%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP335-1 : 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 01:33:03 PM UTC 2026
% Result : Unsatisfiable 7.37s 3.35s
% Output : CNFRefutation 7.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 36
% Syntax : Number of formulae : 275 ( 93 unt; 11 def)
% Number of atoms : 905 ( 495 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 421 ( 144 ~; 277 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 71 !; 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_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c6 = multiply(sk_c8,sk_c7)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c8 = inverse(sk_c3)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f11]) ).
fof(f19,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = inverse(sk_c3)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f35,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f39]) ).
fof(f43,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c6 = multiply(sk_c8,sk_c7)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = inverse(sk_c3)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6
| multiply(sk_c7,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( sk_c8 != inverse(X4)
| multiply(X4,sk_c8) != X3
| sk_c7 != multiply(sk_c8,X3)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(X2,sk_c8)
| sk_c6 != multiply(sk_c8,sk_c7)
| sk_c7 != inverse(X1)
| sk_c8 != multiply(X1,sk_c7)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7)
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X0,X1,X4] :
( sk_c8 != inverse(X4)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X2)
| sk_c7 != multiply(X2,sk_c8)
| sk_c6 != multiply(sk_c8,sk_c7)
| sk_c7 != inverse(X1)
| sk_c8 != multiply(X1,sk_c7)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7)
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(equality_resolution,[],[f66]) ).
tcf(c_83,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_84,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_86,negated_conjecture,
( ( multiply(sk_c8,sk_c7) = sk_c6 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_87,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_89,negated_conjecture,
( ( multiply(sk_c8,sk_c5) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_93,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( 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_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_105,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_106,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_107,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_108,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c7 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c8 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( multiply(sk_c7,sk_c8) != sk_c6 )
| ( multiply(X3,sk_c7) != sk_c8 )
| ( multiply(X2,sk_c8) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 )
| ( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7 ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_409,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_116]) ).
tcf(c_410,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_116]) ).
tcf(c_411,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_116]) ).
tcf(c_412,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_116]) ).
tcf(c_413,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( multiply(sk_c7,sk_c8) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_414,definition,
iPr_def_14 = multiply(sk_c7,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_415,definition,
iPr_def_15 = multiply(sk_c8,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_416,definition,
iPr_def_16 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_417,definition,
iPr_def_17 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_418,definition,
iPr_def_18 = multiply(sk_c4,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_419,definition,
iPr_def_19 = multiply(sk_c8,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_420,definition,
iPr_def_20 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_421,definition,
iPr_def_21 = multiply(sk_c3,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_422,definition,
iPr_def_22 = multiply(sk_c2,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_423,definition,
iPr_def_23 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_424,definition,
iPr_def_24 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_425,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c6 )
| ( iPr_def_14 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_413,c_415,c_414]) ).
tcf(c_426,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_412]) ).
tcf(c_427,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_411]) ).
tcf(c_428,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_410]) ).
tcf(c_429,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_409]) ).
tcf(c_430,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_115,c_417,c_416]) ).
tcf(c_431,negated_conjecture,
( ( iPr_def_18 = sk_c5 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_114,c_418]) ).
tcf(c_432,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_113,c_419]) ).
tcf(c_433,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_112,c_420]) ).
tcf(c_434,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_111,c_421]) ).
tcf(c_435,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_436,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_109,c_422]) ).
tcf(c_437,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_18 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_438,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_439,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_440,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_442,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_103,c_423]) ).
tcf(c_443,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_18 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_444,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_450,negated_conjecture,
( ( iPr_def_24 = sk_c6 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_451,negated_conjecture,
( ( iPr_def_24 = sk_c6 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_452,negated_conjecture,
( ( iPr_def_24 = sk_c6 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_456,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_457,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_458,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_459,negated_conjecture,
( ( iPr_def_15 = sk_c6 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_737,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_20,sk_c7) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_433,c_415]) ).
tcf(c_738,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_16,sk_c7) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_430,c_415]) ).
tcf(c_740,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c8,iPr_def_19) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_432,c_415]) ).
tcf(c_752,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_20) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_433,c_418]) ).
tcf(c_753,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_16) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_430,c_418]) ).
tcf(c_762,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_16,sk_c5) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_430,c_419]) ).
tcf(c_782,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c4,iPr_def_22) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_438,c_418]) ).
