%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP361-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:13:45 AM UTC 2026
% Result : Unsatisfiable 2.62s 1.28s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 47
% Syntax : Number of formulae : 291 ( 19 unt; 14 def)
% Number of atoms : 1038 ( 285 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1409 ( 662 ~; 733 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c7 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c5 = inverse(sk_c7)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f21,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c5 = inverse(sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c5 = inverse(sk_c7)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c5 = inverse(sk_c7)
| sk_c7 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c5 = inverse(sk_c7)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c7,sk_c2) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c7,sk_c2) = sk_c6
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c7,sk_c2) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c7,sk_c2) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c7,sk_c2) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| sk_c7 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c7,sk_c2) = sk_c6
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c2
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c2 = multiply(sk_c1,sk_c7)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c2
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c2 = multiply(sk_c1,sk_c7)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c2
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c2 = multiply(sk_c1,sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c2
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c2 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c2
| multiply(sk_c4,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c2 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c2
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c2 = multiply(sk_c1,sk_c7)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c5) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,X0) != sk_c6
| multiply(X1,sk_c7) != X0
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c5,sk_c7) != sk_c6
| inverse(X2) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| multiply(X3,sk_c5) != sk_c7
| inverse(X3) != sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c5) != sk_c7
| sk_c5 != inverse(sk_c7)
| sk_c6 != multiply(sk_c7,X0)
| multiply(X1,sk_c7) != X0
| sk_c7 != inverse(X1)
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c6 != multiply(sk_c5,sk_c7)
| sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6)
| sk_c7 != multiply(X3,sk_c5)
| sk_c5 != inverse(X3) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X1] :
( multiply(sk_c6,sk_c5) != sk_c7
| sk_c5 != inverse(sk_c7)
| sk_c6 != multiply(sk_c7,multiply(X1,sk_c7))
| sk_c7 != inverse(X1)
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c6 != multiply(sk_c5,sk_c7)
| sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6)
| sk_c7 != multiply(X3,sk_c5)
| sk_c5 != inverse(X3) ),
inference(equality_resolution,[],[f66]) ).
fof(f69,definition,
( spl0_1
<=> ! [X3] :
( sk_c7 != multiply(X3,sk_c5)
| sk_c5 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f70,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c5)
| sk_c5 != inverse(X3) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f73,plain,
( ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f75,definition,
( spl0_3
<=> sk_c6 = multiply(sk_c5,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f76,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f77,plain,
( sk_c6 != multiply(sk_c5,sk_c7)
| spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f79,definition,
( spl0_4
<=> sk_c5 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f80,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f81,plain,
( sk_c5 != multiply(sk_c6,sk_c7)
| spl0_4 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f83,definition,
( spl0_5
<=> ! [X1] :
( sk_c6 != multiply(sk_c7,multiply(X1,sk_c7))
| sk_c7 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f84,plain,
( ! [X1] :
( sk_c6 != multiply(sk_c7,multiply(X1,sk_c7))
| sk_c7 != inverse(X1) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,definition,
( spl0_6
<=> sk_c5 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f87,plain,
( sk_c5 = inverse(sk_c7)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f88,plain,
( sk_c5 != inverse(sk_c7)
| spl0_6 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f90,definition,
( spl0_7
<=> multiply(sk_c6,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f91,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f92,plain,
( multiply(sk_c6,sk_c5) != sk_c7
| spl0_7 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f67,f90,f86,f83,f79,f75,f72,f69]) ).
fof(f95,definition,
( spl0_8
<=> sk_c5 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f97,plain,
( sk_c5 = inverse(sk_c4)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f99,definition,
( spl0_9
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f101,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f64,f99,f95]) ).
fof(f104,definition,
( spl0_10
<=> sk_c7 = multiply(sk_c4,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f106,plain,
( sk_c7 = multiply(sk_c4,sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f62,f99,f104]) ).
fof(f109,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f111,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_11
| spl0_9 ),
inference(avatar_split_clause,[],[f60,f99,f109]) ).
fof(f114,definition,
( spl0_12
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f116,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,plain,
( spl0_12
| spl0_9 ),
inference(avatar_split_clause,[],[f58,f99,f114]) ).
fof(f118,plain,
( spl0_3
| spl0_9 ),
inference(avatar_split_clause,[],[f56,f99,f75]) ).
fof(f119,plain,
( spl0_4
| spl0_9 ),
inference(avatar_split_clause,[],[f54,f99,f79]) ).
fof(f121,definition,
( spl0_13
<=> sk_c2 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f123,plain,
( sk_c2 = multiply(sk_c1,sk_c7)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f52,f121,f95]) ).
