%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP284-1 : 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 : n010.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 0.18s 0.49s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 49
% Syntax : Number of formulae : 341 ( 22 unt; 20 def)
% Number of atoms : 1144 ( 300 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1546 ( 743 ~; 783 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 42 !; 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_c7,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/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/sandbox2/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/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
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/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
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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_c7) = 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_c7)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c5 = multiply(sk_c2,sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c5 = multiply(sk_c2,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c5 = multiply(sk_c2,sk_c7)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c5 = multiply(sk_c2,sk_c7)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = inverse(sk_c2)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c7 = inverse(sk_c2)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c7 = 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_c7) != sk_c5
| inverse(X1) != sk_c7
| 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/sandbox2/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_c7)
| sk_c7 != 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 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f64,definition,
( spl0_3
<=> sk_c5 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f65,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f66,plain,
( sk_c5 != multiply(sk_c6,sk_c7)
| spl0_3 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f68,definition,
( spl0_4
<=> ! [X1] :
( sk_c5 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f69,plain,
( ! [X1] :
( sk_c5 != multiply(X1,sk_c7)
| sk_c7 != 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_c7 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f85,plain,
( sk_c7 = 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_c7) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f106,plain,
( sk_c5 = multiply(sk_c2,sk_c7)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f44,f104,f79]) ).
fof(f108,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f42,f104,f88]) ).
fof(f109,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f40,f104,f93]) ).
fof(f110,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f38,f104,f98]) ).
fof(f111,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f36,f104,f64]) ).
fof(f113,definition,
( spl0_13
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f115,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f34,f113,f79]) ).
fof(f117,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f32,f113,f88]) ).
fof(f118,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f30,f113,f93]) ).
fof(f119,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f28,f113,f98]) ).
fof(f120,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f26,f113,f64]) ).
fof(f122,definition,
( spl0_14
<=> sk_c6 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f124,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f24,f122,f79]) ).
fof(f126,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f22,f122,f88]) ).
fof(f127,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f20,f122,f93]) ).
fof(f128,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f18,f122,f98]) ).
fof(f129,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f16,f122,f64]) ).
fof(f130,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f74,f79]) ).
fof(f131,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f74,f88]) ).
fof(f132,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f74,f93]) ).
fof(f133,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f74,f98]) ).
fof(f134,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f74,f64]) ).
fof(f135,plain,
( identity = multiply(sk_c6,sk_c4)
| ~ spl0_9 ),
inference(superposition,[],[f3,f90]) ).
fof(f136,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_11 ),
inference(superposition,[],[f3,f100]) ).
fof(f139,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f140,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(sk_c5,X0)
| ~ spl0_3 ),
inference(superposition,[],[f4,f65]) ).
fof(f141,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c4,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f135]) ).
fof(f142,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c6,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f95]) ).
fof(f143,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c4,multiply(sk_c5,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f81]) ).
fof(f144,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c4,X0)) = X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f141,f1]) ).
fof(f145,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f139,f1]) ).
fof(f154,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f144,f81]) ).
fof(f157,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f142,f65]) ).
fof(f158,plain,
( multiply(sk_c7,sk_c4) = multiply(sk_c3,identity)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f142,f135]) ).
fof(f181,plain,
( sk_c3 = multiply(inverse(sk_c7),identity)
| ~ spl0_11 ),
inference(superposition,[],[f145,f136]) ).
fof(f188,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_10 ),
inference(superposition,[],[f145,f95]) ).
fof(f197,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f188,f100]) ).
fof(f198,plain,
( multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f140,f197]) ).
fof(f201,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f198,f154]) ).
fof(f207,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c4,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f143,f201]) ).
fof(f208,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f145,f201]) ).
fof(f210,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f208,f3]) ).
fof(f211,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f207,f81]) ).
fof(f216,plain,
( sk_c5 != multiply(identity,sk_c6)
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f76,f210]) ).
