 = iPr_def_17 )
| ( sk_c6 = identity ) ),
inference(light_normalisation,[status(thm)],[c_5457,c_4170]) ).
tcf(c_5504,plain,
! [X0: $i] :
( ( sk_c6 = iPr_def_17 )
| ( multiply(sk_c6,X0) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_5445,c_4258]) ).
tcf(c_6036,plain,
( ( sk_c6 = iPr_def_19 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_455,c_1018]) ).
tcf(c_6043,plain,
( ( sk_c6 = iPr_def_19 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_6036,c_4274]) ).
tcf(c_6109,plain,
( ( sk_c6 = iPr_def_19 )
| ( multiply(iPr_def_16,iPr_def_14) = identity ) ),
inference(superposition,[status(thm)],[c_6043,c_1004]) ).
tcf(c_6111,plain,
( ( sk_c6 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_14) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_6043,c_428]) ).
tcf(c_6128,plain,
( ( sk_c6 = iPr_def_19 )
| ( sk_c6 = identity ) ),
inference(light_normalisation,[status(thm)],[c_6109,c_4170]) ).
tcf(c_6808,plain,
( ( identity = iPr_def_24 )
| ( sk_c6 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_5476,c_454]) ).
tcf(c_7828,plain,
( ( identity = iPr_def_24 )
| ( sk_c6 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_6128,c_455]) ).
tcf(c_7968,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( identity = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_7828,c_6808]) ).
tcf(c_9303,plain,
! [X0: $i] :
( ( iPr_def_17 = iPr_def_19 )
| ( multiply(iPr_def_24,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_7968,c_83]) ).
tcf(c_10523,plain,
multiply(sk_c7,iPr_def_15) = multiply(iPr_def_14,sk_c7),
inference(superposition,[status(thm)],[c_419,c_3139]) ).
tcf(c_10729,plain,
multiply(iPr_def_16,multiply(iPr_def_14,sk_c7)) = iPr_def_15,
inference(superposition,[status(thm)],[c_10523,c_3159]) ).
tcf(c_10837,plain,
multiply(sk_c6,iPr_def_14) = multiply(iPr_def_15,sk_c6),
inference(superposition,[status(thm)],[c_418,c_3140]) ).
tcf(c_11205,plain,
multiply(sk_c3,iPr_def_15) = multiply(iPr_def_20,sk_c7),
inference(superposition,[status(thm)],[c_419,c_3141]) ).
tcf(c_11216,plain,
multiply(sk_c3,multiply(iPr_def_15,sk_c6)) = multiply(iPr_def_20,iPr_def_14),
inference(superposition,[status(thm)],[c_10837,c_3141]) ).
tcf(c_11331,plain,
multiply(iPr_def_21,multiply(iPr_def_20,sk_c7)) = iPr_def_15,
inference(superposition,[status(thm)],[c_11205,c_3162]) ).
tcf(c_11375,plain,
multiply(sk_c1,iPr_def_14) = multiply(iPr_def_24,sk_c6),
inference(superposition,[status(thm)],[c_418,c_3143]) ).
tcf(c_13292,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_24,sk_c6) = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_5459,c_11375]) ).
tcf(c_13327,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(sk_c7,sk_c6) = multiply(iPr_def_23,iPr_def_24) ) ),
inference(superposition,[status(thm)],[c_13292,c_4277]) ).
tcf(c_14003,plain,
( ( iPr_def_18 = iPr_def_24 )
| ( iPr_def_17 = iPr_def_19 )
| ( sk_c6 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_3293,c_455]) ).
tcf(c_14240,plain,
( ( sk_c6 = iPr_def_19 )
| ( multiply(iPr_def_24,sk_c6) = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_6111,c_11375]) ).
tcf(c_14277,plain,
( ( sk_c6 = iPr_def_19 )
| ( multiply(sk_c7,sk_c6) = multiply(iPr_def_23,iPr_def_24) ) ),
inference(superposition,[status(thm)],[c_14240,c_4277]) ).
