%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP360-1 : 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 : n012.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 0.07s 0.38s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 46
% Syntax : Number of formulae : 302 ( 19 unt; 17 def)
% Number of atoms : 1015 ( 293 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1362 ( 649 ~; 696 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 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_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
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,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_3) ).
fof(f10,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c5 = inverse(sk_c7)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c5 = inverse(sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c5 = inverse(sk_c7)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c5 = inverse(sk_c7)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c5 = inverse(sk_c7)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,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_11) ).
fof(f26,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c7,sk_c2) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,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_13) ).
fof(f30,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c7,sk_c2) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c7,sk_c2) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,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_16) ).
fof(f36,plain,
( sk_c2 = multiply(sk_c1,sk_c7)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c2
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c2 = multiply(sk_c1,sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,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_18) ).
fof(f40,plain,
( sk_c2 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c2
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c2 = multiply(sk_c1,sk_c7)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c2
| multiply(sk_c4,sk_c5) = 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_c4,sk_c5) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,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
| inverse(X2) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| inverse(X3) != sk_c6
| multiply(X3,sk_c5) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( multiply(sk_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_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,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_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) ),
inference(equality_resolution,[],[f56]) ).
fof(f59,definition,
( spl0_1
<=> ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f60,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c5)
| sk_c6 != inverse(X3) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f62,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f63,plain,
( ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f65,definition,
( spl0_3
<=> sk_c5 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f66,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f67,plain,
( sk_c5 != multiply(sk_c6,sk_c7)
| spl0_3 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f69,definition,
( spl0_4
<=> ! [X1] :
( sk_c6 != multiply(sk_c7,multiply(X1,sk_c7))
| sk_c7 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f70,plain,
( ! [X1] :
( sk_c6 != multiply(sk_c7,multiply(X1,sk_c7))
| sk_c7 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,definition,
( spl0_5
<=> sk_c5 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f73,plain,
( sk_c5 = inverse(sk_c7)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f74,plain,
( sk_c5 != inverse(sk_c7)
| spl0_5 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f76,definition,
( spl0_6
<=> multiply(sk_c6,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f77,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f78,plain,
( multiply(sk_c6,sk_c5) != sk_c7
| spl0_6 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f79,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f57,f76,f72,f69,f65,f62,f59]) ).
fof(f81,definition,
( spl0_7
<=> sk_c6 = multiply(sk_c4,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f83,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f85,definition,
( spl0_8
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f87,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f54,f85,f81]) ).
fof(f90,definition,
( spl0_9
<=> sk_c6 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f92,plain,
( sk_c6 = inverse(sk_c4)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f52,f85,f90]) ).
fof(f95,definition,
( spl0_10
<=> sk_c7 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f97,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f50,f85,f95]) ).
fof(f100,definition,
( spl0_11
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f102,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f103,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f48,f85,f100]) ).
fof(f104,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f46,f85,f65]) ).
fof(f106,definition,
( spl0_12
<=> sk_c2 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f108,plain,
( sk_c2 = multiply(sk_c1,sk_c7)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f44,f106,f81]) ).
fof(f110,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f42,f106,f90]) ).
fof(f111,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f40,f106,f95]) ).
fof(f112,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f38,f106,f100]) ).
fof(f113,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f36,f106,f65]) ).
fof(f115,definition,
( spl0_13
<=> sk_c6 = multiply(sk_c7,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f117,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f34,f115,f81]) ).
fof(f119,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f32,f115,f90]) ).
fof(f120,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f30,f115,f95]) ).
fof(f121,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f28,f115,f100]) ).
fof(f122,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f26,f115,f65]) ).
fof(f123,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f24,f72,f81]) ).
fof(f124,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f22,f72,f90]) ).
fof(f125,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f20,f72,f95]) ).
fof(f126,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f18,f72,f100]) ).
fof(f127,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f16,f72,f65]) ).
fof(f128,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f76,f81]) ).
fof(f129,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f76,f90]) ).
fof(f130,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f76,f95]) ).
fof(f131,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f76,f100]) ).
fof(f132,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f76,f65]) ).
fof(f133,plain,
( identity = multiply(sk_c6,sk_c4)
| ~ spl0_9 ),
inference(superposition,[],[f3,f92]) ).
