%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP286-1 : 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 : n005.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 0.13s 5.46s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 53
% Syntax : Number of formulae : 325 ( 21 unt; 19 def)
% Number of atoms : 1073 ( 310 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1425 ( 677 ~; 729 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 51 !; 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_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c8 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = inverse(sk_c1)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c8 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c7 = inverse(sk_c2)
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c7 = inverse(sk_c2)
| sk_c8 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c7 = inverse(sk_c2)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c7 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| multiply(X0,sk_c8) != sk_c7
| inverse(X0) != sk_c8
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(X2,sk_c7) != sk_c8
| inverse(X2) != sk_c7
| multiply(sk_c8,X3) != sk_c7
| multiply(X4,sk_c8) != X3
| inverse(X4) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1)
| sk_c6 != multiply(sk_c7,sk_c8)
| sk_c8 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2)
| sk_c7 != multiply(sk_c8,X3)
| multiply(X4,sk_c8) != X3
| sk_c8 != inverse(X4) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X0,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1)
| sk_c6 != multiply(sk_c7,sk_c8)
| sk_c8 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) ),
inference(equality_resolution,[],[f66]) ).
fof(f69,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f70,plain,
( ! [X4] :
( sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,definition,
( spl0_2
<=> ! [X2] :
( sk_c8 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f73,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f75,definition,
( spl0_3
<=> sk_c6 = multiply(sk_c7,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f76,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f77,plain,
( sk_c6 != multiply(sk_c7,sk_c8)
| spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f79,definition,
( spl0_4
<=> ! [X1] :
( sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f80,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,definition,
( spl0_5
<=> ! [X0] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f83,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl0_6
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f86,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f87,plain,
( multiply(sk_c8,sk_c7) != sk_c6
| spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f67,f85,f82,f79,f75,f72,f69]) ).
fof(f90,definition,
( spl0_7
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f92,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f94,definition,
( spl0_8
<=> sk_c7 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f96,plain,
( sk_c7 = inverse(sk_c2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f64,f94,f90]) ).
fof(f99,definition,
( spl0_9
<=> sk_c5 = multiply(sk_c4,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f101,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f62,f94,f99]) ).
fof(f104,definition,
( spl0_10
<=> sk_c7 = multiply(sk_c8,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f106,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f60,f94,f104]) ).
fof(f109,definition,
( spl0_11
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f111,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f58,f94,f109]) ).
fof(f114,definition,
( spl0_12
<=> sk_c8 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f116,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f56,f94,f114]) ).
fof(f118,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f54,f94,f75]) ).
fof(f120,definition,
( spl0_13
<=> sk_c6 = multiply(sk_c2,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f122,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f123,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f52,f120,f90]) ).
fof(f124,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f50,f120,f99]) ).
fof(f125,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f48,f120,f104]) ).
fof(f126,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f46,f120,f109]) ).
fof(f127,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f44,f120,f114]) ).
fof(f128,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f42,f120,f75]) ).
fof(f130,definition,
( spl0_14
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f132,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f40,f130,f90]) ).
fof(f134,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f38,f130,f99]) ).
fof(f135,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f36,f130,f104]) ).
fof(f136,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f130,f109]) ).
fof(f137,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f130,f114]) ).
fof(f138,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f30,f130,f75]) ).
fof(f140,definition,
( spl0_15
<=> sk_c7 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f142,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f143,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f28,f140,f90]) ).
fof(f144,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f26,f140,f99]) ).
fof(f145,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f24,f140,f104]) ).
fof(f146,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f22,f140,f109]) ).
fof(f147,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f20,f140,f114]) ).
fof(f148,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f18,f140,f75]) ).
fof(f149,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f85,f90]) ).
fof(f150,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f85,f99]) ).
fof(f151,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f85,f104]) ).
fof(f152,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f85,f109]) ).
fof(f153,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f85,f114]) ).
fof(f154,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f85,f75]) ).
fof(f155,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_7 ),
inference(superposition,[],[f3,f92]) ).
fof(f158,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f162,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c3,multiply(sk_c7,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f116]) ).
fof(f165,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f158,f1]) ).
fof(f167,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c4,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f155]) ).
fof(f168,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c4,X0)) = X0
| ~ spl0_7 ),
inference(forward_demodulation,[],[f167,f1]) ).
fof(f171,plain,
( sk_c8 = multiply(sk_c8,sk_c5)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f168,f101]) ).
fof(f180,plain,
( sk_c8 = sk_c7
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f171,f106]) ).
fof(f199,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c3,multiply(sk_c8,X0))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(forward_demodulation,[],[f162,f180]) ).
