%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP351-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 10:13:43 AM UTC 2026
% Result : Unsatisfiable 2.24s 1.18s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 46
% Syntax : Number of formulae : 302 ( 20 unt; 17 def)
% Number of atoms : 939 ( 272 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1221 ( 584 ~; 620 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c5 = multiply(sk_c4,sk_c6) ),
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/sandbox2/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
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/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
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c6 = inverse(sk_c2)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = inverse(sk_c2)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c6 = inverse(sk_c2)
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c5) != sk_c7
| multiply(X0,sk_c7) != sk_c6
| inverse(X0) != sk_c7
| multiply(X1,sk_c6) != sk_c5
| inverse(X1) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c6
| inverse(X3) != sk_c5
| multiply(X3,sk_c6) != sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c5) != sk_c7
| sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2)
| sk_c5 != inverse(X3)
| sk_c5 != multiply(X3,sk_c6) ),
inference(reorient_equations,[],[f55]) ).
fof(f58,definition,
( spl0_1
<=> ! [X3] :
( sk_c5 != inverse(X3)
| sk_c5 != multiply(X3,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f59,plain,
( ! [X3] :
( sk_c5 != inverse(X3)
| sk_c5 != multiply(X3,sk_c6) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f62,plain,
( ! [X2] :
( sk_c6 != 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_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f69,plain,
( ! [X1] :
( sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ 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_c6,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f75,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( multiply(sk_c6,sk_c5) != sk_c7
| 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_c5 = multiply(sk_c4,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f81,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f83,definition,
( spl0_8
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f85,plain,
( sk_c6 = 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_c5 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f90,plain,
( sk_c5 = 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_c6 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f95,plain,
( sk_c6 = inverse(sk_c3)
| ~ 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 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f100,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ 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_c5 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f106,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| ~ 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_c5,sk_c4)
| ~ spl0_9 ),
inference(superposition,[],[f3,f90]) ).
fof(f136,plain,
( identity = multiply(sk_c6,sk_c3)
| ~ spl0_10 ),
inference(superposition,[],[f3,f95]) ).
fof(f139,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f142,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c6,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f100]) ).
fof(f143,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c4,multiply(sk_c6,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f81]) ).
fof(f145,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f139,f1]) ).
fof(f148,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c3,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f136]) ).
fof(f149,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c3,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f148,f1]) ).
fof(f157,plain,
( multiply(sk_c7,sk_c3) = multiply(sk_c3,identity)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f142,f136]) ).
fof(f164,plain,
( multiply(sk_c5,sk_c3) = multiply(sk_c4,identity)
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f143,f136]) ).
fof(f182,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_3 ),
inference(superposition,[],[f145,f65]) ).
fof(f183,plain,
( sk_c3 = multiply(inverse(sk_c6),identity)
| ~ spl0_10 ),
inference(superposition,[],[f145,f136]) ).
fof(f186,plain,
( sk_c4 = multiply(inverse(sk_c5),identity)
| ~ spl0_9 ),
inference(superposition,[],[f145,f135]) ).
fof(f189,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f145,f100]) ).
fof(f198,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f189,f95]) ).
fof(f199,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f198,f65]) ).
fof(f203,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f145,f198]) ).
fof(f205,plain,
( identity = sk_c7
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f203,f3]) ).
fof(f219,plain,
( sk_c4 = multiply(inverse(sk_c6),identity)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f186,f199]) ).
fof(f220,plain,
( sk_c3 = sk_c4
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f219,f183]) ).
fof(f239,plain,
( multiply(sk_c7,sk_c3) = multiply(sk_c3,sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f157,f205]) ).
fof(f242,plain,
( multiply(sk_c5,sk_c3) = multiply(sk_c4,sk_c7)
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f164,f205]) ).
fof(f243,plain,
( multiply(sk_c5,sk_c3) = multiply(sk_c3,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f242,f220]) ).
fof(f244,plain,
( multiply(sk_c6,sk_c3) = multiply(sk_c3,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f243,f199]) ).