fof(f220,plain,
( sk_c3 = multiply(inverse(identity),identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f181,f210]) ).
fof(f221,plain,
( sk_c6 = multiply(identity,identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f197,f210]) ).
fof(f223,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f221,f1]) ).
fof(f224,plain,
( identity = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f220,f3]) ).
fof(f228,plain,
( sk_c6 != sk_c5
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f216,f1]) ).
fof(f260,plain,
( sk_c6 = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f157,f197]) ).
fof(f261,plain,
( identity = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f260,f223]) ).
fof(f278,plain,
( identity = multiply(identity,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f261,f224]) ).
fof(f279,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f278,f1]) ).
fof(f295,plain,
( multiply(sk_c7,sk_c4) = multiply(identity,identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f158,f224]) ).
fof(f296,plain,
( identity = multiply(sk_c7,sk_c4)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f295,f1]) ).
fof(f297,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f296,f210]) ).
fof(f298,plain,
( identity = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f297,f1]) ).
fof(f303,plain,
( sk_c6 = inverse(identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f90,f298]) ).
fof(f304,plain,
( identity = inverse(identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f303,f223]) ).
fof(f316,plain,
( identity != sk_c6
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f228,f279]) ).
fof(f317,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f316,f223]) ).
fof(f318,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f317]) ).
fof(f319,plain,
( ! [X1] :
( sk_c5 != multiply(X1,identity)
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f69,f210]) ).
fof(f321,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f319,f279]) ).
fof(f323,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f321,f210]) ).
fof(f325,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f323,f1]) ).
fof(f331,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f325]) ).
fof(f389,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f304,f331]) ).
fof(f390,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f389]) ).
fof(f392,plain,
( identity = multiply(sk_c7,sk_c2)
| ~ spl0_8 ),
inference(superposition,[],[f3,f85]) ).
fof(f394,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_13 ),
inference(superposition,[],[f3,f115]) ).
fof(f398,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f145,f106]) ).
fof(f400,plain,
( sk_c7 = multiply(sk_c7,sk_c5)
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f398,f85]) ).
fof(f401,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_14 ),
inference(superposition,[],[f145,f124]) ).
fof(f403,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f401,f115]) ).
fof(f410,plain,
( sk_c5 != sk_c5
| sk_c7 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_12 ),
inference(superposition,[],[f69,f106]) ).
fof(f411,plain,
( sk_c7 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f410]) ).
fof(f413,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f411,f85]) ).
fof(f414,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f413]) ).
fof(f430,definition,
( spl0_18
<=> identity = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f431,plain,
( identity = sk_c5
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f435,definition,
( spl0_19
<=> sk_c7 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f449,plain,
( sk_c6 != sk_c5
| sk_c6 != inverse(identity)
| ~ spl0_1 ),
inference(superposition,[],[f59,f1]) ).
fof(f458,definition,
( spl0_22
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f460,plain,
( sk_c7 != sk_c6
| spl0_22 ),
inference(avatar_component_clause,[],[f458]) ).
fof(f467,definition,
( spl0_24
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f468,plain,
( identity = sk_c6
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f467]) ).
fof(f472,definition,
( spl0_25
<=> sk_c6 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f473,plain,
( sk_c6 = inverse(identity)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f474,plain,
( sk_c6 != inverse(identity)
| spl0_25 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f499,plain,
( sk_c6 != sk_c6
| sk_c6 != inverse(sk_c3)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f59,f260]) ).
fof(f502,plain,
( sk_c6 != inverse(sk_c3)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f499]) ).
fof(f504,plain,
( sk_c7 != sk_c6
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f502,f100]) ).
fof(f505,plain,
( ~ spl0_22
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f504,f98,f93,f64,f58,f458]) ).
fof(f550,plain,
( sk_c5 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f145,f400]) ).
fof(f552,plain,
( identity = sk_c5
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f550,f3]) ).