fof(f205,plain,
( identity = multiply(sk_c3,identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[],[f199,f155]) ).
fof(f237,plain,
( sk_c7 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_12 ),
inference(superposition,[],[f165,f116]) ).
fof(f249,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f237,f111]) ).
fof(f260,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f249,f180]) ).
fof(f274,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f165,f260]) ).
fof(f276,plain,
( identity = sk_c8
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f274,f3]) ).
fof(f280,plain,
( sk_c6 = multiply(sk_c7,identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f76,f276]) ).
fof(f281,plain,
( sk_c6 != multiply(identity,sk_c7)
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f87,f276]) ).
fof(f300,plain,
( sk_c7 != sk_c6
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f281,f1]) ).
fof(f301,plain,
( sk_c6 = multiply(sk_c8,identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f280,f180]) ).
fof(f305,plain,
( sk_c8 != sk_c6
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f300,f180]) ).
fof(f306,plain,
( sk_c6 = multiply(identity,identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f301,f276]) ).
fof(f309,plain,
( identity != sk_c6
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f305,f276]) ).
fof(f310,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f306,f1]) ).
fof(f345,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f310,f309]) ).
fof(f346,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f345]) ).
fof(f347,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c8)
| sk_c7 != inverse(X1) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f80,f180]) ).
fof(f348,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f86,f180]) ).
fof(f349,plain,
( ! [X1] :
( sk_c6 != multiply(X1,identity)
| sk_c7 != inverse(X1) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f347,f276]) ).
fof(f350,plain,
( sk_c8 = sk_c6
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f348,f260]) ).
fof(f351,plain,
( ! [X1] :
( sk_c8 != inverse(X1)
| sk_c6 != multiply(X1,identity) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f349,f180]) ).
fof(f352,plain,
( identity = sk_c6
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f350,f276]) ).
fof(f353,plain,
( ! [X1] :
( identity != inverse(X1)
| sk_c6 != multiply(X1,identity) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f351,f276]) ).
fof(f357,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f353,f352]) ).
fof(f358,plain,
( identity != identity
| identity != inverse(sk_c3)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f357,f205]) ).
fof(f366,plain,
( identity != inverse(sk_c3)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f358]) ).
fof(f368,plain,
( identity != sk_c7
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f366,f111]) ).
fof(f370,plain,
( identity != sk_c8
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f368,f180]) ).
fof(f373,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f370,f276]) ).
fof(f374,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f373]) ).
fof(f406,plain,
( ! [X4] :
( sk_c7 != multiply(identity,multiply(X4,identity))
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f70,f276]) ).
fof(f407,plain,
( ! [X4] :
( sk_c7 != multiply(X4,identity)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f406,f1]) ).
fof(f408,plain,
( ! [X4] :
( sk_c8 != multiply(X4,identity)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f407,f180]) ).
fof(f409,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f408,f276]) ).
fof(f410,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f409,f276]) ).
fof(f411,plain,
( identity != identity
| identity != inverse(sk_c3)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f410,f205]) ).
fof(f419,plain,
( identity != inverse(sk_c3)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f411]) ).
fof(f424,plain,
( identity != sk_c7
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f419,f111]) ).
fof(f428,plain,
( identity != sk_c8
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f424,f180]) ).
fof(f431,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f428,f276]) ).
fof(f432,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f431]) ).
fof(f433,plain,
( ! [X0] :
( sk_c7 != multiply(X0,identity)
| inverse(X0) != sk_c8 )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f83,f276]) ).
fof(f434,plain,
( ! [X0] :
( sk_c8 != multiply(X0,identity)
| inverse(X0) != sk_c8 )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f433,f180]) ).
fof(f435,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| inverse(X0) != sk_c8 )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f434,f276]) ).
fof(f436,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f435,f276]) ).
fof(f437,plain,
( identity != identity
| identity != inverse(sk_c3)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f436,f205]) ).
fof(f445,plain,
( identity != inverse(sk_c3)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f437]) ).
fof(f450,plain,
( identity != sk_c7
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f445,f111]) ).
fof(f454,plain,
( identity != sk_c8
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f450,f180]) ).
fof(f457,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f454,f276]) ).
fof(f458,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f457]) ).
fof(f466,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c6)
| ~ spl0_13 ),
inference(superposition,[],[f165,f122]) ).
fof(f468,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f466,f96]) ).
fof(f469,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_15 ),
inference(superposition,[],[f165,f142]) ).
fof(f471,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f469,f132]) ).
