%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP262-1 : 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 : 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 01:32:38 PM UTC 2026
% Result : Unsatisfiable 3.90s 6.73s
% Output : CNFRefutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 38
% Syntax : Number of formulae : 266 ( 87 unt; 10 def)
% Number of atoms : 814 ( 463 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 397 ( 140 ~; 257 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 16 ( 14 usr; 15 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/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_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c7 = inverse(sk_c3)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c6 = inverse(sk_c4)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c6 = inverse(sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f24]) ).
fof(f28,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c6 = inverse(sk_c4)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c6 = inverse(sk_c4)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c6 = inverse(sk_c4)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,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
| multiply(sk_c5,sk_c7) != sk_c6
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c5
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,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)
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c6 != multiply(sk_c5,sk_c7)
| sk_c6 != inverse(X1)
| sk_c5 != multiply(X1,sk_c6)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7) ),
inference(reorient_equations,[],[f54]) ).
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_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_82,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_83,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_84,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_85,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_86,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_91,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_93,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_95,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_101,negated_conjecture,
( ( multiply(sk_c5,sk_c7) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_103,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_105,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_106,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c6 )
| ( inverse(X2) != sk_c6 )
| ( inverse(X1) != sk_c7 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c5,sk_c7) != sk_c6 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(X3,sk_c6) != sk_c5 )
| ( multiply(X2,sk_c5) != sk_c6 )
| ( multiply(X1,sk_c6) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_359,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_360,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_361,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_106]) ).
tcf(c_362,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_106]) ).
tcf(c_363,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c5,sk_c7) != sk_c6 )
| ( multiply(sk_c6,sk_c7) != sk_c5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_106]) ).
tcf(c_364,definition,
iPr_def_14 = multiply(sk_c6,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_365,definition,
iPr_def_15 = multiply(sk_c5,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_366,definition,
iPr_def_16 = multiply(sk_c4,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_367,definition,
iPr_def_17 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_368,definition,
iPr_def_18 = multiply(sk_c3,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_369,definition,
iPr_def_19 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_370,definition,
iPr_def_20 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_371,definition,
iPr_def_21 = multiply(sk_c2,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_372,definition,
iPr_def_22 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_373,definition,
iPr_def_23 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_374,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c6 )
| ( iPr_def_14 != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_363,c_365,c_364]) ).
tcf(c_375,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_362]) ).
tcf(c_376,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_361]) ).
tcf(c_377,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_360]) ).
tcf(c_378,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_359]) ).
tcf(c_379,negated_conjecture,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_105,c_366]) ).
tcf(c_380,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_104,c_367]) ).
tcf(c_381,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_103,c_368]) ).
tcf(c_382,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_102,c_369]) ).
tcf(c_383,negated_conjecture,
( ( iPr_def_15 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_384,negated_conjecture,
( ( iPr_def_20 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_100,c_370]) ).
tcf(c_385,negated_conjecture,
( ( iPr_def_20 = sk_c6 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_386,negated_conjecture,
( ( iPr_def_20 = sk_c6 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_387,negated_conjecture,
( ( iPr_def_20 = sk_c6 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_388,negated_conjecture,
( ( iPr_def_20 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_389,negated_conjecture,
( ( iPr_def_21 = sk_c5 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_95,c_371]) ).
tcf(c_390,negated_conjecture,
( ( iPr_def_21 = sk_c5 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_391,negated_conjecture,
( ( iPr_def_21 = sk_c5 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_393,negated_conjecture,
( ( iPr_def_21 = sk_c5 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_394,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_90,c_372]) ).
tcf(c_395,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_396,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_397,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_398,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_399,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_85,c_373]) ).
tcf(c_400,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_401,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_402,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_403,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_739,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c4,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_389,c_366]) ).
tcf(c_740,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_21,sk_c7) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_389,c_365]) ).
tcf(c_759,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_390,c_366]) ).
tcf(c_760,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_21,sk_c7) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_390,c_365]) ).
tcf(c_919,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_394,c_373]) ).
tcf(c_934,plain,
multiply(iPr_def_19,sk_c3) = identity,
inference(superposition,[status(thm)],[c_369,c_79]) ).
tcf(c_935,plain,
multiply(iPr_def_17,sk_c4) = identity,
inference(superposition,[status(thm)],[c_367,c_79]) ).
tcf(c_936,plain,
multiply(iPr_def_22,sk_c1) = identity,
inference(superposition,[status(thm)],[c_372,c_79]) ).
tcf(c_937,plain,
multiply(iPr_def_20,sk_c2) = identity,
inference(superposition,[status(thm)],[c_370,c_79]) ).
