%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP360-1 : 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 : n019.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 01:33:23 PM UTC 2026
% Result : Unsatisfiable 10.44s 2.26s
% Output : CNFRefutation 10.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 36
% Syntax : Number of formulae : 247 ( 120 unt; 10 def)
% Number of atoms : 696 ( 408 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 286 ( 97 ~; 189 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 14 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 79 !; 0 ?; 62 :)
% 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_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c7 = inverse(sk_c3)
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c6 = inverse(sk_c4)
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = inverse(sk_c3)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c6 = multiply(sk_c7,sk_c2) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = multiply(sk_c7,sk_c2) ),
inference(reorient_equations,[],[f27]) ).
fof(f31,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c6 = inverse(sk_c4)
| sk_c6 = multiply(sk_c7,sk_c2) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c6 = multiply(sk_c7,sk_c2) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c2 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = inverse(sk_c3)
| sk_c2 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f37]) ).
fof(f41,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = inverse(sk_c4)
| sk_c2 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c2 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = inverse(sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,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_c7
| multiply(X1,sk_c7) != X0
| multiply(sk_c7,X0) != sk_c6
| inverse(sk_c7) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,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_c7 != inverse(X1)
| multiply(X1,sk_c7) != X0
| sk_c6 != multiply(sk_c7,X0)
| sk_c5 != inverse(sk_c7)
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(reorient_equations,[],[f55]) ).
fof(f57,plain,
! [X2,X3,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_c7 != inverse(X1)
| sk_c6 != multiply(sk_c7,multiply(X1,sk_c7))
| sk_c5 != inverse(sk_c7)
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(equality_resolution,[],[f56]) ).
tcf(c_78,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_79,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_81,negated_conjecture,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_82,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_83,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_84,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_85,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_86,negated_conjecture,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_91,negated_conjecture,
( ( multiply(sk_c7,sk_c2) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c7,sk_c2) = sk_c6 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c7,sk_c2) = sk_c6 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_95,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c7,sk_c2) = sk_c6 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_96,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c2 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c2 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c2 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_100,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c2 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_106,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(sk_c7) != sk_c5 )
| ( inverse(X2) != sk_c7 )
| ( inverse(X1) != sk_c6 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c6,sk_c5) != sk_c7 )
| ( multiply(X2,sk_c6) != sk_c7 )
| ( multiply(X1,sk_c5) != sk_c6 )
| ( multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_355,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_106]) ).
tcf(c_356,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_106]) ).
tcf(c_357,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_106]) ).
tcf(c_358,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c7) != sk_c5 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c6,sk_c5) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_106]) ).
tcf(c_359,definition,
iPr_def_13 = multiply(sk_c6,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_360,definition,
iPr_def_14 = multiply(sk_c6,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_361,definition,
iPr_def_15 = inverse(sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_362,definition,
iPr_def_16 = multiply(sk_c4,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_363,definition,
iPr_def_17 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_364,definition,
iPr_def_18 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_365,definition,
iPr_def_19 = multiply(sk_c3,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_366,definition,
iPr_def_20 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_367,definition,
iPr_def_21 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_368,definition,
iPr_def_22 = multiply(sk_c7,sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_369,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c5 )
| ( iPr_def_14 != sk_c5 )
| ( iPr_def_13 != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_358,c_361,c_360,c_359]) ).
tcf(c_370,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_357]) ).
tcf(c_371,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_356]) ).
tcf(c_372,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_355]) ).
tcf(c_373,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_105,c_363,c_362]) ).
tcf(c_374,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_104,c_364]) ).
tcf(c_375,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_103,c_365]) ).
tcf(c_376,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_102,c_366]) ).
tcf(c_377,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_378,negated_conjecture,
( ( iPr_def_21 = sk_c2 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_100,c_367]) ).
tcf(c_379,negated_conjecture,
( ( iPr_def_21 = sk_c2 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_381,negated_conjecture,
( ( iPr_def_21 = sk_c2 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_382,negated_conjecture,
( ( iPr_def_21 = sk_c2 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_383,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_95,c_368]) ).
tcf(c_384,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_386,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_387,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_388,negated_conjecture,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_15 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_390,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_15 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_391,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_15 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_392,negated_conjecture,
( ( iPr_def_15 = sk_c5 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_393,negated_conjecture,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_394,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_395,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_396,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_397,negated_conjecture,
( ( iPr_def_14 = sk_c5 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_588,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c7 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_373,c_374]) ).