tcf(c_14457,plain,
! [X0: $i] :
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_18,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_434,c_5504]) ).
tcf(c_14689,plain,
( ( sk_c6 = iPr_def_22 )
| ( sk_c6 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_14457,c_4139]) ).
tcf(c_14754,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_3146,c_83]) ).
tcf(c_14777,plain,
multiply(inverse(sk_c6),iPr_def_15) = sk_c7,
inference(superposition,[status(thm)],[c_419,c_14754]) ).
tcf(c_14782,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_83,c_14754]) ).
tcf(c_14783,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_84,c_14754]) ).
tcf(c_14785,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(inverse(iPr_def_21),iPr_def_14) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_4018,c_14754]) ).
tcf(c_14931,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_3162,c_14754]) ).
tcf(c_14932,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_3161,c_14754]) ).
tcf(c_14933,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_3160,c_14754]) ).
tcf(c_14934,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_3159,c_14754]) ).
tcf(c_14935,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_3158,c_14754]) ).
tcf(c_14978,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_14754,c_14754]) ).
tcf(c_15874,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_14783,c_14978]) ).
tcf(c_15886,plain,
multiply(sk_c6,identity) = multiply(iPr_def_16,iPr_def_14),
inference(superposition,[status(thm)],[c_15874,c_4258]) ).
tcf(c_15888,plain,
multiply(sk_c2,sk_c6) = multiply(iPr_def_22,identity),
inference(superposition,[status(thm)],[c_15874,c_3144]) ).
tcf(c_15892,plain,
multiply(sk_c6,sk_c7) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_15874,c_3140]) ).
tcf(c_15894,plain,
multiply(sk_c6,identity) = multiply(iPr_def_21,iPr_def_20),
inference(superposition,[status(thm)],[c_15874,c_4630]) ).
tcf(c_15895,plain,
multiply(sk_c5,identity) = multiply(iPr_def_19,iPr_def_17),
inference(superposition,[status(thm)],[c_15874,c_4598]) ).
tcf(c_15898,plain,
multiply(sk_c7,identity) = multiply(iPr_def_23,iPr_def_24),
inference(superposition,[status(thm)],[c_15874,c_4277]) ).
tcf(c_15905,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_15874,c_14782]) ).
tcf(c_15909,plain,
multiply(sk_c5,identity) = sk_c5,
inference(light_normalisation,[status(thm)],[c_15895,c_4595]) ).
tcf(c_15911,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_15892,c_419]) ).
tcf(c_15915,plain,
multiply(iPr_def_22,identity) = iPr_def_22,
inference(light_normalisation,[status(thm)],[c_15888,c_426]) ).
tcf(c_20439,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_21)) != sk_c7 )
| ( multiply(sk_c3,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_14931,c_430]) ).
tcf(c_20440,plain,
multiply(sk_c3,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_14931,c_84]) ).
tcf(c_20444,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_21)) != sk_c7 )
| ( multiply(sk_c3,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_14931,c_432]) ).
tcf(c_20445,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_21)) != sk_c6 )
| ( multiply(sk_c3,sk_c6) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_14931,c_431]) ).
tcf(c_20446,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_14931,c_14754]) ).
tcf(c_20447,plain,
multiply(sk_c3,identity) = inverse(iPr_def_21),
inference(superposition,[status(thm)],[c_14931,c_15874]) ).
tcf(c_20498,plain,
multiply(iPr_def_21,identity) = iPr_def_21,
inference(superposition,[status(thm)],[c_20440,c_3162]) ).
tcf(c_20685,plain,
( ( iPr_def_18 = iPr_def_24 )
| ( iPr_def_17 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_14003,c_1237]) ).
tcf(c_22294,plain,
inverse(iPr_def_21) = sk_c3,
inference(demodulation,[status(thm)],[c_20447,c_15874]) ).
tcf(c_22335,plain,
multiply(sk_c3,identity) = sk_c3,
inference(superposition,[status(thm)],[c_1001,c_20446]) ).