tcf(c_784,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c7,iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_438,c_414]) ).
tcf(c_869,plain,
( ( sk_c7 = iPr_def_23 )
| ( multiply(iPr_def_16,sk_c5) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_442,c_419]) ).
tcf(c_1004,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c3,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_433,c_421]) ).
tcf(c_1041,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c2,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_434,c_422]) ).
tcf(c_1042,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c2,iPr_def_19) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_432,c_422]) ).
tcf(c_1049,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_444,c_424]) ).
tcf(c_1070,plain,
multiply(iPr_def_20,sk_c3) = identity,
inference(superposition,[status(thm)],[c_420,c_84]) ).
tcf(c_1071,plain,
multiply(iPr_def_16,sk_c4) = identity,
inference(superposition,[status(thm)],[c_416,c_84]) ).
tcf(c_1072,plain,
multiply(iPr_def_23,sk_c1) = identity,
inference(superposition,[status(thm)],[c_423,c_84]) ).
tcf(c_1073,plain,
multiply(iPr_def_17,sk_c2) = identity,
inference(superposition,[status(thm)],[c_417,c_84]) ).
tcf(c_1322,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c7 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_456,c_450]) ).
tcf(c_1383,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c8 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_457,c_451]) ).
tcf(c_1416,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c7 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_458,c_452]) ).
tcf(c_1761,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_19 )
| ( sk_c6 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_456,c_425]) ).
tcf(c_1770,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_17 )
| ( iPr_def_14 != iPr_def_15 )
| ( sk_c6 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_435,c_425]) ).
tcf(c_1891,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_22 )
| ( inverse(sk_c2) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_422,c_427]) ).
tcf(c_1892,plain,
( ~ iPr_def_12
| ( sk_c7 != sk_c8 )
| ( inverse(identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_83,c_427]) ).
tcf(c_1904,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_22 )
| ( sk_c7 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_1891,c_417]) ).
tcf(c_1998,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_15 )
| ( inverse(sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_415,c_428]) ).
tcf(c_2001,plain,
( ~ iPr_def_11
| ( sk_c7 != sk_c6 )
| ( inverse(identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_83,c_428]) ).
tcf(c_2107,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_21 )
| ( inverse(sk_c3) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_421,c_429]) ).
tcf(c_2109,plain,
( ~ iPr_def_10
| ( sk_c7 != sk_c8 )
| ( inverse(identity) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_83,c_429]) ).
tcf(c_2127,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_20 )
| ( sk_c7 != iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_2107,c_420]) ).
tcf(c_2229,plain,
( ~ iPr_def_13
| ( inverse(sk_c7) != sk_c8 )
| ( multiply(sk_c8,iPr_def_14) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_414,c_426]) ).
tcf(c_2233,plain,
( ~ iPr_def_13
| ( inverse(inverse(sk_c8)) != sk_c8 )
| ( multiply(sk_c8,identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_84,c_426]) ).
tcf(c_2359,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( multiply(sk_c8,iPr_def_19) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1322,c_415]) ).
tcf(c_2450,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( multiply(iPr_def_20,sk_c7) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1383,c_415]) ).
tcf(c_2606,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_414,c_85]) ).
tcf(c_2607,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c7,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_415,c_85]) ).
tcf(c_2608,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c8,X0)) = multiply(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_421,c_85]) ).
tcf(c_2609,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c5,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_419,c_85]) ).
tcf(c_2610,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c8,X0)) = multiply(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_418,c_85]) ).
tcf(c_2611,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c7,X0)) = multiply(iPr_def_24,X0),
inference(superposition,[status(thm)],[c_424,c_85]) ).
tcf(c_2614,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_2616,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1070,c_85]) ).
tcf(c_2617,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1071,c_85]) ).
tcf(c_2618,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1072,c_85]) ).
tcf(c_2619,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1073,c_85]) ).
tcf(c_2625,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2619,c_83]) ).
tcf(c_2626,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2618,c_83]) ).
tcf(c_2627,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2617,c_83]) ).
tcf(c_2628,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2616,c_83]) ).
tcf(c_2718,plain,
multiply(iPr_def_17,iPr_def_22) = sk_c7,
inference(superposition,[status(thm)],[c_422,c_2625]) ).
