%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP315-1 : 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 : n004.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 10:17:28 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 38
% Syntax : Number of formulae : 301 ( 26 unt; 17 def)
% Number of atoms : 1057 ( 258 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 1492 ( 736 ~; 739 |; 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 : 47 ( 0 sgn 47 !; 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_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c7) != sk_c5
| multiply(X0,sk_c7) != sk_c6
| inverse(X0) != sk_c7
| multiply(X1,sk_c6) != sk_c5
| inverse(X1) != sk_c6
| inverse(X2) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| inverse(X3) != sk_c6
| multiply(X3,sk_c5) != 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_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) ),
inference(reorient_equations,[],[f38]) ).
fof(f41,definition,
( spl0_1
<=> ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f42,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f44,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f45,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c6)
| sk_c7 != inverse(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f47,definition,
( spl0_3
<=> ! [X1] :
( sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f48,plain,
( ! [X1] :
( sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,definition,
( spl0_4
<=> ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f51,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ 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 = multiply(sk_c4,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f60,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f62,definition,
( spl0_7
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f64,plain,
( sk_c6 = inverse(sk_c2)
| ~ 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_c6 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f69,plain,
( sk_c6 = inverse(sk_c4)
| ~ 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 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f74,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ 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_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f79,plain,
( sk_c7 = inverse(sk_c3)
| ~ 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_c5 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f84,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| ~ 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_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f92,plain,
( sk_c7 = 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_c6 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f100,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| ~ 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(f106,plain,
( sk_c7 != sk_c7
| sk_c7 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_9 ),
inference(superposition,[],[f45,f74]) ).
fof(f107,plain,
( sk_c7 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f106]) ).
fof(f108,plain,
( $false
| ~ spl0_2
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f107,f79]) ).
fof(f109,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f108]) ).
fof(f113,definition,
( spl0_14
<=> sk_c7 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f114,plain,
( sk_c7 = sk_c5
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f115,plain,
( sk_c7 != sk_c5
| spl0_14 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f117,definition,
( spl0_15
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f118,plain,
( sk_c6 = sk_c7
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f119,plain,
( sk_c6 != sk_c7
| spl0_15 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f121,plain,
( sk_c6 != sk_c7
| sk_c7 != inverse(identity)
| ~ spl0_2 ),
inference(superposition,[],[f45,f1]) ).
fof(f123,definition,
( spl0_16
<=> sk_c7 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f124,plain,
( sk_c7 = inverse(identity)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f125,plain,
( sk_c7 != inverse(identity)
| spl0_16 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f126,plain,
( ~ spl0_16
| ~ spl0_15
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f121,f44,f117,f123]) ).
fof(f127,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_12 ),
inference(superposition,[],[f3,f92]) ).
fof(f137,definition,
( spl0_18
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f138,plain,
( identity = sk_c7
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f139,plain,
( identity != sk_c7
| spl0_18 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f143,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f144,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(sk_c5,X0)
| ~ spl0_5 ),
inference(superposition,[],[f4,f54]) ).
fof(f145,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c7,X0)) = multiply(sk_c6,X0)
| ~ spl0_13 ),
inference(superposition,[],[f4,f100]) ).
fof(f149,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f143,f1]) ).
fof(f152,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c1,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f127]) ).
fof(f153,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c1,X0)) = X0
| ~ spl0_12 ),
inference(forward_demodulation,[],[f152,f1]) ).
fof(f165,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f153,f100]) ).
fof(f176,plain,
( multiply(sk_c1,sk_c7) = multiply(sk_c6,sk_c6)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f145,f165]) ).
fof(f177,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c5,sk_c6)
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f144,f165]) ).
fof(f181,plain,
( sk_c5 = multiply(sk_c5,sk_c6)
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f177,f54]) ).
fof(f182,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f176,f100]) ).
fof(f227,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f149,f3]) ).
fof(f228,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f149,f149]) ).
fof(f230,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_5 ),
inference(superposition,[],[f149,f54]) ).
fof(f237,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f149,f181]) ).
fof(f240,plain,
( sk_c5 = multiply(inverse(sk_c4),sk_c6)
| ~ spl0_6 ),
inference(superposition,[],[f149,f60]) ).
fof(f242,plain,
( sk_c6 = multiply(inverse(sk_c2),sk_c5)
| ~ spl0_11 ),
inference(superposition,[],[f149,f84]) ).
fof(f248,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_7
| ~ spl0_11 ),
inference(forward_demodulation,[],[f242,f64]) ).
fof(f250,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f240,f69]) ).
fof(f253,plain,
( identity = sk_c6
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f237,f3]) ).
