%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% 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 10:17:34 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.44s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 42
% Syntax : Number of formulae : 326 ( 24 unt; 15 def)
% Number of atoms : 1123 ( 297 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1566 ( 769 ~; 782 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c6,sk_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(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(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_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) )
| ~ 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] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(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(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(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(f141,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c5,multiply(sk_c4,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f135]) ).
fof(f143,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c4,multiply(sk_c6,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f81]) ).
fof(f144,plain,
( ! [X0] : multiply(sk_c5,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(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(f153,plain,
( sk_c6 = multiply(sk_c5,sk_c5)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f144,f81]) ).
fof(f164,plain,
( multiply(sk_c5,sk_c3) = multiply(sk_c4,identity)
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f143,f136]) ).
fof(f170,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f149,f100]) ).
fof(f180,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f145,f3]) ).
fof(f181,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f145,f145]) ).
fof(f183,plain,
( sk_c3 = multiply(inverse(sk_c6),identity)
| ~ spl0_10 ),
inference(superposition,[],[f145,f136]) ).
fof(f185,plain,
( ! [X0] : multiply(sk_c3,X0) = multiply(inverse(sk_c6),X0)
| ~ spl0_10 ),
inference(superposition,[],[f145,f149]) ).
fof(f186,plain,
( sk_c4 = multiply(inverse(sk_c5),identity)
| ~ spl0_9 ),
inference(superposition,[],[f145,f135]) ).
fof(f187,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(inverse(sk_c5),X0)
| ~ spl0_9 ),
inference(superposition,[],[f145,f144]) ).
fof(f199,plain,
( sk_c4 = multiply(sk_c4,identity)
| ~ spl0_9 ),
inference(forward_demodulation,[],[f186,f187]) ).
fof(f201,plain,
( sk_c3 = multiply(sk_c3,identity)
| ~ spl0_10 ),
inference(forward_demodulation,[],[f183,f185]) ).
fof(f203,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f180,f181]) ).
fof(f224,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f65,f170]) ).
fof(f227,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f145,f170]) ).
fof(f229,plain,
( identity = sk_c7
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f227,f3]) ).
fof(f244,plain,
( sk_c7 != multiply(sk_c6,sk_c6)
| ~ spl0_3
| spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f76,f224]) ).
fof(f247,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f153,f224]) ).
fof(f252,plain,
( sk_c6 != sk_c7
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f244,f247]) ).
fof(f265,plain,
( sk_c3 = multiply(sk_c3,sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f201,f229]) ).
fof(f266,plain,
( sk_c4 = multiply(sk_c4,sk_c7)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f199,f229]) ).
fof(f267,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f1,f229]) ).
fof(f271,plain,
( sk_c4 = multiply(sk_c5,sk_c3)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f199,f164]) ).
fof(f273,plain,
( identity = multiply(inverse(sk_c4),multiply(sk_c5,sk_c3))
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f145,f164]) ).
fof(f276,plain,
( identity = multiply(inverse(sk_c4),multiply(sk_c6,sk_c3))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f273,f224]) ).
fof(f278,plain,
( sk_c4 = multiply(sk_c6,sk_c3)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f271,f224]) ).
fof(f282,plain,
( identity = multiply(inverse(sk_c4),identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f276,f136]) ).
fof(f284,plain,
( identity = inverse(sk_c4)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f282,f203]) ).
fof(f285,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f284,f90]) ).
fof(f286,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f285,f224]) ).
fof(f287,plain,
( sk_c6 = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f286,f229]) ).
fof(f288,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f1,f286]) ).
fof(f291,plain,
( sk_c4 = multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f199,f286]) ).
fof(f292,plain,
( sk_c3 = multiply(sk_c3,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f201,f286]) ).
fof(f296,plain,
( sk_c7 = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f292,f100]) ).
fof(f297,plain,
( sk_c5 = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f291,f81]) ).
fof(f300,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f287,f252]) ).
fof(f301,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f300]) ).
fof(f302,plain,
( sk_c6 = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f297,f224]) ).
fof(f307,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f69,f224]) ).
fof(f313,plain,
( sk_c6 != sk_c7
| sk_c6 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f307,f100]) ).
fof(f314,plain,
( sk_c6 != sk_c5
| sk_c6 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f307,f81]) ).
fof(f316,plain,
( sk_c6 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f314,f224]) ).
fof(f320,plain,
( sk_c6 != sk_c5
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f316,f90]) ).
fof(f324,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f320,f224]) ).
fof(f325,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f324]) ).
fof(f329,plain,
( sk_c6 != sk_c7
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f313,f95]) ).
