%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP333-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 : Tue Sep 29 10:17:31 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.47s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 38
% Syntax : Number of formulae : 310 ( 24 unt; 17 def)
% Number of atoms : 1017 ( 283 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 1386 ( 679 ~; 690 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 60 !; 0 ?)
% 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,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c6 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c6 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c6 = inverse(sk_c1)
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c6 = inverse(sk_c2)
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c6 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c7) != sk_c5
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c6
| inverse(X1) != sk_c6
| multiply(X1,sk_c5) != sk_c6
| multiply(X2,sk_c7) != sk_c6
| inverse(X2) != sk_c7
| multiply(X3,sk_c6) != sk_c5
| inverse(X3) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c7) != sk_c5
| sk_c7 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6
| sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5)
| sk_c6 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2)
| sk_c5 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) ),
inference(reorient_equations,[],[f38]) ).
fof(f41,definition,
( spl0_1
<=> ! [X3] :
( sk_c5 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f42,plain,
( ! [X3] :
( sk_c5 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f44,definition,
( spl0_2
<=> ! [X2] :
( sk_c6 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f45,plain,
( ! [X2] :
( sk_c6 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f47,definition,
( spl0_3
<=> ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f48,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,definition,
( spl0_4
<=> ! [X0] :
( sk_c7 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f51,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f53,definition,
( spl0_5
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f54,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f56,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f39,f53,f50,f47,f44,f41]) ).
fof(f58,definition,
( spl0_6
<=> sk_c6 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f60,plain,
( sk_c6 = inverse(sk_c4)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f62,definition,
( spl0_7
<=> sk_c6 = multiply(sk_c2,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f63,plain,
( sk_c6 != multiply(sk_c2,sk_c5)
| spl0_7 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f64,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f65,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f37,f62,f58]) ).
fof(f67,definition,
( spl0_8
<=> sk_c5 = multiply(sk_c4,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f69,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f70,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f35,f62,f67]) ).
fof(f72,definition,
( spl0_9
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f74,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f75,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f33,f62,f72]) ).
fof(f77,definition,
( spl0_10
<=> sk_c6 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f79,plain,
( sk_c6 = multiply(sk_c3,sk_c7)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f80,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f31,f62,f77]) ).
fof(f82,definition,
( spl0_11
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f84,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,plain,
( spl0_6
| spl0_11 ),
inference(avatar_split_clause,[],[f29,f82,f58]) ).
fof(f86,plain,
( spl0_8
| spl0_11 ),
inference(avatar_split_clause,[],[f27,f82,f67]) ).
fof(f87,plain,
( spl0_9
| spl0_11 ),
inference(avatar_split_clause,[],[f25,f82,f72]) ).
fof(f88,plain,
( spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f23,f82,f77]) ).
fof(f90,definition,
( spl0_12
<=> sk_c6 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f92,plain,
( sk_c6 = inverse(sk_c1)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f21,f90,f58]) ).
fof(f94,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f19,f90,f67]) ).
fof(f95,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f17,f90,f72]) ).
fof(f96,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f15,f90,f77]) ).
fof(f98,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c1,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f100,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,plain,
( spl0_6
| spl0_13 ),
inference(avatar_split_clause,[],[f13,f98,f58]) ).
fof(f102,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f11,f98,f67]) ).
fof(f103,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f9,f98,f72]) ).
fof(f104,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f7,f98,f77]) ).
fof(f105,plain,
spl0_5,
inference(avatar_split_clause,[],[f5,f53]) ).
fof(f111,plain,
( sk_c6 = multiply(sk_c2,multiply(sk_c6,sk_c7))
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f64,f54]) ).
fof(f112,plain,
( sk_c6 != sk_c7
| sk_c7 != inverse(identity)
| ~ spl0_2 ),
inference(superposition,[],[f45,f1]) ).
fof(f114,definition,
( spl0_14
<=> sk_c7 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f115,plain,
( sk_c7 = inverse(identity)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f116,plain,
( sk_c7 != inverse(identity)
| spl0_14 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f118,definition,
( spl0_15
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f119,plain,
( sk_c6 = sk_c7
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f120,plain,
( sk_c6 != sk_c7
| spl0_15 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,plain,
( ~ spl0_14
| ~ spl0_15
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f112,f44,f118,f114]) ).