fof(f476,plain,
( sk_c7 != sk_c7
| sk_c8 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_15 ),
inference(superposition,[],[f83,f142]) ).
fof(f480,plain,
( sk_c8 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f476]) ).
fof(f486,definition,
( spl0_17
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f487,plain,
( identity = sk_c7
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f486]) ).
fof(f499,plain,
( $false
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f480,f132]) ).
fof(f500,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f499]) ).
fof(f506,definition,
( spl0_21
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f507,plain,
( sk_c7 = sk_c6
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f506]) ).
fof(f508,plain,
( sk_c7 != sk_c6
| spl0_21 ),
inference(avatar_component_clause,[],[f506]) ).
fof(f515,plain,
( sk_c7 != multiply(sk_c8,sk_c7)
| sk_c8 != inverse(sk_c1)
| ~ spl0_1
| ~ spl0_15 ),
inference(superposition,[],[f70,f142]) ).
fof(f531,plain,
( sk_c7 != multiply(sk_c8,sk_c7)
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f515,f132]) ).
fof(f538,plain,
( sk_c7 != sk_c6
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f531,f86]) ).
fof(f539,plain,
( ~ spl0_21
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f538,f140,f130,f85,f69,f506]) ).
fof(f550,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f76,f249]) ).
fof(f562,plain,
( spl0_21
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f550,f114,f109,f75,f506]) ).
fof(f563,plain,
( sk_c8 != sk_c8
| sk_c7 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[],[f73,f116]) ).
fof(f565,plain,
( sk_c8 != sk_c6
| sk_c7 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_13 ),
inference(superposition,[],[f73,f122]) ).
fof(f569,plain,
( sk_c7 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f563]) ).
fof(f575,definition,
( spl0_26
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f576,plain,
( identity = sk_c8
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f575]) ).
fof(f579,plain,
( sk_c8 != sk_c6
| ~ spl0_2
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f565,f96]) ).
fof(f585,definition,
( spl0_28
<=> sk_c8 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f587,plain,
( sk_c8 != sk_c6
| spl0_28 ),
inference(avatar_component_clause,[],[f585]) ).
fof(f589,plain,
( $false
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f569,f111]) ).
fof(f590,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f589]) ).
fof(f591,plain,
( ~ spl0_28
| ~ spl0_2
| ~ spl0_8
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f579,f120,f94,f72,f585]) ).
fof(f597,plain,
( ! [X1] :
( sk_c7 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) )
| ~ spl0_4
| ~ spl0_21 ),
inference(forward_demodulation,[],[f80,f507]) ).
fof(f601,plain,
( sk_c7 != sk_c6
| sk_c7 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_13
| ~ spl0_21 ),
inference(superposition,[],[f597,f122]) ).
fof(f607,plain,
( sk_c7 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_13
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f601,f507]) ).
fof(f609,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_13
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f607,f96]) ).
fof(f610,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_13
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f609]) ).
fof(f616,plain,
( sk_c6 = multiply(identity,sk_c7)
| ~ spl0_6
| ~ spl0_26 ),
inference(superposition,[],[f86,f576]) ).
fof(f626,plain,
( sk_c7 = sk_c6
| ~ spl0_6
| ~ spl0_26 ),
inference(forward_demodulation,[],[f616,f1]) ).
fof(f628,plain,
( $false
| ~ spl0_6
| spl0_21
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f626,f508]) ).
fof(f629,plain,
( ~ spl0_6
| spl0_21
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f628]) ).
fof(f632,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f165,f468]) ).
fof(f634,plain,
( identity = sk_c6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f632,f3]) ).
fof(f641,plain,
( identity != sk_c7
| ~ spl0_8
| ~ spl0_13
| spl0_21 ),
inference(superposition,[],[f508,f634]) ).
fof(f642,plain,
( ~ spl0_17
| ~ spl0_8
| ~ spl0_13
| spl0_21 ),
inference(avatar_split_clause,[],[f641,f506,f120,f94,f486]) ).
fof(f649,plain,
( sk_c8 = sk_c6
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f86,f471]) ).
fof(f650,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f165,f471]) ).
fof(f652,plain,
( identity = sk_c7
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f650,f3]) ).
fof(f653,plain,
( identity = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f649,f634]) ).
fof(f665,plain,
( spl0_26
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f653,f140,f130,f120,f94,f85,f575]) ).
fof(f666,plain,
( spl0_17
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f652,f140,f130,f486]) ).
fof(f672,plain,
( sk_c6 != multiply(identity,sk_c8)
| spl0_3
| ~ spl0_17 ),
inference(superposition,[],[f77,f487]) ).
