%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP294-1 : 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 : n005.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 01:32:45 PM UTC 2026
% Result : Unsatisfiable 18.95s 3.29s
% Output : CNFRefutation 18.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 35
% Syntax : Number of formulae : 239 ( 88 unt; 11 def)
% Number of atoms : 750 ( 421 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 302 ( 93 ~; 209 |; 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 : 63 ( 0 sgn 63 !; 0 ?; 49 :)
% 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(f7,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c6 = inverse(sk_c3)
| 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/sandbox/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/sandbox/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(f17,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = inverse(sk_c3)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f27,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c6 = inverse(sk_c3)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f29]) ).
fof(f35,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c6 = inverse(sk_c3)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f39]) ).
fof(f47,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c5 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c6 = inverse(sk_c3)
| sk_c5 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = inverse(sk_c4)
| sk_c5 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c5 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c6 = inverse(sk_c3)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c6 = inverse(sk_c4)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c7 = 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
| inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( sk_c6 != multiply(X3,sk_c5)
| sk_c6 != inverse(X3)
| sk_c6 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6)
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c7 != inverse(X1)
| sk_c5 != multiply(X1,sk_c7)
| sk_c6 != multiply(sk_c7,sk_c5)
| 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_87,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( 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_92,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c3) = sk_c6 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_101,negated_conjecture,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_102,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_107,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c2,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c2,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c5 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c3) = sk_c6 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( 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(X3) != sk_c6 )
| ( inverse(X2) != sk_c7 )
| ( inverse(X1) != sk_c6 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c5) != sk_c6 )
| ( multiply(sk_c7,sk_c6) != sk_c5 )
| ( multiply(X3,sk_c5) != sk_c6 )
| ( multiply(X2,sk_c7) != sk_c5 )
| ( 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_c7 )
| ( multiply(X0,sk_c7) != sk_c5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_116]) ).
tcf(c_414,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_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_c5) != sk_c6 ) ),
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
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c5) != sk_c6 )
| ( 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_c7,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_420,definition,
iPr_def_16 = multiply(sk_c6,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 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_425,definition,
iPr_def_21 = multiply(sk_c3,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_426,definition,
iPr_def_22 = multiply(sk_c2,sk_c7),
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_c6 )
| ( 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_c5) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_415]) ).
tcf(c_432,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( 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_c7 )
| ( multiply(X0,sk_c7) != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_413]) ).
tcf(c_434,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( 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_c7 ) ),
inference(demodulation,[status(thm)],[c_114,c_423]) ).
tcf(c_436,negated_conjecture,
( ( iPr_def_20 = sk_c6 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_113,c_424]) ).
tcf(c_437,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_112,c_425]) ).
tcf(c_438,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_16 = 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_c6 ) ),
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_446,negated_conjecture,
( ( iPr_def_20 = sk_c6 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_447,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_448,negated_conjecture,
( ( iPr_def_16 = sk_c5 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_451,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_20 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_452,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_456,negated_conjecture,
( ( iPr_def_24 = sk_c6 )
| ( iPr_def_20 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_457,negated_conjecture,
( ( iPr_def_24 = sk_c6 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
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_c6 )
| ( 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_752,plain,
( ( sk_c6 = iPr_def_20 )
| ( multiply(iPr_def_18,sk_c5) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_436,c_419]) ).
tcf(c_861,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_20,sk_c7) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_446,c_420]) ).
tcf(c_919,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c7,iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_448,c_419]) ).
tcf(c_1067,plain,
multiply(iPr_def_20,sk_c3) = identity,
inference(superposition,[status(thm)],[c_424,c_84]) ).
tcf(c_1068,plain,
multiply(iPr_def_19,sk_c4) = identity,
inference(superposition,[status(thm)],[c_423,c_84]) ).
tcf(c_1069,plain,
multiply(iPr_def_23,sk_c1) = identity,
inference(superposition,[status(thm)],[c_427,c_84]) ).
tcf(c_1070,plain,
multiply(iPr_def_18,sk_c2) = identity,
inference(superposition,[status(thm)],[c_422,c_84]) ).