tcf(c_2726,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_22,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_2718,c_85]) ).
tcf(c_2728,plain,
multiply(iPr_def_23,iPr_def_24) = sk_c7,
inference(superposition,[status(thm)],[c_424,c_2626]) ).
tcf(c_3153,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_434,c_737]) ).
tcf(c_3253,plain,
multiply(iPr_def_16,iPr_def_18) = sk_c8,
inference(superposition,[status(thm)],[c_418,c_2627]) ).
tcf(c_3256,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_18,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_3253,c_85]) ).
tcf(c_3262,plain,
multiply(iPr_def_20,iPr_def_21) = sk_c8,
inference(superposition,[status(thm)],[c_421,c_2628]) ).
tcf(c_3265,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_21,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_3262,c_85]) ).
tcf(c_3393,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_16,iPr_def_18) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_752,c_2627]) ).
tcf(c_3394,plain,
( ( sk_c8 = iPr_def_20 )
| ( sk_c7 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_3393,c_3253]) ).
tcf(c_3484,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_16,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_431,c_762]) ).
tcf(c_3486,plain,
( ( sk_c8 = iPr_def_19 )
| ( sk_c7 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_3484,c_3253]) ).
tcf(c_3731,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_16,iPr_def_18) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_782,c_2627]) ).
tcf(c_3732,plain,
( ( sk_c8 = iPr_def_22 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_3731,c_3253]) ).
tcf(c_3778,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c7,iPr_def_19) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_3486,c_414]) ).
tcf(c_4616,plain,
( ( sk_c7 = iPr_def_23 )
| ( multiply(iPr_def_16,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_443,c_869]) ).
tcf(c_4620,plain,
( ( sk_c8 = iPr_def_19 )
| ( sk_c7 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_4616,c_3253]) ).
tcf(c_4669,plain,
( ( sk_c7 = iPr_def_23 )
| ( multiply(sk_c7,iPr_def_19) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_4620,c_414]) ).
tcf(c_5895,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_17,iPr_def_22) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1041,c_2625]) ).
tcf(c_5896,plain,
( ( sk_c7 = iPr_def_21 )
| ( sk_c7 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_5895,c_2718]) ).
tcf(c_5907,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_17,iPr_def_22) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1042,c_2625]) ).
tcf(c_5908,plain,
( ( sk_c7 = iPr_def_19 )
| ( sk_c7 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_5907,c_2718]) ).
tcf(c_6678,plain,
( ( sk_c8 = iPr_def_15 )
| ( sk_c7 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_3153,c_3262]) ).
tcf(c_6736,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c3,iPr_def_15) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_6678,c_421]) ).
tcf(c_6743,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_15) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_6678,c_418]) ).
tcf(c_8059,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1416,c_2450]) ).
tcf(c_8071,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_8059,c_3262]) ).
tcf(c_8289,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( multiply(sk_c7,iPr_def_15) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_8071,c_414]) ).
tcf(c_8544,plain,
multiply(sk_c7,iPr_def_15) = multiply(iPr_def_14,sk_c7),
inference(superposition,[status(thm)],[c_415,c_2606]) ).
tcf(c_8545,plain,
multiply(sk_c7,iPr_def_19) = multiply(iPr_def_14,sk_c5),
inference(superposition,[status(thm)],[c_419,c_2606]) ).
tcf(c_9087,plain,
multiply(sk_c8,iPr_def_14) = multiply(iPr_def_15,sk_c8),
inference(superposition,[status(thm)],[c_414,c_2607]) ).
tcf(c_9122,plain,
( ~ iPr_def_13
| ( inverse(sk_c7) != sk_c8 )
| ( multiply(iPr_def_15,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_2607,c_426]) ).
tcf(c_9367,plain,
multiply(sk_c3,iPr_def_15) = multiply(iPr_def_21,sk_c7),
inference(superposition,[status(thm)],[c_415,c_2608]) ).
tcf(c_9769,plain,
multiply(sk_c4,iPr_def_15) = multiply(iPr_def_18,sk_c7),
inference(superposition,[status(thm)],[c_415,c_2610]) ).
tcf(c_10013,plain,
multiply(sk_c1,multiply(iPr_def_14,sk_c5)) = multiply(iPr_def_24,iPr_def_19),
inference(superposition,[status(thm)],[c_8545,c_2611]) ).