fof(f245,plain,
( identity = multiply(sk_c3,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f244,f136]) ).
fof(f246,plain,
( sk_c7 = multiply(sk_c3,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f245,f205]) ).
fof(f247,plain,
( sk_c7 = multiply(sk_c6,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f149,f246]) ).
fof(f251,plain,
( sk_c5 = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f247,f65]) ).
fof(f253,plain,
( sk_c6 = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f251,f199]) ).
fof(f255,plain,
( sk_c7 = multiply(sk_c7,sk_c3)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f239,f246]) ).
fof(f263,plain,
( sk_c6 = multiply(sk_c6,sk_c3)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f255,f253]) ).
fof(f268,plain,
( sk_c3 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f145,f263]) ).
fof(f271,plain,
( identity = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f268,f3]) ).
fof(f274,plain,
( sk_c7 = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f271,f205]) ).
fof(f277,plain,
( sk_c6 = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f274,f253]) ).
fof(f290,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f95,f277]) ).
fof(f332,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f182,f290]) ).
fof(f336,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f332,f76]) ).
fof(f337,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f336]) ).
fof(f341,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c6) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f69,f199]) ).
fof(f396,plain,
( sk_c6 != sk_c5
| sk_c6 != multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f341,f90]) ).
fof(f404,plain,
( sk_c6 != multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f396,f199]) ).
fof(f407,plain,
( sk_c6 != sk_c5
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f404,f81]) ).
fof(f408,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f407,f199]) ).
fof(f409,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f408]) ).
fof(f411,plain,
( sk_c6 = multiply(sk_c2,sk_c6)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f106,f199]) ).
fof(f417,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c2,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f341,f85]) ).
fof(f420,plain,
( sk_c6 != multiply(sk_c2,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f417]) ).
fof(f426,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_14 ),
inference(superposition,[],[f145,f124]) ).
fof(f428,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f426,f115]) ).
fof(f435,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f420,f411]) ).
fof(f436,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f435]) ).
fof(f439,plain,
( sk_c7 != sk_c7
| sk_c6 != multiply(sk_c1,sk_c7)
| ~ spl0_5
| ~ spl0_13 ),
inference(superposition,[],[f72,f115]) ).
fof(f441,plain,
( sk_c6 != multiply(sk_c1,sk_c7)
| ~ spl0_5
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f439]) ).
fof(f442,plain,
( $false
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f441,f124]) ).
fof(f443,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f442]) ).
fof(f448,plain,
( sk_c6 != sk_c6
| sk_c7 != multiply(sk_c3,sk_c6)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f62,f95]) ).
fof(f451,plain,
( sk_c6 != sk_c6
| sk_c7 != multiply(sk_c2,sk_c6)
| ~ spl0_2
| ~ spl0_8 ),
inference(superposition,[],[f62,f85]) ).
fof(f453,plain,
( sk_c7 != multiply(sk_c3,sk_c6)
| ~ spl0_2
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f448]) ).
fof(f456,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f453,f100]) ).
fof(f457,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f456]) ).
fof(f461,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c5 != multiply(X3,sk_c6) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f59,f199]) ).
fof(f462,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c6) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f461,f199]) ).
fof(f471,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f462,f95]) ).
fof(f476,plain,
( sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f471]) ).
fof(f480,plain,
( sk_c6 != sk_c7
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f476,f100]) ).
fof(f486,plain,
( sk_c6 = multiply(inverse(sk_c2),sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f145,f106]) ).
fof(f488,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f486,f85]) ).
fof(f493,plain,
( sk_c5 != sk_c5
| sk_c5 != multiply(sk_c4,sk_c6)
| ~ spl0_1
| ~ spl0_9 ),
inference(superposition,[],[f59,f90]) ).
fof(f495,plain,
( sk_c6 != sk_c5
| sk_c5 != multiply(sk_c2,sk_c6)
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[],[f59,f85]) ).
fof(f496,plain,
( sk_c5 != multiply(sk_c4,sk_c6)
| ~ spl0_1
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f493]) ).
fof(f497,plain,
( sk_c6 != sk_c5
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f495,f106]) ).
