%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP291-1 : 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 : n001.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 10:13:33 AM UTC 2026
% Result : Unsatisfiable 3.26s 1.32s
% Output : Refutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 47
% Syntax : Number of formulae : 297 ( 23 unt; 18 def)
% Number of atoms : 920 ( 264 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1177 ( 554 ~; 605 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 33 !; 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_c7,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c2,sk_c5)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = multiply(sk_c2,sk_c5)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c2,sk_c5)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c2,sk_c5)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c2,sk_c5)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c2) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c5 = inverse(sk_c2)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c2) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c5 = inverse(sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c2) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c5 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c2) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c5 = inverse(sk_c2)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c2) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c5 = inverse(sk_c2)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(sk_c7,sk_c6) != sk_c5
| multiply(X0,sk_c7) != sk_c6
| inverse(X0) != sk_c7
| multiply(X1,sk_c5) != sk_c7
| inverse(X1) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X2) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| inverse(X3) != sk_c6
| multiply(X3,sk_c5) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( multiply(sk_c7,sk_c6) != sk_c5
| sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(X1,sk_c5)
| sk_c5 != inverse(X1)
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) ),
inference(reorient_equations,[],[f55]) ).
fof(f58,definition,
( spl0_1
<=> ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f59,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f62,plain,
( ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f64,definition,
( spl0_3
<=> sk_c5 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f65,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f66,plain,
( sk_c5 != multiply(sk_c6,sk_c7)
| spl0_3 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f68,definition,
( spl0_4
<=> ! [X1] :
( sk_c7 != multiply(X1,sk_c5)
| sk_c5 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f69,plain,
( ! [X1] :
( sk_c5 != inverse(X1)
| sk_c7 != multiply(X1,sk_c5) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,definition,
( spl0_5
<=> ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f72,plain,
( ! [X0] :
( inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,definition,
( spl0_6
<=> multiply(sk_c7,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f75,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( multiply(sk_c7,sk_c6) != sk_c5
| spl0_6 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f56,f74,f71,f68,f64,f61,f58]) ).
fof(f79,definition,
( spl0_7
<=> sk_c6 = multiply(sk_c4,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f81,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f83,definition,
( spl0_8
<=> sk_c5 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f85,plain,
( sk_c5 = inverse(sk_c2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f54,f83,f79]) ).
fof(f88,definition,
( spl0_9
<=> sk_c6 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f90,plain,
( sk_c6 = inverse(sk_c4)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f52,f83,f88]) ).
fof(f93,definition,
( spl0_10
<=> sk_c7 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f95,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f50,f83,f93]) ).
fof(f98,definition,
( spl0_11
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f100,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f48,f83,f98]) ).
fof(f102,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f46,f83,f64]) ).
fof(f104,definition,
( spl0_12
<=> sk_c7 = multiply(sk_c2,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f106,plain,
( sk_c7 = multiply(sk_c2,sk_c5)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f44,f104,f79]) ).
fof(f108,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f42,f104,f88]) ).
fof(f109,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f40,f104,f93]) ).
fof(f110,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f38,f104,f98]) ).
fof(f111,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f36,f104,f64]) ).
fof(f113,definition,
( spl0_13
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f115,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f34,f113,f79]) ).
fof(f117,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f32,f113,f88]) ).
fof(f118,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f30,f113,f93]) ).
fof(f119,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f28,f113,f98]) ).
fof(f120,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f26,f113,f64]) ).
fof(f122,definition,
( spl0_14
<=> sk_c6 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f124,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f24,f122,f79]) ).
fof(f126,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f22,f122,f88]) ).
fof(f127,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f20,f122,f93]) ).
fof(f128,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f18,f122,f98]) ).
fof(f129,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f16,f122,f64]) ).
fof(f130,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f74,f79]) ).
fof(f131,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f74,f88]) ).
fof(f132,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f74,f93]) ).
fof(f133,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f74,f98]) ).
fof(f134,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f74,f64]) ).