fof(f554,plain,
( spl0_18
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f552,f104,f83,f430]) ).
fof(f564,plain,
( sk_c7 = sk_c5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f75,f403]) ).
fof(f568,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f145,f403]) ).
fof(f570,plain,
( identity = sk_c6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f568,f3]) ).
fof(f573,plain,
( identity = sk_c7
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18 ),
inference(forward_demodulation,[],[f564,f431]) ).
fof(f581,plain,
( spl0_24
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f570,f122,f113,f467]) ).
fof(f584,plain,
( sk_c5 = multiply(identity,sk_c7)
| ~ spl0_3
| ~ spl0_24 ),
inference(superposition,[],[f65,f468]) ).
fof(f587,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_9
| ~ spl0_24 ),
inference(superposition,[],[f135,f468]) ).
fof(f602,plain,
( identity = sk_c4
| ~ spl0_9
| ~ spl0_24 ),
inference(forward_demodulation,[],[f587,f1]) ).
fof(f604,plain,
( sk_c7 = sk_c5
| ~ spl0_3
| ~ spl0_24 ),
inference(forward_demodulation,[],[f584,f1]) ).
fof(f608,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_18
| ~ spl0_24 ),
inference(forward_demodulation,[],[f604,f431]) ).
fof(f611,plain,
( sk_c6 != multiply(identity,sk_c5)
| spl0_7
| ~ spl0_9
| ~ spl0_24 ),
inference(superposition,[],[f80,f602]) ).
fof(f618,plain,
( sk_c6 != sk_c5
| spl0_7
| ~ spl0_9
| ~ spl0_24 ),
inference(forward_demodulation,[],[f611,f1]) ).
fof(f620,plain,
( identity != sk_c6
| spl0_7
| ~ spl0_9
| ~ spl0_18
| ~ spl0_24 ),
inference(forward_demodulation,[],[f618,f431]) ).
fof(f621,plain,
( $false
| spl0_7
| ~ spl0_9
| ~ spl0_18
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f620,f468]) ).
fof(f622,plain,
( spl0_7
| ~ spl0_9
| ~ spl0_18
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f621]) ).
fof(f629,plain,
( identity = multiply(identity,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_24 ),
inference(forward_demodulation,[],[f211,f468]) ).
fof(f637,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_24 ),
inference(forward_demodulation,[],[f629,f1]) ).
fof(f640,plain,
( identity != inverse(identity)
| ~ spl0_24
| spl0_25 ),
inference(forward_demodulation,[],[f474,f468]) ).
fof(f648,plain,
( sk_c3 = multiply(inverse(identity),identity)
| ~ spl0_3
| ~ spl0_11
| ~ spl0_18
| ~ spl0_24 ),
inference(superposition,[],[f181,f608]) ).
fof(f650,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_18
| ~ spl0_24 ),
inference(superposition,[],[f392,f608]) ).
fof(f651,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_18
| ~ spl0_24 ),
inference(superposition,[],[f394,f608]) ).
fof(f662,plain,
( identity = sk_c1
| ~ spl0_3
| ~ spl0_13
| ~ spl0_18
| ~ spl0_24 ),
inference(forward_demodulation,[],[f651,f1]) ).
fof(f663,plain,
( identity = sk_c2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_18
| ~ spl0_24 ),
inference(forward_demodulation,[],[f650,f1]) ).
fof(f665,plain,
( identity = sk_c3
| ~ spl0_3
| ~ spl0_11
| ~ spl0_18
| ~ spl0_24 ),
inference(forward_demodulation,[],[f648,f3]) ).
fof(f738,plain,
( sk_c6 = multiply(identity,sk_c7)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| ~ spl0_24 ),
inference(superposition,[],[f124,f662]) ).
fof(f739,plain,
( sk_c7 = inverse(identity)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_18
| ~ spl0_24 ),
inference(superposition,[],[f115,f662]) ).
