%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP289-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 10:17:23 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 46
% Syntax : Number of formulae : 350 ( 26 unt; 19 def)
% Number of atoms : 1121 ( 300 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1490 ( 719 ~; 752 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_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(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_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/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
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/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
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c6 = 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_c6) != sk_c5
| inverse(X1) != sk_c6
| 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_c5 != multiply(X1,sk_c6)
| sk_c6 != 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 != multiply(X3,sk_c5)
| sk_c6 != inverse(X3) )
| ~ 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 != multiply(X2,sk_c6)
| sk_c7 != 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_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(f80,plain,
( sk_c6 != multiply(sk_c4,sk_c5)
| spl0_7 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f81,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| ~ 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_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_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(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(f148,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c3,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f136]) ).
fof(f149,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c3,X0)) = X0
| ~ spl0_11 ),
inference(forward_demodulation,[],[f148,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(f158,plain,
( multiply(sk_c7,sk_c4) = multiply(sk_c3,identity)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f142,f135]) ).
fof(f170,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f149,f95]) ).
fof(f179,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f145,f3]) ).
fof(f180,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f145,f145]) ).
fof(f181,plain,
( sk_c3 = multiply(inverse(sk_c7),identity)
| ~ spl0_11 ),
inference(superposition,[],[f145,f136]) ).
fof(f182,plain,
( ! [X0] : multiply(sk_c3,X0) = multiply(inverse(sk_c7),X0)
| ~ spl0_11 ),
inference(superposition,[],[f145,f149]) ).
fof(f184,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(inverse(sk_c6),X0)
| ~ spl0_9 ),
inference(superposition,[],[f145,f144]) ).
fof(f185,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_3 ),
inference(superposition,[],[f145,f65]) ).
fof(f186,plain,
( sk_c6 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f145,f154]) ).
fof(f187,plain,
( sk_c4 = multiply(inverse(sk_c6),identity)
| ~ spl0_9 ),
inference(superposition,[],[f145,f135]) ).
fof(f198,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f185,f186]) ).
fof(f200,plain,
( sk_c3 = multiply(sk_c3,identity)
| ~ spl0_11 ),
inference(forward_demodulation,[],[f181,f182]) ).
fof(f201,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f179,f180]) ).
fof(f205,plain,
( identity = multiply(sk_c6,sk_c3)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f136,f198]) ).
fof(f206,plain,
( sk_c5 != multiply(sk_c6,sk_c6)
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f76,f198]) ).
fof(f208,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f206,f154]) ).
fof(f209,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f208]) ).
fof(f213,plain,
( identity != sk_c5
| sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_4 ),
inference(superposition,[],[f69,f3]) ).
fof(f214,plain,
( sk_c5 != sk_c5
| sk_c6 != inverse(sk_c6)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f69,f154]) ).
fof(f216,plain,
( sk_c6 != inverse(sk_c6)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f214]) ).
fof(f219,definition,
( spl0_15
<=> sk_c6 = inverse(inverse(sk_c6)) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f220,plain,
( sk_c6 = inverse(inverse(sk_c6))
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f221,plain,
( sk_c6 != inverse(inverse(sk_c6))
| spl0_15 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f223,definition,
( spl0_16
<=> identity = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f224,plain,
( identity = sk_c5
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f225,plain,
( identity != sk_c5
| spl0_16 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f226,plain,
( ~ spl0_15
| ~ spl0_16
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f213,f68,f223,f219]) ).
fof(f232,definition,
( spl0_18
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f233,plain,
( sk_c6 = sk_c5
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f234,plain,
( sk_c6 != sk_c5
| spl0_18 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f288,plain,
( sk_c3 = multiply(inverse(sk_c6),identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f145,f205]) ).
fof(f291,plain,
( sk_c3 = multiply(sk_c4,identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f288,f184]) ).
fof(f293,plain,
( sk_c3 = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f291,f201]) ).
fof(f307,plain,
( sk_c6 = inverse(sk_c3)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f90,f293]) ).
fof(f311,plain,
( identity = multiply(inverse(sk_c3),multiply(sk_c7,sk_c4))
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f145,f158]) ).
fof(f314,plain,
( identity = multiply(inverse(sk_c3),multiply(sk_c7,sk_c3))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f311,f293]) ).
fof(f319,plain,
( identity = multiply(inverse(sk_c3),identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f314,f136]) ).
fof(f322,plain,
( identity = inverse(sk_c3)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f319,f201]) ).
fof(f323,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f322,f100]) ).
fof(f324,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f323,f198]) ).