fof(f135,plain,
( identity = multiply(sk_c6,sk_c4)
| ~ spl0_9 ),
inference(superposition,[],[f3,f90]) ).
fof(f136,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_11 ),
inference(superposition,[],[f3,f100]) ).
fof(f139,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f140,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(sk_c5,X0)
| ~ spl0_3 ),
inference(superposition,[],[f4,f65]) ).
fof(f141,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c4,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f135]) ).
fof(f142,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c6,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f95]) ).
fof(f144,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c4,X0)) = X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f141,f1]) ).
fof(f145,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f139,f1]) ).
fof(f154,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f144,f81]) ).
fof(f157,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f142,f65]) ).
fof(f181,plain,
( sk_c3 = multiply(inverse(sk_c7),identity)
| ~ spl0_11 ),
inference(superposition,[],[f145,f136]) ).
fof(f187,plain,
( sk_c4 = multiply(inverse(sk_c6),identity)
| ~ spl0_9 ),
inference(superposition,[],[f145,f135]) ).
fof(f188,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_10 ),
inference(superposition,[],[f145,f95]) ).
fof(f197,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f188,f100]) ).
fof(f198,plain,
( multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f140,f197]) ).
fof(f201,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f198,f154]) ).
fof(f208,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f145,f201]) ).
fof(f210,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f208,f3]) ).
fof(f216,plain,
( sk_c3 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f181,f210]) ).
fof(f218,plain,
( identity = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f216,f3]) ).
fof(f219,plain,
( sk_c7 = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f218,f210]) ).
fof(f224,plain,
( identity = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f136,f219]) ).
fof(f227,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f224,f197]) ).
fof(f228,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f227,f210]) ).
fof(f231,plain,
( sk_c5 != multiply(sk_c7,sk_c7)
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f76,f228]) ).
fof(f239,plain,
( sk_c4 = multiply(inverse(sk_c7),identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f187,f228]) ).
fof(f240,plain,
( sk_c3 = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f239,f181]) ).
fof(f245,plain,
( sk_c6 != sk_c5
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f231,f197]) ).
fof(f247,plain,
( sk_c7 = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f240,f219]) ).
fof(f249,plain,
( sk_c7 != sk_c5
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f245,f228]) ).
fof(f251,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c7,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f157,f219]) ).
fof(f252,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f251,f197]) ).
fof(f253,plain,
( sk_c7 = multiply(sk_c7,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f252,f228]) ).
fof(f266,plain,
( sk_c5 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f145,f253]) ).
fof(f268,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f266,f3]) ).
fof(f270,plain,
( sk_c7 = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f268,f210]) ).
fof(f285,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f249,f270]) ).
fof(f286,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f285]) ).
fof(f287,plain,
( ! [X1] :
( sk_c7 != multiply(X1,sk_c7)
| sk_c5 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f69,f270]) ).
fof(f288,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f75,f270]) ).
fof(f289,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c7) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f287,f270]) ).
fof(f290,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f288,f228]) ).
fof(f298,plain,
( sk_c7 != sk_c6
| sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f289,f90]) ).
fof(f302,plain,
( sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f298,f228]) ).
fof(f305,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f302,f247]) ).
fof(f306,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f305,f290]) ).
fof(f307,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f306]) ).
fof(f308,plain,
( sk_c6 = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f157,f197]) ).
fof(f316,plain,
( sk_c5 = multiply(inverse(sk_c2),sk_c7)
| ~ spl0_12 ),
inference(superposition,[],[f145,f106]) ).
fof(f318,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f316,f85]) ).
fof(f319,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_14 ),
inference(superposition,[],[f145,f124]) ).
fof(f321,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f319,f115]) ).
fof(f328,plain,
( sk_c5 != sk_c5
| sk_c7 != multiply(sk_c2,sk_c5)
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f69,f85]) ).
fof(f329,plain,
( sk_c7 != multiply(sk_c2,sk_c5)
| ~ spl0_4
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f328]) ).
fof(f330,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f329,f106]) ).