fof(f134,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_11 ),
inference(superposition,[],[f3,f102]) ).
fof(f137,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f138,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(sk_c5,X0)
| ~ spl0_3 ),
inference(superposition,[],[f4,f66]) ).
fof(f139,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c4,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f133]) ).
fof(f140,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c6,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f97]) ).
fof(f142,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c4,X0)) = X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f139,f1]) ).
fof(f143,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f137,f1]) ).
fof(f152,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f142,f83]) ).
fof(f155,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f140,f66]) ).
fof(f156,plain,
( multiply(sk_c7,sk_c4) = multiply(sk_c3,identity)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f140,f133]) ).
fof(f184,plain,
( sk_c3 = multiply(inverse(sk_c7),identity)
| ~ spl0_11 ),
inference(superposition,[],[f143,f134]) ).
fof(f186,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_10 ),
inference(superposition,[],[f143,f97]) ).
fof(f195,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f186,f102]) ).
fof(f196,plain,
( multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f138,f195]) ).
fof(f199,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f196,f152]) ).
fof(f206,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f143,f199]) ).
fof(f208,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f206,f3]) ).
fof(f214,plain,
( sk_c5 != inverse(identity)
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f74,f208]) ).
fof(f218,plain,
( sk_c3 = multiply(inverse(identity),identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f184,f208]) ).
fof(f219,plain,
( sk_c6 = multiply(identity,identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f195,f208]) ).
fof(f221,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f219,f1]) ).
fof(f222,plain,
( identity = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f218,f3]) ).
fof(f254,plain,
( sk_c6 = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f155,f195]) ).
fof(f255,plain,
( identity = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f254,f221]) ).
fof(f272,plain,
( identity = multiply(identity,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f255,f222]) ).
fof(f273,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f272,f1]) ).
fof(f289,plain,
( multiply(sk_c7,sk_c4) = multiply(identity,identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f156,f222]) ).
fof(f290,plain,
( identity = multiply(sk_c7,sk_c4)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f289,f1]) ).
fof(f291,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f290,f208]) ).
fof(f292,plain,
( identity = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f291,f1]) ).
fof(f297,plain,
( sk_c6 = inverse(identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f92,f292]) ).
fof(f298,plain,
( identity = inverse(identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f297,f221]) ).
fof(f333,plain,
( identity != sk_c5
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f214,f298]) ).
fof(f334,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f333,f273]) ).
fof(f335,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f334]) ).
fof(f337,plain,
( identity != multiply(sk_c6,sk_c5)
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f78,f208]) ).
fof(f339,plain,
( identity != multiply(sk_c6,identity)
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f337,f273]) ).
fof(f340,plain,
( identity != multiply(identity,identity)
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f339,f221]) ).
fof(f341,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f340,f1]) ).
fof(f342,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f341]) ).
fof(f346,plain,
( identity = multiply(sk_c5,sk_c7)
| ~ spl0_5 ),
inference(superposition,[],[f3,f73]) ).
fof(f349,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_8 ),
inference(superposition,[],[f3,f87]) ).
fof(f354,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c6,multiply(sk_c5,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f77]) ).
fof(f383,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c2)
| ~ spl0_12 ),
inference(superposition,[],[f143,f108]) ).
fof(f385,plain,
( sk_c7 = multiply(sk_c7,sk_c2)
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f383,f87]) ).
fof(f386,plain,
( sk_c6 = sk_c7
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f385,f117]) ).
fof(f387,plain,
( sk_c1 = multiply(inverse(sk_c7),identity)
| ~ spl0_8 ),
inference(superposition,[],[f143,f349]) ).
fof(f390,plain,
( sk_c1 = multiply(sk_c5,identity)
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_demodulation,[],[f387,f73]) ).
fof(f400,plain,
( sk_c6 != sk_c5
| sk_c6 != inverse(identity)
| ~ spl0_1 ),
inference(superposition,[],[f60,f1]) ).
fof(f404,plain,
( sk_c6 != sk_c6
| sk_c6 != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f60,f83]) ).
fof(f405,plain,
( sk_c6 != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f404]) ).