fof(f125,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f50,f121,f104]) ).
fof(f126,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f48,f121,f109]) ).
fof(f127,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f46,f121,f114]) ).
fof(f128,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f44,f121,f75]) ).
fof(f129,plain,
( spl0_4
| spl0_13 ),
inference(avatar_split_clause,[],[f42,f121,f79]) ).
fof(f131,definition,
( spl0_14
<=> sk_c6 = multiply(sk_c7,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f133,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f40,f131,f95]) ).
fof(f135,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f38,f131,f104]) ).
fof(f136,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f36,f131,f109]) ).
fof(f137,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f131,f114]) ).
fof(f138,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f131,f75]) ).
fof(f139,plain,
( spl0_4
| spl0_14 ),
inference(avatar_split_clause,[],[f30,f131,f79]) ).
fof(f140,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f28,f86,f95]) ).
fof(f141,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f26,f86,f104]) ).
fof(f142,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f24,f86,f109]) ).
fof(f143,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f22,f86,f114]) ).
fof(f145,plain,
( spl0_4
| spl0_6 ),
inference(avatar_split_clause,[],[f18,f86,f79]) ).
fof(f146,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f16,f90,f95]) ).
fof(f147,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f14,f90,f104]) ).
fof(f148,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f12,f90,f109]) ).
fof(f149,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f10,f90,f114]) ).
fof(f150,plain,
( spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f8,f90,f75]) ).
fof(f151,plain,
( spl0_4
| spl0_7 ),
inference(avatar_split_clause,[],[f6,f90,f79]) ).
fof(f152,plain,
( identity = multiply(sk_c5,sk_c4)
| ~ spl0_8 ),
inference(superposition,[],[f3,f97]) ).
fof(f153,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_12 ),
inference(superposition,[],[f3,f116]) ).
fof(f155,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f158,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c4,multiply(sk_c5,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f106]) ).
fof(f159,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c5,multiply(sk_c7,X0))
| ~ spl0_3 ),
inference(superposition,[],[f4,f76]) ).
fof(f162,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f155,f1]) ).
fof(f164,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c5,multiply(sk_c4,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f152]) ).
fof(f165,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c4,X0)) = X0
| ~ spl0_8 ),
inference(forward_demodulation,[],[f164,f1]) ).
fof(f168,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f165,f106]) ).
fof(f175,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f168,f76]) ).
fof(f179,plain,
( multiply(sk_c4,sk_c5) = multiply(sk_c7,sk_c7)
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f158,f168]) ).
fof(f185,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f179,f106]) ).
fof(f189,plain,
( sk_c7 != multiply(sk_c5,sk_c5)
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f92,f175]) ).
fof(f191,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c5,multiply(sk_c7,X0))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f159,f175]) ).
fof(f207,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(inverse(sk_c5),multiply(sk_c5,X0))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f162,f191]) ).
fof(f211,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f162,f111]) ).
fof(f216,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_4 ),
inference(superposition,[],[f162,f80]) ).
fof(f223,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f216,f175]) ).
fof(f228,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f211,f116]) ).
fof(f231,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f207,f162]) ).
fof(f232,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f223,f3]) ).
fof(f235,plain,
( sk_c6 = sk_c7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f228,f185]) ).
fof(f243,plain,
( sk_c5 = multiply(sk_c7,sk_c7)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f80,f235]) ).
fof(f244,plain,
( sk_c5 = sk_c7
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f243,f185]) ).
fof(f248,plain,
( identity = sk_c3
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[],[f153,f231]) ).
fof(f249,plain,
( sk_c7 = sk_c3
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_12 ),
inference(forward_demodulation,[],[f248,f232]) ).
fof(f254,plain,
( identity = multiply(sk_c7,sk_c4)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f152,f244]) ).
fof(f259,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f189,f244]) ).
fof(f261,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f259,f185]) ).
fof(f262,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f261]) ).
fof(f265,plain,
( identity = sk_c4
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f254,f231]) ).
fof(f268,plain,
( sk_c7 = sk_c4
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f265,f232]) ).
fof(f271,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_4
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f88,f244]) ).
fof(f272,plain,
( sk_c7 = multiply(sk_c6,sk_c7)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f91,f244]) ).
fof(f279,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[],[f116,f249]) ).
fof(f280,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f279,f271]) ).
fof(f281,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f280]) ).
fof(f300,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c7,X0)) = X0
| ~ spl0_6 ),
inference(superposition,[],[f162,f87]) ).
fof(f301,plain,
( identity = multiply(sk_c5,sk_c7)
| ~ spl0_6 ),
inference(superposition,[],[f3,f87]) ).