fof(f255,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f227,f228]) ).
fof(f256,plain,
( sk_c6 = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f250,f182]) ).
fof(f257,plain,
( ! [X0] : multiply(X0,sk_c6) = X0
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f255,f253]) ).
fof(f261,plain,
( sk_c6 = multiply(sk_c4,sk_c6)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f60,f256]) ).
fof(f262,plain,
( sk_c6 = sk_c4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f261,f257]) ).
fof(f265,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_7
| ~ spl0_11 ),
inference(superposition,[],[f149,f248]) ).
fof(f267,plain,
( identity = sk_c5
| ~ spl0_7
| ~ spl0_11 ),
inference(forward_demodulation,[],[f265,f3]) ).
fof(f287,plain,
( identity = inverse(sk_c6)
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f3,f257]) ).
fof(f294,plain,
( sk_c5 = sk_c2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f84,f257]) ).
fof(f309,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f230,f256]) ).
fof(f313,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f309,f3]) ).
fof(f318,plain,
( sk_c6 = sk_c7
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f313,f253]) ).
fof(f322,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| spl0_15 ),
inference(forward_subsumption_resolution,[],[f318,f119]) ).
fof(f323,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| spl0_15 ),
inference(avatar_contradiction_clause,[],[f322]) ).
fof(f328,plain,
( sk_c6 = sk_c5
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f267,f253]) ).
fof(f329,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f287,f253]) ).
fof(f340,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f230,f328]) ).
fof(f342,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f340,f3]) ).
fof(f344,plain,
( sk_c6 = sk_c7
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f342,f253]) ).
fof(f345,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_15 ),
inference(forward_subsumption_resolution,[],[f344,f119]) ).
fof(f346,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_15 ),
inference(avatar_contradiction_clause,[],[f345]) ).
fof(f347,plain,
( sk_c7 != inverse(sk_c6)
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| spl0_16 ),
inference(forward_demodulation,[],[f125,f253]) ).
fof(f360,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c6)
| inverse(X0) != sk_c7 )
| ~ spl0_4
| ~ spl0_15 ),
inference(forward_demodulation,[],[f51,f118]) ).
fof(f362,plain,
( identity = sk_c6
| ~ spl0_15
| ~ spl0_18 ),
inference(forward_demodulation,[],[f138,f118]) ).
fof(f363,plain,
( ! [X0] :
( sk_c6 != X0
| inverse(X0) != sk_c7 )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f360,f257]) ).
fof(f364,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c6 != X0 )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f363,f118]) ).
fof(f365,plain,
( sk_c6 != sk_c7
| sk_c6 != sk_c1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(superposition,[],[f364,f92]) ).
fof(f367,plain,
( sk_c6 != sk_c6
| sk_c6 != sk_c2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(superposition,[],[f364,f64]) ).
fof(f368,plain,
( sk_c6 != sk_c2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f367]) ).
fof(f370,plain,
( sk_c6 != sk_c5
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f368,f294]) ).
fof(f371,plain,
( sk_c6 != sk_c1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f365,f118]) ).
fof(f372,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f370,f328]) ).
fof(f373,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f372]) ).
fof(f374,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f42,f328]) ).
fof(f375,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != X3 )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f374,f257]) ).
fof(f377,plain,
( sk_c6 = multiply(sk_c1,sk_c6)
| ~ spl0_13
| ~ spl0_15 ),
inference(superposition,[],[f100,f118]) ).
fof(f386,plain,
( sk_c6 = sk_c1
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f377,f257]) ).
fof(f390,plain,
( sk_c6 != sk_c6
| sk_c6 != sk_c2
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f375,f64]) ).
fof(f391,plain,
( sk_c6 != sk_c2
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f390]) ).
fof(f393,plain,
( sk_c6 != sk_c5
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f391,f294]) ).
fof(f395,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f393,f328]) ).
fof(f396,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f395]) ).
fof(f399,plain,
( ! [X1] :
( sk_c5 != X1
| sk_c6 != inverse(X1) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f48,f257]) ).
fof(f400,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != X1 )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f399,f328]) ).
fof(f414,plain,
( sk_c6 != sk_c7
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| spl0_16 ),
inference(forward_demodulation,[],[f347,f329]) ).
fof(f416,plain,
( $false
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| spl0_16 ),
inference(forward_subsumption_resolution,[],[f414,f118]) ).
fof(f417,plain,
( ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| spl0_16 ),
inference(avatar_contradiction_clause,[],[f416]) ).
fof(f422,plain,
( sk_c6 != sk_c6
| sk_c6 != sk_c2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f400,f64]) ).
