%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP305-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 10:17:26 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 40
% Syntax : Number of formulae : 292 ( 25 unt; 16 def)
% Number of atoms : 933 ( 262 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1206 ( 565 ~; 625 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c6,sk_c5) = sk_c4
| sk_c4 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c6,sk_c5) = sk_c4
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c6,sk_c5) = sk_c4
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| inverse(sk_c3) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c6,sk_c5) = sk_c4
| sk_c5 = inverse(sk_c3) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| multiply(sk_c3,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c6,sk_c5) = sk_c4
| sk_c5 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f13]) ).
fof(f17,negated_conjecture,
( multiply(sk_c5,sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c6 = multiply(sk_c5,sk_c4)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c5,sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = multiply(sk_c5,sk_c4)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c5,sk_c4) = sk_c6
| inverse(sk_c3) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = multiply(sk_c5,sk_c4)
| sk_c5 = inverse(sk_c3) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c5,sk_c4) = sk_c6
| multiply(sk_c3,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = multiply(sk_c5,sk_c4)
| sk_c5 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c4 = inverse(sk_c6)
| sk_c4 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c6) = sk_c4
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c4 = inverse(sk_c6)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c6) = sk_c4
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c4 = inverse(sk_c6)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c6) = sk_c4
| inverse(sk_c3) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c4 = inverse(sk_c6)
| sk_c5 = inverse(sk_c3) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c6) = sk_c4
| multiply(sk_c3,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c4 = inverse(sk_c6)
| sk_c5 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c4 = multiply(sk_c1,sk_c6)
| sk_c4 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f35]) ).
fof(f41,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c4
| inverse(sk_c3) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c4 = multiply(sk_c1,sk_c6)
| sk_c5 = inverse(sk_c3) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c4
| multiply(sk_c3,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c4 = multiply(sk_c1,sk_c6)
| sk_c5 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c6 = inverse(sk_c1)
| sk_c4 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f45]) ).
fof(f51,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c3) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = inverse(sk_c1)
| sk_c5 = inverse(sk_c3) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c3,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c6 = inverse(sk_c1)
| sk_c5 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
! [X2,X0,X1] :
( multiply(sk_c6,sk_c5) != sk_c4
| multiply(sk_c5,sk_c4) != sk_c6
| inverse(sk_c6) != sk_c4
| multiply(X0,sk_c6) != sk_c4
| inverse(X0) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| inverse(X1) != sk_c6
| multiply(X1,sk_c5) != sk_c6
| inverse(X2) != sk_c5
| multiply(X2,sk_c4) != sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
! [X2,X0,X1] :
( multiply(sk_c6,sk_c5) != sk_c4
| sk_c6 != multiply(sk_c5,sk_c4)
| sk_c4 != inverse(sk_c6)
| sk_c4 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6
| sk_c4 != multiply(sk_c5,sk_c6)
| sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5)
| sk_c5 != inverse(X2)
| sk_c5 != multiply(X2,sk_c4) ),
inference(reorient_equations,[],[f55]) ).
fof(f58,definition,
( spl0_1
<=> ! [X2] :
( sk_c5 != inverse(X2)
| sk_c5 != multiply(X2,sk_c4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f59,plain,
( ! [X2] :
( sk_c5 != inverse(X2)
| sk_c5 != multiply(X2,sk_c4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,definition,
( spl0_2
<=> ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f62,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c5)
| sk_c6 != inverse(X1) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f64,definition,
( spl0_3
<=> sk_c4 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f65,plain,
( sk_c4 = multiply(sk_c5,sk_c6)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f66,plain,
( sk_c4 != multiply(sk_c5,sk_c6)
| spl0_3 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f68,definition,
( spl0_4
<=> ! [X0] :
( sk_c4 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f69,plain,
( ! [X0] :
( sk_c4 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,definition,
( spl0_5
<=> sk_c4 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f72,plain,
( sk_c4 = inverse(sk_c6)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f73,plain,
( sk_c4 != inverse(sk_c6)
| spl0_5 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f75,definition,
( spl0_6
<=> sk_c6 = multiply(sk_c5,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f76,plain,
( sk_c6 = multiply(sk_c5,sk_c4)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f77,plain,
( sk_c6 != multiply(sk_c5,sk_c4)
| spl0_6 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f79,definition,
( spl0_7
<=> multiply(sk_c6,sk_c5) = sk_c4 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f80,plain,
( multiply(sk_c6,sk_c5) = sk_c4
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f81,plain,
( multiply(sk_c6,sk_c5) != sk_c4
| spl0_7 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f56,f79,f75,f71,f68,f64,f61,f58]) ).