tcf(c_773,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c4,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_388,c_362]) ).
tcf(c_774,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c6,iPr_def_15) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_388,c_359]) ).
tcf(c_803,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c7,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_378,c_368]) ).
tcf(c_828,plain,
multiply(iPr_def_20,sk_c3) = identity,
inference(superposition,[status(thm)],[c_366,c_79]) ).
tcf(c_829,plain,
multiply(iPr_def_18,sk_c4) = identity,
inference(superposition,[status(thm)],[c_364,c_79]) ).
tcf(c_830,plain,
multiply(iPr_def_15,sk_c7) = identity,
inference(superposition,[status(thm)],[c_361,c_79]) ).
tcf(c_831,plain,
multiply(iPr_def_17,sk_c1) = identity,
inference(superposition,[status(thm)],[c_363,c_79]) ).
tcf(c_995,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c7 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_394,c_393]) ).
tcf(c_1070,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c7 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_396,c_395]) ).
tcf(c_1307,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c5,X0)) = multiply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_359,c_80]) ).
tcf(c_1308,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_360,c_80]) ).
tcf(c_1309,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c6,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_365,c_80]) ).
tcf(c_1312,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c7,X0)) = multiply(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_367,c_80]) ).
tcf(c_1314,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_79,c_80]) ).
tcf(c_1316,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_828,c_80]) ).
tcf(c_1317,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_829,c_80]) ).
tcf(c_1318,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c7,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_830,c_80]) ).
tcf(c_1319,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_831,c_80]) ).
tcf(c_1322,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1319,c_78]) ).
tcf(c_1323,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c7,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1318,c_78]) ).
tcf(c_1324,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1317,c_78]) ).
tcf(c_1325,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1316,c_78]) ).
tcf(c_1609,plain,
multiply(iPr_def_17,iPr_def_21) = sk_c7,
inference(superposition,[status(thm)],[c_367,c_1322]) ).
tcf(c_1624,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_21,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_1609,c_80]) ).
tcf(c_1626,plain,
multiply(iPr_def_15,iPr_def_22) = sk_c2,
inference(superposition,[status(thm)],[c_368,c_1323]) ).
tcf(c_1627,plain,
! [X0: $i] :
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_15,multiply(iPr_def_13,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_1070,c_1323]) ).
tcf(c_1628,plain,
! [X0: $i] :
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(iPr_def_15,multiply(iPr_def_13,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_995,c_1323]) ).
tcf(c_1683,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_16 )
| ( inverse(sk_c4) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_362,c_372]) ).
tcf(c_1698,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_18 )
| ( sk_c6 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_1683,c_364]) ).
tcf(c_1971,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_13 != iPr_def_17 )
| ( sk_c5 != iPr_def_15 )
| ( sk_c5 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_588,c_369]) ).
tcf(c_2263,plain,
multiply(iPr_def_18,iPr_def_16) = sk_c5,
inference(superposition,[status(thm)],[c_362,c_1324]) ).
tcf(c_2266,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_16,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2263,c_80]) ).
tcf(c_2268,plain,
multiply(iPr_def_20,iPr_def_19) = sk_c6,
inference(superposition,[status(thm)],[c_365,c_1325]) ).
tcf(c_2271,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_19,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_2268,c_80]) ).
tcf(c_3397,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_773,c_1324]) ).
tcf(c_3398,plain,
( ( sk_c5 = iPr_def_15 )
| ( sk_c6 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_3397,c_2263]) ).
tcf(c_3850,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_17,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_588,c_803]) ).
tcf(c_3868,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c7 = iPr_def_22 )
| ( sk_c6 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_3850,c_1609]) ).
tcf(c_5288,plain,
multiply(sk_c3,iPr_def_13) = multiply(iPr_def_19,sk_c5),
inference(superposition,[status(thm)],[c_359,c_1309]) ).
tcf(c_5374,plain,
multiply(iPr_def_20,multiply(iPr_def_19,sk_c5)) = iPr_def_13,
inference(superposition,[status(thm)],[c_5288,c_1325]) ).
tcf(c_5703,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1314,c_78]) ).