fof(f423,plain,
( sk_c6 != sk_c2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f422]) ).
fof(f425,plain,
( sk_c6 != sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f423,f294]) ).
fof(f427,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f425,f328]) ).
fof(f428,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f427]) ).
fof(f435,plain,
( sk_c6 = inverse(sk_c3)
| ~ spl0_10
| ~ spl0_15 ),
inference(forward_demodulation,[],[f79,f118]) ).
fof(f439,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != X1 )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f399,f256]) ).
fof(f449,plain,
( identity = multiply(sk_c6,sk_c3)
| ~ spl0_10
| ~ spl0_15 ),
inference(superposition,[],[f3,f435]) ).
fof(f470,plain,
( sk_c6 != sk_c6
| sk_c6 != sk_c4
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f439,f69]) ).
fof(f473,plain,
( sk_c6 != sk_c4
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f470]) ).
fof(f475,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f473,f262]) ).
fof(f476,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f475]) ).
fof(f486,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f371,f386]) ).
fof(f487,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f486]) ).
fof(f531,plain,
( sk_c7 = inverse(sk_c6)
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f124,f362]) ).
fof(f532,plain,
( sk_c6 = multiply(sk_c3,sk_c6)
| ~ spl0_9
| ~ spl0_15 ),
inference(forward_demodulation,[],[f74,f118]) ).
fof(f533,plain,
( sk_c6 = sk_c5
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f114,f118]) ).
fof(f534,plain,
( sk_c6 = multiply(sk_c6,sk_c3)
| ~ spl0_10
| ~ spl0_15
| ~ spl0_18 ),
inference(forward_demodulation,[],[f449,f362]) ).
fof(f537,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f531,f118]) ).
fof(f538,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_15
| ~ spl0_18 ),
inference(superposition,[],[f1,f362]) ).
fof(f547,plain,
( sk_c7 = multiply(sk_c6,sk_c5)
| ~ spl0_5
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(superposition,[],[f230,f537]) ).
fof(f552,plain,
( sk_c7 = sk_c5
| ~ spl0_5
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f547,f538]) ).
fof(f555,plain,
( sk_c6 != sk_c5
| sk_c6 != inverse(identity)
| ~ spl0_3 ),
inference(superposition,[],[f48,f1]) ).
fof(f562,plain,
( sk_c6 != inverse(identity)
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f555,f533]) ).
fof(f566,plain,
( sk_c6 != inverse(sk_c6)
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18 ),
inference(forward_demodulation,[],[f562,f362]) ).
fof(f569,plain,
( $false
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f566,f537]) ).
fof(f570,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f569]) ).
fof(f571,plain,
( sk_c6 != sk_c5
| spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f115,f118]) ).
fof(f573,plain,
( sk_c6 = sk_c5
| ~ spl0_5
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f552,f118]) ).
fof(f579,plain,
( $false
| ~ spl0_5
| spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f573,f571]) ).
fof(f580,plain,
( ~ spl0_5
| spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f579]) ).
fof(f581,plain,
( sk_c7 != inverse(sk_c6)
| ~ spl0_15
| spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f125,f362]) ).
fof(f582,plain,
( sk_c6 != inverse(sk_c6)
| ~ spl0_15
| spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f581,f118]) ).
fof(f583,plain,
( sk_c3 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_10
| ~ spl0_15
| ~ spl0_18 ),
inference(superposition,[],[f149,f534]) ).
fof(f586,plain,
( identity = sk_c3
| ~ spl0_10
| ~ spl0_15
| ~ spl0_18 ),
inference(forward_demodulation,[],[f583,f3]) ).
fof(f587,plain,
( sk_c6 = sk_c3
| ~ spl0_10
| ~ spl0_15
| ~ spl0_18 ),
inference(forward_demodulation,[],[f586,f362]) ).
fof(f597,plain,
( sk_c3 = multiply(inverse(sk_c6),identity)
| ~ spl0_10
| ~ spl0_15 ),
inference(superposition,[],[f149,f449]) ).
fof(f600,plain,
( sk_c3 = inverse(sk_c6)
| ~ spl0_10
| ~ spl0_15 ),
inference(forward_demodulation,[],[f597,f255]) ).
fof(f611,plain,
( sk_c6 != sk_c3
| ~ spl0_10
| ~ spl0_15
| spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f582,f600]) ).
fof(f614,plain,
( $false
| ~ spl0_10
| ~ spl0_15
| spl0_16
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f611,f587]) ).
fof(f615,plain,
( ~ spl0_10
| ~ spl0_15
| spl0_16
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f614]) ).