fof(f84,definition,
( spl0_8
<=> sk_c5 = multiply(sk_c3,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f86,plain,
( sk_c5 = multiply(sk_c3,sk_c4)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f88,definition,
( spl0_9
<=> sk_c6 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f90,plain,
( sk_c6 = inverse(sk_c1)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f54,f88,f84]) ).
fof(f93,definition,
( spl0_10
<=> sk_c5 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f95,plain,
( sk_c5 = inverse(sk_c3)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f52,f88,f93]) ).
fof(f98,definition,
( spl0_11
<=> sk_c6 = multiply(sk_c2,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f100,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f103,definition,
( spl0_12
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f105,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f107,plain,
( spl0_3
| spl0_9 ),
inference(avatar_split_clause,[],[f46,f88,f64]) ).
fof(f109,definition,
( spl0_13
<=> sk_c4 = multiply(sk_c1,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f111,plain,
( sk_c4 = multiply(sk_c1,sk_c6)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f44,f109,f84]) ).
fof(f113,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f42,f109,f93]) ).
fof(f116,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f36,f109,f64]) ).
fof(f117,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f34,f71,f84]) ).
fof(f118,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f32,f71,f93]) ).
fof(f119,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f30,f71,f98]) ).
fof(f120,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f28,f71,f103]) ).
fof(f121,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f26,f71,f64]) ).
fof(f122,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f24,f75,f84]) ).
fof(f123,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f22,f75,f93]) ).
fof(f124,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f20,f75,f98]) ).
fof(f125,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f18,f75,f103]) ).
fof(f127,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f14,f79,f84]) ).
fof(f128,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f12,f79,f93]) ).
fof(f129,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f10,f79,f98]) ).
fof(f130,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f8,f79,f103]) ).
fof(f131,plain,
( spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f6,f79,f64]) ).
fof(f132,plain,
( identity = multiply(sk_c5,sk_c3)
| ~ spl0_10 ),
inference(superposition,[],[f3,f95]) ).
fof(f133,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_12 ),
inference(superposition,[],[f3,f105]) ).
fof(f136,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f137,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c6,X0)) = multiply(sk_c4,X0)
| ~ spl0_3 ),
inference(superposition,[],[f4,f65]) ).
fof(f138,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c5,multiply(sk_c3,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f132]) ).
fof(f139,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c2,multiply(sk_c5,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f100]) ).
fof(f140,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c3,multiply(sk_c4,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f86]) ).
fof(f141,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c3,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f138,f1]) ).
fof(f142,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f136,f1]) ).
fof(f145,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c2,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f133]) ).
fof(f146,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c2,X0)) = X0
| ~ spl0_12 ),
inference(forward_demodulation,[],[f145,f1]) ).
fof(f151,plain,
( sk_c4 = multiply(sk_c5,sk_c5)
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f141,f86]) ).
fof(f154,plain,
( multiply(sk_c6,sk_c6) = multiply(sk_c2,sk_c4)
| ~ spl0_3
| ~ spl0_11 ),
inference(superposition,[],[f139,f65]) ).
fof(f155,plain,
( multiply(sk_c6,sk_c3) = multiply(sk_c2,identity)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f139,f132]) ).
fof(f168,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f146,f100]) ).
fof(f175,plain,
! [X0] : multiply(inverse(identity),X0) = X0,
inference(superposition,[],[f142,f1]) ).
fof(f177,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f142,f3]) ).
fof(f178,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f142,f142]) ).
fof(f179,plain,
( sk_c2 = multiply(inverse(sk_c6),identity)
| ~ spl0_12 ),
inference(superposition,[],[f142,f133]) ).
fof(f180,plain,
( ! [X0] : multiply(sk_c2,X0) = multiply(inverse(sk_c6),X0)
| ~ spl0_12 ),
inference(superposition,[],[f142,f146]) ).
fof(f181,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(inverse(sk_c5),multiply(sk_c4,X0))
| ~ spl0_3 ),
inference(superposition,[],[f142,f137]) ).
fof(f182,plain,
( ! [X0] : multiply(sk_c3,X0) = multiply(inverse(sk_c5),X0)
| ~ spl0_10 ),
inference(superposition,[],[f142,f141]) ).