tcf(c_5716,plain,
multiply(inverse(sk_c6),iPr_def_13) = sk_c5,
inference(superposition,[status(thm)],[c_359,c_5703]) ).
tcf(c_5717,plain,
multiply(inverse(sk_c6),iPr_def_14) = sk_c7,
inference(superposition,[status(thm)],[c_360,c_5703]) ).
tcf(c_5722,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_78,c_5703]) ).
tcf(c_5723,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_79,c_5703]) ).
tcf(c_5724,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[status(thm)],[c_80,c_5703]) ).
tcf(c_5805,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_1325,c_5703]) ).
tcf(c_5806,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_1324,c_5703]) ).
tcf(c_5807,plain,
! [X0: $i] : multiply(inverse(iPr_def_15),X0) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_1323,c_5703]) ).
tcf(c_5808,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_1322,c_5703]) ).
tcf(c_5839,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_5703,c_5703]) ).
tcf(c_6386,plain,
( ~ iPr_def_10
| ( sk_c6 != sk_c5 )
| ( inverse(inverse(identity)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_5722,c_372]) ).
tcf(c_6414,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_5723,c_5839]) ).
tcf(c_6419,plain,
multiply(sk_c6,sk_c7) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_6414,c_1308]) ).
tcf(c_6427,plain,
multiply(sk_c6,sk_c5) = multiply(iPr_def_13,identity),
inference(superposition,[status(thm)],[c_6414,c_1307]) ).
tcf(c_6432,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_6414,c_5722]) ).
tcf(c_6434,plain,
multiply(iPr_def_13,identity) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_6427,c_359]) ).
tcf(c_6437,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_6419,c_360]) ).
tcf(c_6735,plain,
multiply(sk_c5,identity) = multiply(iPr_def_18,iPr_def_16),
inference(superposition,[status(thm)],[c_6414,c_2266]) ).
tcf(c_6738,plain,
multiply(sk_c5,identity) = sk_c5,
inference(light_normalisation,[status(thm)],[c_6735,c_2263]) ).
tcf(c_6802,plain,
multiply(sk_c6,identity) = multiply(iPr_def_20,iPr_def_19),
inference(superposition,[status(thm)],[c_6414,c_2271]) ).
tcf(c_7142,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_20)) != sk_c7 )
| ( multiply(sk_c7,multiply(sk_c3,sk_c7)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_5805,c_370]) ).
tcf(c_7143,plain,
multiply(sk_c3,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_5805,c_79]) ).
tcf(c_7147,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_20)) != sk_c7 )
| ( multiply(sk_c3,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_5805,c_371]) ).
tcf(c_7148,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_5805,c_5703]) ).
tcf(c_7149,plain,
multiply(sk_c3,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_5805,c_6414]) ).
tcf(c_7174,plain,
inverse(iPr_def_20) = sk_c3,
inference(demodulation,[status(thm)],[c_7149,c_6414]) ).
tcf(c_7190,plain,
multiply(sk_c3,sk_c6) = iPr_def_19,
inference(superposition,[status(thm)],[c_2268,c_7148]) ).
tcf(c_7611,plain,
( ( sk_c6 = iPr_def_16 )
| ~ iPr_def_10
| ( iPr_def_16 != iPr_def_22 )
| ( sk_c6 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_383,c_1698]) ).
tcf(c_7864,plain,
multiply(sk_c4,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_5806,c_79]) ).
tcf(c_7869,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_5806,c_5703]) ).
tcf(c_7870,plain,
multiply(sk_c4,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_5806,c_6414]) ).
tcf(c_8051,plain,
inverse(iPr_def_18) = sk_c4,
inference(demodulation,[status(thm)],[c_7870,c_6414]) ).
tcf(c_8065,plain,
multiply(sk_c4,sk_c5) = iPr_def_16,
inference(superposition,[status(thm)],[c_2263,c_7869]) ).
tcf(c_8491,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c6)),multiply(X0,iPr_def_13)) = sk_c5,
inference(superposition,[status(thm)],[c_359,c_5724]) ).
tcf(c_8498,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c1)),multiply(X0,iPr_def_21)) = sk_c7,
inference(superposition,[status(thm)],[c_367,c_5724]) ).
