%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n003.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 10:13:35 AM UTC 2026
% Result : Unsatisfiable 2.78s 1.29s
% Output : Refutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 43
% Syntax : Number of formulae : 276 ( 19 unt; 15 def)
% Number of atoms : 925 ( 254 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1228 ( 579 ~; 634 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/theBenchmark.p',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(f37,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c4
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c4 = multiply(sk_c1,sk_c6)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c4
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c4 = multiply(sk_c1,sk_c6)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f39]) ).
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(f47,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f49]) ).
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 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) )
| ~ 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(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] :
( inverse(X0) != sk_c6
| sk_c4 != multiply(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(f101,plain,
( spl0_11
| spl0_9 ),
inference(avatar_split_clause,[],[f50,f88,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(f106,plain,
( spl0_12
| spl0_9 ),
inference(avatar_split_clause,[],[f48,f88,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(f110,plain,
( sk_c4 != multiply(sk_c1,sk_c6)
| spl0_13 ),
inference(avatar_component_clause,[],[f109]) ).
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(f114,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f40,f109,f98]) ).
fof(f115,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f38,f109,f103]) ).
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(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(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(f178,plain,
( sk_c2 = multiply(inverse(sk_c6),identity)
| ~ spl0_12 ),
inference(superposition,[],[f142,f133]) ).
fof(f185,plain,
( sk_c5 = multiply(inverse(sk_c2),sk_c6)
| ~ spl0_11 ),
inference(superposition,[],[f142,f100]) ).
fof(f194,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f185,f105]) ).
fof(f195,plain,
( multiply(sk_c5,sk_c5) = multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f137,f194]) ).
fof(f198,plain,
( sk_c4 = multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f195,f151]) ).
fof(f205,plain,
( sk_c6 = multiply(inverse(sk_c4),sk_c4)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f142,f198]) ).
fof(f207,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f205,f3]) ).
fof(f213,plain,
( sk_c2 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f178,f207]) ).
fof(f215,plain,
( identity = sk_c2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f213,f3]) ).
fof(f216,plain,
( sk_c6 = sk_c2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f215,f207]) ).
fof(f221,plain,
( identity = multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f133,f216]) ).
fof(f223,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f105,f216]) ).
fof(f224,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f221,f194]) ).
fof(f225,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f224,f207]) ).
fof(f245,plain,
( multiply(sk_c6,sk_c6) = multiply(sk_c6,sk_c4)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f154,f216]) ).
fof(f246,plain,
( sk_c5 = multiply(sk_c6,sk_c4)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f245,f194]) ).
fof(f247,plain,
( sk_c6 = multiply(sk_c6,sk_c4)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f246,f225]) ).
fof(f260,plain,
( sk_c4 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f142,f247]) ).
fof(f262,plain,
( identity = sk_c4
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f260,f3]) ).
fof(f264,plain,
( sk_c6 = sk_c4
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f262,f207]) ).
fof(f296,plain,
( sk_c6 != sk_c4
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f73,f223]) ).
fof(f300,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f296,f264]) ).
fof(f301,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f300]) ).
fof(f307,plain,
( sk_c6 != multiply(sk_c6,sk_c5)
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f81,f264]) ).
fof(f308,plain,
( sk_c6 != multiply(sk_c6,sk_c6)
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f307,f225]) ).
fof(f309,plain,
( sk_c6 != sk_c5
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f308,f194]) ).
fof(f310,plain,
( $false
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f309,f225]) ).
fof(f311,plain,
( ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f310]) ).
fof(f312,plain,
( sk_c6 != multiply(sk_c5,sk_c6)
| ~ spl0_3
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f77,f264]) ).
fof(f313,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f80,f264]) ).
fof(f314,plain,
( sk_c6 != sk_c4
| ~ spl0_3
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f312,f65]) ).
fof(f315,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f313,f225]) ).
fof(f316,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f314,f264]) ).
fof(f317,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f316]) ).
fof(f382,plain,
( identity = multiply(sk_c4,sk_c6)
| ~ spl0_5 ),
inference(superposition,[],[f3,f72]) ).
fof(f384,plain,
( identity = multiply(sk_c6,sk_c1)
| ~ spl0_9 ),
inference(superposition,[],[f3,f90]) ).
fof(f388,plain,
( multiply(sk_c5,sk_c4) = multiply(sk_c4,sk_c5)
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f137,f80]) ).
fof(f389,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c4)
| ~ spl0_7 ),
inference(superposition,[],[f142,f80]) ).
fof(f390,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(sk_c6,multiply(sk_c5,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f80]) ).
fof(f391,plain,
( sk_c5 = multiply(sk_c4,sk_c4)
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f389,f72]) ).
fof(f392,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f388,f76]) ).