fof(f619,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 )
| ~ spl0_4
| ~ spl0_15 ),
inference(forward_demodulation,[],[f360,f118]) ).
fof(f631,plain,
( sk_c6 != sk_c6
| sk_c6 != inverse(sk_c3)
| ~ spl0_4
| ~ spl0_9
| ~ spl0_15 ),
inference(superposition,[],[f619,f532]) ).
fof(f632,plain,
( sk_c6 != inverse(sk_c3)
| ~ spl0_4
| ~ spl0_9
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f631]) ).
fof(f634,plain,
( $false
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f632,f435]) ).
fof(f635,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f634]) ).
fof(f643,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f42,f533]) ).
fof(f645,plain,
( sk_c6 != sk_c6
| sk_c6 != inverse(identity)
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f643,f1]) ).
fof(f650,plain,
( sk_c6 != inverse(identity)
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f645]) ).
fof(f654,plain,
( sk_c6 != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18 ),
inference(forward_demodulation,[],[f650,f362]) ).
fof(f656,plain,
( $false
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f654,f537]) ).
fof(f657,plain,
( ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f656]) ).
fof(f666,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_18 ),
inference(superposition,[],[f1,f138]) ).
fof(f667,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_9 ),
inference(superposition,[],[f149,f74]) ).
fof(f670,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f667,f79]) ).
fof(f671,plain,
( sk_c6 = sk_c7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_18 ),
inference(forward_demodulation,[],[f670,f666]) ).
fof(f672,plain,
( $false
| ~ spl0_9
| ~ spl0_10
| spl0_15
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f671,f119]) ).
fof(f673,plain,
( ~ spl0_9
| ~ spl0_10
| spl0_15
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f672]) ).
fof(f788,plain,
( multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f144,f670]) ).
fof(f796,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f788,f250]) ).
fof(f830,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f149,f796]) ).
fof(f832,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f830,f3]) ).
fof(f839,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f832,f139]) ).
fof(f840,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_18 ),
inference(avatar_contradiction_clause,[],[f839]) ).
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(s19,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f109]) ).
cnf(s21,plain,
( ~ spl0_2
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f126]) ).
cnf(s26,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f323]) ).
cnf(s27,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f346]) ).
cnf(s30,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(sat_conversion,[],[f373]) ).
cnf(s31,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f396]) ).
cnf(s34,plain,
( ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| spl0_16 ),
inference(sat_conversion,[],[f417]) ).
cnf(s35,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f428]) ).
cnf(s37,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f476]) ).
cnf(s40,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(sat_conversion,[],[f487]) ).
cnf(s50,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f570]) ).
cnf(s52,plain,
( ~ spl0_5
| spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f580]) ).
cnf(s55,plain,
( ~ spl0_10
| ~ spl0_15
| spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f615]) ).
cnf(s57,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15 ),
inference(sat_conversion,[],[f635]) ).
cnf(s61,plain,
( ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f657]) ).
cnf(s63,plain,
( ~ spl0_9
| ~ spl0_10
| spl0_15
| ~ spl0_18 ),
inference(sat_conversion,[],[f673]) ).
cnf(s70,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f840]) ).
cnf(s71,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(rat,[],[s1,s18]) ).
cnf(s72,plain,
( spl0_6
| ~ spl0_4 ),
inference(rat,[],[s27,s40,s2,s6,s10,s14,s18]) ).
cnf(s73,plain,
( ~ spl0_13
| ~ spl0_12
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11 ),
inference(rat,[],[s27,s30,s18]) ).
cnf(s74,plain,
( spl0_13
| ~ spl0_4 ),
inference(rat,[],[s63,s57,s70,s15,s16,s17,s72,s18]) ).
cnf(s75,plain,
( spl0_12
| ~ spl0_4 ),
inference(rat,[],[s63,s57,s70,s11,s12,s13,s72,s18]) ).
cnf(s76,plain,
~ spl0_4,
inference(rat,[],[s73,s3,s7,s26,s40,s75,s74,s72,s18]) ).
cnf(s77,plain,
( ~ spl0_15
| ~ spl0_18
| ~ spl0_3
| ~ spl0_16 ),
inference(rat,[],[s52,s50,s18]) ).
cnf(s78,plain,
( spl0_13
| ~ spl0_3 ),
inference(rat,[],[s77,s55,s63,s70,s14,s15,s16,s17,s18]) ).
cnf(s79,plain,
( spl0_12
| ~ spl0_3 ),
inference(rat,[],[s77,s55,s63,s70,s10,s11,s12,s13,s18]) ).
cnf(s80,plain,
( spl0_11
| ~ spl0_3 ),
inference(rat,[],[s37,s6,s7,s78,s79,s18]) ).
