%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP361-1 : 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 : n017.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 10:17:35 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 48
% Syntax : Number of formulae : 324 ( 21 unt; 14 def)
% Number of atoms : 1128 ( 319 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1519 ( 715 ~; 790 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 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 : 55 ( 0 sgn 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(f19,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c5 = inverse(sk_c7)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(f100,plain,
( sk_c7 != inverse(sk_c1)
| spl0_9 ),
inference(avatar_component_clause,[],[f99]) ).
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(f144,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f20,f86,f75]) ).
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(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(f160,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c7,X0))
| ~ spl0_4 ),
inference(superposition,[],[f4,f80]) ).
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(f176,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f76,f168]) ).
fof(f179,plain,
( multiply(sk_c4,sk_c5) = multiply(sk_c7,sk_c7)
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f158,f168]) ).
fof(f186,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f179,f106]) ).
fof(f190,plain,
( sk_c7 = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f111,f176]) ).
fof(f220,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f162,f3]) ).
fof(f223,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(inverse(sk_c5),X0)
| ~ spl0_8 ),
inference(superposition,[],[f162,f165]) ).
fof(f224,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(inverse(sk_c5),multiply(sk_c6,X0))
| ~ spl0_3 ),
inference(superposition,[],[f162,f159]) ).
fof(f227,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f162,f162]) ).
fof(f228,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f162,f111]) ).
fof(f230,plain,
( sk_c5 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f162,f190]) ).
fof(f234,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f162,f186]) ).
fof(f239,plain,
( identity = sk_c7
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f234,f3]) ).
fof(f243,plain,
( sk_c5 = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f230,f116]) ).
fof(f245,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f228,f116]) ).
fof(f248,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(inverse(sk_c5),multiply(sk_c5,X0))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f224,f176]) ).
fof(f250,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f220,f227]) ).
fof(f253,plain,
( sk_c5 = sk_c7
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f243,f186]) ).
fof(f254,plain,
( sk_c6 = sk_c7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f245,f186]) ).
fof(f256,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f248,f162]) ).
fof(f258,plain,
( ! [X0] : multiply(X0,sk_c7) = X0
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f250,f239]) ).
fof(f262,plain,
( sk_c7 != multiply(sk_c7,sk_c5)
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f92,f254]) ).
fof(f263,plain,
( sk_c7 = multiply(sk_c3,sk_c7)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f111,f254]) ).
fof(f269,plain,
( sk_c7 = sk_c3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f263,f258]) ).
fof(f270,plain,
( sk_c5 != sk_c7
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f262,f256]) ).
fof(f272,plain,
( $false
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f270,f253]) ).
fof(f273,plain,
( ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f272]) ).
fof(f274,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_3
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f88,f253]) ).
fof(f281,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f116,f269]) ).
fof(f282,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f281,f274]) ).
fof(f283,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f282]) ).
fof(f290,plain,
( sk_c2 = sk_c1
| ~ spl0_8
| ~ spl0_10
| ~ spl0_13 ),
inference(forward_demodulation,[],[f123,f258]) ).
fof(f291,plain,
( sk_c7 = multiply(sk_c7,sk_c2)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14 ),
inference(forward_demodulation,[],[f133,f254]) ).
fof(f317,plain,
( identity = multiply(sk_c5,sk_c7)
| ~ spl0_6 ),
inference(superposition,[],[f3,f87]) ).
fof(f318,plain,
( identity = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f317,f168]) ).
fof(f319,plain,
( sk_c5 = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f318,f239]) ).
fof(f329,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_9 ),
inference(superposition,[],[f3,f101]) ).
fof(f346,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c6,multiply(sk_c5,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f91]) ).
fof(f347,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c2)
| ~ spl0_13 ),
inference(superposition,[],[f162,f123]) ).
fof(f349,plain,
( sk_c7 = multiply(sk_c7,sk_c2)
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f347,f101]) ).
fof(f351,plain,
( sk_c2 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_14 ),
inference(superposition,[],[f162,f133]) ).