fof(f332,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_8 ),
inference(superposition,[],[f3,f85]) ).
fof(f333,plain,
( sk_c7 = multiply(sk_c6,sk_c2)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f332,f229]) ).
fof(f335,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_13 ),
inference(superposition,[],[f3,f115]) ).
fof(f336,plain,
( identity = sk_c1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f335,f267]) ).
fof(f338,plain,
( sk_c7 = sk_c1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f336,f229]) ).
fof(f339,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_14 ),
inference(superposition,[],[f145,f124]) ).
fof(f342,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f339,f115]) ).
fof(f344,plain,
( sk_c6 = sk_c7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f342,f267]) ).
fof(f345,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f344,f329]) ).
fof(f346,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f345]) ).
fof(f348,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(superposition,[],[f115,f338]) ).
fof(f349,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f348,f344]) ).
fof(f377,plain,
( sk_c2 = multiply(inverse(sk_c6),sk_c7)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f145,f333]) ).
fof(f380,plain,
( sk_c2 = multiply(sk_c3,sk_c7)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f377,f185]) ).
fof(f382,plain,
( sk_c3 = sk_c2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f380,f265]) ).
fof(f387,plain,
( identity != sk_c6
| sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_5 ),
inference(superposition,[],[f72,f3]) ).
fof(f388,plain,
( sk_c6 != sk_c6
| sk_c7 != inverse(sk_c6)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f72,f170]) ).
fof(f389,plain,
( sk_c6 != sk_c5
| sk_c7 != inverse(sk_c6)
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f72,f65]) ).
fof(f390,plain,
( sk_c6 != sk_c6
| sk_c7 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_14 ),
inference(superposition,[],[f72,f124]) ).
fof(f391,plain,
( sk_c7 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f390]) ).
fof(f393,plain,
( $false
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f391,f115]) ).
fof(f394,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f393]) ).
fof(f397,plain,
( sk_c6 != sk_c7
| sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f387,f229]) ).
fof(f446,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c5 != multiply(X3,sk_c6) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f59,f224]) ).
fof(f447,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f446,f224]) ).
fof(f468,plain,
( sk_c6 != sk_c6
| sk_c6 != inverse(identity)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f447,f1]) ).
fof(f472,plain,
( sk_c6 != sk_c7
| sk_c6 != inverse(sk_c3)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f447,f100]) ).
fof(f475,plain,
( sk_c6 != inverse(identity)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f468]) ).
fof(f481,plain,
( sk_c6 != inverse(sk_c7)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f475,f229]) ).
fof(f487,plain,
( sk_c6 != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f481,f344]) ).
fof(f490,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f487,f349]) ).
fof(f491,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f490]) ).
fof(f500,plain,
( sk_c2 = multiply(inverse(sk_c6),identity)
| ~ spl0_8 ),
inference(superposition,[],[f145,f332]) ).
fof(f503,plain,
( sk_c2 = inverse(sk_c6)
| ~ spl0_8 ),
inference(forward_demodulation,[],[f500,f203]) ).
fof(f507,plain,
( identity != sk_c7
| sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_2 ),
inference(superposition,[],[f62,f3]) ).
fof(f508,plain,
( sk_c7 != sk_c7
| sk_c6 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f62,f100]) ).
fof(f512,plain,
( sk_c6 != inverse(sk_c2)
| identity != sk_c7
| ~ spl0_2
| ~ spl0_8 ),
inference(forward_demodulation,[],[f507,f503]) ).
fof(f518,definition,
( spl0_16
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f519,plain,
( sk_c6 = sk_c7
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f518]) ).
fof(f520,plain,
( sk_c6 != sk_c7
| spl0_16 ),
inference(avatar_component_clause,[],[f518]) ).
fof(f522,plain,
( identity != sk_c7
| ~ spl0_2
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f512,f85]) ).
fof(f524,plain,
( sk_c1 = multiply(inverse(sk_c7),identity)
| ~ spl0_13 ),
inference(superposition,[],[f145,f335]) ).
fof(f527,plain,
( sk_c1 = inverse(sk_c7)
| ~ spl0_13 ),
inference(forward_demodulation,[],[f524,f203]) ).
fof(f530,plain,
( identity = multiply(sk_c2,sk_c6)
| ~ spl0_8 ),
inference(superposition,[],[f3,f503]) ).
fof(f531,plain,
( identity = sk_c5
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f530,f106]) ).
fof(f555,plain,
( identity = multiply(sk_c1,sk_c7)
| ~ spl0_13 ),
inference(superposition,[],[f3,f527]) ).
fof(f556,plain,
( identity = sk_c6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f555,f124]) ).
fof(f575,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f1,f556]) ).