fof(f393,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c4)
| ~ spl0_13 ),
inference(superposition,[],[f142,f111]) ).
fof(f395,plain,
( sk_c6 = multiply(sk_c6,sk_c4)
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f393,f90]) ).
fof(f399,plain,
( sk_c6 != sk_c4
| sk_c6 != multiply(sk_c6,sk_c5)
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[],[f62,f72]) ).
fof(f400,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c2,sk_c5)
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[],[f62,f105]) ).
fof(f404,plain,
( sk_c6 != multiply(sk_c2,sk_c5)
| ~ spl0_2
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f400]) ).
fof(f410,definition,
( spl0_15
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f416,plain,
( sk_c6 != sk_c4
| sk_c6 != sk_c4
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f399,f80]) ).
fof(f417,plain,
( sk_c6 != sk_c4
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(duplicate_literal_removal,[],[f416]) ).
fof(f418,plain,
( ~ spl0_11
| ~ spl0_2
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f404,f103,f61,f98]) ).
fof(f420,plain,
( sk_c1 = multiply(inverse(sk_c6),identity)
| ~ spl0_9 ),
inference(superposition,[],[f142,f384]) ).
fof(f423,plain,
( sk_c2 = sk_c1
| ~ spl0_9
| ~ spl0_12 ),
inference(forward_demodulation,[],[f420,f178]) ).
fof(f436,plain,
( multiply(sk_c4,sk_c6) = multiply(sk_c6,sk_c4)
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f390,f65]) ).
fof(f445,plain,
( identity = multiply(sk_c6,sk_c4)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f436,f382]) ).
fof(f470,plain,
( sk_c4 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f142,f395]) ).
fof(f472,plain,
( identity = sk_c4
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f470,f3]) ).
fof(f475,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f445,f395]) ).
fof(f485,plain,
( sk_c6 = sk_c4
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f472,f475]) ).
fof(f486,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f485,f417]) ).
fof(f487,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f486]) ).
fof(f488,plain,
( sk_c1 = multiply(sk_c4,identity)
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f420,f72]) ).
fof(f491,plain,
( sk_c1 = multiply(sk_c4,sk_c4)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f488,f472]) ).
fof(f492,plain,
( sk_c5 = sk_c1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f491,f391]) ).
fof(f507,plain,
( sk_c4 = multiply(sk_c5,sk_c6)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f111,f492]) ).
fof(f513,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f507,f109,f88,f79,f71,f64]) ).
fof(f522,plain,
( sk_c6 != sk_c4
| sk_c4 != multiply(sk_c6,sk_c6)
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f69,f72]) ).
fof(f524,plain,
( sk_c6 != sk_c6
| sk_c4 != multiply(sk_c1,sk_c6)
| ~ spl0_4
| ~ spl0_9 ),
inference(superposition,[],[f69,f90]) ).
fof(f525,plain,
( sk_c4 != multiply(sk_c1,sk_c6)
| ~ spl0_4
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f524]) ).
fof(f526,plain,
( $false
| ~ spl0_4
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f525,f111]) ).
fof(f527,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f526]) ).
fof(f533,definition,
( spl0_17
<=> sk_c6 = sk_c4 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f534,plain,
( sk_c6 = sk_c4
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f533]) ).
fof(f538,plain,
( sk_c5 != sk_c5
| sk_c5 != multiply(sk_c3,sk_c4)
| ~ spl0_1
| ~ spl0_10 ),
inference(superposition,[],[f59,f95]) ).
fof(f539,plain,
( sk_c6 != sk_c5
| sk_c5 != multiply(sk_c1,sk_c4)
| ~ spl0_1
| ~ spl0_9 ),
inference(superposition,[],[f59,f90]) ).
fof(f540,plain,
( sk_c5 != multiply(sk_c3,sk_c4)
| ~ spl0_1
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f538]) ).
fof(f541,plain,
( ~ spl0_8
| ~ spl0_1
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f540,f93,f58,f84]) ).
fof(f543,plain,
( spl0_17
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f485,f109,f88,f79,f71,f64,f533]) ).
fof(f576,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17 ),
inference(forward_demodulation,[],[f392,f534]) ).
fof(f589,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17 ),
inference(superposition,[],[f142,f576]) ).
fof(f591,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17 ),
inference(forward_demodulation,[],[f589,f3]) ).
fof(f593,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f591,f475]) ).
fof(f597,plain,
( sk_c5 != multiply(sk_c1,sk_c6)
| sk_c6 != sk_c5
| ~ spl0_1
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_demodulation,[],[f539,f534]) ).
fof(f602,plain,
( spl0_15
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f593,f533,f109,f88,f79,f75,f71,f64,f410]) ).