tcf(c_946,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_395,c_373]) ).
tcf(c_984,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_396,c_373]) ).
tcf(c_1029,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_397,c_373]) ).
tcf(c_1107,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_23) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_399,c_371]) ).
tcf(c_1155,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(sk_c2,iPr_def_23) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_400,c_371]) ).
tcf(c_1189,plain,
( ( sk_c6 = iPr_def_23 )
| ( multiply(sk_c1,iPr_def_18) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_401,c_373]) ).
tcf(c_1257,plain,
( ( sk_c6 = iPr_def_23 )
| ( multiply(sk_c1,iPr_def_19) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_402,c_373]) ).
tcf(c_1369,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c6 = iPr_def_23 )
| ( sk_c6 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_403,c_374]) ).
tcf(c_1370,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_22 )
| ( sk_c6 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_398,c_374]) ).
tcf(c_1530,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_364,c_80]) ).
tcf(c_1532,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c5,X0)) = multiply(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_366,c_80]) ).
tcf(c_1533,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c6,X0)) = multiply(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_371,c_80]) ).
tcf(c_1534,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c7,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_365,c_80]) ).
tcf(c_1536,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_79,c_80]) ).
tcf(c_1538,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_934,c_80]) ).
tcf(c_1539,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_935,c_80]) ).
tcf(c_1540,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_936,c_80]) ).
tcf(c_1541,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_937,c_80]) ).
tcf(c_1543,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1541,c_78]) ).
tcf(c_1544,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1540,c_78]) ).
tcf(c_1545,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1539,c_78]) ).
tcf(c_1546,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1538,c_78]) ).
tcf(c_1973,plain,
multiply(iPr_def_20,iPr_def_21) = sk_c6,
inference(superposition,[status(thm)],[c_371,c_1543]) ).
tcf(c_1976,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_21,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_1973,c_80]) ).
tcf(c_1993,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_23 )
| ( inverse(sk_c1) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_373,c_375]) ).
tcf(c_1995,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_15 )
| ( inverse(sk_c5) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_365,c_375]) ).
tcf(c_1997,plain,
( ~ iPr_def_13
| ( sk_c6 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_79,c_375]) ).
tcf(c_2018,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_23 )
| ( sk_c7 != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_1993,c_372]) ).
tcf(c_2126,plain,
( ~ iPr_def_12
| ( sk_c5 != iPr_def_21 )
| ( inverse(sk_c2) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_371,c_376]) ).
tcf(c_2128,plain,
( ~ iPr_def_12
| ( sk_c5 != identity )
| ( inverse(inverse(sk_c6)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_79,c_376]) ).
tcf(c_2145,plain,
( ~ iPr_def_12
| ( sk_c5 != iPr_def_21 )
| ( sk_c6 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_2126,c_370]) ).
tcf(c_2295,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_18 )
| ( inverse(sk_c3) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_368,c_377]) ).
tcf(c_2319,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_19 )
| ( sk_c7 != iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_2295,c_369]) ).
tcf(c_2447,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_16 )
| ( inverse(sk_c4) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_366,c_378]) ).
tcf(c_2448,plain,
( ~ iPr_def_10
| ( sk_c6 != sk_c5 )
| ( inverse(identity) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_78,c_378]) ).
tcf(c_2463,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_17 )
| ( sk_c6 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_2447,c_367]) ).
tcf(c_2876,plain,
multiply(iPr_def_22,iPr_def_23) = sk_c7,
inference(superposition,[status(thm)],[c_373,c_1544]) ).
tcf(c_2881,plain,
multiply(iPr_def_17,iPr_def_16) = sk_c5,
inference(superposition,[status(thm)],[c_366,c_1545]) ).
tcf(c_2893,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_16,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2881,c_80]) ).
tcf(c_2895,plain,
multiply(iPr_def_19,iPr_def_18) = sk_c6,
inference(superposition,[status(thm)],[c_368,c_1546]) ).
tcf(c_2937,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(iPr_def_18,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_2895,c_80]) ).
tcf(c_3703,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_17,iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_739,c_1545]) ).
tcf(c_3704,plain,
( ( sk_c5 = iPr_def_21 )
| ( sk_c6 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_3703,c_2881]) ).
tcf(c_3756,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_17,iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_759,c_1545]) ).
tcf(c_3757,plain,
( ( sk_c5 = iPr_def_21 )
| ( sk_c6 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_3756,c_2881]) ).
tcf(c_4266,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_919,c_1544]) ).
tcf(c_4267,plain,
( ( sk_c6 = iPr_def_16 )
| ( sk_c7 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_4266,c_2876]) ).