fof(f124,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_11 ),
inference(superposition,[],[f3,f84]) ).
fof(f125,plain,
( identity = multiply(sk_c6,sk_c1)
| ~ spl0_12 ),
inference(superposition,[],[f3,f92]) ).
fof(f126,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[],[f1,f3]) ).
fof(f127,plain,
( identity != sk_c6
| sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_2 ),
inference(superposition,[],[f45,f3]) ).
fof(f129,definition,
( spl0_16
<=> sk_c7 = inverse(inverse(sk_c7)) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f131,plain,
( sk_c7 != inverse(inverse(sk_c7))
| spl0_16 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f133,definition,
( spl0_17
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f134,plain,
( identity = sk_c6
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f135,plain,
( identity != sk_c6
| spl0_17 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,plain,
( ~ spl0_16
| ~ spl0_17
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f127,f44,f133,f129]) ).
fof(f137,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f126,f4]) ).
fof(f145,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c2,multiply(multiply(sk_c6,sk_c7),X0))
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f4,f111]) ).
fof(f147,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c2,multiply(sk_c6,multiply(sk_c7,X0)))
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f145,f4]) ).
fof(f153,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c2,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f124]) ).
fof(f154,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c2,X0)) = X0
| ~ spl0_11 ),
inference(forward_demodulation,[],[f153,f1]) ).
fof(f155,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c1,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f125]) ).
fof(f156,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c1,X0)) = X0
| ~ spl0_12 ),
inference(forward_demodulation,[],[f155,f1]) ).
fof(f172,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c6,sk_c6)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11 ),
inference(superposition,[],[f154,f111]) ).
fof(f181,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f156,f100]) ).
fof(f265,plain,
! [X0] : multiply(inverse(identity),X0) = X0,
inference(superposition,[],[f137,f1]) ).
fof(f267,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f137,f3]) ).
fof(f268,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f137,f137]) ).
fof(f272,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f137,f181]) ).
fof(f275,plain,
( sk_c2 = multiply(inverse(sk_c6),identity)
| ~ spl0_11 ),
inference(superposition,[],[f137,f124]) ).
fof(f293,plain,
( identity = sk_c7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f272,f3]) ).
fof(f297,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f267,f268]) ).
fof(f310,plain,
( identity != inverse(identity)
| ~ spl0_12
| ~ spl0_13
| spl0_14 ),
inference(superposition,[],[f116,f293]) ).
fof(f315,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c2,multiply(sk_c6,multiply(identity,X0)))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f147,f293]) ).
fof(f318,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c2,multiply(sk_c6,X0))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f315,f1]) ).
fof(f324,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(multiply(inverse(sk_c6),identity),multiply(sk_c6,X0))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f318,f275]) ).
fof(f325,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(inverse(sk_c6),multiply(identity,multiply(sk_c6,X0)))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f324,f4]) ).
fof(f431,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(inverse(sk_c6),multiply(sk_c6,X0))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f325,f1]) ).
fof(f445,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f431,f137]) ).
fof(f465,plain,
( sk_c6 = multiply(multiply(inverse(sk_c6),identity),multiply(sk_c6,sk_c7))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11 ),
inference(superposition,[],[f111,f275]) ).
fof(f466,plain,
( sk_c6 = inverse(multiply(inverse(sk_c6),identity))
| ~ spl0_11 ),
inference(superposition,[],[f84,f275]) ).
fof(f468,plain,
( sk_c6 = multiply(inverse(sk_c6),multiply(identity,multiply(sk_c6,sk_c7)))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11 ),
inference(forward_demodulation,[],[f465,f4]) ).
fof(f532,plain,
( sk_c6 = inverse(inverse(sk_c6))
| ~ spl0_11 ),
inference(forward_demodulation,[],[f466,f297]) ).
fof(f533,plain,
( sk_c6 = multiply(inverse(sk_c6),multiply(sk_c6,sk_c7))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11 ),
inference(forward_demodulation,[],[f468,f1]) ).
fof(f537,plain,
( sk_c6 = sk_c7
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11 ),
inference(forward_demodulation,[],[f533,f137]) ).
fof(f544,plain,
( identity = sk_c6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f119,f293]) ).
fof(f547,plain,
( identity = sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f537,f293]) ).
fof(f548,plain,
( $false
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f544,f135]) ).