fof(f196,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c3,multiply(sk_c4,X0))
| ~ spl0_3
| ~ spl0_10 ),
inference(forward_demodulation,[],[f181,f182]) ).
fof(f197,plain,
( sk_c2 = multiply(sk_c2,identity)
| ~ spl0_12 ),
inference(forward_demodulation,[],[f179,f180]) ).
fof(f198,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f177,f178]) ).
fof(f206,plain,
( multiply(sk_c5,sk_c5) = multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f137,f168]) ).
fof(f210,plain,
( sk_c4 = multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f206,f151]) ).
fof(f216,plain,
( sk_c6 = multiply(inverse(sk_c4),sk_c4)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f142,f210]) ).
fof(f218,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f216,f3]) ).
fof(f229,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f1,f218]) ).
fof(f232,plain,
( sk_c4 = multiply(inverse(sk_c2),multiply(sk_c6,sk_c6))
| ~ spl0_3
| ~ spl0_11 ),
inference(superposition,[],[f142,f154]) ).
fof(f235,plain,
( sk_c4 = multiply(inverse(sk_c2),sk_c5)
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f232,f168]) ).
fof(f237,plain,
( multiply(sk_c6,sk_c5) = sk_c4
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f235,f105]) ).
fof(f238,plain,
( sk_c5 = sk_c4
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f237,f229]) ).
fof(f242,plain,
( multiply(sk_c2,sk_c5) = multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f154,f238]) ).
fof(f246,plain,
( sk_c5 = multiply(sk_c2,sk_c5)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f242,f168]) ).
fof(f248,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f246,f100]) ).
fof(f251,plain,
( sk_c2 = multiply(sk_c6,sk_c3)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f197,f155]) ).
fof(f253,plain,
( identity = multiply(inverse(sk_c2),multiply(sk_c6,sk_c3))
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f142,f155]) ).
fof(f256,plain,
( identity = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f253,f229]) ).
fof(f258,plain,
( sk_c2 = sk_c3
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f251,f229]) ).
fof(f262,plain,
( identity = multiply(sk_c6,sk_c3)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f256,f105]) ).
fof(f264,plain,
( identity = sk_c3
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f262,f229]) ).
fof(f265,plain,
( identity = sk_c2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f264,f258]) ).
fof(f266,plain,
( sk_c6 = sk_c2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f265,f218]) ).
fof(f287,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c5,X0)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f140,f196]) ).
fof(f309,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f105,f266]) ).
fof(f457,plain,
( sk_c6 != sk_c4
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f73,f309]) ).
fof(f462,plain,
( sk_c6 != sk_c5
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f457,f238]) ).
fof(f464,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f462,f248]) ).
fof(f465,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f464]) ).
fof(f466,plain,
( sk_c6 = sk_c4
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f72,f309]) ).
fof(f467,plain,
( sk_c5 != multiply(sk_c6,sk_c5)
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f81,f238]) ).
fof(f468,plain,
( $false
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f467,f229]) ).
fof(f469,plain,
( ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f468]) ).
fof(f470,plain,
( sk_c6 != multiply(sk_c5,sk_c5)
| ~ spl0_3
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f77,f238]) ).
fof(f472,plain,
( sk_c6 != sk_c4
| ~ spl0_3
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f470,f151]) ).
fof(f473,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f472,f466]) ).
fof(f474,plain,
( ~ spl0_3
| ~ spl0_5
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f473]) ).
fof(f562,plain,
( sk_c6 = multiply(sk_c6,sk_c4)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f76,f287]) ).
fof(f566,plain,
( identity = multiply(sk_c4,sk_c6)
| ~ spl0_5 ),
inference(superposition,[],[f3,f72]) ).
fof(f568,plain,
( identity = multiply(sk_c6,sk_c1)
| ~ spl0_9 ),
inference(superposition,[],[f3,f90]) ).
fof(f575,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c4)
| ~ spl0_7 ),
inference(superposition,[],[f142,f80]) ).
fof(f581,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c4)
| ~ spl0_13 ),
inference(superposition,[],[f142,f111]) ).
fof(f582,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(sk_c1,multiply(sk_c6,X0))
| ~ spl0_13 ),
inference(superposition,[],[f4,f111]) ).
fof(f583,plain,
( sk_c6 = multiply(sk_c6,sk_c4)
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f581,f90]) ).
fof(f585,plain,
( sk_c4 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f142,f562]) ).
fof(f587,plain,
( identity = sk_c4
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f585,f3]) ).