tcf(c_4426,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_946,c_1544]) ).
tcf(c_4427,plain,
( ( sk_c6 = iPr_def_17 )
| ( sk_c7 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_4426,c_2876]) ).
tcf(c_4529,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_984,c_1544]) ).
tcf(c_4530,plain,
( ( sk_c7 = iPr_def_22 )
| ( sk_c7 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_4529,c_2876]) ).
tcf(c_4673,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1029,c_1544]) ).
tcf(c_4674,plain,
( ( sk_c7 = iPr_def_22 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_4673,c_2876]) ).
tcf(c_4939,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1107,c_1543]) ).
tcf(c_4940,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c6 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_4939,c_1973]) ).
tcf(c_4996,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1155,c_1543]) ).
tcf(c_4997,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c6 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_4996,c_1973]) ).
tcf(c_5050,plain,
( ( sk_c6 = iPr_def_23 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1189,c_1544]) ).
tcf(c_5051,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c7 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_5050,c_2876]) ).
tcf(c_5121,plain,
( ( sk_c6 = iPr_def_23 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1257,c_1544]) ).
tcf(c_5122,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_5121,c_2876]) ).
tcf(c_6048,plain,
multiply(sk_c4,iPr_def_15) = multiply(iPr_def_16,sk_c7),
inference(superposition,[status(thm)],[c_365,c_1532]) ).
tcf(c_6375,plain,
multiply(sk_c2,iPr_def_14) = multiply(iPr_def_21,sk_c7),
inference(superposition,[status(thm)],[c_364,c_1533]) ).
tcf(c_6473,plain,
multiply(iPr_def_20,multiply(iPr_def_21,sk_c7)) = iPr_def_14,
inference(superposition,[status(thm)],[c_6375,c_1543]) ).
tcf(c_6837,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(sk_c6,sk_c7) = multiply(iPr_def_20,iPr_def_15) ) ),
inference(superposition,[status(thm)],[c_760,c_1976]) ).
tcf(c_6838,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c6,sk_c7) = multiply(iPr_def_20,iPr_def_15) ) ),
inference(superposition,[status(thm)],[c_740,c_1976]) ).
tcf(c_6852,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_20,iPr_def_15) = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_6838,c_364]) ).
tcf(c_6855,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_20,iPr_def_15) = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_6837,c_364]) ).
tcf(c_6960,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1536,c_78]) ).
tcf(c_6966,plain,
multiply(inverse(sk_c6),iPr_def_14) = sk_c7,
inference(superposition,[status(thm)],[c_364,c_6960]) ).
tcf(c_6970,plain,
multiply(inverse(sk_c5),iPr_def_15) = sk_c7,
inference(superposition,[status(thm)],[c_365,c_6960]) ).
tcf(c_6971,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_78,c_6960]) ).
tcf(c_6972,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_79,c_6960]) ).
tcf(c_7069,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_1546,c_6960]) ).
tcf(c_7070,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_1545,c_6960]) ).
tcf(c_7071,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_1544,c_6960]) ).
tcf(c_7072,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_1543,c_6960]) ).
tcf(c_7102,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_6960,c_6960]) ).
tcf(c_7783,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_6972,c_7102]) ).
tcf(c_7795,plain,
multiply(sk_c5,sk_c7) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_7783,c_1534]) ).
tcf(c_7796,plain,
multiply(sk_c6,sk_c7) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_7783,c_1530]) ).
tcf(c_7798,plain,
multiply(sk_c6,identity) = multiply(iPr_def_19,iPr_def_18),
inference(superposition,[status(thm)],[c_7783,c_2937]) ).
tcf(c_7801,plain,
multiply(sk_c5,identity) = multiply(iPr_def_17,iPr_def_16),
inference(superposition,[status(thm)],[c_7783,c_2893]) ).
tcf(c_7803,plain,
multiply(sk_c6,identity) = multiply(iPr_def_20,iPr_def_21),
inference(superposition,[status(thm)],[c_7783,c_1976]) ).
tcf(c_7808,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_7783,c_6971]) ).
tcf(c_7809,plain,
multiply(sk_c6,identity) = sk_c6,
inference(light_normalisation,[status(thm)],[c_7803,c_1973]) ).
tcf(c_7811,plain,
multiply(sk_c5,identity) = sk_c5,
inference(light_normalisation,[status(thm)],[c_7801,c_2881]) ).
tcf(c_7816,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_7796,c_364]) ).
tcf(c_7817,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_7795,c_365]) ).