fof(f685,plain,
( sk_c8 != sk_c6
| spl0_3
| ~ spl0_17 ),
inference(forward_demodulation,[],[f672,f1]) ).
fof(f686,plain,
( identity != sk_c8
| spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f685,f634]) ).
fof(f687,plain,
( ~ spl0_26
| spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f686,f486,f120,f94,f75,f575]) ).
fof(f696,plain,
( identity != sk_c8
| ~ spl0_8
| ~ spl0_13
| spl0_28 ),
inference(forward_demodulation,[],[f587,f634]) ).
fof(f709,plain,
( ~ spl0_26
| ~ spl0_8
| ~ spl0_13
| spl0_28 ),
inference(avatar_split_clause,[],[f696,f585,f120,f94,f575]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f88]) ).
cnf(s2,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f97]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f102]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f107]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f112]) ).
cnf(s6,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f117]) ).
cnf(s7,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f118]) ).
cnf(s8,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f123]) ).
cnf(s9,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f124]) ).
cnf(s10,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f125]) ).
cnf(s11,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f126]) ).
cnf(s12,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f127]) ).
cnf(s13,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f128]) ).
cnf(s14,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f133]) ).
cnf(s15,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f134]) ).
cnf(s16,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f135]) ).
cnf(s17,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f136]) ).
cnf(s18,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s19,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f138]) ).
cnf(s20,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f143]) ).
cnf(s21,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f144]) ).
cnf(s22,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f145]) ).
cnf(s23,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f146]) ).
cnf(s24,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f147]) ).
cnf(s25,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f148]) ).
cnf(s26,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f149]) ).
cnf(s27,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f150]) ).
cnf(s28,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f151]) ).
cnf(s29,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f152]) ).
cnf(s30,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f153]) ).
cnf(s31,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f154]) ).
cnf(s32,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f346]) ).
cnf(s34,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f374]) ).
cnf(s42,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f432]) ).
cnf(s46,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f458]) ).
cnf(s49,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f500]) ).
cnf(s55,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_21 ),
inference(sat_conversion,[],[f539]) ).
cnf(s58,plain,
( ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| spl0_21 ),
inference(sat_conversion,[],[f562]) ).
cnf(s62,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f590]) ).
cnf(s63,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_13
| ~ spl0_28 ),
inference(sat_conversion,[],[f591]) ).
cnf(s67,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_13
| ~ spl0_21 ),
inference(sat_conversion,[],[f610]) ).
cnf(s72,plain,
( ~ spl0_6
| spl0_21
| ~ spl0_26 ),
inference(sat_conversion,[],[f629]) ).
cnf(s73,plain,
( ~ spl0_8
| ~ spl0_13
| ~ spl0_17
| spl0_21 ),
inference(sat_conversion,[],[f642]) ).
cnf(s80,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| spl0_26 ),
inference(sat_conversion,[],[f665]) ).
cnf(s82,plain,
( ~ spl0_14
| ~ spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f666]) ).
cnf(s88,plain,
( spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_17
| ~ spl0_26 ),
inference(sat_conversion,[],[f687]) ).
cnf(s92,plain,
( ~ spl0_8
| ~ spl0_13
| ~ spl0_26
| spl0_28 ),
inference(sat_conversion,[],[f709]) ).
cnf(s97,plain,
spl0_3,
inference(rat,[],[s88,s80,s82,s7,s13,s19,s25,s31]) ).
cnf(s98,plain,
spl0_6,
inference(rat,[],[s32,s26,s27,s28,s29,s30,s97]) ).
cnf(s99,plain,
( spl0_12
| ~ spl0_5 ),
inference(rat,[],[s49,s18,s24]) ).
cnf(s100,plain,
( spl0_11
| ~ spl0_5 ),
inference(rat,[],[s49,s17,s23]) ).
cnf(s101,plain,
( spl0_10
| ~ spl0_5 ),
inference(rat,[],[s49,s16,s22]) ).
cnf(s102,plain,
( spl0_9
| ~ spl0_5 ),
inference(rat,[],[s49,s15,s21]) ).
cnf(s103,plain,
( ~ spl0_9
| ~ spl0_12
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(rat,[],[s49,s14,s20,s46]) ).
cnf(s104,plain,
~ spl0_5,
inference(rat,[],[s103,s102,s101,s100,s99]) ).
cnf(s105,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s73,s67,s82,s4,s10,s16,s22]) ).
cnf(s106,plain,
( spl0_12
| ~ spl0_17
| ~ spl0_4 ),
inference(rat,[],[s73,s67,s6,s12]) ).