fof(f549,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| spl0_17 ),
inference(avatar_contradiction_clause,[],[f548]) ).
fof(f550,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f547,f135]) ).
fof(f551,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_17 ),
inference(avatar_contradiction_clause,[],[f550]) ).
fof(f558,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_11
| ~ spl0_17 ),
inference(superposition,[],[f124,f134]) ).
fof(f559,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_12
| ~ spl0_17 ),
inference(superposition,[],[f125,f134]) ).
fof(f571,plain,
( identity = sk_c1
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f559,f1]) ).
fof(f572,plain,
( identity = sk_c2
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f558,f1]) ).
fof(f596,plain,
( sk_c6 = inverse(identity)
| ~ spl0_12
| ~ spl0_17 ),
inference(superposition,[],[f92,f571]) ).
fof(f605,plain,
( identity = inverse(identity)
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f596,f134]) ).
fof(f608,plain,
( $false
| ~ spl0_12
| ~ spl0_13
| spl0_14
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f605,f310]) ).
fof(f609,plain,
( ~ spl0_12
| ~ spl0_13
| spl0_14
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f608]) ).
fof(f611,plain,
( ! [X0] :
( sk_c7 != multiply(X0,identity)
| inverse(X0) != sk_c6 )
| ~ spl0_4
| ~ spl0_17 ),
inference(forward_demodulation,[],[f51,f134]) ).
fof(f615,plain,
( ! [X0] :
( sk_c7 != X0
| inverse(X0) != sk_c6 )
| ~ spl0_4
| ~ spl0_17 ),
inference(forward_demodulation,[],[f611,f297]) ).
fof(f618,plain,
( ! [X0] :
( identity != X0
| inverse(X0) != sk_c6 )
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f615,f293]) ).
fof(f619,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f618,f134]) ).
fof(f622,plain,
( identity != sk_c6
| identity != sk_c1
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(superposition,[],[f619,f92]) ).
fof(f625,plain,
( identity != sk_c1
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f622,f134]) ).
fof(f628,plain,
( $false
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f625,f571]) ).
fof(f629,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f628]) ).
fof(f642,plain,
( identity = multiply(inverse(sk_c6),identity)
| ~ spl0_11
| ~ spl0_17 ),
inference(superposition,[],[f275,f572]) ).
fof(f656,plain,
( ! [X3] :
( sk_c5 != multiply(X3,identity)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_17 ),
inference(forward_demodulation,[],[f42,f134]) ).
fof(f657,plain,
( ! [X3] :
( sk_c5 != X3
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_17 ),
inference(forward_demodulation,[],[f656,f297]) ).
fof(f658,plain,
( ! [X3] :
( multiply(sk_c6,sk_c7) != X3
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f657,f54]) ).
fof(f659,plain,
( ! [X3] :
( multiply(sk_c6,sk_c6) != X3
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f658,f172]) ).
fof(f660,plain,
( ! [X3] :
( sk_c6 != X3
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f659,f445]) ).
fof(f661,plain,
( ! [X3] :
( identity != X3
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f660,f134]) ).
fof(f662,plain,
( ! [X3] :
( identity != inverse(X3)
| identity != X3 )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f661,f134]) ).
fof(f664,plain,
( identity != sk_c6
| identity != sk_c1
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(superposition,[],[f662,f92]) ).
fof(f667,plain,
( identity != sk_c1
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f664,f134]) ).
fof(f670,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f667,f571]) ).
fof(f671,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f670]) ).
fof(f674,plain,
( identity = inverse(sk_c4)
| ~ spl0_6
| ~ spl0_17 ),
inference(forward_demodulation,[],[f60,f134]) ).
fof(f675,plain,
( sk_c6 != multiply(sk_c2,multiply(sk_c6,sk_c7))
| ~ spl0_5
| spl0_7 ),
inference(forward_demodulation,[],[f63,f54]) ).
fof(f689,plain,
( identity = inverse(sk_c6)
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f642,f297]) ).
fof(f706,plain,
( identity = inverse(identity)
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f689,f134]) ).
fof(f727,plain,
( ! [X1] :
( sk_c6 != multiply(X1,multiply(sk_c6,sk_c7))
| sk_c6 != inverse(X1) )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f48,f54]) ).
fof(f728,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c4,sk_c6)
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_demodulation,[],[f69,f54]) ).