tcf(c_8483,plain,
multiply(sk_c3,iPr_def_19) = identity,
inference(superposition,[status(thm)],[c_7069,c_79]) ).
tcf(c_8487,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_19)) != sk_c7 )
| ( multiply(sk_c3,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_7069,c_377]) ).
tcf(c_8489,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_19,X0)) = X0,
inference(superposition,[status(thm)],[c_7069,c_6960]) ).
tcf(c_8490,plain,
multiply(sk_c3,identity) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_7069,c_7783]) ).
tcf(c_8547,plain,
( ( sk_c7 = iPr_def_19 )
| ~ iPr_def_13
| ( sk_c6 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_397,c_2018]) ).
tcf(c_8549,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_13
| ( sk_c6 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_395,c_2018]) ).
tcf(c_8550,plain,
( ( sk_c6 = iPr_def_16 )
| ~ iPr_def_13
| ( sk_c6 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_394,c_2018]) ).
tcf(c_8583,plain,
( ( sk_c7 = iPr_def_19 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_8547,c_5122,c_8547]) ).
tcf(c_8595,plain,
inverse(iPr_def_19) = sk_c3,
inference(demodulation,[status(thm)],[c_8490,c_7783]) ).
tcf(c_8600,plain,
multiply(sk_c3,sk_c6) = iPr_def_18,
inference(superposition,[status(thm)],[c_2895,c_8489]) ).
tcf(c_8634,plain,
multiply(sk_c4,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_7070,c_79]) ).
tcf(c_8637,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_17)) != sk_c6 )
| ( multiply(sk_c4,sk_c5) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_7070,c_378]) ).
tcf(c_8639,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_17)) != sk_c6 )
| ( multiply(sk_c4,sk_c6) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_7070,c_376]) ).
tcf(c_8640,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_7070,c_6960]) ).
tcf(c_8641,plain,
multiply(sk_c4,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_7070,c_7783]) ).
tcf(c_8676,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_8549,c_4997,c_8549]) ).
tcf(c_8682,plain,
( ( sk_c6 = iPr_def_16 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_8550,c_4940,c_8550]) ).
tcf(c_8690,plain,
( iPr_def_13
| iPr_def_12
| ( sk_c6 = iPr_def_23 )
| ( sk_c6 != iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_1369,c_1369,c_2319,c_2463,c_4940,c_4997,c_5051,c_5122]) ).
tcf(c_8746,plain,
( iPr_def_13
| iPr_def_12
| ( sk_c7 = iPr_def_22 )
| ( sk_c6 != iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_1370,c_1370,c_2319,c_2463,c_4267,c_4427,c_4530,c_4674]) ).
tcf(c_8951,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_12
| ( sk_c5 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_385,c_2145]) ).
tcf(c_8952,plain,
( ( sk_c6 = iPr_def_16 )
| ~ iPr_def_12
| ( sk_c5 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_384,c_2145]) ).
tcf(c_9117,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_8951,c_3757,c_8951]) ).
tcf(c_9123,plain,
( ( sk_c6 = iPr_def_16 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_8952,c_3704,c_8952]) ).
tcf(c_9129,plain,
inverse(iPr_def_17) = sk_c4,
inference(demodulation,[status(thm)],[c_8641,c_7783]) ).
tcf(c_9138,plain,
multiply(sk_c4,sk_c5) = iPr_def_16,
inference(superposition,[status(thm)],[c_2881,c_8640]) ).
tcf(c_9221,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_22)) != sk_c7 )
| ( multiply(sk_c1,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_7071,c_375]) ).
tcf(c_9222,plain,
multiply(sk_c1,iPr_def_22) = identity,
inference(superposition,[status(thm)],[c_7071,c_79]) ).
tcf(c_9226,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_22)) != sk_c7 )
| ( multiply(sk_c1,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_7071,c_377]) ).
tcf(c_9228,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_22,X0)) = X0,
inference(superposition,[status(thm)],[c_7071,c_6960]) ).
tcf(c_9229,plain,
multiply(sk_c1,identity) = inverse(iPr_def_22),
inference(superposition,[status(thm)],[c_7071,c_7783]) ).
tcf(c_9239,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_23 )
| ( inverse(inverse(iPr_def_22)) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_9221,c_373]) ).
tcf(c_9616,plain,
( ~ iPr_def_10
| ( sk_c6 != identity )
| ( sk_c6 != sk_c5 ) ),
inference(light_normalisation,[status(thm)],[c_2448,c_7808]) ).
tcf(c_10478,plain,
inverse(iPr_def_22) = sk_c1,
inference(demodulation,[status(thm)],[c_9229,c_7783]) ).