fof(f593,plain,
( sk_c6 != sk_c4
| sk_c6 != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[],[f62,f80]) ).
fof(f596,plain,
( sk_c6 != sk_c4
| sk_c6 != sk_c4
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f593,f72]) ).
fof(f597,plain,
( sk_c6 != sk_c4
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(duplicate_literal_removal,[],[f596]) ).
fof(f602,definition,
( spl0_14
<=> sk_c6 = sk_c4 ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f603,plain,
( sk_c6 = sk_c4
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f602]) ).
fof(f604,plain,
( sk_c6 != sk_c4
| spl0_14 ),
inference(avatar_component_clause,[],[f602]) ).
fof(f610,plain,
( ~ spl0_14
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f597,f79,f71,f61,f602]) ).
fof(f617,definition,
( spl0_16
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f618,plain,
( sk_c6 = sk_c5
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f619,plain,
( sk_c6 != sk_c5
| spl0_16 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f624,plain,
( ! [X0] : multiply(inverse(sk_c4),X0) = X0
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f175,f587]) ).
fof(f631,plain,
( sk_c6 = multiply(inverse(sk_c4),identity)
| ~ spl0_5 ),
inference(superposition,[],[f142,f566]) ).
fof(f634,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f631,f624]) ).
fof(f640,plain,
( sk_c6 = sk_c4
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f634,f587]) ).
fof(f651,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| spl0_14 ),
inference(forward_subsumption_resolution,[],[f640,f604]) ).
fof(f652,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| spl0_14 ),
inference(avatar_contradiction_clause,[],[f651]) ).
fof(f655,definition,
( spl0_17
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f656,plain,
( identity = sk_c6
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f655]) ).
fof(f657,plain,
( identity != sk_c6
| spl0_17 ),
inference(avatar_component_clause,[],[f655]) ).
fof(f660,plain,
( sk_c6 = inverse(sk_c4)
| ~ spl0_5 ),
inference(forward_demodulation,[],[f631,f198]) ).
fof(f666,plain,
( sk_c1 = multiply(inverse(sk_c6),identity)
| ~ spl0_9 ),
inference(superposition,[],[f142,f568]) ).
fof(f688,plain,
( identity = multiply(sk_c6,sk_c4)
| ~ spl0_5 ),
inference(superposition,[],[f3,f660]) ).
fof(f689,plain,
( identity = sk_c6
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f688,f583]) ).
fof(f690,plain,
( spl0_17
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f689,f109,f88,f71,f655]) ).
fof(f691,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_17 ),
inference(superposition,[],[f1,f656]) ).
fof(f692,plain,
( ! [X0] : multiply(inverse(sk_c6),X0) = X0
| ~ spl0_17 ),
inference(superposition,[],[f175,f656]) ).
fof(f695,plain,
( ! [X0] : multiply(X0,sk_c6) = X0
| ~ spl0_17 ),
inference(superposition,[],[f198,f656]) ).
fof(f697,plain,
( ! [X0] : multiply(sk_c4,X0) = X0
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f692,f72]) ).
fof(f708,plain,
( multiply(sk_c1,sk_c6) = multiply(sk_c4,identity)
| ~ spl0_13 ),
inference(superposition,[],[f582,f198]) ).
fof(f713,plain,
( identity = multiply(sk_c1,sk_c6)
| ~ spl0_5
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f708,f697]) ).
fof(f721,plain,
( identity = sk_c4
| ~ spl0_5
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f713,f111]) ).
fof(f726,plain,
( sk_c6 = sk_c4
| ~ spl0_5
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f721,f656]) ).
fof(f728,plain,
( $false
| ~ spl0_5
| ~ spl0_13
| spl0_14
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f726,f604]) ).
fof(f729,plain,
( ~ spl0_5
| ~ spl0_13
| spl0_14
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f728]) ).
fof(f745,plain,
( sk_c4 != multiply(sk_c6,sk_c6)
| spl0_3
| ~ spl0_16 ),
inference(superposition,[],[f66,f618]) ).
fof(f764,plain,
( sk_c6 != sk_c4
| spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f745,f691]) ).
fof(f770,plain,
( $false
| spl0_3
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f764,f603]) ).
fof(f771,plain,
( spl0_3
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f770]) ).
fof(f776,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f575,f603]) ).
fof(f777,plain,
( inverse(sk_c6) = sk_c1
| ~ spl0_9 ),
inference(forward_demodulation,[],[f666,f198]) ).