fof(f740,plain,
( identity = inverse(identity)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_18
| ~ spl0_24 ),
inference(forward_demodulation,[],[f739,f608]) ).
fof(f741,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| ~ spl0_24 ),
inference(forward_demodulation,[],[f738,f1]) ).
fof(f743,plain,
( $false
| ~ spl0_3
| ~ spl0_13
| ~ spl0_18
| ~ spl0_24
| spl0_25 ),
inference(forward_subsumption_resolution,[],[f740,f640]) ).
fof(f744,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_18
| ~ spl0_24
| spl0_25 ),
inference(avatar_contradiction_clause,[],[f743]) ).
fof(f745,plain,
( $false
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| spl0_22
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f741,f460]) ).
fof(f746,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| spl0_22
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f745]) ).
fof(f747,plain,
( ! [X0] :
( sk_c6 != multiply(X0,identity)
| inverse(X0) != sk_c7 )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_18
| ~ spl0_24 ),
inference(forward_demodulation,[],[f72,f608]) ).
fof(f749,plain,
( identity = inverse(identity)
| ~ spl0_24
| ~ spl0_25 ),
inference(forward_demodulation,[],[f473,f468]) ).
fof(f751,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| inverse(X0) != sk_c7 )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_18
| ~ spl0_24 ),
inference(forward_demodulation,[],[f747,f468]) ).
fof(f752,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_18
| ~ spl0_24 ),
inference(forward_demodulation,[],[f751,f608]) ).
fof(f755,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_18
| ~ spl0_24 ),
inference(superposition,[],[f752,f3]) ).
fof(f758,plain,
( identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_18
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f755]) ).
fof(f779,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_18
| ~ spl0_24
| ~ spl0_25 ),
inference(forward_demodulation,[],[f758,f749]) ).
fof(f783,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_18
| ~ spl0_24
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f779,f749]) ).
fof(f784,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_18
| ~ spl0_24
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f783]) ).
fof(f789,plain,
( ! [X2] :
( identity != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_18
| ~ spl0_24 ),
inference(forward_demodulation,[],[f62,f608]) ).
fof(f790,plain,
( ! [X2] :
( sk_c7 != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_18
| ~ spl0_24 ),
inference(forward_demodulation,[],[f789,f468]) ).
fof(f791,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_18
| ~ spl0_24 ),
inference(forward_demodulation,[],[f790,f608]) ).
fof(f793,plain,
( sk_c7 = inverse(identity)
| ~ spl0_3
| ~ spl0_11
| ~ spl0_18
| ~ spl0_24 ),
inference(superposition,[],[f100,f665]) ).
fof(f820,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_18
| ~ spl0_24 ),
inference(superposition,[],[f791,f3]) ).
fof(f823,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_18
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f820]) ).
fof(f827,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_18
| ~ spl0_24
| ~ spl0_25 ),
inference(forward_demodulation,[],[f823,f749]) ).
fof(f832,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_18
| ~ spl0_24
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f827,f749]) ).
fof(f833,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_18
| ~ spl0_24
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f832]) ).
fof(f840,plain,
( sk_c5 != multiply(identity,sk_c7)
| spl0_3
| ~ spl0_24 ),
inference(forward_demodulation,[],[f66,f468]) ).
fof(f846,plain,
( sk_c7 != sk_c5
| spl0_3
| ~ spl0_24 ),
inference(forward_demodulation,[],[f840,f1]) ).
fof(f852,plain,
( identity != sk_c7
| spl0_3
| ~ spl0_18
| ~ spl0_24 ),
inference(forward_demodulation,[],[f846,f431]) ).
fof(f860,plain,
( $false
| spl0_3
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f573,f852]) ).
fof(f861,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f860]) ).
fof(f864,plain,
( identity != sk_c5
| sk_c6 != inverse(identity)
| ~ spl0_1
| ~ spl0_24 ),
inference(forward_demodulation,[],[f449,f468]) ).