tcf(c_1161,plain,
( ( sk_c6 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_451,c_428]) ).
tcf(c_1166,plain,
( ( sk_c6 = iPr_def_20 )
| ( multiply(iPr_def_23,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_451,c_418]) ).
tcf(c_1213,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_452,c_428]) ).
tcf(c_1423,plain,
( ( sk_c6 = iPr_def_24 )
| ( multiply(sk_c6,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_457,c_420]) ).
tcf(c_1565,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c6 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_459,c_439]) ).
tcf(c_1657,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c6 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_460,c_440]) ).
tcf(c_1745,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c6 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_461,c_441]) ).
tcf(c_1812,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c7 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_462,c_442]) ).
tcf(c_2221,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_16 )
| ( inverse(sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_420,c_430]) ).
tcf(c_2550,plain,
( ~ iPr_def_11
| ( sk_c7 != sk_c6 )
| ( inverse(identity) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_83,c_432]) ).
tcf(c_2667,plain,
( ~ iPr_def_10
| ( sk_c5 != iPr_def_16 )
| ( inverse(sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_420,c_433]) ).
tcf(c_2671,plain,
( ~ iPr_def_10
| ( sk_c5 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_84,c_433]) ).
tcf(c_3207,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_3208,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_420,c_85]) ).
tcf(c_3209,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c6,X0)) = multiply(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_425,c_85]) ).
tcf(c_3212,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c5,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_419,c_85]) ).
tcf(c_3213,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c7,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_426,c_85]) ).
tcf(c_3215,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_3217,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1067,c_85]) ).
tcf(c_3218,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1068,c_85]) ).
tcf(c_3219,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1069,c_85]) ).
tcf(c_3220,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1070,c_85]) ).
tcf(c_3226,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3220,c_83]) ).
tcf(c_3227,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3219,c_83]) ).
tcf(c_3228,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3218,c_83]) ).
tcf(c_3229,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3217,c_83]) ).
tcf(c_3340,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(iPr_def_19,sk_c7) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_1657,c_420]) ).
tcf(c_3460,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1745,c_425]) ).
tcf(c_3463,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(iPr_def_20,sk_c7) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_1745,c_420]) ).
tcf(c_3556,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(iPr_def_21,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1812,c_418]) ).
tcf(c_3608,plain,
multiply(iPr_def_18,iPr_def_22) = sk_c7,
inference(superposition,[status(thm)],[c_426,c_3226]) ).
tcf(c_4019,plain,
( ( sk_c6 = iPr_def_20 )
| ( multiply(iPr_def_18,iPr_def_22) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_441,c_752]) ).
tcf(c_4025,plain,
( ( sk_c6 = iPr_def_20 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_4019,c_3608]) ).
tcf(c_4282,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_22,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_3608,c_85]) ).
tcf(c_4294,plain,
multiply(iPr_def_23,iPr_def_24) = sk_c7,
inference(superposition,[status(thm)],[c_428,c_3227]) ).
tcf(c_4357,plain,
multiply(iPr_def_19,iPr_def_17) = sk_c5,
inference(superposition,[status(thm)],[c_421,c_3228]) ).
tcf(c_4380,plain,
multiply(iPr_def_20,iPr_def_21) = sk_c6,
inference(superposition,[status(thm)],[c_425,c_3229]) ).
tcf(c_4383,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_21,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_4380,c_85]) ).
tcf(c_6763,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_447,c_861]) ).
tcf(c_6771,plain,
( ( sk_c6 = iPr_def_16 )
| ( sk_c6 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_6763,c_4380]) ).
tcf(c_7347,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c7,iPr_def_16) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_6771,c_418]) ).
tcf(c_10988,plain,
( ( sk_c6 = iPr_def_20 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_456,c_1166]) ).
tcf(c_10996,plain,
( ( sk_c6 = iPr_def_20 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_10988,c_4294]) ).
tcf(c_12118,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( sk_c6 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_10996,c_4025]) ).
tcf(c_14568,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( sk_c6 = iPr_def_24 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_12118,c_1423]) ).