fof(f503,definition,
( spl0_16
<=> sk_c5 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f504,plain,
( sk_c5 = sk_c7
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f505,plain,
( sk_c5 != sk_c7
| spl0_16 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f519,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f145,f428]) ).
fof(f521,plain,
( identity = sk_c6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f519,f3]) ).
fof(f544,plain,
( sk_c6 = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f488,f75]) ).
fof(f548,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f145,f488]) ).
fof(f550,plain,
( identity = sk_c5
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f548,f3]) ).
fof(f553,plain,
( sk_c6 = sk_c5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f550,f521]) ).
fof(f554,plain,
( $false
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f553,f497]) ).
fof(f555,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f554]) ).
fof(f556,plain,
( sk_c7 != multiply(sk_c2,sk_c6)
| ~ spl0_2
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f451]) ).
fof(f562,definition,
( spl0_18
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f563,plain,
( sk_c6 = sk_c5
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f571,definition,
( spl0_20
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f572,plain,
( sk_c6 = sk_c7
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f571]) ).
fof(f575,plain,
( sk_c5 != sk_c7
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f556,f106]) ).
fof(f577,plain,
( spl0_18
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f553,f122,f113,f104,f83,f562]) ).
fof(f578,plain,
( ~ spl0_16
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f575,f104,f83,f61,f503]) ).
fof(f645,plain,
( ~ spl0_20
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f480,f98,f93,f64,f58,f571]) ).
fof(f647,plain,
( spl0_20
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f253,f98,f93,f88,f79,f64,f571]) ).
fof(f648,plain,
( sk_c6 = sk_c7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f205,f521]) ).
fof(f649,plain,
( ~ spl0_7
| ~ spl0_1
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f496,f88,f58,f79]) ).
fof(f650,plain,
( spl0_18
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f199,f98,f93,f64,f562]) ).
fof(f651,plain,
( spl0_20
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f648,f122,f113,f98,f93,f571]) ).
fof(f730,plain,
( ! [X0] :
( inverse(X0) != sk_c5
| sk_c6 != multiply(X0,sk_c7) )
| ~ spl0_5
| ~ spl0_16 ),
inference(forward_demodulation,[],[f72,f504]) ).
fof(f731,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c6 != multiply(X0,sk_c7) )
| ~ spl0_5
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f730,f563]) ).
fof(f732,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c5)
| inverse(X0) != sk_c6 )
| ~ spl0_5
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f731,f504]) ).
fof(f733,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c6 != multiply(X0,sk_c6) )
| ~ spl0_5
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f732,f563]) ).
fof(f734,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18 ),
inference(superposition,[],[f733,f95]) ).
fof(f736,plain,
( sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f734]) ).
fof(f738,plain,
( sk_c6 != sk_c7
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f736,f100]) ).
fof(f740,plain,
( $false
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f738,f572]) ).
fof(f741,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_18
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f740]) ).
fof(f745,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c6) )
| ~ spl0_4
| ~ spl0_18 ),
inference(forward_demodulation,[],[f69,f563]) ).
fof(f769,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c2,sk_c6)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_18 ),
inference(superposition,[],[f745,f85]) ).
fof(f770,plain,
( sk_c6 != multiply(sk_c2,sk_c6)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f769]) ).
fof(f773,plain,
( sk_c6 != sk_c5
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_18 ),
inference(forward_demodulation,[],[f770,f106]) ).
fof(f775,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f773,f563]) ).
fof(f776,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f775]) ).
fof(f777,plain,
( sk_c5 != multiply(sk_c6,sk_c5)
| spl0_3
| ~ spl0_16 ),
inference(forward_demodulation,[],[f66,f504]) ).
fof(f778,plain,
( sk_c5 != sk_c7
| spl0_3
| ~ spl0_6
| ~ spl0_16 ),
inference(forward_demodulation,[],[f777,f75]) ).
fof(f779,plain,
( $false
| spl0_3
| ~ spl0_6
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f778,f504]) ).
fof(f780,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f779]) ).
fof(f781,plain,
( sk_c6 != sk_c7
| spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f505,f563]) ).
fof(f782,plain,
( spl0_20
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f544,f104,f83,f74,f571]) ).
fof(f784,plain,
( ~ spl0_20
| spl0_16
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f781,f562,f503,f571]) ).