fof(f578,plain,
( sk_c6 != sk_c7
| ~ spl0_2
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f522,f556]) ).
fof(f579,plain,
( sk_c6 = sk_c5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f531,f556]) ).
fof(f580,plain,
( ~ spl0_16
| ~ spl0_2
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f578,f122,f113,f83,f61,f518]) ).
fof(f582,plain,
( sk_c7 = multiply(sk_c6,sk_c6)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f75,f579]) ).
fof(f591,plain,
( sk_c6 = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f582,f575]) ).
fof(f594,plain,
( $false
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_16 ),
inference(forward_subsumption_resolution,[],[f591,f520]) ).
fof(f595,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_16 ),
inference(avatar_contradiction_clause,[],[f594]) ).
fof(f597,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c5 != multiply(X3,sk_c6) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f59,f579]) ).
fof(f598,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f597,f579]) ).
fof(f601,plain,
( identity != sk_c6
| sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f598,f3]) ).
fof(f606,plain,
( sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f601,f556]) ).
fof(f609,plain,
( sk_c6 != inverse(sk_c2)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f606,f503]) ).
fof(f610,plain,
( $false
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f609,f85]) ).
fof(f611,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f610]) ).
fof(f612,plain,
( sk_c5 != sk_c7
| spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f66,f575]) ).
fof(f613,plain,
( sk_c6 != sk_c5
| spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_demodulation,[],[f612,f519]) ).
fof(f614,plain,
( $false
| spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f613,f579]) ).
fof(f615,plain,
( spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f614]) ).
fof(f619,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f69,f579]) ).
fof(f635,plain,
( identity != sk_c6
| sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f619,f3]) ).
fof(f640,plain,
( sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f635,f556]) ).
fof(f643,plain,
( sk_c6 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f640,f503]) ).
fof(f644,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f643,f85]) ).
fof(f645,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f644]) ).
fof(f646,plain,
( sk_c6 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f508]) ).
fof(f650,plain,
( ~ spl0_10
| ~ spl0_2
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f646,f98,f61,f93]) ).
fof(f654,plain,
( sk_c6 = multiply(sk_c6,sk_c3)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f278,f302]) ).
fof(f688,plain,
( sk_c6 = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f654,f288]) ).
fof(f717,plain,
( sk_c7 != inverse(sk_c6)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f389,f224]) ).
fof(f722,plain,
( sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f397,f519]) ).
fof(f727,plain,
( sk_c7 != sk_c2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f717,f503]) ).
fof(f730,plain,
( sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_demodulation,[],[f722,f519]) ).
fof(f734,plain,
( sk_c7 != sk_c3
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f727,f382]) ).
fof(f737,plain,
( sk_c6 != inverse(sk_c2)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_demodulation,[],[f730,f503]) ).
fof(f748,plain,
( $false
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f737,f85]) ).
fof(f749,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f748]) ).
fof(f764,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f266,f302]) ).
fof(f781,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f734,f296]) ).
fof(f782,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f781]) ).
fof(f786,plain,
( sk_c6 = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f764,f288]) ).
fof(f799,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_16 ),
inference(forward_subsumption_resolution,[],[f786,f520]) ).
fof(f800,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_16 ),
inference(avatar_contradiction_clause,[],[f799]) ).
fof(f805,plain,
( sk_c6 != sk_c7
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f472,f95]) ).
fof(f826,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f805,f519]) ).
fof(f827,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f826]) ).
fof(f858,plain,
( sk_c7 != inverse(sk_c6)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f388]) ).
fof(f863,plain,
( sk_c6 != inverse(sk_c6)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_demodulation,[],[f858,f519]) ).
fof(f897,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f95,f688]) ).
fof(f902,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f897,f863]) ).
fof(f903,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f902]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f77]) ).
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(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(s28,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f301]) ).
cnf(s30,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f325]) ).
cnf(s31,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f346]) ).
cnf(s32,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f394]) ).
cnf(s46,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f491]) ).
cnf(s48,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(sat_conversion,[],[f580]) ).
cnf(s49,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_16 ),
inference(sat_conversion,[],[f595]) ).
cnf(s51,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f611]) ).
cnf(s52,plain,
( spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(sat_conversion,[],[f615]) ).
cnf(s54,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f645]) ).
cnf(s55,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f650]) ).
cnf(s65,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(sat_conversion,[],[f749]) ).
cnf(s75,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f782]) ).
cnf(s82,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f800]) ).
cnf(s83,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(sat_conversion,[],[f827]) ).
cnf(s87,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(sat_conversion,[],[f903]) ).