fof(f327,plain,
( sk_c3 = multiply(sk_c3,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f200,f324]) ).
fof(f329,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f1,f324]) ).
fof(f330,plain,
( sk_c7 = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f327,f95]) ).
fof(f333,plain,
( sk_c6 = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f330,f198]) ).
fof(f344,plain,
( sk_c7 = inverse(sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f100,f333]) ).
fof(f345,plain,
( identity = multiply(sk_c7,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f136,f333]) ).
fof(f349,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c6,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f157,f333]) ).
fof(f355,plain,
( sk_c5 = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f349,f329]) ).
fof(f359,plain,
( identity = multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f345,f198]) ).
fof(f360,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f344,f198]) ).
fof(f365,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f355,f170]) ).
fof(f369,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f359,f154]) ).
fof(f370,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f360,f216]) ).
fof(f371,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f370]) ).
fof(f372,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f365,f234]) ).
fof(f373,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_18 ),
inference(avatar_contradiction_clause,[],[f372]) ).
fof(f377,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_16 ),
inference(forward_subsumption_resolution,[],[f369,f225]) ).
fof(f378,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_16 ),
inference(avatar_contradiction_clause,[],[f377]) ).
fof(f380,plain,
( sk_c6 = inverse(sk_c1)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f115,f198]) ).
fof(f381,plain,
( sk_c6 = multiply(sk_c1,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_demodulation,[],[f124,f198]) ).
fof(f394,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_8 ),
inference(superposition,[],[f3,f85]) ).
fof(f398,plain,
( sk_c5 != sk_c5
| sk_c6 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_12 ),
inference(superposition,[],[f69,f106]) ).
fof(f401,plain,
( sk_c6 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f398]) ).
fof(f403,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f401,f85]) ).
fof(f404,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f403]) ).
fof(f405,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f62,f198]) ).
fof(f406,plain,
( ! [X2] :
( sk_c6 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f405,f198]) ).
fof(f413,plain,
( sk_c6 != sk_c5
| sk_c6 != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f406,f154]) ).
fof(f415,plain,
( sk_c6 != sk_c6
| sk_c6 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(superposition,[],[f406,f381]) ).
fof(f417,plain,
( sk_c6 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f415]) ).
fof(f419,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f417,f380]) ).
fof(f420,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f419]) ).
fof(f422,definition,
( spl0_20
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f423,plain,
( identity = sk_c6
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f427,plain,
( sk_c2 = multiply(inverse(sk_c6),identity)
| ~ spl0_8 ),
inference(superposition,[],[f145,f394]) ).
fof(f430,plain,
( sk_c4 = sk_c2
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f427,f187]) ).
fof(f436,plain,
( identity != sk_c6
| sk_c6 != inverse(inverse(sk_c5))
| ~ spl0_1 ),
inference(superposition,[],[f59,f3]) ).
fof(f438,plain,
( sk_c6 != sk_c6
| sk_c6 != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f59,f81]) ).
fof(f439,plain,
( sk_c6 != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f438]) ).
fof(f440,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f439,f90]) ).
fof(f441,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f440]) ).
fof(f452,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c6)
| inverse(X0) != sk_c7 )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f72,f198]) ).
fof(f453,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f452,f198]) ).
fof(f455,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12 ),
inference(superposition,[],[f106,f430]) ).
fof(f461,plain,
( sk_c7 != sk_c6
| sk_c6 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f453,f95]) ).
fof(f462,plain,
( sk_c6 != sk_c6
| sk_c6 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(superposition,[],[f453,f381]) ).
fof(f464,plain,
( sk_c6 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f462]) ).
fof(f466,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f464,f380]) ).
fof(f467,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f466]) ).
fof(f471,plain,
( sk_c2 = inverse(sk_c6)
| ~ spl0_8 ),
inference(forward_demodulation,[],[f427,f201]) ).
fof(f474,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_13 ),
inference(superposition,[],[f3,f115]) ).
fof(f480,plain,
( identity = multiply(sk_c2,sk_c6)
| ~ spl0_8 ),
inference(superposition,[],[f3,f471]) ).
fof(f481,plain,
( identity = sk_c5
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f480,f106]) ).
fof(f482,plain,
( $false
| ~ spl0_8
| ~ spl0_12
| spl0_16 ),
inference(forward_subsumption_resolution,[],[f481,f225]) ).
fof(f483,plain,
( ~ spl0_8
| ~ spl0_12
| spl0_16 ),
inference(avatar_contradiction_clause,[],[f482]) ).
fof(f484,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_14 ),
inference(superposition,[],[f145,f124]) ).