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,[],[f337]) ).
cnf(s30,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f409]) ).
cnf(s31,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f436]) ).
cnf(s32,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f443]) ).
cnf(s33,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f457]) ).
cnf(s37,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f555]) ).
cnf(s40,plain,
( ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f577]) ).
cnf(s41,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_16 ),
inference(sat_conversion,[],[f578]) ).
cnf(s52,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_20 ),
inference(sat_conversion,[],[f645]) ).
cnf(s54,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_20 ),
inference(sat_conversion,[],[f647]) ).
cnf(s56,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f649]) ).
cnf(s58,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f650]) ).
cnf(s59,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14
| spl0_20 ),
inference(sat_conversion,[],[f651]) ).
cnf(s66,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_18
| ~ spl0_20 ),
inference(sat_conversion,[],[f741]) ).
cnf(s69,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_18 ),
inference(sat_conversion,[],[f776]) ).
cnf(s70,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_16 ),
inference(sat_conversion,[],[f780]) ).
cnf(s71,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| spl0_20 ),
inference(sat_conversion,[],[f782]) ).
cnf(s73,plain,
( spl0_16
| ~ spl0_18
| ~ spl0_20 ),
inference(sat_conversion,[],[f784]) ).
cnf(s74,plain,
spl0_3,
inference(rat,[],[s73,s40,s71,s70,s6,s11,s16,s21,s26]) ).
cnf(s75,plain,
spl0_6,
inference(rat,[],[s27,s22,s23,s24,s25,s74]) ).
cnf(s76,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_9
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s66,s73,s54,s58,s74]) ).
cnf(s77,plain,
( spl0_11
| ~ spl0_5 ),
inference(rat,[],[s32,s15,s20]) ).
cnf(s78,plain,
( spl0_10
| ~ spl0_5 ),
inference(rat,[],[s32,s14,s19]) ).
cnf(s79,plain,
( spl0_9
| ~ spl0_5 ),
inference(rat,[],[s32,s13,s18]) ).
cnf(s80,plain,
( ~ spl0_9
| ~ spl0_5
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s32,s12,s17,s76]) ).
cnf(s81,plain,
~ spl0_5,
inference(rat,[],[s80,s79,s78,s77]) ).
cnf(s82,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s69,s40,s5,s10,s15,s20]) ).
cnf(s83,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s69,s40,s4,s9,s14,s19]) ).
cnf(s84,plain,
( spl0_9
| ~ spl0_4 ),
inference(rat,[],[s69,s3,s8,s58,s83,s82,s74]) ).
cnf(s85,plain,
( ~ spl0_9
| ~ spl0_11
| ~ spl0_4
| ~ spl0_10 ),
inference(rat,[],[s31,s2,s7,s30,s74]) ).
cnf(s86,plain,
~ spl0_4,
inference(rat,[],[s85,s84,s83,s82]) ).
cnf(s87,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s73,s41,s40,s71,s5,s10,s15,s20,s75]) ).
cnf(s88,plain,
( ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s73,s41,s40,s71,s4,s9,s14,s19,s33,s75]) ).
cnf(s89,plain,
~ spl0_2,
inference(rat,[],[s88,s87]) ).
cnf(s90,plain,
spl0_1,
inference(rat,[],[s1,s74,s75,s81,s86,s89]) ).
cnf(s91,plain,
( spl0_9
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s59,s13,s18,s52,s74,s90]) ).
cnf(s92,plain,
( ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s59,s12,s17,s56,s91,s52,s74,s90]) ).
cnf(s93,plain,
spl0_11,
inference(rat,[],[s37,s5,s10,s15,s20,s90]) ).
cnf(s94,plain,
~ spl0_10,
inference(rat,[],[s92,s93]) ).