tcf(c_10014,plain,
multiply(sk_c1,multiply(iPr_def_14,sk_c7)) = multiply(iPr_def_24,iPr_def_15),
inference(superposition,[status(thm)],[c_8544,c_2611]) ).
tcf(c_11156,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_14,sk_c5) = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_3778,c_8545]) ).
tcf(c_11722,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2614,c_83]) ).
tcf(c_11727,plain,
multiply(inverse(sk_c7),iPr_def_14) = sk_c8,
inference(superposition,[status(thm)],[c_414,c_11722]) ).
tcf(c_11728,plain,
multiply(inverse(sk_c8),iPr_def_15) = sk_c7,
inference(superposition,[status(thm)],[c_415,c_11722]) ).
tcf(c_11734,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_83,c_11722]) ).
tcf(c_11735,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_84,c_11722]) ).
tcf(c_11763,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( multiply(inverse(sk_c8),iPr_def_15) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_2359,c_11722]) ).
tcf(c_11764,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(inverse(sk_c8),iPr_def_15) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_740,c_11722]) ).
tcf(c_11836,plain,
multiply(inverse(sk_c7),multiply(iPr_def_14,sk_c5)) = iPr_def_19,
inference(superposition,[status(thm)],[c_8545,c_11722]) ).
tcf(c_11837,plain,
multiply(inverse(sk_c7),multiply(iPr_def_14,sk_c7)) = iPr_def_15,
inference(superposition,[status(thm)],[c_8544,c_11722]) ).
tcf(c_11847,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_2628,c_11722]) ).
tcf(c_11848,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2627,c_11722]) ).
tcf(c_11849,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2626,c_11722]) ).
tcf(c_11850,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2625,c_11722]) ).
tcf(c_11895,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_11722,c_11722]) ).
tcf(c_12626,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_11735,c_11895]) ).
tcf(c_12640,plain,
multiply(sk_c7,sk_c8) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_12626,c_2606]) ).
tcf(c_12643,plain,
multiply(sk_c8,sk_c7) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_12626,c_2607]) ).
tcf(c_12645,plain,
multiply(sk_c8,sk_c5) = multiply(iPr_def_19,identity),
inference(superposition,[status(thm)],[c_12626,c_2609]) ).
tcf(c_12646,plain,
multiply(sk_c8,identity) = multiply(iPr_def_16,iPr_def_18),
inference(superposition,[status(thm)],[c_12626,c_3256]) ).
tcf(c_12648,plain,
multiply(sk_c7,identity) = multiply(iPr_def_17,iPr_def_22),
inference(superposition,[status(thm)],[c_12626,c_2726]) ).
tcf(c_12653,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_12626,c_11734]) ).
tcf(c_12654,plain,
multiply(sk_c7,identity) = sk_c7,
inference(light_normalisation,[status(thm)],[c_12648,c_2718]) ).
tcf(c_12656,plain,
multiply(sk_c8,identity) = sk_c8,
inference(light_normalisation,[status(thm)],[c_12646,c_3253]) ).
tcf(c_12657,plain,
multiply(iPr_def_19,identity) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_12645,c_419]) ).
tcf(c_12659,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_12643,c_415]) ).
tcf(c_12662,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_12640,c_414]) ).
tcf(c_14718,plain,
( ( sk_c7 = iPr_def_23 )
| ( multiply(iPr_def_14,sk_c5) = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_4669,c_8545]) ).
tcf(c_15099,plain,
multiply(sk_c3,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_11847,c_84]) ).
tcf(c_15104,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_11847,c_11722]) ).
tcf(c_15121,plain,
( ( identity = iPr_def_21 )
| ( sk_c7 = iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_1004,c_15099]) ).
tcf(c_15204,plain,
multiply(sk_c3,sk_c8) = iPr_def_21,
inference(superposition,[status(thm)],[c_3262,c_15104]) ).
tcf(c_16802,plain,
multiply(sk_c4,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_11848,c_84]) ).
tcf(c_16807,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_11848,c_11722]) ).
tcf(c_16808,plain,
multiply(sk_c4,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_11848,c_12626]) ).
tcf(c_16825,plain,
( ( identity = iPr_def_18 )
| ( sk_c7 = iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_753,c_16802]) ).