fof(f485,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c1,multiply(sk_c7,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f124]) ).
fof(f486,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f484,f115]) ).
fof(f488,plain,
( ! [X0] : multiply(sk_c5,X0) = X0
| ~ spl0_16 ),
inference(superposition,[],[f1,f224]) ).
fof(f490,plain,
( ! [X0,X1] :
( sk_c7 != multiply(X0,multiply(X1,sk_c6))
| sk_c7 != inverse(multiply(X0,X1)) )
| ~ spl0_2 ),
inference(superposition,[],[f62,f4]) ).
fof(f509,definition,
( spl0_25
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f510,plain,
( sk_c7 = sk_c6
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f511,plain,
( sk_c7 != sk_c6
| spl0_25 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f521,plain,
( multiply(sk_c6,identity) = multiply(sk_c5,sk_c1)
| ~ spl0_3
| ~ spl0_13 ),
inference(superposition,[],[f140,f474]) ).
fof(f522,plain,
( sk_c1 = multiply(inverse(sk_c7),identity)
| ~ spl0_13 ),
inference(superposition,[],[f145,f474]) ).
fof(f525,plain,
( sk_c1 = inverse(sk_c7)
| ~ spl0_13 ),
inference(forward_demodulation,[],[f522,f201]) ).
fof(f526,plain,
( sk_c1 = multiply(sk_c6,identity)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f521,f488]) ).
fof(f527,plain,
( sk_c6 = sk_c1
| ~ spl0_3
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f526,f201]) ).
fof(f530,plain,
( sk_c7 = inverse(sk_c6)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_16 ),
inference(superposition,[],[f115,f527]) ).
fof(f545,plain,
( identity = multiply(sk_c1,sk_c7)
| ~ spl0_13 ),
inference(superposition,[],[f3,f525]) ).
fof(f546,plain,
( identity = sk_c6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f545,f124]) ).
fof(f548,plain,
( spl0_20
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f546,f122,f113,f422]) ).
fof(f549,plain,
( sk_c6 = sk_c5
| ~ spl0_16
| ~ spl0_20 ),
inference(superposition,[],[f423,f224]) ).
fof(f552,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_20 ),
inference(superposition,[],[f1,f423]) ).
fof(f556,plain,
( $false
| ~ spl0_16
| spl0_18
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f549,f234]) ).
fof(f557,plain,
( ~ spl0_16
| spl0_18
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f556]) ).
fof(f618,plain,
( sk_c7 != multiply(sk_c6,sk_c6)
| sk_c7 != inverse(multiply(sk_c1,sk_c7))
| ~ spl0_2
| ~ spl0_14 ),
inference(superposition,[],[f490,f485]) ).
fof(f621,plain,
( sk_c7 != sk_c6
| sk_c7 != inverse(multiply(sk_c1,sk_c7))
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f618,f552]) ).
fof(f675,plain,
( sk_c7 != inverse(sk_c6)
| sk_c7 != sk_c6
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f621,f124]) ).
fof(f687,plain,
( sk_c7 != sk_c6
| ~ spl0_2
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f675,f530]) ).
fof(f692,plain,
( ~ spl0_25
| ~ spl0_2
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f687,f422,f223,f122,f113,f64,f61,f509]) ).
fof(f714,plain,
( sk_c7 = sk_c5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f486,f75]) ).
fof(f729,plain,
( sk_c7 = sk_c6
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18 ),
inference(forward_demodulation,[],[f714,f233]) ).
fof(f734,plain,
( $false
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| spl0_25 ),
inference(forward_subsumption_resolution,[],[f729,f511]) ).
fof(f735,plain,
( ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| spl0_25 ),
inference(avatar_contradiction_clause,[],[f734]) ).
fof(f743,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| spl0_25 ),
inference(forward_subsumption_resolution,[],[f198,f511]) ).
fof(f744,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| spl0_25 ),
inference(avatar_contradiction_clause,[],[f743]) ).
fof(f752,plain,
( sk_c6 != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f413,f233]) ).
fof(f761,plain,
( sk_c6 != inverse(sk_c2)
| ~ spl0_8
| spl0_15 ),
inference(forward_demodulation,[],[f221,f471]) ).
fof(f771,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f752,f360]) ).
fof(f772,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f771]) ).
fof(f781,plain,
( $false
| ~ spl0_8
| spl0_15 ),
inference(forward_subsumption_resolution,[],[f761,f85]) ).
fof(f782,plain,
( ~ spl0_8
| spl0_15 ),
inference(avatar_contradiction_clause,[],[f781]) ).