fof(f603,plain,
( sk_c5 != sk_c4
| sk_c6 != sk_c5
| ~ spl0_1
| ~ spl0_9
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f597,f111]) ).
fof(f606,plain,
( sk_c6 != sk_c5
| sk_c6 != sk_c5
| ~ spl0_1
| ~ spl0_9
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f603,f534]) ).
fof(f607,plain,
( sk_c6 != sk_c5
| ~ spl0_1
| ~ spl0_9
| ~ spl0_13
| ~ spl0_17 ),
inference(duplicate_literal_removal,[],[f606]) ).
fof(f608,plain,
( ~ spl0_15
| ~ spl0_1
| ~ spl0_9
| ~ spl0_13
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f607,f533,f109,f88,f58,f410]) ).
fof(f666,plain,
( sk_c6 = sk_c4
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f72,f223]) ).
fof(f676,plain,
( sk_c6 != sk_c4
| sk_c6 != sk_c4
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f522,f315]) ).
fof(f677,plain,
( sk_c6 != sk_c4
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(duplicate_literal_removal,[],[f676]) ).
fof(f687,plain,
( sk_c4 != multiply(sk_c2,sk_c6)
| ~ spl0_9
| ~ spl0_12
| spl0_13 ),
inference(forward_demodulation,[],[f110,f423]) ).
fof(f693,plain,
( spl0_17
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f666,f103,f98,f93,f84,f71,f64,f533]) ).
fof(f694,plain,
( ~ spl0_17
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f677,f103,f98,f93,f84,f79,f71,f68,f64,f533]) ).
fof(f701,plain,
( sk_c4 != multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_13 ),
inference(forward_demodulation,[],[f687,f216]) ).
fof(f708,plain,
( sk_c6 != sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_13 ),
inference(forward_demodulation,[],[f701,f315]) ).
fof(f711,plain,
( ~ spl0_17
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f708,f109,f103,f98,f93,f88,f84,f79,f64,f533]) ).
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(s4,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f101]) ).
cnf(s5,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f106]) ).
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(s9,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f114]) ).
cnf(s10,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f115]) ).
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,[],[f301]) ).
cnf(s28,plain,
( ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f311]) ).
cnf(s29,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f317]) ).
cnf(s38,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f418]) ).
cnf(s39,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(sat_conversion,[],[f487]) ).
cnf(s41,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(sat_conversion,[],[f513]) ).
cnf(s42,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_13 ),
inference(sat_conversion,[],[f527]) ).
cnf(s44,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_10 ),
inference(sat_conversion,[],[f541]) ).
cnf(s45,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f543]) ).
cnf(s47,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f602]) ).
cnf(s50,plain,
( ~ spl0_1
| ~ spl0_9
| ~ spl0_13
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f608]) ).
cnf(s56,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f693]) ).
cnf(s58,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_17 ),
inference(sat_conversion,[],[f694]) ).
cnf(s66,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_13
| ~ spl0_17 ),
inference(sat_conversion,[],[f711]) ).
cnf(s67,plain,
spl0_3,
inference(rat,[],[s41,s6,s11,s16,s26]) ).
cnf(s68,plain,
spl0_7,
inference(rat,[],[s28,s22,s23,s24,s25,s67]) ).
cnf(s69,plain,
spl0_6,
inference(rat,[],[s29,s17,s18,s19,s20,s67]) ).
cnf(s70,plain,
spl0_5,
inference(rat,[],[s27,s12,s13,s14,s15,s67]) ).
cnf(s71,plain,
( spl0_13
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_8 ),
inference(rat,[],[s56,s66,s68,s70,s67]) ).
cnf(s72,plain,
( ~ spl0_9
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s71,s8,s9,s10,s42]) ).
cnf(s73,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_8
| ~ spl0_4
| ~ spl0_12 ),
inference(rat,[],[s56,s58,s68,s70,s67]) ).
cnf(s74,plain,
( ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s73,s3,s4,s5,s72]) ).
cnf(s75,plain,
~ spl0_4,
inference(rat,[],[s42,s2,s7,s74]) ).
cnf(s76,plain,
( spl0_12
| ~ spl0_2 ),
inference(rat,[],[s39,s5,s10,s68,s67,s70]) ).
cnf(s77,plain,
( ~ spl0_12
| ~ spl0_2 ),
inference(rat,[],[s39,s4,s9,s38,s70,s67,s68]) ).
cnf(s78,plain,
~ spl0_2,
inference(rat,[],[s77,s76]) ).
cnf(s79,plain,
spl0_1,
inference(rat,[],[s1,s68,s70,s69,s67,s75,s78]) ).
cnf(s80,plain,
( ~ spl0_9
| ~ spl0_17
| ~ spl0_13 ),
inference(rat,[],[s47,s50,s79,s68,s69,s70,s67]) ).