tcf(c_8561,plain,
! [X0: $i] : multiply(inverse(multiply(X0,iPr_def_15)),multiply(X0,identity)) = sk_c7,
inference(superposition,[status(thm)],[c_830,c_5724]) ).
tcf(c_8562,plain,
! [X0: $i] : multiply(inverse(multiply(X0,iPr_def_17)),multiply(X0,identity)) = sk_c1,
inference(superposition,[status(thm)],[c_831,c_5724]) ).
tcf(c_8644,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c4)),multiply(X0,identity)) = iPr_def_18,
inference(superposition,[status(thm)],[c_7864,c_5724]) ).
tcf(c_8658,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c4)),X0) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_8644,c_6414]) ).
tcf(c_8660,plain,
! [X0: $i] : multiply(inverse(multiply(X0,iPr_def_17)),X0) = sk_c1,
inference(light_normalisation,[status(thm)],[c_8562,c_6414]) ).
tcf(c_8661,plain,
! [X0: $i] : multiply(inverse(multiply(X0,iPr_def_15)),X0) = sk_c7,
inference(light_normalisation,[status(thm)],[c_8561,c_6414]) ).
tcf(c_10893,plain,
multiply(sk_c7,iPr_def_15) = identity,
inference(superposition,[status(thm)],[c_5807,c_79]) ).
tcf(c_10901,plain,
! [X0: $i] : multiply(sk_c7,multiply(iPr_def_15,X0)) = X0,
inference(superposition,[status(thm)],[c_5807,c_5703]) ).
tcf(c_10902,plain,
multiply(sk_c7,identity) = inverse(iPr_def_15),
inference(superposition,[status(thm)],[c_5807,c_6414]) ).
tcf(c_10972,plain,
multiply(sk_c1,identity) = multiply(iPr_def_21,iPr_def_15),
inference(superposition,[status(thm)],[c_10893,c_1312]) ).
tcf(c_10973,plain,
multiply(sk_c6,identity) = multiply(iPr_def_14,iPr_def_15),
inference(superposition,[status(thm)],[c_10893,c_1308]) ).
tcf(c_11017,plain,
inverse(iPr_def_15) = sk_c7,
inference(demodulation,[status(thm)],[c_10902,c_6414]) ).
tcf(c_11220,plain,
multiply(inverse(iPr_def_19),multiply(sk_c3,iPr_def_13)) = sk_c5,
inference(superposition,[status(thm)],[c_7190,c_8491]) ).
tcf(c_11242,plain,
multiply(inverse(multiply(inverse(iPr_def_13),sk_c6)),identity) = sk_c5,
inference(superposition,[status(thm)],[c_79,c_8491]) ).
tcf(c_11257,plain,
multiply(inverse(iPr_def_19),multiply(iPr_def_19,sk_c5)) = sk_c5,
inference(light_normalisation,[status(thm)],[c_11220,c_5288]) ).
tcf(c_11354,plain,
multiply(sk_c7,sk_c2) = iPr_def_22,
inference(superposition,[status(thm)],[c_1626,c_10901]) ).
tcf(c_11372,plain,
( ~ iPr_def_12
| ( sk_c6 != sk_c7 )
| ( inverse(iPr_def_15) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_10901,c_370]) ).
tcf(c_11399,plain,
( ~ iPr_def_12
| ( sk_c6 != sk_c7 ) ),
inference(ground_joinability,[status(thm)],[c_11372,c_11017]) ).
tcf(c_11506,plain,
( ( sk_c6 = iPr_def_16 )
| ~ iPr_def_12
| ( sk_c7 != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_383,c_11399]) ).
tcf(c_11554,plain,
multiply(iPr_def_21,iPr_def_15) = sk_c1,
inference(demodulation,[status(thm)],[c_10972,c_6414]) ).
tcf(c_11559,plain,
multiply(sk_c7,iPr_def_15) = multiply(iPr_def_17,sk_c1),
inference(superposition,[status(thm)],[c_11554,c_1624]) ).
tcf(c_12137,plain,
inverse(multiply(inverse(iPr_def_13),sk_c6)) = sk_c5,
inference(demodulation,[status(thm)],[c_11242,c_6414]) ).
tcf(c_12157,plain,
multiply(sk_c5,multiply(inverse(iPr_def_13),sk_c6)) = identity,
inference(superposition,[status(thm)],[c_12137,c_79]) ).