tcf(c_14663,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( sk_c6 = iPr_def_24 )
| ( sk_c6 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_14568,c_4380]) ).
tcf(c_17315,plain,
multiply(sk_c7,iPr_def_16) = multiply(iPr_def_14,sk_c7),
inference(superposition,[status(thm)],[c_420,c_3207]) ).
tcf(c_17446,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_14,sk_c7) = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_919,c_17315]) ).
tcf(c_17779,plain,
multiply(sk_c6,iPr_def_14) = multiply(iPr_def_16,sk_c6),
inference(superposition,[status(thm)],[c_418,c_3208]) ).
tcf(c_18570,plain,
multiply(sk_c3,iPr_def_16) = multiply(iPr_def_21,sk_c7),
inference(superposition,[status(thm)],[c_420,c_3209]) ).
tcf(c_18581,plain,
multiply(sk_c3,multiply(iPr_def_16,sk_c6)) = multiply(iPr_def_21,iPr_def_14),
inference(superposition,[status(thm)],[c_17779,c_3209]) ).
tcf(c_19161,plain,
multiply(sk_c2,multiply(iPr_def_14,sk_c7)) = multiply(iPr_def_22,iPr_def_16),
inference(superposition,[status(thm)],[c_17315,c_3213]) ).
tcf(c_19565,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_1812,c_3463]) ).
tcf(c_19579,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c6 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_19565,c_4380]) ).
tcf(c_19695,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_19579,c_425]) ).
tcf(c_19712,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(iPr_def_21,sk_c7) = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_19695,c_18570]) ).
tcf(c_25366,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_3215,c_83]) ).
tcf(c_25371,plain,
multiply(inverse(sk_c7),iPr_def_14) = sk_c6,
inference(superposition,[status(thm)],[c_418,c_25366]) ).
tcf(c_25372,plain,
multiply(inverse(sk_c6),iPr_def_16) = sk_c7,
inference(superposition,[status(thm)],[c_420,c_25366]) ).
tcf(c_25376,plain,
multiply(inverse(sk_c7),iPr_def_15) = sk_c5,
inference(superposition,[status(thm)],[c_419,c_25366]) ).
tcf(c_25378,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_83,c_25366]) ).
tcf(c_25379,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_84,c_25366]) ).
tcf(c_25400,plain,
multiply(inverse(sk_c7),multiply(iPr_def_14,sk_c7)) = iPr_def_16,
inference(superposition,[status(thm)],[c_17315,c_25366]) ).
tcf(c_25518,plain,
multiply(inverse(sk_c6),multiply(iPr_def_16,sk_c6)) = iPr_def_14,
inference(superposition,[status(thm)],[c_17779,c_25366]) ).
tcf(c_25537,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_3229,c_25366]) ).
tcf(c_25538,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_3228,c_25366]) ).
tcf(c_25539,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_3227,c_25366]) ).
tcf(c_25540,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_3226,c_25366]) ).
tcf(c_25631,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_25366,c_25366]) ).
tcf(c_29841,plain,
( ~ iPr_def_12
| ( sk_c6 != sk_c5 )
| ( inverse(inverse(identity)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_25378,c_431]) ).
tcf(c_29887,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_25379,c_25631]) ).
tcf(c_29900,plain,
multiply(sk_c7,sk_c6) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_29887,c_3207]) ).
tcf(c_29903,plain,
multiply(sk_c6,sk_c7) = multiply(iPr_def_16,identity),
inference(superposition,[status(thm)],[c_29887,c_3208]) ).
tcf(c_29904,plain,
multiply(sk_c6,identity) = multiply(iPr_def_20,iPr_def_21),
inference(superposition,[status(thm)],[c_29887,c_4383]) ).
tcf(c_29906,plain,
multiply(sk_c7,sk_c5) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_29887,c_3212]) ).
tcf(c_29909,plain,
multiply(sk_c7,identity) = multiply(iPr_def_18,iPr_def_22),
inference(superposition,[status(thm)],[c_29887,c_4282]) ).