fof(f414,definition,
( spl0_15
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f415,plain,
( identity = sk_c6
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f419,definition,
( spl0_16
<=> sk_c6 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f420,plain,
( sk_c6 = inverse(identity)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f419]) ).
fof(f423,definition,
( spl0_17
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f424,plain,
( sk_c6 = sk_c5
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f423]) ).
fof(f426,plain,
( ~ spl0_16
| ~ spl0_17
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f400,f59,f423,f419]) ).
fof(f427,plain,
( ~ spl0_9
| ~ spl0_1
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f405,f81,f59,f90]) ).
fof(f441,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c6,multiply(sk_c5,X0))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f354,f386]) ).
fof(f474,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c6),multiply(sk_c6,X0))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f143,f441]) ).
fof(f477,plain,
( ! [X0] : multiply(sk_c5,X0) = X0
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f474,f143]) ).
fof(f543,plain,
( identity = sk_c1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f477,f390]) ).
fof(f545,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f477,f346]) ).
fof(f563,plain,
( sk_c7 = inverse(identity)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f87,f543]) ).
fof(f574,plain,
( sk_c5 = inverse(identity)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f73,f545]) ).
fof(f579,plain,
( identity = sk_c6
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f386,f545]) ).
fof(f580,plain,
( spl0_15
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f579,f115,f106,f85,f76,f72,f414]) ).
fof(f584,plain,
( sk_c6 = sk_c5
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f574,f420]) ).
fof(f588,plain,
( sk_c6 = inverse(identity)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f563,f386]) ).
fof(f589,plain,
( spl0_16
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f588,f115,f106,f85,f76,f72,f419]) ).
fof(f590,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f63,f386]) ).
fof(f591,plain,
( spl0_17
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f584,f419,f115,f106,f85,f76,f72,f423]) ).
fof(f592,plain,
( ! [X2] :
( sk_c6 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f590,f386]) ).
fof(f593,plain,
( sk_c6 != sk_c6
| sk_c6 != inverse(identity)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f592,f1]) ).
fof(f600,plain,
( sk_c6 != inverse(identity)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f593]) ).
fof(f604,plain,
( ~ spl0_16
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f600,f115,f106,f85,f62,f419]) ).
fof(f610,plain,
( ! [X1] :
( sk_c6 != multiply(sk_c6,multiply(X1,sk_c6))
| sk_c7 != inverse(X1) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f70,f386]) ).
fof(f611,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(sk_c6,multiply(X1,sk_c6)) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f610,f386]) ).
fof(f633,plain,
( ! [X1] :
( identity != inverse(X1)
| sk_c6 != multiply(sk_c6,multiply(X1,sk_c6)) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f611,f415]) ).
fof(f634,plain,
( ! [X1] :
( identity != multiply(identity,multiply(X1,identity))
| identity != inverse(X1) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f633,f415]) ).
fof(f635,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f634,f1]) ).
fof(f636,plain,
( identity = sk_c5
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f424,f415]) ).
fof(f637,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(superposition,[],[f635,f1]) ).
fof(f645,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f637]) ).
fof(f666,plain,
( identity = inverse(identity)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f420,f415]) ).
fof(f667,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f666,f645]) ).
fof(f668,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f667]) ).
fof(f669,plain,
( sk_c5 != multiply(sk_c6,sk_c6)
| spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f67,f386]) ).
fof(f672,plain,
( sk_c5 != multiply(identity,identity)
| spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f669,f415]) ).
fof(f675,plain,
( identity != sk_c5
| spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f672,f1]) ).
fof(f680,plain,
( $false
| spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f675,f636]) ).
fof(f681,plain,
( spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f680]) ).
fof(f682,plain,
( sk_c5 = multiply(identity,sk_c7)
| ~ spl0_3
| ~ spl0_15 ),
inference(forward_demodulation,[],[f66,f415]) ).
fof(f690,plain,
( ! [X1] :
( identity != multiply(sk_c7,multiply(X1,sk_c7))
| sk_c7 != inverse(X1) )
| ~ spl0_4
| ~ spl0_15 ),
inference(forward_demodulation,[],[f70,f415]) ).
fof(f691,plain,
( identity = inverse(sk_c4)
| ~ spl0_9
| ~ spl0_15 ),
inference(forward_demodulation,[],[f92,f415]) ).