tcf(c_12315,plain,
multiply(iPr_def_13,multiply(inverse(iPr_def_13),sk_c6)) = multiply(sk_c6,identity),
inference(superposition,[status(thm)],[c_12157,c_1307]) ).
tcf(c_12316,plain,
multiply(iPr_def_13,multiply(inverse(iPr_def_13),sk_c6)) = multiply(iPr_def_14,iPr_def_15),
inference(light_normalisation,[status(thm)],[c_12315,c_10973]) ).
tcf(c_12624,plain,
multiply(iPr_def_14,iPr_def_15) = sk_c6,
inference(demodulation,[status(thm)],[c_10973,c_6414]) ).
tcf(c_12626,plain,
multiply(inverse(iPr_def_14),sk_c6) = iPr_def_15,
inference(superposition,[status(thm)],[c_12624,c_5703]) ).
tcf(c_12649,plain,
! [X0: $i] : multiply(inverse(iPr_def_14),multiply(sk_c6,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_12626,c_80]) ).
tcf(c_12928,plain,
multiply(sk_c1,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_5808,c_79]) ).
tcf(c_12938,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_5808,c_5703]) ).
tcf(c_12941,plain,
multiply(sk_c1,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_5808,c_6414]) ).
tcf(c_12943,plain,
multiply(inverse(multiply(sk_c1,sk_c1)),multiply(inverse(iPr_def_17),iPr_def_21)) = sk_c7,
inference(superposition,[status(thm)],[c_5808,c_8498]) ).
tcf(c_13678,plain,
multiply(inverse(iPr_def_14),iPr_def_13) = multiply(iPr_def_15,sk_c5),
inference(superposition,[status(thm)],[c_359,c_12649]) ).
tcf(c_13679,plain,
multiply(inverse(iPr_def_14),iPr_def_14) = multiply(iPr_def_15,sk_c7),
inference(superposition,[status(thm)],[c_360,c_12649]) ).
tcf(c_13722,plain,
multiply(inverse(iPr_def_14),iPr_def_14) = identity,
inference(light_normalisation,[status(thm)],[c_13679,c_830]) ).
tcf(c_13916,plain,
inverse(iPr_def_17) = sk_c1,
inference(demodulation,[status(thm)],[c_12941,c_6414]) ).
tcf(c_13926,plain,
multiply(sk_c1,identity) = sk_c1,
inference(superposition,[status(thm)],[c_831,c_12938]) ).
tcf(c_13929,plain,
multiply(sk_c1,sk_c7) = iPr_def_21,
inference(superposition,[status(thm)],[c_1609,c_12938]) ).
tcf(c_15880,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,multiply(X1,sk_c4))),multiply(X0,X1)) = iPr_def_18,
inference(superposition,[status(thm)],[c_80,c_8658]) ).
tcf(c_15890,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_18 )
| ( inverse(inverse(multiply(sk_c5,sk_c4))) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_8658,c_372]) ).
tcf(c_15892,plain,
multiply(inverse(iPr_def_18),multiply(inverse(multiply(sk_c6,sk_c4)),iPr_def_13)) = sk_c5,
inference(superposition,[status(thm)],[c_8658,c_8491]) ).
tcf(c_15904,plain,
multiply(sk_c4,multiply(inverse(multiply(sk_c6,sk_c4)),iPr_def_13)) = sk_c5,
inference(light_normalisation,[status(thm)],[c_15892,c_8051]) ).
tcf(c_17176,plain,
multiply(inverse(identity),sk_c1) = sk_c1,
inference(superposition,[status(thm)],[c_12928,c_8660]) ).
tcf(c_17194,plain,
multiply(inverse(sk_c1),inverse(multiply(iPr_def_17,iPr_def_17))) = sk_c1,
inference(superposition,[status(thm)],[c_8660,c_8660]) ).
tcf(c_17198,plain,
multiply(identity,sk_c1) = sk_c1,
inference(light_normalisation,[status(thm)],[c_17176,c_6432]) ).
tcf(c_17202,plain,
multiply(iPr_def_17,inverse(multiply(iPr_def_17,iPr_def_17))) = sk_c1,
inference(light_normalisation,[status(thm)],[c_17194,c_363]) ).