tcf(c_29914,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_29887,c_25378]) ).
tcf(c_29915,plain,
multiply(sk_c7,identity) = sk_c7,
inference(light_normalisation,[status(thm)],[c_29909,c_3608]) ).
tcf(c_29918,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_29906,c_419]) ).
tcf(c_29920,plain,
multiply(sk_c6,identity) = sk_c6,
inference(light_normalisation,[status(thm)],[c_29904,c_4380]) ).
tcf(c_29921,plain,
multiply(iPr_def_16,identity) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_29903,c_420]) ).
tcf(c_29924,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_29900,c_418]) ).
tcf(c_30030,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_14,sk_c7) = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_7347,c_17315]) ).
tcf(c_33610,plain,
multiply(sk_c3,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_25537,c_84]) ).
tcf(c_33613,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_20)) != sk_c6 )
| ( multiply(sk_c3,sk_c5) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_25537,c_431]) ).
tcf(c_33614,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_20)) != sk_c6 )
| ( multiply(sk_c3,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_25537,c_432]) ).
tcf(c_33615,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_25537,c_25366]) ).
tcf(c_33616,plain,
multiply(sk_c3,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_25537,c_29887]) ).
tcf(c_33632,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_21 )
| ( inverse(inverse(iPr_def_20)) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_33614,c_425]) ).
tcf(c_33647,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( identity = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_3460,c_33610]) ).
tcf(c_33794,plain,
inverse(iPr_def_20) = sk_c3,
inference(demodulation,[status(thm)],[c_33616,c_29887]) ).
tcf(c_33818,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_16) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_3463,c_33615]) ).
tcf(c_33822,plain,
multiply(sk_c3,sk_c6) = iPr_def_21,
inference(superposition,[status(thm)],[c_4380,c_33615]) ).
tcf(c_33840,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(iPr_def_21,sk_c7) = sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_33818,c_18570]) ).
tcf(c_34252,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( inverse(iPr_def_21) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_33647,c_29914]) ).
tcf(c_34254,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(iPr_def_21,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_33647,c_83]) ).
tcf(c_34829,plain,
multiply(sk_c4,iPr_def_19) = identity,
inference(superposition,[status(thm)],[c_25538,c_84]) ).
tcf(c_34834,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_19,X0)) = X0,
inference(superposition,[status(thm)],[c_25538,c_25366]) ).
tcf(c_34835,plain,
multiply(sk_c4,identity) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_25538,c_29887]) ).
tcf(c_35157,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(sk_c4,iPr_def_16) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_3340,c_34834]) ).
tcf(c_35161,plain,
multiply(sk_c4,sk_c5) = iPr_def_17,
inference(superposition,[status(thm)],[c_4357,c_34834]) ).
tcf(c_35288,plain,
multiply(sk_c1,iPr_def_23) = identity,
inference(superposition,[status(thm)],[c_25539,c_84]) ).
tcf(c_35330,plain,
( ( identity = iPr_def_24 )
| ( sk_c7 = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_1213,c_35288]) ).
tcf(c_35331,plain,
( ( identity = iPr_def_24 )
| ( sk_c6 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_1161,c_35288]) ).
tcf(c_35627,plain,
( ( identity = iPr_def_24 )
| ( multiply(sk_c6,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_35330,c_420]) ).
tcf(c_37362,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_18)) != sk_c7 )
| ( multiply(sk_c2,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_25540,c_430]) ).
tcf(c_37363,plain,
multiply(sk_c2,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_25540,c_84]) ).
tcf(c_37368,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_25540,c_25366]) ).
tcf(c_37369,plain,
multiply(sk_c2,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_25540,c_29887]) ).
tcf(c_38752,plain,
inverse(iPr_def_18) = sk_c2,
inference(demodulation,[status(thm)],[c_37369,c_29887]) ).
tcf(c_38766,plain,
multiply(sk_c2,sk_c7) = iPr_def_22,
inference(superposition,[status(thm)],[c_3608,c_37368]) ).