fof(f302,plain,
( identity = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f301,f168]) ).
fof(f322,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c2)
| ~ spl0_13 ),
inference(superposition,[],[f162,f123]) ).
fof(f324,plain,
( sk_c7 = multiply(sk_c7,sk_c2)
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f322,f101]) ).
fof(f389,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c7)
| ~ spl0_7 ),
inference(superposition,[],[f162,f91]) ).
fof(f390,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c6,multiply(sk_c5,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f91]) ).
fof(f401,plain,
( sk_c6 = sk_c7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f324,f133]) ).
fof(f422,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c7,multiply(sk_c5,X0))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f390,f401]) ).
fof(f426,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c7),multiply(sk_c7,X0))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f162,f422]) ).
fof(f429,plain,
( ! [X0] : multiply(sk_c5,X0) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f426,f162]) ).
fof(f438,plain,
( identity = sk_c7
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f429,f301]) ).
fof(f443,plain,
( sk_c6 != sk_c7
| spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f77,f429]) ).
fof(f444,plain,
( $false
| spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f443,f401]) ).
fof(f445,plain,
( spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f444]) ).
fof(f447,plain,
( sk_c5 != multiply(sk_c7,sk_c7)
| spl0_4
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f81,f401]) ).
fof(f481,plain,
( sk_c5 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f389,f401]) ).
fof(f482,plain,
( identity = sk_c5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f481,f3]) ).
fof(f483,plain,
( sk_c5 = sk_c7
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f482,f438]) ).
fof(f505,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f300,f429]) ).
fof(f517,plain,
( sk_c5 != sk_c7
| spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f447,f505]) ).
fof(f525,plain,
( $false
| spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f517,f483]) ).
fof(f526,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f525]) ).
fof(f536,plain,
( ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c7) )
| ~ spl0_2
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f73,f401]) ).
fof(f544,plain,
( sk_c5 != sk_c7
| sk_c7 != multiply(sk_c7,sk_c7)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f536,f87]) ).
fof(f552,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f544,f483]) ).
fof(f559,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f552,f505]) ).
fof(f560,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f559]) ).
fof(f561,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c7)
| sk_c5 != inverse(X3) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f70,f483]) ).
fof(f562,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| sk_c7 != multiply(X3,sk_c7) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f561,f483]) ).
fof(f564,plain,
( sk_c5 != sk_c7
| sk_c7 != multiply(sk_c7,sk_c7)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f562,f87]) ).
fof(f572,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f564,f483]) ).
fof(f579,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f572,f505]) ).
fof(f580,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f579]) ).
fof(f581,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f84,f505]) ).
fof(f582,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c7) )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f581,f401]) ).
fof(f584,plain,
( sk_c5 != sk_c7
| sk_c7 != multiply(sk_c7,sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f582,f87]) ).
fof(f592,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f584,f483]) ).
fof(f599,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f592,f505]) ).
fof(f600,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f599]) ).
fof(f609,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f301,f76]) ).
fof(f613,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f609,f302]) ).
fof(f630,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f272,f235]) ).
fof(f631,plain,
( sk_c5 = sk_c7
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f613,f235]) ).
fof(f667,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c7 != multiply(sk_c7,multiply(X1,sk_c7)) )
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f84,f235]) ).
fof(f669,plain,
( sk_c5 != sk_c7
| sk_c7 != multiply(sk_c7,multiply(sk_c7,sk_c7))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f667,f87]) ).
fof(f675,plain,
( sk_c7 != multiply(sk_c7,multiply(sk_c7,sk_c7))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f669,f631]) ).
fof(f677,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f675,f630]) ).
fof(f680,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f677,f630]) ).
fof(f681,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f680]) ).
fof(f682,plain,
( ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c7) )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f73,f235]) ).
fof(f684,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c3,sk_c7)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f682,f116]) ).
fof(f686,plain,
( sk_c7 != multiply(sk_c3,sk_c7)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f684]) ).
fof(f688,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f686,f249]) ).
fof(f690,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f688,f630]) ).
fof(f691,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f690]) ).
fof(f694,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c7)
| sk_c5 != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f70,f631]) ).
fof(f695,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| sk_c7 != multiply(X3,sk_c7) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f694,f631]) ).
fof(f705,plain,
( sk_c5 != sk_c7
| sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f695,f97]) ).
fof(f707,plain,
( sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f705,f631]) ).
fof(f710,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f707,f268]) ).
fof(f715,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f710,f630]) ).
fof(f716,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f715]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f93]) ).