fof(f331,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f330]) ).
fof(f337,definition,
( spl0_16
<=> sk_c7 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f338,plain,
( sk_c7 = sk_c5
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f337]) ).
fof(f346,definition,
( spl0_18
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f348,plain,
( sk_c6 != sk_c5
| spl0_18 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f360,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c3,sk_c6)
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f62,f100]) ).
fof(f365,plain,
( sk_c7 != multiply(sk_c3,sk_c6)
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f360]) ).
fof(f367,definition,
( spl0_20
<=> sk_c7 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f368,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f369,plain,
( sk_c7 != multiply(sk_c2,sk_c6)
| spl0_20 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f376,definition,
( spl0_22
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f377,plain,
( sk_c7 = sk_c6
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f380,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f365,f95]) ).
fof(f381,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f380]) ).
fof(f385,plain,
( sk_c7 != sk_c7
| sk_c6 != multiply(sk_c3,sk_c7)
| ~ spl0_5
| ~ spl0_11 ),
inference(superposition,[],[f72,f100]) ).
fof(f387,plain,
( sk_c7 != sk_c7
| sk_c6 != multiply(sk_c1,sk_c7)
| ~ spl0_5
| ~ spl0_13 ),
inference(superposition,[],[f72,f115]) ).
fof(f389,plain,
( sk_c6 != multiply(sk_c1,sk_c7)
| ~ spl0_5
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f387]) ).
fof(f396,plain,
( $false
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f389,f124]) ).
fof(f397,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f396]) ).
fof(f407,plain,
( sk_c7 != sk_c6
| sk_c6 != multiply(sk_c3,sk_c5)
| ~ spl0_1
| ~ spl0_11 ),
inference(superposition,[],[f59,f100]) ).
fof(f410,plain,
( sk_c6 != sk_c5
| sk_c6 != multiply(sk_c2,sk_c5)
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[],[f59,f85]) ).
fof(f412,plain,
( sk_c7 != sk_c6
| sk_c6 != sk_c5
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f410,f106]) ).
fof(f414,plain,
( sk_c7 != sk_c6
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f407,f308]) ).
fof(f415,plain,
( ~ spl0_18
| ~ spl0_22
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f412,f104,f83,f58,f376,f346]) ).
fof(f417,plain,
( ~ spl0_22
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f414,f98,f93,f64,f58,f376]) ).
fof(f428,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f145,f318]) ).
fof(f430,plain,
( identity = sk_c7
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f428,f3]) ).
fof(f451,plain,
( sk_c7 = sk_c5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f75,f321]) ).
fof(f453,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f145,f321]) ).
fof(f455,plain,
( identity = sk_c6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f453,f3]) ).
fof(f457,plain,
( spl0_16
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f451,f122,f113,f74,f337]) ).
fof(f458,plain,
( sk_c7 = sk_c6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f455,f430]) ).
fof(f459,plain,
( spl0_22
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f458,f122,f113,f104,f83,f376]) ).
fof(f461,plain,
( sk_c7 = multiply(sk_c2,sk_c7)
| ~ spl0_12
| ~ spl0_16 ),
inference(superposition,[],[f106,f338]) ).
fof(f466,plain,
( sk_c7 != sk_c6
| ~ spl0_16
| spl0_18 ),
inference(superposition,[],[f348,f338]) ).
fof(f470,plain,
( ~ spl0_22
| ~ spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f466,f346,f337,f376]) ).
fof(f501,plain,
( ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c7) )
| ~ spl0_2
| ~ spl0_22 ),
inference(forward_demodulation,[],[f62,f377]) ).
fof(f513,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c1,sk_c7)
| ~ spl0_2
| ~ spl0_13
| ~ spl0_22 ),
inference(superposition,[],[f501,f115]) ).
fof(f515,plain,
( sk_c7 != multiply(sk_c1,sk_c7)
| ~ spl0_2
| ~ spl0_13
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f513]) ).