tcf(c_17265,plain,
( ~ iPr_def_11
| ( inverse(inverse(multiply(sk_c6,iPr_def_15))) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_8661,c_371]) ).
tcf(c_17558,plain,
( ( sk_c6 = iPr_def_16 )
| ~ iPr_def_11
| ( inverse(inverse(iPr_def_13)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_774,c_17265]) ).
tcf(c_18051,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(inverse(sk_c4),multiply(iPr_def_15,iPr_def_13)) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1628,c_15880]) ).
tcf(c_18052,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(inverse(sk_c4),multiply(iPr_def_15,iPr_def_13)) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1627,c_15880]) ).
tcf(c_18061,plain,
multiply(inverse(multiply(sk_c6,sk_c4)),multiply(iPr_def_20,iPr_def_19)) = iPr_def_18,
inference(superposition,[status(thm)],[c_2271,c_15880]) ).
tcf(c_18321,plain,
multiply(inverse(multiply(sk_c6,sk_c4)),sk_c6) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_18061,c_2268]) ).
tcf(c_20851,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_18321,c_18052,c_18051,c_17558,c_17265,c_17202,c_17198,c_15904,c_15890,c_13929,c_13926,c_13916,c_13722,c_13679,c_13678,c_12943,c_12928,c_12626,c_12624,c_12316,c_12315,c_11559,c_11506,c_11399,c_11354,c_11257,c_11017,c_10902,c_10893,c_8065,c_8051,c_7864,c_7611,c_7190,c_7174,c_7147,c_7142,c_7143,c_6802,c_6738,c_6735,c_6437,c_6434,c_6427,c_6432,c_6386,c_5717,c_5716,c_5374,c_5288,c_3868,c_3398,c_1971,c_829,c_397,c_396,c_394,c_393,c_392,c_391,c_390,c_387,c_386,c_384,c_382,c_381,c_379,c_377,c_376,c_375,c_374,c_373,c_369,c_366,c_364,c_363,c_361]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP360-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 14:34:19 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 10.44/2.26 % SZS status Started for theBenchmark.p
% 10.44/2.26 % SZS status Unsatisfiable for theBenchmark.p
% 10.44/2.26
% 10.44/2.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.44/2.26
% 10.44/2.26 % ------ iProver source info
% 10.44/2.26
% 10.44/2.26 % git: date: 2026-07-19 20:42:38 +0200
% 10.44/2.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.44/2.26 % git: non_committed_changes: false
% 10.44/2.26
% 10.44/2.26 % ------ Parsing...% successful
% 10.44/2.26
% 10.44/2.26
% 10.44/2.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.44/2.26
% 10.44/2.26 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.44/2.26
% 10.44/2.26 % ------ Preprocessing... gs_s sp: 3 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.44/2.26
% 10.44/2.26 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.44/2.26 % ------ Proving...
% 10.44/2.26 % ------ Problem Properties
% 10.44/2.26
% 10.44/2.26 %
% 10.44/2.26 % clauses 42
% 10.44/2.26 % conjectures 29
% 10.44/2.26 % EPR 26
% 10.44/2.26 % Horn 16
% 10.44/2.26 % unary 13
% 10.44/2.26 % binary 25
% 10.44/2.26 % lits 78
% 10.44/2.26 % lits eq 72
% 10.44/2.26 % fd_pure 0
% 10.44/2.26 % fd_pseudo 0
% 10.44/2.26 % fd_cond 0
% 10.44/2.26 % fd_pseudo_cond 0
% 10.44/2.26 % AC symbols 0
% 10.44/2.26
% 10.44/2.26 % ------ Schedule dynamic 5 is on
% 10.44/2.26
% 10.44/2.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.44/2.26
% 10.44/2.26
% 10.44/2.26 % ------
% 10.44/2.26 % Current options:
% 10.44/2.26 % ------
% 10.44/2.26
% 10.44/2.26
% 10.44/2.26 %
% 10.44/2.26
% 10.44/2.26 % ------ Proving...
% 10.44/2.26 %
% 10.44/2.26
% 10.44/2.26 % SZS status Unsatisfiable for theBenchmark.p
% 10.44/2.26
% 10.44/2.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.44/2.26
% 10.44/2.26
%------------------------------------------------------------------------------