cnf(s81,plain,
( ~ spl0_9
| ~ spl0_13 ),
inference(rat,[],[s80,s45,s68,s70,s67]) ).
cnf(s82,plain,
spl0_12,
inference(rat,[],[s81,s5,s10]) ).
cnf(s83,plain,
( ~ spl0_9
| ~ spl0_11 ),
inference(rat,[],[s71,s7,s8,s81,s82]) ).
cnf(s84,plain,
spl0_9,
inference(rat,[],[s44,s2,s3,s79]) ).
cnf(s85,plain,
~ spl0_13,
inference(rat,[],[s81,s84]) ).
cnf(s86,plain,
~ spl0_11,
inference(rat,[],[s83,s84]) ).
cnf(s89,plain,
$false,
inference(rat,[],[s9,s85,s86]) ).
fof(f712,plain,
$false,
inference(avatar_sat_refutation,[],[s89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP305-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:50:55 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.78/1.29 % (259926)Input is clausal, will run a generic CNF schedule.
% 2.78/1.29 % (259933)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=600679919:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.78/1.29 % (259932)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3786125653:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.78/1.29 % (259935)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3779630682:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.78/1.29 % (259931)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1629485613:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.78/1.29 % (259937)dis-21_1_sil=8000:lcm=predicate:random_seed=1164478473:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.78/1.29 % (259934)lrs+10_1_sil=8000:sp=occurrence:random_seed=336883232:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.78/1.29 % (259936)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1895186060:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.78/1.29 % (259937)Refutation not found, incomplete strategy
% 2.78/1.29 % (259937)------------------------------
% 2.78/1.29 % (259937)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.29 % (259937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.29 % (259937)CaDiCaL version: 2.1.3
% 2.78/1.29 % (259937)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.29 % (259937)Time elapsed: 0.002 s
% 2.78/1.29 % (259937)Peak memory usage: 88 MB
% 2.78/1.29 % (259937)Instructions burned: 1 (million)
% 2.78/1.29 % (259934)Refutation not found, incomplete strategy
% 2.78/1.29 % (259934)------------------------------
% 2.78/1.29 % (259934)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.29 % (259934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.29 % (259934)CaDiCaL version: 2.1.3
% 2.78/1.29 % (259934)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.29 % (259934)Time elapsed: 0.002 s
% 2.78/1.29 % (259934)Peak memory usage: 88 MB
% 2.78/1.29 % (259934)Instructions burned: 2 (million)
% 2.78/1.29 % (259936)First to succeed.
% 2.78/1.29 % (259936)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-259926"
% 2.78/1.29 % (259935)Instruction limit reached!
% 2.78/1.29 % (259935)------------------------------
% 2.78/1.29 % (259935)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.29 % (259935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.29 % (259935)CaDiCaL version: 2.1.3
% 2.78/1.29 % (259935)Termination reason: Instruction limit
% 2.78/1.29 % (259935)Termination phase: Saturation
% 2.78/1.29 % (259935)Time elapsed: 0.067 s
% 2.78/1.29 % (259935)Peak memory usage: 89 MB
% 2.78/1.29 % (259935)Instructions burned: 114 (million)
% 2.78/1.29 % (259945)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3634678191:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.78/1.29 % (259937)------------------------------
% 2.78/1.29 % (259937)------------------------------
% 2.78/1.29 % (259934)------------------------------
% 2.78/1.29 % (259934)------------------------------
% 2.78/1.29 % (259945)Refutation not found, incomplete strategy
% 2.78/1.29 % (259945)------------------------------
% 2.78/1.29 % (259945)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.29 % (259945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.29 % (259945)CaDiCaL version: 2.1.3
% 2.78/1.29 % (259945)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.29 % (259945)Time elapsed: 0.003 s
% 2.78/1.29 % (259945)Peak memory usage: 88 MB
% 2.78/1.29 % (259945)Instructions burned: 3 (million)
% 2.78/1.29 % (259936)Refutation found. Thanks to Tanya!
% 2.78/1.29 % SZS status Unsatisfiable for theBenchmark
% 2.78/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.70/1.49 % (259936)------------------------------
% 3.70/1.49 % (259936)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.49 % (259936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.49 % (259936)CaDiCaL version: 2.1.3
% 3.70/1.49 % (259936)Termination reason: Refutation
% 3.70/1.49 % (259936)Time elapsed: 0.018 s
% 3.70/1.49 % (259936)Peak memory usage: 89 MB
% 3.70/1.49 % (259936)Instructions burned: 26 (million)
% 3.70/1.49 % (259936)------------------------------
% 3.70/1.49 % (259936)------------------------------
% 3.70/1.49 % (259926)Success in time 0.448 s
% 3.70/1.49 % Vampire exiting
%------------------------------------------------------------------------------