cnf(s81,plain,
( ~ spl0_11
| ~ spl0_13
| ~ spl0_3
| ~ spl0_12 ),
inference(rat,[],[s37,s2,s3,s35,s18]) ).
cnf(s82,plain,
~ spl0_3,
inference(rat,[],[s81,s80,s79,s78]) ).
cnf(s83,plain,
( ~ spl0_13
| ~ spl0_12
| ~ spl0_11
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s21,s34,s27,s18]) ).
cnf(s84,plain,
( spl0_13
| ~ spl0_2 ),
inference(rat,[],[s19,s16,s17]) ).
cnf(s85,plain,
( spl0_12
| ~ spl0_2 ),
inference(rat,[],[s19,s12,s13]) ).
cnf(s86,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s19,s8,s9]) ).
cnf(s87,plain,
( ~ spl0_11
| ~ spl0_2
| ~ spl0_13
| ~ spl0_12 ),
inference(rat,[],[s19,s4,s5,s83]) ).
cnf(s88,plain,
~ spl0_2,
inference(rat,[],[s87,s86,s85,s84]) ).
cnf(s89,plain,
spl0_1,
inference(rat,[],[s71,s76,s82,s88]) ).
cnf(s90,plain,
( ~ spl0_15
| ~ spl0_18
| ~ spl0_16 ),
inference(rat,[],[s52,s61,s89,s18]) ).
cnf(s91,plain,
( ~ spl0_15
| ~ spl0_18
| ~ spl0_10 ),
inference(rat,[],[s90,s55]) ).
cnf(s92,plain,
( ~ spl0_18
| ~ spl0_10
| ~ spl0_9 ),
inference(rat,[],[s91,s63]) ).
cnf(s93,plain,
( ~ spl0_9
| ~ spl0_10
| ~ spl0_6
| ~ spl0_8 ),
inference(rat,[],[s92,s70,s18]) ).
cnf(s94,plain,
spl0_13,
inference(rat,[],[s93,s14,s15,s16,s17]) ).
cnf(s95,plain,
spl0_12,
inference(rat,[],[s93,s10,s11,s12,s13]) ).
cnf(s96,plain,
spl0_11,
inference(rat,[],[s93,s6,s7,s8,s9]) ).
cnf(s97,plain,
~ spl0_7,
inference(rat,[],[s31,s94,s95,s89,s18,s96]) ).
cnf(s98,plain,
spl0_10,
inference(rat,[],[s5,s97]) ).
cnf(s99,plain,
spl0_9,
inference(rat,[],[s4,s97]) ).
cnf(s100,plain,
spl0_8,
inference(rat,[],[s3,s97]) ).
cnf(s101,plain,
spl0_6,
inference(rat,[],[s2,s97]) ).
cnf(s104,plain,
$false,
inference(rat,[],[s93,s100,s101,s98,s99]) ).
fof(f841,plain,
$false,
inference(avatar_sat_refutation,[],[s104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP315-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n004.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 09:49:36 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.41 Running first-order model finding
% 0.13/0.41 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
% 0.18/0.47 % (3258907)Will run a generic schedule for satisfiability detection.
% 0.18/0.47 % (3258916)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=618908779:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.47 % (3258913)% WARNING: option uhcvi not known.
% 0.18/0.47 % (3258914)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3599006054:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.47 % (3258912)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1366448788_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.47 % (3258917)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2450242587:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.47 % (3258913)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2904919294:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.47 % (3258915)dis+10_1_sil=32000:sp=arity:random_seed=1139388331:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.47 % (3258918)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3475831275:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.47 % (3258916) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3258907-3258916"...
% 0.18/0.47 % TRYING [1]
% 0.18/0.47 % TRYING [2]
% 0.18/0.47 % TRYING [3]
% 0.18/0.47 % (3258916)...printing done.
% 0.18/0.47 % TRYING [4]
% 0.18/0.47 % (3258916)Refutation found. Thanks to Tanya!
% 0.18/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.48 % (3258916)------------------------------
% 0.18/0.48 % (3258916)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.48 % (3258916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.48 % (3258916)CaDiCaL version: 2.1.3
% 0.18/0.48 % (3258916)Termination reason: Refutation
% 0.18/0.48 % (3258916)Time elapsed: 0.011 s
% 0.18/0.48 % (3258916)Peak memory usage: 12 MB
% 0.18/0.48 % (3258916)Instructions burned: 28 (million)
% 0.18/0.48 % (3258907)Success in time 0.051 s
% 0.18/0.48 % Vampire exiting
%------------------------------------------------------------------------------