fof(f738,plain,
( identity = multiply(sk_c6,sk_c4)
| ~ spl0_6 ),
inference(superposition,[],[f3,f60]) ).
fof(f759,plain,
( inverse(sk_c3) = inverse(identity)
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_demodulation,[],[f74,f115]) ).
fof(f760,plain,
( sk_c6 = multiply(sk_c3,inverse(identity))
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f79,f115]) ).
fof(f763,plain,
( sk_c6 != inverse(identity)
| ~ spl0_14
| spl0_15 ),
inference(forward_demodulation,[],[f120,f115]) ).
fof(f790,plain,
( inverse(identity) = multiply(inverse(sk_c3),sk_c6)
| ~ spl0_10
| ~ spl0_14 ),
inference(superposition,[],[f137,f760]) ).
fof(f793,plain,
( inverse(identity) = multiply(inverse(identity),sk_c6)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f790,f759]) ).
fof(f797,plain,
( sk_c6 = inverse(identity)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f793,f265]) ).
fof(f802,plain,
( $false
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14
| spl0_15 ),
inference(forward_subsumption_resolution,[],[f797,f763]) ).
fof(f803,plain,
( ~ spl0_9
| ~ spl0_10
| ~ spl0_14
| spl0_15 ),
inference(avatar_contradiction_clause,[],[f802]) ).
fof(f811,plain,
( sk_c6 != multiply(multiply(inverse(sk_c6),identity),multiply(sk_c6,sk_c7))
| ~ spl0_5
| spl0_7
| ~ spl0_11 ),
inference(forward_demodulation,[],[f675,f275]) ).
fof(f813,plain,
( sk_c6 != multiply(inverse(sk_c6),multiply(identity,multiply(sk_c6,sk_c7)))
| ~ spl0_5
| spl0_7
| ~ spl0_11 ),
inference(forward_demodulation,[],[f811,f4]) ).
fof(f815,plain,
( sk_c6 != multiply(inverse(sk_c6),multiply(sk_c6,sk_c7))
| ~ spl0_5
| spl0_7
| ~ spl0_11 ),
inference(forward_demodulation,[],[f813,f1]) ).
fof(f817,plain,
( sk_c6 != sk_c7
| ~ spl0_5
| spl0_7
| ~ spl0_11 ),
inference(forward_demodulation,[],[f815,f137]) ).
fof(f818,plain,
( $false
| ~ spl0_5
| spl0_7
| ~ spl0_11
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f817,f119]) ).
fof(f819,plain,
( ~ spl0_5
| spl0_7
| ~ spl0_11
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f818]) ).
fof(f823,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_9 ),
inference(superposition,[],[f3,f74]) ).
fof(f832,plain,
( sk_c4 = multiply(inverse(sk_c6),identity)
| ~ spl0_6 ),
inference(superposition,[],[f137,f738]) ).
fof(f835,plain,
( sk_c4 = inverse(sk_c6)
| ~ spl0_6 ),
inference(forward_demodulation,[],[f832,f297]) ).
fof(f840,plain,
( sk_c6 != sk_c7
| sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f727,f137]) ).
fof(f860,plain,
( identity = multiply(sk_c6,inverse(sk_c6))
| ~ spl0_6 ),
inference(superposition,[],[f738,f835]) ).
fof(f861,plain,
( multiply(sk_c6,sk_c7) = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f728,f835]) ).
fof(f863,plain,
( identity = multiply(sk_c6,sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f861,f3]) ).
fof(f864,plain,
( sk_c3 = multiply(inverse(sk_c7),identity)
| ~ spl0_9 ),
inference(superposition,[],[f137,f823]) ).
fof(f867,plain,
( sk_c3 = inverse(sk_c7)
| ~ spl0_9 ),
inference(forward_demodulation,[],[f864,f297]) ).
fof(f869,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f79,f867]) ).
fof(f870,plain,
( sk_c7 = inverse(inverse(sk_c7))
| ~ spl0_9 ),
inference(superposition,[],[f74,f867]) ).
fof(f871,plain,
( $false
| ~ spl0_9
| spl0_16 ),
inference(forward_subsumption_resolution,[],[f870,f131]) ).
fof(f872,plain,
( ~ spl0_9
| spl0_16 ),
inference(avatar_contradiction_clause,[],[f871]) ).
fof(f873,plain,
( identity = sk_c6
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f869,f3]) ).