cnf(s2,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f102]) ).
cnf(s3,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f107]) ).
cnf(s4,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f112]) ).
cnf(s5,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f117]) ).
cnf(s6,plain,
( spl0_3
| spl0_9 ),
inference(sat_conversion,[],[f118]) ).
cnf(s7,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f119]) ).
cnf(s8,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f124]) ).
cnf(s9,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f125]) ).
cnf(s10,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f126]) ).
cnf(s11,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f127]) ).
cnf(s12,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f128]) ).
cnf(s13,plain,
( spl0_4
| spl0_13 ),
inference(sat_conversion,[],[f129]) ).
cnf(s14,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f134]) ).
cnf(s15,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f135]) ).
cnf(s16,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f136]) ).
cnf(s17,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s18,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f138]) ).
cnf(s19,plain,
( spl0_4
| spl0_14 ),
inference(sat_conversion,[],[f139]) ).
cnf(s20,plain,
( spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f140]) ).
cnf(s21,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f141]) ).
cnf(s22,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f142]) ).
cnf(s23,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f143]) ).
cnf(s25,plain,
( spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f145]) ).
cnf(s26,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f146]) ).
cnf(s27,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f147]) ).
cnf(s28,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f148]) ).
cnf(s29,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f149]) ).
cnf(s30,plain,
( spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f150]) ).
cnf(s31,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f151]) ).
cnf(s32,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f262]) ).
cnf(s34,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f281]) ).
cnf(s40,plain,
( spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f445]) ).
cnf(s41,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f526]) ).
cnf(s45,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f560]) ).
cnf(s49,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f580]) ).
cnf(s53,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f600]) ).
cnf(s56,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f681]) ).
cnf(s57,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f691]) ).
cnf(s61,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f716]) ).
cnf(s62,plain,
spl0_3,
inference(rat,[],[s40,s6,s12,s18,s30]) ).
cnf(s63,plain,
spl0_4,
inference(rat,[],[s41,s7,s13,s19,s25,s31]) ).
cnf(s64,plain,
spl0_7,
inference(rat,[],[s32,s26,s27,s28,s29,s62,s63]) ).
cnf(s65,plain,
spl0_6,
inference(rat,[],[s34,s20,s21,s22,s23,s62,s63]) ).
cnf(s66,plain,
( spl0_12
| ~ spl0_9
| ~ spl0_5 ),
inference(rat,[],[s53,s11,s17,s65,s64]) ).
cnf(s67,plain,
( spl0_11
| ~ spl0_9
| ~ spl0_5 ),
inference(rat,[],[s53,s10,s16,s65,s64]) ).
cnf(s68,plain,
( ~ spl0_9
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s53,s9,s15,s56,s67,s66,s65,s64,s62,s63]) ).
cnf(s69,plain,
( ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s56,s3,s4,s5,s68,s64,s65,s63,s62]) ).
cnf(s70,plain,
~ spl0_5,
inference(rat,[],[s53,s2,s8,s14,s69,s65,s64]) ).
cnf(s71,plain,
( spl0_12
| ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s45,s11,s17,s65,s64]) ).
cnf(s72,plain,
( spl0_11
| ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s45,s10,s16,s65,s64]) ).
cnf(s73,plain,
( ~ spl0_9
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s45,s9,s15,s57,s72,s71,s65,s64,s62,s63]) ).
cnf(s74,plain,
( ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s57,s3,s4,s5,s73,s64,s63,s62]) ).
cnf(s75,plain,
~ spl0_2,
inference(rat,[],[s45,s2,s8,s14,s74,s65,s64]) ).
cnf(s76,plain,
spl0_1,
inference(rat,[],[s1,s64,s62,s65,s63,s70,s75]) ).
cnf(s77,plain,
( spl0_12
| ~ spl0_9 ),
inference(rat,[],[s49,s11,s17,s65,s64,s76]) ).
cnf(s78,plain,
( spl0_11
| ~ spl0_9 ),
inference(rat,[],[s49,s10,s16,s65,s64,s76]) ).
cnf(s79,plain,
( ~ spl0_9
| ~ spl0_8 ),
inference(rat,[],[s49,s9,s15,s61,s78,s77,s65,s64,s76,s62,s63]) ).
cnf(s80,plain,
~ spl0_8,
inference(rat,[],[s61,s3,s4,s5,s79,s62,s63,s65,s64,s76]) ).
cnf(s81,plain,
spl0_14,
inference(rat,[],[s14,s80]) ).
cnf(s82,plain,
spl0_13,
inference(rat,[],[s8,s80]) ).
cnf(s83,plain,
spl0_9,
inference(rat,[],[s2,s80]) ).
cnf(s84,plain,
$false,
inference(rat,[],[s49,s76,s64,s65,s83,s82,s81]) ).
fof(f717,plain,
$false,
inference(avatar_sat_refutation,[],[s84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP361-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n018.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 09:57:39 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.62/1.28 % (2090497)Input is clausal, will run a generic CNF schedule.