tcf(c_22337,plain,
multiply(sk_c3,sk_c6) = iPr_def_20,
inference(superposition,[status(thm)],[c_4627,c_20446]) ).
tcf(c_29909,plain,
( ~ iPr_def_12
| ( sk_c6 != identity )
| ( sk_c6 != sk_c5 ) ),
inference(light_normalisation,[status(thm)],[c_2206,c_15905]) ).
tcf(c_29954,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_12
| ( sk_c6 != iPr_def_22 )
| ( sk_c6 != identity ) ),
inference(superposition,[status(thm)],[c_439,c_29909]) ).
tcf(c_30325,plain,
( ~ iPr_def_10
| ( sk_c6 != identity )
| ( sk_c6 != sk_c5 ) ),
inference(light_normalisation,[status(thm)],[c_2436,c_15905]) ).
tcf(c_30370,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_10
| ( sk_c6 != iPr_def_22 )
| ( sk_c6 != identity ) ),
inference(superposition,[status(thm)],[c_439,c_30325]) ).
tcf(c_31099,plain,
( ~ iPr_def_10
| ( inverse(inverse(sk_c5)) != sk_c6 ) ),
inference(global_subsumption_just,[status(thm)],[c_2437,c_2459,c_2437,c_5476,c_6128,c_14689,c_30370]) ).
tcf(c_31132,plain,
( ( sk_c7 = iPr_def_21 )
| ~ iPr_def_10
| ( inverse(inverse(iPr_def_16)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_447,c_31099]) ).
tcf(c_31134,plain,
( ( sk_c6 = iPr_def_19 )
| ~ iPr_def_10
| ( inverse(inverse(iPr_def_16)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_445,c_31099]) ).
tcf(c_31462,plain,
multiply(sk_c4,iPr_def_19) = identity,
inference(superposition,[status(thm)],[c_14932,c_84]) ).
tcf(c_31465,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_19)) != sk_c6 )
| ( multiply(sk_c4,sk_c5) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_14932,c_433]) ).
tcf(c_31467,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_19)) != sk_c6 )
| ( multiply(sk_c4,sk_c6) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_14932,c_431]) ).
tcf(c_31468,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_19,X0)) = X0,
inference(superposition,[status(thm)],[c_14932,c_14754]) ).
tcf(c_31469,plain,
multiply(sk_c4,identity) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_14932,c_15874]) ).
tcf(c_31496,plain,
multiply(iPr_def_19,identity) = iPr_def_19,
inference(superposition,[status(thm)],[c_31462,c_3161]) ).
tcf(c_31503,plain,
inverse(iPr_def_19) = sk_c4,
inference(demodulation,[status(thm)],[c_31469,c_15874]) ).
tcf(c_31539,plain,
( ( inverse(inverse(iPr_def_16)) != sk_c6 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_31132,c_2459,c_5476,c_14689,c_30370,c_31134]) ).
tcf(c_31540,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_16)) != sk_c6 ) ),
inference(renaming,[status(thm)],[c_31539]) ).
tcf(c_31847,plain,
multiply(sk_c4,identity) = sk_c4,
inference(superposition,[status(thm)],[c_1002,c_31468]) ).
tcf(c_31850,plain,
multiply(sk_c4,sk_c5) = iPr_def_17,
inference(superposition,[status(thm)],[c_4595,c_31468]) ).
tcf(c_31935,plain,
multiply(sk_c1,iPr_def_23) = identity,
inference(superposition,[status(thm)],[c_14933,c_84]) ).
tcf(c_31939,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_23)) != sk_c7 )
| ( multiply(sk_c1,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_14933,c_432]) ).
tcf(c_31940,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_23)) != sk_c6 )
| ( multiply(sk_c1,sk_c6) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_14933,c_431]) ).
tcf(c_31941,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_23,X0)) = X0,
inference(superposition,[status(thm)],[c_14933,c_14754]) ).
tcf(c_31942,plain,
multiply(sk_c1,identity) = inverse(iPr_def_23),
inference(superposition,[status(thm)],[c_14933,c_15874]) ).