cnf(s88,plain,
spl0_3,
inference(rat,[],[s52,s49,s6,s11,s16,s21,s26]) ).
cnf(s89,plain,
spl0_6,
inference(rat,[],[s28,s22,s23,s24,s25,s88]) ).
cnf(s90,plain,
( spl0_11
| ~ spl0_5 ),
inference(rat,[],[s32,s15,s20]) ).
cnf(s91,plain,
( spl0_10
| ~ spl0_5 ),
inference(rat,[],[s32,s14,s19]) ).
cnf(s92,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_11
| ~ spl0_5
| ~ spl0_10 ),
inference(rat,[],[s49,s8,s13,s18,s65,s75,s88,s89]) ).
cnf(s93,plain,
( ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_5 ),
inference(rat,[],[s87,s82,s3,s92,s88]) ).
cnf(s94,plain,
( ~ spl0_10
| ~ spl0_5
| ~ spl0_11 ),
inference(rat,[],[s32,s12,s17,s93]) ).
cnf(s95,plain,
~ spl0_5,
inference(rat,[],[s94,s91,s90]) ).
cnf(s96,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s54,s5,s10,s15,s20]) ).
cnf(s97,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s31,s13,s18,s30,s88]) ).
cnf(s98,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s54,s4,s9,s14,s19]) ).
cnf(s99,plain,
( ~ spl0_10
| ~ spl0_4
| ~ spl0_11 ),
inference(rat,[],[s31,s12,s17,s97,s88]) ).
cnf(s100,plain,
~ spl0_4,
inference(rat,[],[s99,s98,s96]) ).
cnf(s101,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s49,s48,s5,s10,s15,s20,s89]) ).
cnf(s102,plain,
( ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s49,s48,s4,s9,s14,s19,s55,s89]) ).
cnf(s103,plain,
~ spl0_2,
inference(rat,[],[s102,s101]) ).
cnf(s104,plain,
spl0_1,
inference(rat,[],[s1,s88,s89,s95,s100,s103]) ).
cnf(s105,plain,
spl0_11,
inference(rat,[],[s51,s5,s10,s15,s20,s104]) ).
cnf(s106,plain,
( ~ spl0_14
| ~ spl0_13 ),
inference(rat,[],[s51,s4,s9,s46,s88,s105,s104]) ).
cnf(s107,plain,
spl0_14,
inference(rat,[],[s82,s83,s17,s18,s19,s88,s105,s104]) ).
cnf(s108,plain,
~ spl0_13,
inference(rat,[],[s106,s107]) ).
cnf(s109,plain,
spl0_10,
inference(rat,[],[s14,s108]) ).
cnf(s110,plain,
spl0_9,
inference(rat,[],[s13,s108]) ).
cnf(s111,plain,
spl0_7,
inference(rat,[],[s12,s108]) ).
cnf(s112,plain,
~ spl0_16,
inference(rat,[],[s83,s104,s88,s105,s109]) ).
cnf(s113,plain,
$false,
inference(rat,[],[s82,s109,s105,s111,s88,s110,s112]) ).
fof(f905,plain,
$false,
inference(avatar_sat_refutation,[],[s113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP351-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.35 % Computer : n001.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 27 10:01:15 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 Running first-order model finding
% 0.12/0.38 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.44 % (3316079)Will run a generic schedule for satisfiability detection.
% 0.12/0.44 % (3316088)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2607338964:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.44 % (3316085)% WARNING: option uhcvi not known.
% 0.12/0.44 % (3316087)dis+10_1_sil=32000:sp=arity:random_seed=1915400529:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.44 % (3316089)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3547137826:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.44 % (3316084)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4088294929_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.44 % (3316086)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=441103722:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.44 % (3316090)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2379981574:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.44 % (3316088) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3316079-3316088"...
% 0.12/0.44 % (3316085)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1601809098:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.44 % TRYING [1]
% 0.12/0.44 % (3316088)...printing done.
% 0.12/0.44 % TRYING [2]
% 0.12/0.44 % (3316088)Refutation found. Thanks to Tanya!
% 0.12/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.44 % (3316088)------------------------------
% 0.12/0.44 % (3316088)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.44 % (3316088)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.44 % (3316088)CaDiCaL version: 2.1.3
% 0.12/0.44 % (3316088)Termination reason: Refutation
% 0.12/0.44 % (3316088)Time elapsed: 0.010 s
% 0.12/0.44 % (3316088)Peak memory usage: 12 MB
% 0.12/0.44 % (3316088)Instructions burned: 27 (million)
% 0.12/0.44 % (3316079)Success in time 0.046 s
% 0.12/0.44 % Vampire exiting
%------------------------------------------------------------------------------