tcf(c_17091,plain,
( iPr_def_13
| ( sk_c6 != iPr_def_15 )
| ( sk_c7 = iPr_def_19 )
| iPr_def_10
| iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_1761,c_1761,c_1904,c_3732,c_5908]) ).
tcf(c_17092,plain,
( iPr_def_13
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_19 )
| ( sk_c6 != iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_17091]) ).
tcf(c_17119,plain,
( iPr_def_13
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_19 )
| ( iPr_def_15 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_450,c_17092]) ).
tcf(c_17651,plain,
inverse(iPr_def_16) = sk_c4,
inference(demodulation,[status(thm)],[c_16808,c_12626]) ).
tcf(c_17657,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_15) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_738,c_16807]) ).
tcf(c_17687,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_18,sk_c7) = sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_17657,c_9769]) ).
tcf(c_17976,plain,
( ~ iPr_def_12
| ( sk_c7 != identity )
| ( sk_c7 != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_1892,c_12653]) ).
tcf(c_18017,plain,
( ( sk_c7 = iPr_def_17 )
| ~ iPr_def_12
| ( identity != iPr_def_21 )
| ( sk_c7 != sk_c8 ) ),
inference(superposition,[status(thm)],[c_434,c_17976]) ).
tcf(c_18276,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( sk_c7 != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_2001,c_12653]) ).
tcf(c_18302,plain,
( ( sk_c7 = iPr_def_19 )
| ~ iPr_def_11
| ( sk_c7 != iPr_def_24 )
| ( sk_c7 != identity ) ),
inference(superposition,[status(thm)],[c_450,c_18276]) ).
tcf(c_18306,plain,
( ( sk_c7 = iPr_def_17 )
| ~ iPr_def_11
| ( sk_c7 != iPr_def_15 )
| ( sk_c7 != identity ) ),
inference(superposition,[status(thm)],[c_435,c_18276]) ).
tcf(c_18373,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_21,sk_c7) = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_6736,c_9367]) ).
tcf(c_18412,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_21,iPr_def_19) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_432,c_18373]) ).
tcf(c_18495,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_18,sk_c7) = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_6743,c_9769]) ).
tcf(c_18534,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_18,iPr_def_19) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_432,c_18495]) ).
tcf(c_18915,plain,
multiply(sk_c1,iPr_def_23) = identity,
inference(superposition,[status(thm)],[c_11849,c_84]) ).
tcf(c_18920,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_23,X0)) = X0,
inference(superposition,[status(thm)],[c_11849,c_11722]) ).
tcf(c_18921,plain,
multiply(sk_c1,identity) = inverse(iPr_def_23),
inference(superposition,[status(thm)],[c_11849,c_12626]) ).
tcf(c_18952,plain,
( ( identity = iPr_def_24 )
| ( sk_c7 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_1049,c_18915]) ).
tcf(c_19056,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c8,iPr_def_19) = multiply(iPr_def_20,iPr_def_21) ) ),
inference(superposition,[status(thm)],[c_18412,c_3265]) ).
tcf(c_19065,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c8,iPr_def_19) = sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_19056,c_3262]) ).
tcf(c_19383,plain,
( ~ iPr_def_10
| ( sk_c8 != identity )
| ( sk_c7 != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_2109,c_12653]) ).
tcf(c_20516,plain,
inverse(iPr_def_23) = sk_c1,
inference(demodulation,[status(thm)],[c_18921,c_12626]) ).
tcf(c_20541,plain,
multiply(sk_c1,sk_c7) = iPr_def_24,
inference(superposition,[status(thm)],[c_2728,c_18920]) ).
tcf(c_21931,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_17)) != sk_c7 )
| ( multiply(sk_c2,sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_11850,c_427]) ).
tcf(c_21932,plain,
multiply(sk_c2,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_11850,c_84]) ).
tcf(c_21936,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_17)) != sk_c8 )
| ( multiply(sk_c2,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_11850,c_429]) ).
tcf(c_21937,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_11850,c_11722]) ).
tcf(c_21938,plain,
multiply(sk_c2,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_11850,c_12626]) ).
tcf(c_21942,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_22 )
| ( inverse(inverse(iPr_def_17)) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_21931,c_422]) ).
tcf(c_23193,plain,
inverse(iPr_def_17) = sk_c2,
inference(demodulation,[status(thm)],[c_21938,c_12626]) ).