fof(f874,plain,
( $false
| ~ spl0_9
| ~ spl0_10
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f873,f135]) ).
fof(f875,plain,
( ~ spl0_9
| ~ spl0_10
| spl0_17 ),
inference(avatar_contradiction_clause,[],[f874]) ).
fof(f877,plain,
( spl0_15
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f537,f82,f62,f53,f118]) ).
fof(f887,plain,
( identity = inverse(inverse(sk_c6))
| ~ spl0_6
| ~ spl0_17 ),
inference(forward_demodulation,[],[f674,f835]) ).
fof(f890,plain,
( sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f840,f119]) ).
fof(f896,plain,
( identity = inverse(inverse(identity))
| ~ spl0_6
| ~ spl0_17 ),
inference(forward_demodulation,[],[f887,f134]) ).
fof(f898,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_11
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f890,f532]) ).
fof(f899,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_11
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f898]) ).
fof(f914,plain,
( ! [X3] :
( identity != X3
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_17 ),
inference(forward_demodulation,[],[f658,f863]) ).
fof(f920,plain,
( ! [X3] :
( identity != inverse(X3)
| identity != X3 )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_17 ),
inference(forward_demodulation,[],[f914,f134]) ).
fof(f937,plain,
( identity != sk_c6
| identity != sk_c4
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_17 ),
inference(superposition,[],[f920,f60]) ).
fof(f940,plain,
( identity != sk_c4
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f937,f134]) ).
fof(f944,plain,
( identity != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_17 ),
inference(forward_demodulation,[],[f940,f835]) ).
fof(f947,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_17 ),
inference(forward_demodulation,[],[f944,f134]) ).
fof(f951,plain,
( ! [X0] :
( sk_c6 != X0
| inverse(X0) != sk_c6 )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f615,f119]) ).
fof(f953,plain,
( ! [X0] :
( identity != X0
| inverse(X0) != sk_c6 )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f951,f134]) ).
fof(f955,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f953,f134]) ).
fof(f962,plain,
( multiply(identity,sk_c7) = multiply(sk_c4,identity)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_17 ),
inference(superposition,[],[f728,f134]) ).
fof(f963,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_6
| ~ spl0_17 ),
inference(superposition,[],[f738,f134]) ).
fof(f964,plain,
( identity = sk_c4
| ~ spl0_6
| ~ spl0_17 ),
inference(forward_demodulation,[],[f963,f1]) ).
fof(f965,plain,
( sk_c4 = multiply(identity,sk_c7)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_17 ),
inference(forward_demodulation,[],[f962,f297]) ).
fof(f970,plain,
( sk_c7 = sk_c4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_17 ),
inference(forward_demodulation,[],[f965,f1]) ).
fof(f974,plain,
( sk_c7 = inverse(sk_c6)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_17 ),
inference(forward_demodulation,[],[f970,f835]) ).
fof(f977,plain,
( sk_c7 = inverse(identity)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_17 ),
inference(forward_demodulation,[],[f974,f134]) ).
fof(f984,plain,
( identity != sk_c6
| identity != sk_c4
| ~ spl0_4
| ~ spl0_6
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[],[f955,f60]) ).
fof(f985,plain,
( identity != sk_c6
| identity != sk_c2
| ~ spl0_4
| ~ spl0_11
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[],[f955,f84]) ).
fof(f986,plain,
( identity != sk_c2
| ~ spl0_4
| ~ spl0_11
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f985,f134]) ).
fof(f987,plain,
( identity != sk_c4
| ~ spl0_4
| ~ spl0_6
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f984,f134]) ).
fof(f989,plain,
( $false
| ~ spl0_4
| ~ spl0_11
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f986,f572]) ).
fof(f990,plain,
( ~ spl0_4
| ~ spl0_11
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f989]) ).
fof(f991,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f987,f964]) ).
fof(f992,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f991]) ).
fof(f995,plain,
( sk_c6 != multiply(sk_c2,multiply(sk_c6,sk_c7))
| ~ spl0_5
| spl0_7 ),
inference(forward_demodulation,[],[f63,f54]) ).
fof(f1001,plain,
( sk_c6 != multiply(sk_c2,identity)
| ~ spl0_5
| ~ spl0_6
| spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f995,f863]) ).