fof(f781,plain,
( identity = sk_c5
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f776,f3]) ).
fof(f782,plain,
( sk_c4 = sk_c1
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f777,f72]) ).
fof(f787,plain,
( sk_c6 = sk_c5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f781,f656]) ).
fof(f788,plain,
( sk_c6 = sk_c1
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_demodulation,[],[f782,f603]) ).
fof(f790,plain,
( $false
| ~ spl0_7
| ~ spl0_14
| spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f787,f619]) ).
fof(f791,plain,
( ~ spl0_7
| ~ spl0_14
| spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f790]) ).
fof(f792,plain,
( ! [X2] :
( sk_c5 != multiply(X2,sk_c6)
| sk_c5 != inverse(X2) )
| ~ spl0_1
| ~ spl0_14 ),
inference(forward_demodulation,[],[f59,f603]) ).
fof(f796,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f587,f603]) ).
fof(f805,plain,
( ! [X2] :
( sk_c5 != X2
| sk_c5 != inverse(X2) )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f792,f695]) ).
fof(f811,plain,
( ! [X2] :
( sk_c6 != X2
| sk_c5 != inverse(X2) )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f805,f618]) ).
fof(f814,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| sk_c6 != X2 )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f811,f618]) ).
fof(f849,plain,
( sk_c6 != sk_c4
| sk_c6 != sk_c6
| ~ spl0_1
| ~ spl0_5
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f814,f72]) ).
fof(f856,plain,
( sk_c6 != sk_c4
| ~ spl0_1
| ~ spl0_5
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f849]) ).
fof(f863,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f856,f603]) ).
fof(f864,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f863]) ).
fof(f869,plain,
( ! [X0] :
( sk_c4 != X0
| inverse(X0) != sk_c6 )
| ~ spl0_4
| ~ spl0_17 ),
inference(forward_demodulation,[],[f69,f695]) ).
fof(f870,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c6 != X0 )
| ~ spl0_4
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f869,f603]) ).
fof(f871,plain,
( sk_c6 != sk_c4
| sk_c6 != sk_c6
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f870,f72]) ).
fof(f875,plain,
( sk_c6 != sk_c6
| sk_c6 != sk_c1
| ~ spl0_4
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f870,f90]) ).
fof(f876,plain,
( sk_c6 != sk_c1
| ~ spl0_4
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f875]) ).
fof(f878,plain,
( sk_c6 != sk_c4
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f871]) ).
fof(f879,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f876,f788]) ).
fof(f880,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f879]) ).
fof(f885,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f878,f603]) ).
fof(f886,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_14
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f885]) ).
fof(f922,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f634,f657]) ).
fof(f923,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| spl0_17 ),
inference(avatar_contradiction_clause,[],[f922]) ).
fof(f931,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f796,f657]) ).
fof(f932,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14
| spl0_17 ),
inference(avatar_contradiction_clause,[],[f931]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f82]) ).
cnf(s2,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f91]) ).
cnf(s3,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f96]) ).
cnf(s6,plain,
( spl0_3
| spl0_9 ),
inference(sat_conversion,[],[f107]) ).
cnf(s7,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f112]) ).
cnf(s8,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f113]) ).
cnf(s11,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f116]) ).
cnf(s12,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f117]) ).
cnf(s13,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f118]) ).
cnf(s14,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f119]) ).
cnf(s15,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f120]) ).
cnf(s16,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f121]) ).
cnf(s17,plain,
( spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f122]) ).
cnf(s18,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f123]) ).
cnf(s19,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f124]) ).
cnf(s20,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f125]) ).
cnf(s22,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f127]) ).
cnf(s23,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f128]) ).
cnf(s24,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f129]) ).
cnf(s25,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f130]) ).
cnf(s26,plain,
( spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f131]) ).
cnf(s27,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f465]) ).
cnf(s28,plain,
( ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f469]) ).
cnf(s29,plain,
( ~ spl0_3
| ~ spl0_5
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f474]) ).
cnf(s37,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14 ),
inference(sat_conversion,[],[f610]) ).
cnf(s42,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f652]) ).
cnf(s46,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f690]) ).
cnf(s47,plain,
( ~ spl0_5
| ~ spl0_13
| spl0_14
| ~ spl0_17 ),
inference(sat_conversion,[],[f729]) ).
cnf(s50,plain,
( spl0_3
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f771]) ).
cnf(s52,plain,
( ~ spl0_7
| ~ spl0_14
| spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f791]) ).