fof(f353,plain,
( sk_c2 = multiply(sk_c5,sk_c6)
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_demodulation,[],[f351,f87]) ).
fof(f354,plain,
( identity != sk_c6
| spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f77,f317]) ).
fof(f355,plain,
( sk_c7 = multiply(inverse(sk_c5),identity)
| ~ spl0_6 ),
inference(superposition,[],[f162,f317]) ).
fof(f358,plain,
( sk_c7 = multiply(sk_c4,identity)
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f355,f223]) ).
fof(f359,plain,
( sk_c7 = sk_c4
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f358,f250]) ).
fof(f360,plain,
( multiply(sk_c6,identity) = multiply(sk_c5,sk_c1)
| ~ spl0_4
| ~ spl0_9 ),
inference(superposition,[],[f160,f329]) ).
fof(f361,plain,
( sk_c1 = multiply(inverse(sk_c7),identity)
| ~ spl0_9 ),
inference(superposition,[],[f162,f329]) ).
fof(f364,plain,
( inverse(sk_c7) = sk_c1
| ~ spl0_9 ),
inference(forward_demodulation,[],[f361,f250]) ).
fof(f365,plain,
( sk_c6 = multiply(sk_c5,sk_c1)
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_demodulation,[],[f360,f250]) ).
fof(f366,plain,
( sk_c5 = sk_c1
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f364,f87]) ).
fof(f372,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c6,identity)
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f346,f317]) ).
fof(f379,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f372,f250]) ).
fof(f385,plain,
( sk_c7 = inverse(sk_c5)
| ~ spl0_6
| ~ spl0_9 ),
inference(superposition,[],[f101,f366]) ).
fof(f399,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c5,X0)) = X0
| ~ spl0_6
| ~ spl0_9 ),
inference(superposition,[],[f162,f385]) ).
fof(f414,plain,
( sk_c6 = sk_c7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f133,f349]) ).
fof(f417,plain,
( sk_c2 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f162,f349]) ).
fof(f419,plain,
( identity = sk_c2
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f417,f3]) ).
fof(f431,plain,
( sk_c7 = multiply(sk_c7,sk_c5)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f91,f414]) ).
fof(f435,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c7,multiply(sk_c5,X0))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f346,f414]) ).
fof(f437,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f435,f399]) ).
fof(f442,plain,
( sk_c5 = sk_c7
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f431,f437]) ).
fof(f447,plain,
( multiply(sk_c7,sk_c1) = multiply(sk_c6,sk_c6)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f346,f365]) ).
fof(f452,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c7,sk_c1)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f447,f414]) ).
fof(f456,plain,
( identity = multiply(sk_c7,sk_c7)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f452,f329]) ).
fof(f459,plain,
( identity = sk_c6
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f456,f379]) ).
fof(f462,plain,
( $false
| spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f459,f354]) ).
fof(f463,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f462]) ).
fof(f465,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2) )
| ~ spl0_2
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f73,f414]) ).
fof(f471,plain,
( sk_c5 != sk_c7
| sk_c7 != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f465,f80]) ).
fof(f482,plain,
( sk_c7 != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f471,f442]) ).
fof(f489,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f482,f414]) ).
fof(f493,plain,
( sk_c5 != sk_c7
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f489,f87]) ).
fof(f496,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f493,f442]) ).
fof(f497,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f496]) ).
fof(f498,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,f437]) ).
fof(f499,plain,
( ! [X1] :
( sk_c7 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f498,f414]) ).
fof(f504,plain,
( sk_c2 = multiply(sk_c7,sk_c6)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f353,f442]) ).
fof(f506,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f385,f442]) ).
fof(f508,plain,
( sk_c6 = sk_c2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f504,f437]) ).
fof(f517,plain,
( sk_c5 != sk_c7
| sk_c7 != inverse(sk_c6)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f499,f80]) ).
fof(f528,plain,
( sk_c7 != inverse(sk_c6)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f517,f442]) ).
fof(f535,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f528,f414]) ).
fof(f540,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f535,f506]) ).