fof(f876,plain,
( spl0_18
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f279,f98,f93,f88,f79,f64,f430]) ).
fof(f882,plain,
( identity != sk_c7
| spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f460,f468]) ).
fof(f908,plain,
( spl0_24
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f223,f98,f93,f88,f79,f64,f467]) ).
fof(f913,plain,
( ~ spl0_25
| ~ spl0_18
| ~ spl0_1
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f864,f467,f58,f430,f472]) ).
fof(f915,definition,
( spl0_26
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f924,plain,
( spl0_19
| ~ spl0_3
| ~ spl0_11
| ~ spl0_18
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f793,f467,f430,f98,f64,f435]) ).
fof(f925,plain,
( spl0_26
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f637,f467,f98,f93,f88,f79,f64,f915]) ).
fof(f927,plain,
( ~ spl0_26
| spl0_22
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f882,f467,f458,f915]) ).
fof(f969,plain,
( ! [X2] :
( sk_c7 != multiply(X2,identity)
| sk_c7 != inverse(X2) )
| ~ spl0_2
| ~ spl0_24 ),
inference(forward_demodulation,[],[f62,f468]) ).
fof(f991,plain,
( identity != sk_c7
| sk_c7 != inverse(identity)
| ~ spl0_2
| ~ spl0_24 ),
inference(superposition,[],[f969,f1]) ).
fof(f1007,plain,
( ~ spl0_19
| ~ spl0_26
| ~ spl0_2
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f991,f467,f61,f915,f435]) ).
fof(f1012,plain,
( ! [X0] :
( identity != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_5
| ~ spl0_24 ),
inference(forward_demodulation,[],[f72,f468]) ).
fof(f1019,plain,
( sk_c7 = inverse(identity)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_18
| ~ spl0_24 ),
inference(superposition,[],[f85,f663]) ).
fof(f1020,plain,
( spl0_19
| ~ spl0_3
| ~ spl0_8
| ~ spl0_18
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f1019,f467,f430,f83,f64,f435]) ).
fof(f1034,plain,
( identity != sk_c7
| sk_c7 != inverse(identity)
| ~ spl0_5
| ~ spl0_24 ),
inference(superposition,[],[f1012,f1]) ).
fof(f1041,plain,
( ~ spl0_19
| ~ spl0_26
| ~ spl0_5
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f1034,f467,f71,f915,f435]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f77]) ).
cnf(s2,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f86]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f91]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f96]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f101]) ).
cnf(s6,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f102]) ).
cnf(s7,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f107]) ).
cnf(s8,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f108]) ).
cnf(s9,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f109]) ).
cnf(s10,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f110]) ).
cnf(s11,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f111]) ).
cnf(s12,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f116]) ).
cnf(s13,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f117]) ).
cnf(s14,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f118]) ).
cnf(s15,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f119]) ).
cnf(s16,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f120]) ).
cnf(s17,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f125]) ).
cnf(s18,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f126]) ).
cnf(s19,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f127]) ).
cnf(s20,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f128]) ).
cnf(s21,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f129]) ).
cnf(s22,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f130]) ).
cnf(s23,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f131]) ).
cnf(s24,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f132]) ).
cnf(s25,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f133]) ).
cnf(s26,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f134]) ).
cnf(s27,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f318]) ).
cnf(s28,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f390]) ).
cnf(s29,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(sat_conversion,[],[f414]) ).
cnf(s37,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_22 ),
inference(sat_conversion,[],[f505]) ).
cnf(s38,plain,
( ~ spl0_8
| ~ spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f554]) ).
cnf(s41,plain,
( ~ spl0_13
| ~ spl0_14
| spl0_24 ),
inference(sat_conversion,[],[f581]) ).
cnf(s43,plain,
( spl0_7
| ~ spl0_9
| ~ spl0_18
| ~ spl0_24 ),
inference(sat_conversion,[],[f622]) ).