fof(f517,plain,
( sk_c7 != sk_c6
| ~ spl0_2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(forward_demodulation,[],[f515,f124]) ).
fof(f519,plain,
( $false
| ~ spl0_2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f517,f377]) ).
fof(f520,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f519]) ).
fof(f522,plain,
( sk_c5 != multiply(sk_c7,sk_c7)
| spl0_3
| ~ spl0_22 ),
inference(forward_demodulation,[],[f66,f377]) ).
fof(f524,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| spl0_3
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f522,f338]) ).
fof(f529,plain,
( sk_c7 != multiply(sk_c2,sk_c7)
| spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f369,f377]) ).
fof(f534,plain,
( $false
| ~ spl0_12
| ~ spl0_16
| spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f461,f529]) ).
fof(f535,plain,
( ~ spl0_12
| ~ spl0_16
| spl0_20
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f534]) ).
fof(f536,plain,
( sk_c7 = multiply(sk_c2,sk_c7)
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f368,f377]) ).
fof(f537,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c7)
| ~ spl0_20
| ~ spl0_22 ),
inference(superposition,[],[f145,f536]) ).
fof(f539,plain,
( sk_c7 = multiply(sk_c5,sk_c7)
| ~ spl0_8
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f537,f85]) ).
fof(f540,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_8
| ~ spl0_16
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f539,f338]) ).
fof(f541,plain,
( $false
| spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f540,f524]) ).
fof(f542,plain,
( spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f541]) ).
fof(f543,plain,
( sk_c6 != multiply(sk_c3,sk_c7)
| ~ spl0_5
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f385]) ).
fof(f644,plain,
( spl0_22
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f228,f98,f93,f88,f79,f64,f376]) ).
fof(f645,plain,
( sk_c6 != multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f543,f219]) ).
fof(f656,plain,
( sk_c7 != sk_c6
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f645,f290]) ).
fof(f662,plain,
( ~ spl0_22
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f656,f98,f93,f88,f79,f74,f71,f64,f376]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f77]) ).
cnf(s2,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f86]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f91]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f96]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f101]) ).
cnf(s6,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f102]) ).
cnf(s7,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f107]) ).
cnf(s8,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f108]) ).
cnf(s9,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f109]) ).
cnf(s10,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f110]) ).
cnf(s11,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f111]) ).
cnf(s12,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f116]) ).
cnf(s13,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f117]) ).
cnf(s14,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f118]) ).
cnf(s15,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f119]) ).
cnf(s16,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f120]) ).
cnf(s17,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f125]) ).
cnf(s18,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f126]) ).
cnf(s19,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f127]) ).
cnf(s20,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f128]) ).
cnf(s21,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f129]) ).
cnf(s22,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f130]) ).
cnf(s23,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f131]) ).
cnf(s24,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f132]) ).
cnf(s25,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f133]) ).
cnf(s26,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f134]) ).
cnf(s27,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f286]) ).
cnf(s29,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f307]) ).
cnf(s30,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(sat_conversion,[],[f331]) ).
cnf(s36,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f381]) ).
cnf(s38,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f397]) ).
cnf(s40,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_18
| ~ spl0_22 ),
inference(sat_conversion,[],[f415]) ).
cnf(s41,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_22 ),
inference(sat_conversion,[],[f417]) ).
cnf(s45,plain,
( ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| spl0_16 ),
inference(sat_conversion,[],[f457]) ).
cnf(s47,plain,
( ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_22 ),
inference(sat_conversion,[],[f459]) ).
cnf(s49,plain,
( ~ spl0_16
| spl0_18
| ~ spl0_22 ),
inference(sat_conversion,[],[f470]) ).
cnf(s54,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(sat_conversion,[],[f520]) ).
cnf(s55,plain,
( ~ spl0_12
| ~ spl0_16
| spl0_20
| ~ spl0_22 ),
inference(sat_conversion,[],[f535]) ).
cnf(s56,plain,
( spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_20
| ~ spl0_22 ),
inference(sat_conversion,[],[f542]) ).