cnf(s107,plain,
( ~ spl0_17
| ~ spl0_9
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s73,s67,s5,s11,s34,s106,s105,s98]) ).
cnf(s108,plain,
( spl0_15
| ~ spl0_9
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s34,s23,s24,s105,s98]) ).
cnf(s109,plain,
( ~ spl0_9
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s34,s17,s18,s82,s108,s107,s105,s98]) ).
cnf(s110,plain,
( spl0_9
| ~ spl0_4 ),
inference(rat,[],[s73,s67,s82,s3,s9,s15,s21]) ).
cnf(s111,plain,
( ~ spl0_9
| ~ spl0_4 ),
inference(rat,[],[s73,s67,s82,s2,s8,s14,s20,s109]) ).
cnf(s112,plain,
~ spl0_4,
inference(rat,[],[s111,s110]) ).
cnf(s114,plain,
( spl0_12
| ~ spl0_15
| ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s92,s80,s63,s6,s12,s98]) ).
cnf(s115,plain,
( ~ spl0_15
| ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s92,s80,s63,s5,s11,s62,s114,s98]) ).
cnf(s116,plain,
( spl0_15
| ~ spl0_2 ),
inference(rat,[],[s62,s23,s24]) ).
cnf(s117,plain,
( ~ spl0_15
| ~ spl0_2 ),
inference(rat,[],[s62,s17,s18,s115]) ).
cnf(s118,plain,
~ spl0_2,
inference(rat,[],[s117,s116]) ).
cnf(s119,plain,
spl0_1,
inference(rat,[],[s1,s97,s98,s104,s112,s118]) ).
cnf(s120,plain,
( spl0_12
| ~ spl0_15
| ~ spl0_14 ),
inference(rat,[],[s80,s6,s12,s72,s55,s98,s119]) ).
cnf(s121,plain,
( ~ spl0_15
| ~ spl0_14 ),
inference(rat,[],[s80,s5,s11,s58,s120,s72,s55,s119,s97,s98]) ).
cnf(s122,plain,
spl0_15,
inference(rat,[],[s42,s20,s21,s22,s23,s24,s119]) ).
cnf(s123,plain,
~ spl0_14,
inference(rat,[],[s121,s122]) ).
cnf(s124,plain,
spl0_12,
inference(rat,[],[s18,s123]) ).
cnf(s125,plain,
spl0_11,
inference(rat,[],[s17,s123]) ).
cnf(s126,plain,
spl0_10,
inference(rat,[],[s16,s123]) ).
cnf(s127,plain,
spl0_9,
inference(rat,[],[s15,s123]) ).
cnf(s128,plain,
spl0_7,
inference(rat,[],[s14,s123]) ).
cnf(s131,plain,
$false,
inference(rat,[],[s42,s124,s127,s125,s119,s128,s126]) ).
fof(f722,plain,
$false,
inference(avatar_sat_refutation,[],[s131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP286-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/5.38 % Computer : n005.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sun Sep 27 09:48:08 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/5.41 Running first-order model finding
% 0.13/5.41 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
% 0.13/5.46 % (3745312)Will run a generic schedule for satisfiability detection.
% 0.13/5.46 % (3745320)dis+10_1_sil=32000:sp=arity:random_seed=2042304885:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/5.46 % (3745318)% WARNING: option uhcvi not known.
% 0.13/5.46 % (3745317)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1176734885_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/5.46 % (3745319)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1866354479:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/5.46 % (3745318)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1378525394:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/5.46 % (3745321)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2872103156:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/5.46 % (3745322)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=503227696:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/5.46 % (3745320) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3745312-3745320"...
% 0.13/5.46 % (3745323)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3659357132:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/5.46 % TRYING [1]
% 0.13/5.46 % (3745320)...printing done.
% 0.13/5.46 % TRYING [2]
% 0.13/5.46 % (3745320)Refutation found. Thanks to Tanya!
% 0.13/5.46 % SZS status Unsatisfiable for theBenchmark
% 0.13/5.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/5.46 % (3745320)------------------------------
% 0.13/5.46 % (3745320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/5.46 % (3745320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/5.46 % (3745320)CaDiCaL version: 2.1.3
% 0.13/5.46 % (3745320)Termination reason: Refutation
% 0.13/5.46 % (3745320)Time elapsed: 0.009 s
% 0.13/5.46 % (3745320)Peak memory usage: 12 MB
% 0.13/5.46 % (3745320)Instructions burned: 24 (million)
% 0.13/5.46 % (3745312)Success in time 0.037 s
% 0.13/5.46 % Vampire exiting
%------------------------------------------------------------------------------