tcf(c_31973,plain,
multiply(iPr_def_23,identity) = iPr_def_23,
inference(superposition,[status(thm)],[c_31935,c_3160]) ).
tcf(c_32127,plain,
inverse(iPr_def_23) = sk_c1,
inference(demodulation,[status(thm)],[c_31942,c_15874]) ).
tcf(c_32154,plain,
multiply(sk_c1,sk_c7) = iPr_def_24,
inference(superposition,[status(thm)],[c_4274,c_31941]) ).
tcf(c_32637,plain,
multiply(sk_c7,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_14934,c_84]) ).
tcf(c_32641,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_16)) != sk_c7 )
| ( multiply(sk_c7,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_14934,c_432]) ).
tcf(c_32643,plain,
! [X0: $i] : multiply(sk_c7,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_14934,c_14754]) ).
tcf(c_32644,plain,
multiply(sk_c7,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_14934,c_15874]) ).
tcf(c_32709,plain,
multiply(sk_c1,identity) = multiply(iPr_def_24,iPr_def_16),
inference(superposition,[status(thm)],[c_32637,c_3143]) ).
tcf(c_32710,plain,
multiply(sk_c6,identity) = multiply(iPr_def_15,iPr_def_16),
inference(superposition,[status(thm)],[c_32637,c_3140]) ).
tcf(c_32711,plain,
multiply(iPr_def_16,identity) = iPr_def_16,
inference(superposition,[status(thm)],[c_32637,c_3159]) ).
tcf(c_32871,plain,
inverse(iPr_def_16) = sk_c7,
inference(demodulation,[status(thm)],[c_32644,c_15874]) ).
tcf(c_32877,plain,
( ~ iPr_def_10
| ( inverse(sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_31540,c_32871]) ).
tcf(c_32884,plain,
( ~ iPr_def_13
| ( sk_c6 != identity )
| ( sk_c7 != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_2107,c_32871]) ).
tcf(c_32885,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_32877,c_420]) ).
tcf(c_32888,plain,
( ~ iPr_def_13
| ( sk_c6 != identity ) ),
inference(equality_resolution_simp,[status(thm)],[c_32884]) ).
tcf(c_32944,plain,
( ( sk_c6 = iPr_def_19 )
| ~ iPr_def_10
| ( iPr_def_16 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_455,c_32885]) ).
tcf(c_32947,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_10
| ( iPr_def_16 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_434,c_32885]) ).
tcf(c_33430,plain,
( ( iPr_def_16 != iPr_def_24 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_32944,c_2459,c_5476,c_14689,c_30370,c_32944]) ).
tcf(c_33431,plain,
( ~ iPr_def_10
| ( iPr_def_16 != iPr_def_24 ) ),
inference(renaming,[status(thm)],[c_33430]) ).
tcf(c_33441,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_32947,c_5476,c_14689,c_30370]) ).
tcf(c_33934,plain,
multiply(sk_c7,sk_c6) = iPr_def_14,
inference(superposition,[status(thm)],[c_4170,c_32643]) ).
tcf(c_34180,plain,
multiply(iPr_def_24,iPr_def_16) = sk_c1,
inference(demodulation,[status(thm)],[c_32709,c_15874]) ).
tcf(c_34183,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( multiply(iPr_def_18,iPr_def_16) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_20685,c_34180]) ).
tcf(c_34187,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( sk_c1 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_34180,c_9303]) ).
tcf(c_34746,plain,
multiply(iPr_def_15,iPr_def_16) = sk_c6,
inference(demodulation,[status(thm)],[c_32710,c_15874]) ).
tcf(c_34747,plain,
multiply(inverse(iPr_def_15),sk_c6) = iPr_def_16,
inference(superposition,[status(thm)],[c_34746,c_14754]) ).
tcf(c_35049,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( inverse(iPr_def_16) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_34187,c_427]) ).
tcf(c_35050,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( sk_c7 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_35049,c_32871]) ).
tcf(c_35711,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_35050,c_428]) ).