fof(f797,plain,
( sk_c7 != sk_c6
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f461,f307]) ).
fof(f810,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f797,f510]) ).
fof(f811,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f810]) ).
fof(f825,plain,
( sk_c6 != inverse(inverse(sk_c5))
| ~ spl0_1
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f436,f423]) ).
fof(f827,plain,
( sk_c6 != multiply(sk_c4,sk_c6)
| spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f80,f233]) ).
fof(f831,plain,
( sk_c6 = multiply(sk_c4,sk_c6)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_18 ),
inference(forward_demodulation,[],[f455,f233]) ).
fof(f863,plain,
( sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_1
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f825,f233]) ).
fof(f865,plain,
( $false
| spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f831,f827]) ).
fof(f866,plain,
( spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f865]) ).
fof(f878,plain,
( $false
| ~ spl0_1
| ~ spl0_15
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f863,f220]) ).
fof(f879,plain,
( ~ spl0_1
| ~ spl0_15
| ~ spl0_18
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f878]) ).
fof(f892,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c6)
| inverse(X0) != sk_c7 )
| ~ spl0_5
| ~ spl0_25 ),
inference(forward_demodulation,[],[f72,f510]) ).
fof(f898,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 )
| ~ spl0_5
| ~ spl0_25 ),
inference(forward_demodulation,[],[f892,f510]) ).
fof(f919,plain,
( identity != sk_c6
| sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_5
| ~ spl0_25 ),
inference(superposition,[],[f898,f3]) ).
fof(f923,plain,
( sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_5
| ~ spl0_20
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f919,f423]) ).
fof(f926,plain,
( $false
| ~ spl0_5
| ~ spl0_15
| ~ spl0_20
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f923,f220]) ).
fof(f927,plain,
( ~ spl0_5
| ~ spl0_15
| ~ spl0_20
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f926]) ).
fof(f933,plain,
( sk_c7 != sk_c5
| spl0_3
| ~ spl0_20 ),
inference(forward_demodulation,[],[f66,f552]) ).
fof(f936,plain,
( sk_c7 != sk_c6
| spl0_3
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f933,f233]) ).
fof(f939,plain,
( $false
| spl0_3
| ~ spl0_18
| ~ spl0_20
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f936,f510]) ).
fof(f940,plain,
( spl0_3
| ~ spl0_18
| ~ spl0_20
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f939]) ).
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(s26,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f134]) ).
cnf(s27,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f209]) ).
cnf(s28,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f226]) ).
cnf(s32,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f371]) ).
cnf(s33,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f373]) ).
cnf(s35,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f378]) ).
cnf(s37,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(sat_conversion,[],[f404]) ).
cnf(s38,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f420]) ).
cnf(s40,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f441]) ).
cnf(s42,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f467]) ).
cnf(s44,plain,
( ~ spl0_8
| ~ spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f483]) ).
cnf(s49,plain,
( ~ spl0_13
| ~ spl0_14
| spl0_20 ),
inference(sat_conversion,[],[f548]) ).
cnf(s51,plain,
( ~ spl0_16
| spl0_18
| ~ spl0_20 ),
inference(sat_conversion,[],[f557]) ).
cnf(s61,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_20
| ~ spl0_25 ),
inference(sat_conversion,[],[f692]) ).
cnf(s67,plain,
( ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| spl0_25 ),
inference(sat_conversion,[],[f735]) ).
cnf(s68,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| spl0_25 ),
inference(sat_conversion,[],[f744]) ).
cnf(s70,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(sat_conversion,[],[f772]) ).
cnf(s74,plain,
( ~ spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f782]) ).
cnf(s81,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_25 ),
inference(sat_conversion,[],[f811]) ).
cnf(s85,plain,
( spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_18 ),
inference(sat_conversion,[],[f866]) ).
cnf(s86,plain,
( ~ spl0_1
| ~ spl0_15
| ~ spl0_18
| ~ spl0_20 ),
inference(sat_conversion,[],[f879]) ).
cnf(s89,plain,
( ~ spl0_5
| ~ spl0_15
| ~ spl0_20
| ~ spl0_25 ),
inference(sat_conversion,[],[f927]) ).
cnf(s92,plain,
( spl0_3
| ~ spl0_18
| ~ spl0_20
| ~ spl0_25 ),
inference(sat_conversion,[],[f940]) ).
cnf(s93,plain,
spl0_3,
inference(rat,[],[s67,s92,s51,s44,s49,s6,s11,s16,s21,s26]) ).
cnf(s94,plain,
spl0_6,
inference(rat,[],[s27,s22,s23,s93]) ).