tcf(c_10483,plain,
multiply(sk_c1,sk_c7) = iPr_def_23,
inference(superposition,[status(thm)],[c_2876,c_9228]) ).
tcf(c_11069,plain,
multiply(sk_c2,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_7072,c_79]) ).
tcf(c_11074,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_20)) != sk_c6 )
| ( multiply(sk_c2,sk_c6) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_7072,c_376]) ).
tcf(c_11075,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_7072,c_6960]) ).
tcf(c_11076,plain,
multiply(sk_c2,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_7072,c_7783]) ).
tcf(c_11081,plain,
( ~ iPr_def_12
| ( sk_c5 != iPr_def_21 )
| ( inverse(inverse(iPr_def_20)) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_11074,c_371]) ).
tcf(c_12136,plain,
inverse(iPr_def_20) = sk_c2,
inference(demodulation,[status(thm)],[c_11076,c_7783]) ).
tcf(c_12159,plain,
multiply(sk_c2,identity) = sk_c2,
inference(superposition,[status(thm)],[c_937,c_11075]) ).
tcf(c_12160,plain,
multiply(sk_c2,sk_c6) = iPr_def_21,
inference(superposition,[status(thm)],[c_1973,c_11075]) ).
tcf(c_12365,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_12160,c_12159,c_12136,c_11081,c_11069,c_10483,c_10478,c_9616,c_9239,c_9226,c_9229,c_9222,c_9138,c_9129,c_9123,c_9117,c_8746,c_8690,c_8682,c_8676,c_8639,c_8637,c_8634,c_8600,c_8595,c_8583,c_8487,c_8483,c_7817,c_7816,c_7811,c_7809,c_7801,c_7798,c_7796,c_7795,c_7808,c_6970,c_6966,c_6855,c_6852,c_6473,c_6375,c_6048,c_2463,c_2128,c_1997,c_1995,c_403,c_401,c_398,c_396,c_393,c_391,c_388,c_387,c_386,c_385,c_384,c_383,c_382,c_381,c_380,c_379,c_374,c_372,c_370,c_369,c_367]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP262-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.37 % Computer : n005.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Wed Sep 23 14:18:09 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.41 Running first-order theorem proving
% 0.13/5.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/5.42
% 0.13/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.42
% 0.13/5.42 % Detected problem language: tptp
% 0.13/5.43 % Proving...
% 3.90/6.73 % SZS status Started for theBenchmark.p
% 3.90/6.73 % SZS status Unsatisfiable for theBenchmark.p
% 3.90/6.73
% 3.90/6.73 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.90/6.73
% 3.90/6.73 % ------ iProver source info
% 3.90/6.73
% 3.90/6.73 % git: date: 2026-07-19 20:42:38 +0200
% 3.90/6.73 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.90/6.73 % git: non_committed_changes: false
% 3.90/6.73
% 3.90/6.73 % ------ Parsing...% successful
% 3.90/6.73
% 3.90/6.73
% 3.90/6.73 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.90/6.73
% 3.90/6.73 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.90/6.73
% 3.90/6.73 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.90/6.73
% 3.90/6.73 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.90/6.73 % ------ Proving...
% 3.90/6.73 % ------ Problem Properties
% 3.90/6.73
% 3.90/6.73 %
% 3.90/6.73 % clauses 43
% 3.90/6.73 % conjectures 30
% 3.90/6.73 % EPR 26
% 3.90/6.73 % Horn 17
% 3.90/6.73 % unary 13
% 3.90/6.73 % binary 25
% 3.90/6.73 % lits 81
% 3.90/6.73 % lits eq 73
% 3.90/6.73 % fd_pure 0
% 3.90/6.73 % fd_pseudo 0
% 3.90/6.73 % fd_cond 0
% 3.90/6.73 % fd_pseudo_cond 0
% 3.90/6.73 % AC symbols 0
% 3.90/6.73
% 3.90/6.73 % ------ Schedule dynamic 5 is on
% 3.90/6.73
% 3.90/6.73 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.90/6.73
% 3.90/6.73
% 3.90/6.73 % ------
% 3.90/6.73 % Current options:
% 3.90/6.73 % ------
% 3.90/6.73
% 3.90/6.73
% 3.90/6.73 %
% 3.90/6.73
% 3.90/6.73 % ------ Proving...
% 3.90/6.73 %
% 3.90/6.73
% 3.90/6.73 % SZS status Unsatisfiable for theBenchmark.p
% 3.90/6.73
% 3.90/6.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.90/6.74
% 3.90/6.74
%------------------------------------------------------------------------------