tcf(c_23202,plain,
multiply(sk_c2,sk_c7) = iPr_def_22,
inference(superposition,[status(thm)],[c_2718,c_21937]) ).
tcf(c_29674,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( multiply(iPr_def_14,sk_c7) = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_8289,c_8544]) ).
tcf(c_29711,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( multiply(iPr_def_14,iPr_def_19) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1322,c_29674]) ).
tcf(c_32387,plain,
( ~ iPr_def_13
| ( sk_c7 != sk_c8 )
| ( inverse(inverse(sk_c8)) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_2233,c_12626]) ).
tcf(c_32421,plain,
( ( sk_c7 = iPr_def_17 )
| ~ iPr_def_13
| ( sk_c7 != sk_c8 )
| ( inverse(inverse(iPr_def_16)) != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_430,c_32387]) ).
tcf(c_32422,plain,
( ( sk_c7 = iPr_def_17 )
| ~ iPr_def_13
| ( sk_c7 != sk_c8 ) ),
inference(ground_joinability,[status(thm)],[c_32421,c_416,c_17651]) ).
tcf(c_35511,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_32422,c_29711,c_23202,c_23193,c_21942,c_21936,c_21938,c_21932,c_20541,c_20516,c_19383,c_19065,c_18952,c_18921,c_18915,c_18534,c_18306,c_18302,c_18017,c_17687,c_17119,c_16825,c_15204,c_15121,c_15099,c_14718,c_12662,c_12659,c_12657,c_12656,c_12654,c_12648,c_12646,c_12645,c_12643,c_12640,c_12653,c_11837,c_11836,c_11764,c_11763,c_11728,c_11727,c_11156,c_10014,c_10013,c_9122,c_9087,c_8545,c_8544,c_5896,c_3394,c_2229,c_2127,c_1998,c_1770,c_784,c_459,c_440,c_439,c_438,c_437,c_436,c_435,c_425,c_417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP335-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 14:32:17 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.44
% 0.11/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.44
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.46 % Proving...
% 7.37/3.35 % SZS status Started for theBenchmark.p
% 7.37/3.35 % SZS status Unsatisfiable for theBenchmark.p
% 7.37/3.35
% 7.37/3.35 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.37/3.35
% 7.37/3.35 % ------ iProver source info
% 7.37/3.35
% 7.37/3.35 % git: date: 2026-07-19 20:42:38 +0200
% 7.37/3.35 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.37/3.35 % git: non_committed_changes: false
% 7.37/3.35
% 7.37/3.35 % ------ Parsing...% successful
% 7.37/3.35
% 7.37/3.35
% 7.37/3.35 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.37/3.35
% 7.37/3.35 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 7.37/3.35
% 7.37/3.35 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.37/3.35
% 7.37/3.35 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 7.37/3.35 % ------ Proving...
% 7.37/3.35 % ------ Problem Properties
% 7.37/3.35
% 7.37/3.35 %
% 7.37/3.35 % clauses 49
% 7.37/3.35 % conjectures 35
% 7.37/3.35 % EPR 31
% 7.37/3.35 % Horn 18
% 7.37/3.35 % unary 14
% 7.37/3.35 % binary 30
% 7.37/3.35 % lits 92
% 7.37/3.35 % lits eq 84
% 7.37/3.36 % fd_pure 0
% 7.37/3.36 % fd_pseudo 0
% 7.37/3.36 % fd_cond 0
% 7.37/3.36 % fd_pseudo_cond 0
% 7.37/3.36 % AC symbols 0
% 7.37/3.36
% 7.37/3.36 % ------ Schedule dynamic 5 is on
% 7.37/3.36
% 7.37/3.36 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.37/3.36
% 7.37/3.36
% 7.37/3.36 % ------
% 7.37/3.36 % Current options:
% 7.37/3.36 % ------
% 7.37/3.36
% 7.37/3.36
% 7.37/3.36 %
% 7.37/3.36
% 7.37/3.36 % ------ Proving...
% 7.37/3.36 %
% 7.37/3.36
% 7.37/3.36 % SZS status Unsatisfiable for theBenchmark.p
% 7.37/3.36
% 7.37/3.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.37/3.36
% 7.37/3.36
%------------------------------------------------------------------------------