cnf(s57,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f864]) ).
cnf(s60,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17 ),
inference(sat_conversion,[],[f880]) ).
cnf(s62,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_14
| ~ spl0_17 ),
inference(sat_conversion,[],[f886]) ).
cnf(s66,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f923]) ).
cnf(s67,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f932]) ).
cnf(s74,plain,
spl0_3,
inference(rat,[],[s50,s52,s47,s46,s6,s11,s16,s26]) ).
cnf(s75,plain,
spl0_7,
inference(rat,[],[s28,s22,s23,s24,s25,s74]) ).
cnf(s76,plain,
( ~ spl0_5
| spl0_4
| spl0_1
| spl0_2 ),
inference(rat,[],[s29,s17,s18,s19,s20,s1,s75,s74]) ).
cnf(s77,plain,
spl0_5,
inference(rat,[],[s27,s12,s13,s14,s15,s74]) ).
cnf(s78,plain,
( ~ spl0_10
| ~ spl0_8
| ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s62,s66,s42,s77,s74]) ).
cnf(s79,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s47,s60,s46,s3,s8,s77]) ).
cnf(s80,plain,
( spl0_8
| ~ spl0_4 ),
inference(rat,[],[s47,s60,s46,s2,s7,s77]) ).
cnf(s81,plain,
( ~ spl0_8
| ~ spl0_4
| ~ spl0_10 ),
inference(rat,[],[s29,s19,s20,s78,s77,s74]) ).
cnf(s82,plain,
~ spl0_4,
inference(rat,[],[s81,s80,s79]) ).
cnf(s83,plain,
( spl0_10
| spl0_14 ),
inference(rat,[],[s46,s47,s3,s8,s77]) ).
cnf(s84,plain,
( spl0_8
| spl0_14 ),
inference(rat,[],[s46,s47,s2,s7,s77]) ).
cnf(s85,plain,
( ~ spl0_8
| spl0_14
| ~ spl0_10 ),
inference(rat,[],[s29,s19,s20,s42,s77,s74]) ).
cnf(s86,plain,
spl0_14,
inference(rat,[],[s85,s84,s83]) ).
cnf(s87,plain,
~ spl0_2,
inference(rat,[],[s37,s77,s75,s86]) ).
cnf(s88,plain,
spl0_1,
inference(rat,[],[s76,s77,s82,s87]) ).
cnf(s89,plain,
~ spl0_17,
inference(rat,[],[s57,s52,s77,s86,s88,s75]) ).
cnf(s91,plain,
spl0_10,
inference(rat,[],[s46,s3,s8,s77,s89]) ).
cnf(s92,plain,
spl0_8,
inference(rat,[],[s46,s2,s7,s77,s89]) ).
cnf(s93,plain,
~ spl0_6,
inference(rat,[],[s67,s89,s86,s91,s74,s92]) ).
cnf(s94,plain,
spl0_12,
inference(rat,[],[s20,s93]) ).
cnf(s95,plain,
spl0_11,
inference(rat,[],[s19,s93]) ).
cnf(s96,plain,
$false,
inference(rat,[],[s29,s94,s92,s91,s77,s74,s95,s93]) ).
fof(f990,plain,
$false,
inference(avatar_sat_refutation,[],[s96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP305-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 09:49:15 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.41 Running first-order model finding
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.47 % (1785225)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (1785234)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3497742130:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (1785231)% WARNING: option uhcvi not known.
% 0.16/0.47 % (1785233)dis+10_1_sil=32000:sp=arity:random_seed=2867741312:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (1785230)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3456420715_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % (1785231)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2236603889:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (1785235)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3875814397:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % (1785232)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3350915448:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (1785236)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2853723982:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % (1785234) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1785225-1785234"...
% 0.16/0.47 % TRYING [1]
% 0.16/0.47 % TRYING [2]
% 0.16/0.47 % (1785234)...printing done.
% 0.16/0.47 % TRYING [3]
% 0.16/0.47 % (1785234)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (1785234)------------------------------
% 0.16/0.47 % (1785234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (1785234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (1785234)CaDiCaL version: 2.1.3
% 0.16/0.47 % (1785234)Termination reason: Refutation
% 0.16/0.47 % (1785234)Time elapsed: 0.010 s
% 0.16/0.47 % (1785234)Peak memory usage: 12 MB
% 0.16/0.47 % (1785234)Instructions burned: 27 (million)
% 0.16/0.47 % (1785225)Success in time 0.054 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------