cnf(s71,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_22 ),
inference(sat_conversion,[],[f644]) ).
cnf(s77,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_22 ),
inference(sat_conversion,[],[f662]) ).
cnf(s81,plain,
spl0_3,
inference(rat,[],[s56,s55,s47,s45,s6,s11,s16,s21,s26]) ).
cnf(s82,plain,
spl0_6,
inference(rat,[],[s27,s22,s23,s24,s25,s81]) ).
cnf(s83,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_9
| ~ spl0_5
| ~ spl0_7 ),
inference(rat,[],[s71,s77,s82,s81]) ).
cnf(s84,plain,
( spl0_11
| ~ spl0_5 ),
inference(rat,[],[s38,s15,s20]) ).
cnf(s85,plain,
( spl0_10
| ~ spl0_5 ),
inference(rat,[],[s38,s14,s19]) ).
cnf(s86,plain,
( spl0_9
| ~ spl0_5 ),
inference(rat,[],[s38,s13,s18]) ).
cnf(s87,plain,
( ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_5 ),
inference(rat,[],[s38,s12,s17,s83]) ).
cnf(s88,plain,
~ spl0_5,
inference(rat,[],[s87,s86,s85,s84]) ).
cnf(s89,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s30,s5,s10]) ).
cnf(s90,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s30,s4,s9]) ).
cnf(s91,plain,
( spl0_9
| ~ spl0_4 ),
inference(rat,[],[s30,s3,s8]) ).
cnf(s92,plain,
( ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_4 ),
inference(rat,[],[s30,s2,s7,s29,s82,s81]) ).
cnf(s93,plain,
~ spl0_4,
inference(rat,[],[s92,s91,s90,s89]) ).
cnf(s94,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s47,s54,s5,s10,s15,s20]) ).
cnf(s95,plain,
( ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s47,s54,s4,s9,s14,s19,s36]) ).
cnf(s96,plain,
~ spl0_2,
inference(rat,[],[s95,s94]) ).
cnf(s97,plain,
spl0_1,
inference(rat,[],[s1,s81,s82,s88,s93,s96]) ).
cnf(s98,plain,
( spl0_9
| spl0_22 ),
inference(rat,[],[s47,s3,s8,s13,s18]) ).
cnf(s99,plain,
( ~ spl0_9
| ~ spl0_11
| spl0_22
| ~ spl0_10 ),
inference(rat,[],[s47,s2,s7,s12,s17,s71,s81]) ).
cnf(s100,plain,
( ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s99,s98,s41,s81,s97]) ).
cnf(s101,plain,
spl0_11,
inference(rat,[],[s49,s40,s47,s45,s5,s10,s15,s20,s97,s82]) ).
cnf(s102,plain,
~ spl0_10,
inference(rat,[],[s100,s101]) ).
cnf(s103,plain,
spl0_14,
inference(rat,[],[s19,s102]) ).
cnf(s104,plain,
spl0_13,
inference(rat,[],[s14,s102]) ).
cnf(s105,plain,
spl0_12,
inference(rat,[],[s9,s102]) ).
cnf(s106,plain,
spl0_8,
inference(rat,[],[s4,s102]) ).
cnf(s107,plain,
spl0_16,
inference(rat,[],[s45,s103,s82,s104]) ).
cnf(s108,plain,
spl0_22,
inference(rat,[],[s47,s104,s103,s106,s105]) ).
cnf(s109,plain,
~ spl0_18,
inference(rat,[],[s40,s108,s97,s105,s106]) ).
cnf(s111,plain,
$false,
inference(rat,[],[s49,s108,s109,s107]) ).
fof(f665,plain,
$false,
inference(avatar_sat_refutation,[],[s111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP291-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:51:15 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.26/1.32 % (3311102)Input is clausal, will run a generic CNF schedule.