tcf(c_43387,plain,
( ~ iPr_def_11
| ( sk_c6 != identity )
| ( sk_c7 != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_2550,c_29914]) ).
tcf(c_44297,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(iPr_def_21,iPr_def_21) = identity ) ),
inference(superposition,[status(thm)],[c_34252,c_84]) ).
tcf(c_48000,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( sk_c6 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_17446,c_30030]) ).
tcf(c_49057,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(iPr_def_21,iPr_def_21) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1812,c_19712]) ).
tcf(c_50104,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c6 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_34254,c_3556]) ).
tcf(c_50620,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( iPr_def_14 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_50104,c_1565]) ).
tcf(c_52551,plain,
( ( identity = iPr_def_24 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_35331,c_35627]) ).
tcf(c_52609,plain,
( ( identity = iPr_def_24 )
| ( sk_c6 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_52551,c_4380]) ).
tcf(c_52902,plain,
( ( iPr_def_15 = iPr_def_16 )
| ( iPr_def_14 = iPr_def_15 )
| ( identity = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_52609,c_48000]) ).
tcf(c_53540,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_52902,c_50620,c_50104,c_49057,c_44297,c_43387,c_38766,c_38752,c_37362,c_37369,c_37363,c_35161,c_35157,c_34835,c_34829,c_33840,c_33822,c_33794,c_33632,c_33613,c_33616,c_33610,c_29924,c_29921,c_29920,c_29918,c_29915,c_29906,c_29904,c_29903,c_29900,c_29914,c_29841,c_25518,c_25400,c_25376,c_25372,c_25371,c_19579,c_19161,c_18581,c_18570,c_17779,c_17315,c_14663,c_2671,c_2667,c_2221,c_448,c_447,c_446,c_438,c_437,c_436,c_435,c_434,c_429,c_424,c_422]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP294-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n005.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 14:23:17 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.43 % Proving...
% 18.95/3.29 % SZS status Started for theBenchmark.p
% 18.95/3.29 % SZS status Unsatisfiable for theBenchmark.p
% 18.95/3.29
% 18.95/3.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 18.95/3.29
% 18.95/3.29 % ------ iProver source info
% 18.95/3.29
% 18.95/3.29 % git: date: 2026-07-19 20:42:38 +0200
% 18.95/3.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 18.95/3.29 % git: non_committed_changes: false
% 18.95/3.29
% 18.95/3.29 % ------ Parsing...% successful
% 18.95/3.29
% 18.95/3.29
% 18.95/3.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 18.95/3.29
% 18.95/3.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 18.95/3.29
% 18.95/3.29 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 18.95/3.29
% 18.95/3.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 18.95/3.29 % ------ Proving...
% 18.95/3.29 % ------ Problem Properties
% 18.95/3.29
% 18.95/3.29 %
% 18.95/3.29 % clauses 49
% 18.95/3.29 % conjectures 35
% 18.95/3.29 % EPR 31
% 18.95/3.29 % Horn 18
% 18.95/3.29 % unary 14
% 18.95/3.29 % binary 30
% 18.95/3.29 % lits 93
% 18.95/3.29 % lits eq 85
% 18.95/3.29 % fd_pure 0
% 18.95/3.29 % fd_pseudo 0
% 18.95/3.29 % fd_cond 0
% 18.95/3.29 % fd_pseudo_cond 0
% 18.95/3.29 % AC symbols 0
% 18.95/3.29
% 18.95/3.29 % ------ Schedule dynamic 5 is on
% 18.95/3.29
% 18.95/3.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 18.95/3.29
% 18.95/3.29
% 18.95/3.29 % ------
% 18.95/3.29 % Current options:
% 18.95/3.29 % ------
% 18.95/3.29
% 18.95/3.29
% 18.95/3.29 %
% 18.95/3.29
% 18.95/3.29 % ------ Proving...
% 18.95/3.29 %
% 18.95/3.29
% 18.95/3.29 % SZS status Unsatisfiable for theBenchmark.p
% 18.95/3.29
% 18.95/3.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.96/3.30
% 18.96/3.30
%------------------------------------------------------------------------------