fof(f1010,plain,
( sk_c6 != sk_c2
| ~ spl0_5
| ~ spl0_6
| spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f1001,f297]) ).
fof(f1011,plain,
( sk_c6 != multiply(inverse(sk_c6),identity)
| ~ spl0_5
| ~ spl0_6
| spl0_7
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1010,f275]) ).
fof(f1012,plain,
( sk_c6 != inverse(sk_c6)
| ~ spl0_5
| ~ spl0_6
| spl0_7
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1011,f297]) ).
fof(f1013,plain,
( identity != inverse(identity)
| ~ spl0_5
| ~ spl0_6
| spl0_7
| ~ spl0_8
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1012,f134]) ).
fof(f1014,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| spl0_7
| ~ spl0_8
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1013,f706]) ).
fof(f1015,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_7
| ~ spl0_8
| ~ spl0_11
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f1014]) ).
fof(f1021,plain,
( identity != sk_c7
| sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f840,f134]) ).
fof(f1024,plain,
( identity = sk_c7
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f119,f134]) ).
fof(f1029,plain,
( identity = multiply(identity,inverse(identity))
| ~ spl0_6
| ~ spl0_17 ),
inference(forward_demodulation,[],[f860,f134]) ).
fof(f1031,plain,
( spl0_14
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f977,f133,f67,f58,f53,f114]) ).
fof(f1038,plain,
( identity != inverse(inverse(identity))
| identity != sk_c7
| ~ spl0_3
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1021,f134]) ).
fof(f1041,plain,
( identity = inverse(identity)
| ~ spl0_6
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1029,f1]) ).
fof(f1047,plain,
( identity != sk_c7
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1038,f896]) ).
fof(f1056,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1047,f1024]) ).
fof(f1057,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f1056]) ).
fof(f1072,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1041,f947]) ).
fof(f1073,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f1072]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f56]) ).
cnf(s2,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f65]) ).
cnf(s3,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f70]) ).
cnf(s4,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f75]) ).
cnf(s5,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f80]) ).
cnf(s6,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f85]) ).
cnf(s7,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f86]) ).
cnf(s8,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f87]) ).
cnf(s9,plain,
( spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f88]) ).
cnf(s10,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f93]) ).
cnf(s11,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f94]) ).
cnf(s12,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f95]) ).
cnf(s13,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f96]) ).
cnf(s14,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f101]) ).
cnf(s15,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f102]) ).
cnf(s16,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f103]) ).
cnf(s17,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f104]) ).
cnf(s18,plain,
spl0_5,
inference(sat_conversion,[],[f105]) ).
cnf(s20,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f121]) ).
cnf(s21,plain,
( ~ spl0_2
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f136]) ).
cnf(s32,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f549]) ).
cnf(s33,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f551]) ).
cnf(s34,plain,
( ~ spl0_12
| ~ spl0_13
| spl0_14
| ~ spl0_17 ),
inference(sat_conversion,[],[f609]) ).
cnf(s38,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(sat_conversion,[],[f629]) ).
cnf(s42,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(sat_conversion,[],[f671]) ).
cnf(s49,plain,
( ~ spl0_9
| ~ spl0_10
| ~ spl0_14
| spl0_15 ),
inference(sat_conversion,[],[f803]) ).
cnf(s53,plain,
( ~ spl0_5
| spl0_7
| ~ spl0_11
| ~ spl0_15 ),
inference(sat_conversion,[],[f819]) ).
cnf(s57,plain,
( ~ spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f872]) ).
cnf(s58,plain,
( ~ spl0_9
| ~ spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f875]) ).
cnf(s59,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f877]) ).
cnf(s61,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_11
| ~ spl0_15 ),
inference(sat_conversion,[],[f899]) ).
cnf(s65,plain,
( ~ spl0_4
| ~ spl0_11
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f990]) ).
cnf(s66,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f992]) ).
cnf(s71,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_7
| ~ spl0_8
| ~ spl0_11
| ~ spl0_17 ),
inference(sat_conversion,[],[f1015]) ).
cnf(s72,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| spl0_14
| ~ spl0_17 ),
inference(sat_conversion,[],[f1031]) ).
cnf(s76,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f1057]) ).
cnf(s77,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_17 ),
inference(sat_conversion,[],[f1073]) ).
cnf(s85,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(rat,[],[s1,s18]) ).