cnf(s95,plain,
( spl0_11
| ~ spl0_9
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s42,s15,s20,s93]) ).
cnf(s96,plain,
( ~ spl0_11
| ~ spl0_25
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(rat,[],[s42,s14,s19,s81,s93]) ).
cnf(s97,plain,
( ~ spl0_9
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s96,s95,s68,s93]) ).
cnf(s98,plain,
( ~ spl0_8
| spl0_9
| ~ spl0_5 ),
inference(rat,[],[s67,s51,s89,s44,s74,s8,s49,s13,s18,s94]) ).
cnf(s99,plain,
( spl0_9
| ~ spl0_5 ),
inference(rat,[],[s3,s98]) ).
cnf(s100,plain,
( ~ spl0_9
| ~ spl0_5 ),
inference(rat,[],[s51,s85,s44,s49,s2,s7,s12,s17,s97]) ).
cnf(s101,plain,
~ spl0_5,
inference(rat,[],[s100,s99]) ).
cnf(s102,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_9
| ~ spl0_4 ),
inference(rat,[],[s35,s9,s10,s28,s37,s74,s93]) ).
cnf(s103,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_4 ),
inference(rat,[],[s32,s4,s5,s102,s93]) ).
cnf(s104,plain,
( spl0_7
| ~ spl0_4 ),
inference(rat,[],[s37,s2,s7]) ).
cnf(s105,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s37,s3,s8,s103]) ).
cnf(s106,plain,
~ spl0_4,
inference(rat,[],[s105,s104]) ).
cnf(s107,plain,
( spl0_11
| ~ spl0_7
| ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s38,s15,s20,s93]) ).
cnf(s108,plain,
( spl0_10
| ~ spl0_7
| ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s38,s14,s19,s93]) ).
cnf(s109,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s70,s33,s108,s107,s93]) ).
cnf(s110,plain,
( ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s51,s85,s44,s49,s2,s7,s12,s17,s109]) ).
cnf(s111,plain,
~ spl0_2,
inference(rat,[],[s67,s61,s51,s44,s49,s3,s8,s13,s18,s110,s94,s93]) ).
cnf(s112,plain,
spl0_1,
inference(rat,[],[s1,s101,s94,s93,s106,s111]) ).
cnf(s113,plain,
~ spl0_9,
inference(rat,[],[s51,s44,s49,s85,s2,s7,s12,s17,s40,s112]) ).
cnf(s114,plain,
spl0_14,
inference(rat,[],[s18,s113]) ).
cnf(s115,plain,
spl0_13,
inference(rat,[],[s13,s113]) ).
cnf(s116,plain,
spl0_12,
inference(rat,[],[s8,s113]) ).
cnf(s117,plain,
spl0_8,
inference(rat,[],[s3,s113]) ).
cnf(s118,plain,
spl0_20,
inference(rat,[],[s49,s114,s115]) ).
cnf(s119,plain,
spl0_16,
inference(rat,[],[s44,s117,s116]) ).
cnf(s120,plain,
spl0_15,
inference(rat,[],[s74,s117]) ).
cnf(s121,plain,
spl0_18,
inference(rat,[],[s51,s118,s119]) ).
cnf(s122,plain,
$false,
inference(rat,[],[s86,s118,s112,s121,s120]) ).
fof(f941,plain,
$false,
inference(avatar_sat_refutation,[],[s122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP289-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n016.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 09:50:47 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.47 % (2383360)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (2383369)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3259320254:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (2383366)% WARNING: option uhcvi not known.
% 0.17/0.47 % (2383367)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2028194523:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (2383365)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2160877765_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (2383366)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=320080638:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (2383370)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2973945205:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (2383368)dis+10_1_sil=32000:sp=arity:random_seed=371595868:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (2383371)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3033695224:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % (2383369) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2383360-2383369"...
% 0.17/0.47 % TRYING [1]
% 0.17/0.47 % TRYING [2]
% 0.17/0.47 % TRYING [3]
% 0.17/0.47 % (2383369)...printing done.
% 0.17/0.47 % (2383369)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (2383369)------------------------------
% 0.17/0.47 % (2383369)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (2383369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (2383369)CaDiCaL version: 2.1.3
% 0.17/0.47 % (2383369)Termination reason: Refutation
% 0.17/0.47 % (2383369)Time elapsed: 0.011 s
% 0.17/0.47 % (2383369)Peak memory usage: 12 MB
% 0.17/0.47 % (2383369)Instructions burned: 30 (million)
% 0.17/0.47 % (2383360)Success in time 0.047 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------