% 2.62/1.28 % (2090506)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1791704922:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.62/1.28 % (2090506)Instruction limit reached!
% 2.62/1.28 % (2090506)------------------------------
% 2.62/1.28 % (2090506)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.28 % (2090506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.28 % (2090506)CaDiCaL version: 2.1.3
% 2.62/1.28 % (2090506)Termination reason: Instruction limit
% 2.62/1.28 % (2090506)Termination phase: Saturation
% 2.62/1.28 % (2090506)Time elapsed: 0.039 s
% 2.62/1.28 % (2090506)Peak memory usage: 89 MB
% 2.62/1.28 % (2090506)Instructions burned: 123 (million)
% 2.62/1.28 % (2090505)lrs+10_1_sil=8000:sp=occurrence:random_seed=2195271768:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.62/1.28 % (2090503)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4053560784:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.62/1.28 % (2090504)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=702612176:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.62/1.28 % (2090502)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3579725102:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.62/1.28 % (2090507)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2152254674:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.62/1.28 % (2090508)dis-21_1_sil=8000:lcm=predicate:random_seed=1568132013:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.62/1.28 % (2090505)Refutation not found, incomplete strategy
% 2.62/1.28 % (2090505)------------------------------
% 2.62/1.28 % (2090505)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.28 % (2090505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.28 % (2090505)CaDiCaL version: 2.1.3
% 2.62/1.28 % (2090505)Termination reason: Refutation not found, incomplete strategy
% 2.62/1.28 % (2090505)Time elapsed: 0.004 s
% 2.62/1.28 % (2090505)Peak memory usage: 88 MB
% 2.62/1.28 % (2090505)Instructions burned: 4 (million)
% 2.62/1.28 % (2090508)Refutation not found, incomplete strategy
% 2.62/1.28 % (2090508)------------------------------
% 2.62/1.28 % (2090508)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.28 % (2090508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.28 % (2090508)CaDiCaL version: 2.1.3
% 2.62/1.28 % (2090508)Termination reason: Refutation not found, incomplete strategy
% 2.62/1.28 % (2090508)Time elapsed: 0.002 s
% 2.62/1.28 % (2090508)Peak memory usage: 88 MB
% 2.62/1.28 % (2090508)Instructions burned: 2 (million)
% 2.62/1.28 % (2090507)First to succeed.
% 2.62/1.28 % (2090507)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2090497"
% 2.62/1.28 % (2090510)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=966383506:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.62/1.28 % (2090510)Refutation not found, incomplete strategy
% 2.62/1.28 % (2090510)------------------------------
% 2.62/1.28 % (2090510)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.28 % (2090510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.28 % (2090510)CaDiCaL version: 2.1.3
% 2.62/1.28 % (2090510)Termination reason: Refutation not found, incomplete strategy
% 2.62/1.28 % (2090510)Time elapsed: 0.002 s
% 2.62/1.28 % (2090510)Peak memory usage: 88 MB
% 2.62/1.28 % (2090510)Instructions burned: 4 (million)
% 2.62/1.28 % (2090510)------------------------------
% 2.62/1.28 % (2090510)------------------------------
% 2.62/1.28 % (2090505)------------------------------
% 2.62/1.28 % (2090505)------------------------------
% 2.62/1.28 % (2090508)------------------------------
% 2.62/1.28 % (2090508)------------------------------
% 2.62/1.28 % (2090507)Refutation found. Thanks to Tanya!
% 2.62/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.62/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.50 % (2090507)------------------------------
% 0.18/1.50 % (2090507)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.50 % (2090507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.50 % (2090507)CaDiCaL version: 2.1.3
% 0.18/1.50 % (2090507)Termination reason: Refutation
% 0.18/1.50 % (2090507)Time elapsed: 0.018 s
% 0.18/1.50 % (2090507)Peak memory usage: 89 MB
% 0.18/1.50 % (2090507)Instructions burned: 27 (million)
% 0.18/1.50 % (2090507)------------------------------
% 0.18/1.50 % (2090507)------------------------------
% 0.18/1.50 % (2090497)Success in time 0.418 s
% 0.18/1.50 % Vampire exiting
%------------------------------------------------------------------------------