fof(f541,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f540]) ).
fof(f542,plain,
( sk_c5 != multiply(sk_c7,sk_c7)
| spl0_4
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f81,f414]) ).
fof(f543,plain,
( sk_c7 = sk_c2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f508,f414]) ).
fof(f547,plain,
( sk_c6 != sk_c5
| spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f542,f379]) ).
fof(f553,plain,
( sk_c6 != sk_c7
| spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f547,f442]) ).
fof(f556,plain,
( $false
| spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f553,f414]) ).
fof(f557,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f556]) ).
fof(f558,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,f442]) ).
fof(f566,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f558,f442]) ).
fof(f578,plain,
( sk_c7 != sk_c7
| sk_c7 != inverse(identity)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f566,f1]) ).
fof(f581,plain,
( sk_c7 != inverse(identity)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f578]) ).
fof(f583,plain,
( sk_c7 != inverse(sk_c2)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f581,f419]) ).
fof(f587,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f583,f543]) ).
fof(f594,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f587,f506]) ).
fof(f595,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f594]) ).
fof(f600,plain,
( sk_c7 = sk_c2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14 ),
inference(forward_demodulation,[],[f291,f256]) ).
fof(f602,plain,
( sk_c7 != inverse(sk_c2)
| ~ spl0_8
| spl0_9
| ~ spl0_10
| ~ spl0_13 ),
inference(forward_demodulation,[],[f100,f290]) ).
fof(f617,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_3
| ~ spl0_8
| spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f602,f600]) ).
fof(f630,plain,
( $false
| ~ spl0_3
| ~ spl0_8
| spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f617,f281]) ).
fof(f631,plain,
( ~ spl0_3
| ~ spl0_8
| spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f630]) ).
fof(f672,plain,
( sk_c6 != multiply(sk_c7,sk_c7)
| sk_c7 != inverse(identity)
| ~ spl0_5 ),
inference(superposition,[],[f84,f1]) ).
fof(f679,plain,
( sk_c7 != inverse(identity)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f672,f379]) ).
fof(f684,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f679,f239]) ).
fof(f690,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f684,f281]) ).
fof(f691,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f690]) ).
fof(f700,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2) )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f73,f254]) ).
fof(f701,plain,
( ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != X2 )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f700,f258]) ).
fof(f707,plain,
( sk_c5 != sk_c7
| sk_c7 != sk_c4
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f701,f97]) ).
fof(f709,plain,
( sk_c7 != sk_c4
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f707,f319]) ).
fof(f712,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f709,f359]) ).
fof(f713,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f712]) ).
fof(f714,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c7)
| sk_c5 != inverse(X3) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f70,f319]) ).
fof(f715,plain,
( ! [X3] :
( sk_c7 != X3
| sk_c5 != inverse(X3) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f714,f258]) ).
fof(f716,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| sk_c7 != X3 )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f715,f319]) ).
fof(f719,plain,
( sk_c5 != sk_c7
| sk_c7 != sk_c4
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f716,f97]) ).
fof(f721,plain,
( sk_c7 != sk_c4
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f719,f319]) ).
fof(f724,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f721,f359]) ).
fof(f725,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f724]) ).
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(s24,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f144]) ).
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_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f273]) ).
cnf(s33,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f283]) ).
cnf(s37,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f463]) ).
cnf(s42,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f497]) ).
cnf(s47,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f541]) ).
cnf(s51,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f557]) ).
cnf(s55,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f595]) ).
cnf(s56,plain,
( ~ spl0_3
| ~ spl0_8
| spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f631]) ).
cnf(s58,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f691]) ).
cnf(s62,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f713]) ).
cnf(s64,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(sat_conversion,[],[f725]) ).
cnf(s65,plain,
( spl0_3
| ~ spl0_14
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(rat,[],[s51,s37]) ).
cnf(s66,plain,
spl0_3,
inference(rat,[],[s65,s6,s12,s18,s24,s30]) ).
cnf(s67,plain,
spl0_4,
inference(rat,[],[s51,s7,s13,s19,s25,s31]) ).