tcf(c_35713,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( inverse(iPr_def_23) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_35050,c_420]) ).
tcf(c_35714,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( multiply(iPr_def_23,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_35050,c_418]) ).
tcf(c_35795,plain,
multiply(sk_c2,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_14935,c_84]) ).
tcf(c_35800,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_18)) != sk_c6 )
| ( multiply(sk_c2,sk_c6) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_14935,c_431]) ).
tcf(c_35802,plain,
multiply(sk_c2,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_14935,c_15874]) ).
tcf(c_35803,plain,
( ~ iPr_def_12
| ( sk_c5 != iPr_def_22 )
| ( inverse(inverse(iPr_def_18)) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_35800,c_426]) ).
tcf(c_37642,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_35803,c_35802,c_35795,c_35713,c_35711,c_35714,c_34747,c_34746,c_34183,c_34187,c_34180,c_33934,c_33441,c_33431,c_32888,c_32885,c_32871,c_32711,c_32710,c_32709,c_32641,c_32644,c_32637,c_32154,c_32127,c_31973,c_31940,c_31939,c_31935,c_31850,c_31847,c_31503,c_31496,c_31467,c_31465,c_31462,c_29954,c_22337,c_22335,c_22294,c_20498,c_20445,c_20444,c_20439,c_20440,c_15915,c_15911,c_15909,c_15898,c_15895,c_15894,c_15892,c_15888,c_15886,c_15905,c_14785,c_14777,c_14689,c_14277,c_13327,c_11331,c_11216,c_11205,c_10837,c_10729,c_4726,c_2635,c_2459,c_2122,c_1004,c_780,c_463,c_461,c_456,c_451,c_448,c_447,c_446,c_445,c_444,c_441,c_438,c_437,c_436,c_429,c_427,c_425,c_423,c_420]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP301-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n013.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Wed Sep 23 14:23:51 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 10.76/2.74 % SZS status Started for theBenchmark.p
% 10.76/2.74 % SZS status Unsatisfiable for theBenchmark.p
% 10.76/2.74
% 10.76/2.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.76/2.74
% 10.76/2.74 % ------ iProver source info
% 10.76/2.74
% 10.76/2.74 % git: date: 2026-07-19 20:42:38 +0200
% 10.76/2.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.76/2.74 % git: non_committed_changes: false
% 10.76/2.74
% 10.76/2.74 % ------ Parsing...% successful
% 10.76/2.74
% 10.76/2.74
% 10.76/2.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.76/2.74
% 10.76/2.74 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.76/2.74
% 10.76/2.74 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.76/2.74
% 10.76/2.74 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.76/2.74 % ------ Proving...
% 10.76/2.74 % ------ Problem Properties
% 10.76/2.74
% 10.76/2.74 %
% 10.76/2.74 % clauses 49
% 10.76/2.74 % conjectures 35
% 10.76/2.74 % EPR 31
% 10.76/2.74 % Horn 18
% 10.76/2.74 % unary 14
% 10.76/2.74 % binary 30
% 10.76/2.74 % lits 93
% 10.76/2.74 % lits eq 85
% 10.76/2.74 % fd_pure 0
% 10.76/2.74 % fd_pseudo 0
% 10.76/2.74 % fd_cond 0
% 10.76/2.74 % fd_pseudo_cond 0
% 10.76/2.74 % AC symbols 0
% 10.76/2.74
% 10.76/2.74 % ------ Schedule dynamic 5 is on
% 10.76/2.74
% 10.76/2.74 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.76/2.74
% 10.76/2.74
% 10.76/2.74 % ------
% 10.76/2.74 % Current options:
% 10.76/2.74 % ------
% 10.76/2.74
% 10.76/2.74
% 10.76/2.74 %
% 10.76/2.74
% 10.76/2.74 % ------ Proving...
% 10.76/2.74 %
% 10.76/2.74
% 10.76/2.74 % SZS status Unsatisfiable for theBenchmark.p
% 10.76/2.74
% 10.76/2.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.76/2.75
% 10.76/2.75
%------------------------------------------------------------------------------