cnf(s95,plain,
spl0_14,
inference(rat,[],[s19,s94]) ).
cnf(s96,plain,
spl0_13,
inference(rat,[],[s14,s94]) ).
cnf(s97,plain,
spl0_12,
inference(rat,[],[s9,s94]) ).
cnf(s98,plain,
spl0_8,
inference(rat,[],[s4,s94]) ).
cnf(s99,plain,
$false,
inference(rat,[],[s37,s95,s96,s90,s97,s98]) ).
fof(f785,plain,
$false,
inference(avatar_sat_refutation,[],[s99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP351-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n006.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
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 09:54:55 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.24/1.18 % (2745881)Input is clausal, will run a generic CNF schedule.
% 2.24/1.18 % (2745904)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3835584537:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.24/1.18 % (2745904)First to succeed.
% 2.24/1.18 % (2745904)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2745881"
% 2.24/1.18 % (2745901)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3585628727:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.24/1.18 % (2745899)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=1433924216:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.24/1.18 % (2745900)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4159111788:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.24/1.18 % (2745902)lrs+10_1_sil=8000:sp=occurrence:random_seed=2633853682:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.24/1.18 % (2745902)Refutation not found, incomplete strategy
% 2.24/1.18 % (2745902)------------------------------
% 2.24/1.18 % (2745902)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.24/1.18 % (2745902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/1.18 % (2745902)CaDiCaL version: 2.1.3
% 2.24/1.18 % (2745902)Termination reason: Refutation not found, incomplete strategy
% 2.24/1.18 % (2745902)Time elapsed: 0.003 s
% 2.24/1.18 % (2745902)Peak memory usage: 88 MB
% 2.24/1.18 % (2745902)Instructions burned: 3 (million)
% 2.24/1.18 % (2745905)dis-21_1_sil=8000:lcm=predicate:random_seed=1242898073: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)
% 2.24/1.18 % (2745905)Refutation not found, incomplete strategy
% 2.24/1.18 % (2745905)------------------------------
% 2.24/1.18 % (2745905)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.24/1.18 % (2745905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/1.18 % (2745905)CaDiCaL version: 2.1.3
% 2.24/1.18 % (2745905)Termination reason: Refutation not found, incomplete strategy
% 2.24/1.18 % (2745905)Time elapsed: 0.002 s
% 2.24/1.18 % (2745905)Peak memory usage: 88 MB
% 2.24/1.18 % (2745905)Instructions burned: 1 (million)
% 2.24/1.18 % (2745903)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2733180274:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.24/1.18 % (2745903)Instruction limit reached!
% 2.24/1.18 % (2745903)------------------------------
% 2.24/1.18 % (2745903)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.24/1.18 % (2745903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/1.18 % (2745903)CaDiCaL version: 2.1.3
% 2.24/1.18 % (2745903)Termination reason: Instruction limit
% 2.24/1.18 % (2745903)Termination phase: Saturation
% 2.24/1.18 % (2745903)Time elapsed: 0.080 s
% 2.24/1.18 % (2745903)Peak memory usage: 89 MB
% 2.24/1.18 % (2745903)Instructions burned: 116 (million)
% 2.24/1.18 % (2745904)Refutation found. Thanks to Tanya!
% 2.24/1.18 % SZS status Unsatisfiable for theBenchmark
% 2.24/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.51 % (2745904)------------------------------
% 0.18/1.51 % (2745904)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.51 % (2745904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.51 % (2745904)CaDiCaL version: 2.1.3
% 0.18/1.51 % (2745904)Termination reason: Refutation
% 0.18/1.51 % (2745904)Time elapsed: 0.010 s
% 0.18/1.51 % (2745904)Peak memory usage: 89 MB
% 0.18/1.51 % (2745904)Instructions burned: 28 (million)
% 0.18/1.51 % (2745904)------------------------------
% 0.18/1.51 % (2745904)------------------------------
% 0.18/1.51 % (2745881)Success in time 0.327 s
% 0.18/1.51 % Vampire exiting
%------------------------------------------------------------------------------