cnf(s44,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_18
| ~ spl0_24
| spl0_25 ),
inference(sat_conversion,[],[f744]) ).
cnf(s45,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| spl0_22
| ~ spl0_24 ),
inference(sat_conversion,[],[f746]) ).
cnf(s47,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_18
| ~ spl0_24
| ~ spl0_25 ),
inference(sat_conversion,[],[f784]) ).
cnf(s50,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_18
| ~ spl0_24
| ~ spl0_25 ),
inference(sat_conversion,[],[f833]) ).
cnf(s53,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| ~ spl0_24 ),
inference(sat_conversion,[],[f861]) ).
cnf(s55,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f876]) ).
cnf(s70,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_24 ),
inference(sat_conversion,[],[f908]) ).
cnf(s73,plain,
( ~ spl0_1
| ~ spl0_18
| ~ spl0_24
| ~ spl0_25 ),
inference(sat_conversion,[],[f913]) ).
cnf(s77,plain,
( ~ spl0_3
| ~ spl0_11
| ~ spl0_18
| spl0_19
| ~ spl0_24 ),
inference(sat_conversion,[],[f924]) ).
cnf(s79,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_24
| spl0_26 ),
inference(sat_conversion,[],[f925]) ).
cnf(s86,plain,
( spl0_22
| ~ spl0_24
| ~ spl0_26 ),
inference(sat_conversion,[],[f927]) ).
cnf(s102,plain,
( ~ spl0_2
| ~ spl0_19
| ~ spl0_24
| ~ spl0_26 ),
inference(sat_conversion,[],[f1007]) ).
cnf(s108,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_18
| spl0_19
| ~ spl0_24 ),
inference(sat_conversion,[],[f1020]) ).
cnf(s116,plain,
( ~ spl0_5
| ~ spl0_19
| ~ spl0_24
| ~ spl0_26 ),
inference(sat_conversion,[],[f1041]) ).
cnf(s118,plain,
spl0_3,
inference(rat,[],[s53,s38,s41,s6,s11,s16,s21,s26]) ).
cnf(s119,plain,
spl0_6,
inference(rat,[],[s27,s22,s23,s24,s25,s118]) ).
cnf(s120,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_9
| ~ spl0_8
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s108,s116,s79,s55,s70,s118]) ).
cnf(s121,plain,
( spl0_11
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s44,s47,s38,s41,s10,s15,s20,s118]) ).
cnf(s122,plain,
( spl0_10
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s44,s47,s38,s41,s9,s14,s19,s118]) ).
cnf(s123,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_5
| ~ spl0_8
| ~ spl0_7 ),
inference(rat,[],[s44,s47,s38,s41,s8,s13,s18,s120,s118]) ).
cnf(s124,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s123,s122,s121]) ).
cnf(s125,plain,
( ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s116,s77,s79,s55,s70,s3,s4,s5,s124,s118]) ).
cnf(s126,plain,
~ spl0_5,
inference(rat,[],[s44,s47,s38,s41,s2,s7,s12,s17,s125,s118]) ).
cnf(s127,plain,
( spl0_12
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s28,s8,s9,s10,s118]) ).
cnf(s128,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s28,s3,s4,s5,s29,s127,s118]) ).
cnf(s129,plain,
~ spl0_4,
inference(rat,[],[s29,s2,s7,s128]) ).
cnf(s130,plain,
( ~ spl0_9
| ~ spl0_11
| ~ spl0_10
| ~ spl0_8
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s102,s108,s79,s55,s70,s118]) ).
cnf(s131,plain,
( spl0_9
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s44,s50,s38,s41,s8,s13,s18,s118]) ).
cnf(s132,plain,
( spl0_11
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s44,s50,s38,s41,s10,s15,s20,s118]) ).
cnf(s133,plain,
( ~ spl0_11
| ~ spl0_9
| ~ spl0_2
| ~ spl0_8
| ~ spl0_7 ),
inference(rat,[],[s44,s50,s38,s41,s9,s14,s19,s130,s118]) ).