% 3.26/1.32 % (3311111)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1794752984:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.26/1.32 % (3311107)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=141046639:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.26/1.32 % (3311110)lrs+10_1_sil=8000:sp=occurrence:random_seed=19443544:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.26/1.32 % (3311109)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=985003641:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.26/1.32 % (3311108)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3184396006:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.26/1.32 % (3311110)Refutation not found, incomplete strategy
% 3.26/1.32 % (3311110)------------------------------
% 3.26/1.32 % (3311110)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.32 % (3311110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.32 % (3311110)CaDiCaL version: 2.1.3
% 3.26/1.32 % (3311110)Termination reason: Refutation not found, incomplete strategy
% 3.26/1.32 % (3311110)Time elapsed: 0.003 s
% 3.26/1.32 % (3311110)Peak memory usage: 88 MB
% 3.26/1.32 % (3311110)Instructions burned: 3 (million)
% 3.26/1.32 % (3311111)Instruction limit reached!
% 3.26/1.32 % (3311111)------------------------------
% 3.26/1.32 % (3311111)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.32 % (3311111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.32 % (3311111)CaDiCaL version: 2.1.3
% 3.26/1.32 % (3311111)Termination reason: Instruction limit
% 3.26/1.32 % (3311111)Termination phase: Saturation
% 3.26/1.32 % (3311111)Time elapsed: 0.037 s
% 3.26/1.32 % (3311111)Peak memory usage: 89 MB
% 3.26/1.32 % (3311111)Instructions burned: 115 (million)
% 3.26/1.32 % (3311113)dis-21_1_sil=8000:lcm=predicate:random_seed=4214282542: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)
% 3.26/1.32 % (3311113)Refutation not found, incomplete strategy
% 3.26/1.32 % (3311113)------------------------------
% 3.26/1.32 % (3311113)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.32 % (3311113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.32 % (3311113)CaDiCaL version: 2.1.3
% 3.26/1.32 % (3311113)Termination reason: Refutation not found, incomplete strategy
% 3.26/1.32 % (3311113)Time elapsed: 0.002 s
% 3.26/1.32 % (3311113)Peak memory usage: 88 MB
% 3.26/1.32 % (3311113)Instructions burned: 1 (million)
% 3.26/1.32 % (3311112)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2990358757:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.26/1.32 % (3311112)First to succeed.
% 3.26/1.32 % (3311112)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3311102"
% 3.26/1.32 % (3311120)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=3419879777:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.26/1.32 % (3311120)Refutation not found, incomplete strategy
% 3.26/1.32 % (3311120)------------------------------
% 3.26/1.32 % (3311120)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.32 % (3311120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.32 % (3311120)CaDiCaL version: 2.1.3
% 3.26/1.32 % (3311120)Termination reason: Refutation not found, incomplete strategy
% 3.26/1.32 % (3311120)Time elapsed: 0.002 s
% 3.26/1.32 % (3311120)Peak memory usage: 88 MB
% 3.26/1.32 % (3311120)Instructions burned: 3 (million)
% 3.26/1.32 % (3311110)------------------------------
% 3.26/1.32 % (3311110)------------------------------
% 3.26/1.32 % (3311113)------------------------------
% 3.26/1.32 % (3311113)------------------------------
% 3.26/1.32 % (3311112)Refutation found. Thanks to Tanya!
% 3.26/1.32 % SZS status Unsatisfiable for theBenchmark
% 3.26/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.89/1.52 % (3311112)------------------------------
% 3.89/1.52 % (3311112)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.52 % (3311112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.52 % (3311112)CaDiCaL version: 2.1.3
% 3.89/1.52 % (3311112)Termination reason: Refutation
% 3.89/1.52 % (3311112)Time elapsed: 0.017 s
% 3.89/1.52 % (3311112)Peak memory usage: 89 MB
% 3.89/1.52 % (3311112)Instructions burned: 24 (million)
% 3.89/1.52 % (3311112)------------------------------
% 3.89/1.52 % (3311112)------------------------------
% 3.89/1.52 % (3311102)Success in time 0.457 s
% 3.89/1.52 % Vampire exiting
%------------------------------------------------------------------------------