cnf(s68,plain,
( spl0_14
| ~ spl0_5
| ~ spl0_7
| ~ spl0_6 ),
inference(rat,[],[s58,s14,s15,s16,s17]) ).
cnf(s69,plain,
( spl0_13
| ~ spl0_5
| ~ spl0_7
| ~ spl0_6 ),
inference(rat,[],[s58,s8,s9,s10,s11]) ).
cnf(s70,plain,
( ~ spl0_13
| ~ spl0_5
| ~ spl0_14
| ~ spl0_6
| ~ spl0_7 ),
inference(rat,[],[s56,s2,s3,s4,s5,s47,s67,s66]) ).
cnf(s71,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_6 ),
inference(rat,[],[s70,s69,s68]) ).
cnf(s72,plain,
( ~ spl0_7
| ~ spl0_6
| spl0_1
| spl0_2 ),
inference(rat,[],[s71,s1,s66,s67]) ).
cnf(s73,plain,
spl0_7,
inference(rat,[],[s32,s26,s27,s28,s29,s66]) ).
cnf(s74,plain,
spl0_6,
inference(rat,[],[s33,s20,s21,s22,s23,s66]) ).
cnf(s76,plain,
( spl0_14
| ~ spl0_2 ),
inference(rat,[],[s62,s14,s15,s16,s17,s74]) ).
cnf(s77,plain,
( ~ spl0_14
| ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s56,s2,s3,s4,s5,s42,s73,s74,s67,s66]) ).
cnf(s78,plain,
( ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s62,s8,s9,s10,s11,s77,s74]) ).
cnf(s79,plain,
~ spl0_2,
inference(rat,[],[s78,s76]) ).
cnf(s80,plain,
spl0_1,
inference(rat,[],[s72,s73,s74,s79]) ).
cnf(s81,plain,
spl0_14,
inference(rat,[],[s64,s14,s15,s74,s80]) ).
cnf(s82,plain,
~ spl0_13,
inference(rat,[],[s56,s2,s3,s4,s5,s55,s66,s81,s73,s74,s80]) ).
cnf(s85,plain,
spl0_10,
inference(rat,[],[s9,s82]) ).
cnf(s86,plain,
spl0_8,
inference(rat,[],[s8,s82]) ).
cnf(s87,plain,
$false,
inference(rat,[],[s64,s80,s74,s85,s86]) ).
fof(f726,plain,
$false,
inference(avatar_sat_refutation,[],[s87]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:50:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.16/0.47 % (2299532)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (2299537)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1608687444_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % TRYING [1]
% 0.16/0.47 % TRYING [2]
% 0.16/0.47 % TRYING [3]
% 0.16/0.47 % (2299538)% WARNING: option uhcvi not known.
% 0.16/0.47 % TRYING [4]
% 0.16/0.47 % (2299539)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=991877725:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (2299538)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1010601843:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (2299540)dis+10_1_sil=32000:sp=arity:random_seed=1912945471:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (2299541)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4066519487:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (2299543)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1076684711:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % (2299542)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3423057536:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % TRYING [5]
% 0.16/0.47 % (2299541) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2299532-2299541"...
% 0.16/0.47 % (2299540) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2299532-2299540"...
% 0.16/0.47 % TRYING [6]
% 0.16/0.47 % (2299542) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2299532-2299542"...
% 0.16/0.47 % (2299541)...printing done.
% 0.16/0.47 % (2299541)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (2299541)------------------------------
% 0.16/0.47 % (2299541)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (2299541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (2299541)CaDiCaL version: 2.1.3
% 0.16/0.47 % (2299541)Termination reason: Refutation
% 0.16/0.47 % (2299541)Time elapsed: 0.016 s
% 0.16/0.47 % (2299541)Peak memory usage: 12 MB
% 0.16/0.47 % (2299541)Instructions burned: 24 (million)
% 0.16/0.47 % (2299532)Success in time 0.057 s
% 0.16/0.47 % Vampire exiting
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