cnf(s134,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s133,s132,s131]) ).
cnf(s135,plain,
( ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s102,s77,s79,s55,s70,s3,s4,s5,s134,s118]) ).
cnf(s136,plain,
~ spl0_2,
inference(rat,[],[s43,s131,s38,s41,s2,s7,s12,s17,s135]) ).
cnf(s137,plain,
spl0_1,
inference(rat,[],[s1,s118,s119,s126,s129,s136]) ).
cnf(s138,plain,
( ~ spl0_10
| ~ spl0_9
| ~ spl0_11
| ~ spl0_7 ),
inference(rat,[],[s79,s86,s70,s37,s118,s137]) ).
cnf(s139,plain,
( spl0_10
| ~ spl0_8 ),
inference(rat,[],[s44,s73,s38,s41,s9,s14,s19,s118,s137]) ).
cnf(s140,plain,
( ~ spl0_11
| ~ spl0_8
| ~ spl0_7 ),
inference(rat,[],[s38,s45,s41,s8,s13,s18,s138,s37,s139,s118,s137]) ).
cnf(s141,plain,
( ~ spl0_8
| ~ spl0_7 ),
inference(rat,[],[s44,s73,s38,s41,s10,s15,s20,s140,s137,s118]) ).
cnf(s142,plain,
~ spl0_7,
inference(rat,[],[s138,s3,s4,s5,s141]) ).
cnf(s143,plain,
spl0_14,
inference(rat,[],[s17,s142]) ).
cnf(s144,plain,
spl0_13,
inference(rat,[],[s12,s142]) ).
cnf(s145,plain,
spl0_12,
inference(rat,[],[s7,s142]) ).
cnf(s146,plain,
spl0_8,
inference(rat,[],[s2,s142]) ).
cnf(s148,plain,
spl0_24,
inference(rat,[],[s41,s143,s144]) ).
cnf(s149,plain,
spl0_18,
inference(rat,[],[s38,s146,s145]) ).
cnf(s153,plain,
~ spl0_25,
inference(rat,[],[s73,s148,s137,s149]) ).
cnf(s157,plain,
$false,
inference(rat,[],[s44,s118,s148,s144,s149,s153]) ).
fof(f1043,plain,
$false,
inference(avatar_sat_refutation,[],[s157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP284-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n010.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:45:02 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.43 Running first-order model finding
% 0.15/0.43 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
% 0.18/0.49 % (708452)Will run a generic schedule for satisfiability detection.
% 0.18/0.49 % (708461)dis+10_1_sil=32000:sp=arity:random_seed=629766209:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.49 % (708459)% WARNING: option uhcvi not known.
% 0.18/0.49 % (708458)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=308607473_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.49 % (708460)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=883770403:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.49 % (708462)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2598903463:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.49 % (708463)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2165307204:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.49 % (708459)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3066664116:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.49 % (708461) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-708452-708461"...
% 0.18/0.49 % (708464)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=671220919:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.49 % TRYING [1]
% 0.18/0.49 % TRYING [2]
% 0.18/0.49 % (708461)...printing done.
% 0.18/0.49 % TRYING [3]
% 0.18/0.49 % (708461)Refutation found. Thanks to Tanya!
% 0.18/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.49 % (708461)------------------------------
% 0.18/0.49 % (708461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.49 % (708461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.49 % (708461)CaDiCaL version: 2.1.3
% 0.18/0.49 % (708461)Termination reason: Refutation
% 0.18/0.49 % (708461)Time elapsed: 0.019 s
% 0.18/0.49 % (708461)Peak memory usage: 12 MB
% 0.18/0.49 % (708461)Instructions burned: 34 (million)
% 0.18/0.49 % (708452)Success in time 0.044 s
% 0.18/0.49 % Vampire exiting
%------------------------------------------------------------------------------