cnf(s86,plain,
( spl0_6
| ~ spl0_4 ),
inference(rat,[],[s33,s38,s2,s6,s10,s14,s18]) ).
cnf(s87,plain,
( spl0_13
| spl0_17 ),
inference(rat,[],[s58,s16,s17]) ).
cnf(s88,plain,
( ~ spl0_13
| spl0_17
| ~ spl0_15 ),
inference(rat,[],[s58,s12,s13,s32]) ).
cnf(s89,plain,
( ~ spl0_15
| ~ spl0_11
| ~ spl0_4 ),
inference(rat,[],[s88,s87,s65]) ).
cnf(s90,plain,
( ~ spl0_11
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s89,s59,s18]) ).
cnf(s91,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s49,s66,s72,s58,s7,s8,s9,s86,s18]) ).
cnf(s92,plain,
~ spl0_4,
inference(rat,[],[s71,s58,s3,s4,s5,s90,s91,s86,s18]) ).
cnf(s93,plain,
( ~ spl0_15
| ~ spl0_3 ),
inference(rat,[],[s76,s58,s6,s8,s9,s61,s18]) ).
cnf(s94,plain,
( ~ spl0_11
| spl0_15 ),
inference(rat,[],[s58,s71,s2,s3,s4,s5,s59,s18]) ).
cnf(s95,plain,
spl0_15,
inference(rat,[],[s72,s49,s58,s6,s7,s8,s9,s94,s18]) ).
cnf(s96,plain,
~ spl0_3,
inference(rat,[],[s93,s95]) ).
cnf(s97,plain,
spl0_17,
inference(rat,[],[s88,s87,s95]) ).
cnf(s98,plain,
~ spl0_2,
inference(rat,[],[s34,s12,s16,s57,s21,s20,s97,s95]) ).
cnf(s99,plain,
spl0_1,
inference(rat,[],[s85,s92,s96,s98]) ).
cnf(s100,plain,
( spl0_8
| ~ spl0_11 ),
inference(rat,[],[s42,s11,s15,s53,s18,s97,s99,s95]) ).
cnf(s101,plain,
~ spl0_11,
inference(rat,[],[s42,s10,s14,s77,s100,s53,s18,s97,s99,s95]) ).
cnf(s104,plain,
spl0_8,
inference(rat,[],[s7,s101]) ).
cnf(s105,plain,
spl0_6,
inference(rat,[],[s6,s101]) ).
cnf(s107,plain,
$false,
inference(rat,[],[s77,s99,s97,s18,s105,s104]) ).
fof(f1099,plain,
$false,
inference(avatar_sat_refutation,[],[s107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP333-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:54:24 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.47 % (991291)Will run a generic schedule for satisfiability detection.
% 0.10/0.47 % (991298)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3310226526:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.47 % (991297)% WARNING: option uhcvi not known.
% 0.10/0.47 % (991296)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2336918527_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.47 % (991297)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1144272577:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.47 % (991299)dis+10_1_sil=32000:sp=arity:random_seed=1503393576:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.47 % (991302)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3968741082:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.47 % (991300)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=915639259:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.47 % (991301)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2643468463:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.47 % TRYING [1]
% 0.10/0.47 % TRYING [2]
% 0.10/0.47 % TRYING [3]
% 0.10/0.47 % TRYING [4]
% 0.10/0.47 % TRYING [5]
% 0.10/0.47 % (991301) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-991291-991301"...
% 0.10/0.47 % (991299) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-991291-991299"...
% 0.10/0.47 % (991301)...printing done.
% 0.10/0.47 % (991300) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-991291-991300"...
% 0.10/0.47 % (991299)...printing done.
% 0.10/0.47 % (991301)Refutation found. Thanks to Tanya!
% 0.10/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.47 % (991301)------------------------------
% 0.10/0.47 % (991301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.47 % (991301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.47 % (991301)CaDiCaL version: 2.1.3
% 0.10/0.47 % (991301)Termination reason: Refutation
% 0.10/0.47 % (991301)Time elapsed: 0.021 s
% 0.10/0.47 % (991301)Peak memory usage: 12 MB
% 0.10/0.47 % (991301)Instructions burned: 33 (million)
% 0.10/0.47 % (991291)Success in time 0.055 s
% 0.10/0.47 % Vampire exiting
%------------------------------------------------------------------------------