fof(f699,plain,
( sk_c5 = sk_c7
| ~ spl0_3
| ~ spl0_15 ),
inference(forward_demodulation,[],[f682,f1]) ).
fof(f707,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f699,f636]) ).
fof(f725,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_9
| ~ spl0_15 ),
inference(superposition,[],[f3,f691]) ).
fof(f726,plain,
( identity = sk_c4
| ~ spl0_9
| ~ spl0_15 ),
inference(forward_demodulation,[],[f725,f1]) ).
fof(f729,plain,
( identity = inverse(identity)
| ~ spl0_9
| ~ spl0_15 ),
inference(superposition,[],[f691,f726]) ).
fof(f731,plain,
( sk_c6 = multiply(identity,sk_c5)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_15 ),
inference(superposition,[],[f83,f726]) ).
fof(f732,plain,
( sk_c6 = sk_c5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_15 ),
inference(forward_demodulation,[],[f731,f1]) ).
fof(f751,plain,
( ! [X1] :
( identity != multiply(identity,multiply(X1,identity))
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f690,f707]) ).
fof(f752,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f751,f1]) ).
fof(f753,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f752,f707]) ).
fof(f754,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[],[f753,f1]) ).
fof(f767,definition,
( spl0_20
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f773,plain,
( spl0_15
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f221,f100,f95,f90,f81,f65,f414]) ).
fof(f774,plain,
( spl0_20
| ~ spl0_9
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f729,f414,f90,f767]) ).
fof(f777,plain,
( spl0_17
| ~ spl0_7
| ~ spl0_9
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f732,f414,f90,f81,f423]) ).
fof(f857,plain,
( ! [X2] :
( sk_c5 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_15 ),
inference(forward_demodulation,[],[f63,f699]) ).
fof(f858,plain,
( ! [X2] :
( identity != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f857,f636]) ).
fof(f859,plain,
( ! [X2] :
( sk_c7 != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f858,f415]) ).
fof(f860,plain,
( ! [X2] :
( sk_c5 != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f859,f699]) ).
fof(f861,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f860,f636]) ).
fof(f862,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[],[f861,f1]) ).
fof(f868,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_15
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f862]) ).
fof(f870,plain,
( ~ spl0_20
| ~ spl0_2
| ~ spl0_3
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f868,f423,f414,f65,f62,f767]) ).
fof(f872,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_15
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f754]) ).
fof(f876,plain,
( ~ spl0_20
| ~ spl0_3
| ~ spl0_4
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f872,f423,f414,f69,f65,f767]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f79]) ).
cnf(s2,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f88]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f93]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f98]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f103]) ).
cnf(s6,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f104]) ).
cnf(s7,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f109]) ).
cnf(s8,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f110]) ).
cnf(s9,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f111]) ).
cnf(s10,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f112]) ).
cnf(s11,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f113]) ).
cnf(s12,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f118]) ).
cnf(s13,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f119]) ).
cnf(s14,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f120]) ).
cnf(s15,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f121]) ).
cnf(s16,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f122]) ).
cnf(s17,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f123]) ).
cnf(s18,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f124]) ).
cnf(s19,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f125]) ).
cnf(s20,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f126]) ).
cnf(s21,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f127]) ).
cnf(s22,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f128]) ).
cnf(s23,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f129]) ).
cnf(s24,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f130]) ).
cnf(s25,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f131]) ).
cnf(s26,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f132]) ).
cnf(s27,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f335]) ).
cnf(s28,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f342]) ).
cnf(s33,plain,
( ~ spl0_1
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f426]) ).
cnf(s34,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f427]) ).
cnf(s40,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f580]) ).
cnf(s43,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f589]) ).
cnf(s44,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| spl0_17 ),
inference(sat_conversion,[],[f591]) ).
cnf(s45,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(sat_conversion,[],[f604]) ).
cnf(s47,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f668]) ).
cnf(s50,plain,
( spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f681]) ).
cnf(s54,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f773]) ).
cnf(s55,plain,
( ~ spl0_9
| ~ spl0_15
| spl0_20 ),
inference(sat_conversion,[],[f774]) ).
cnf(s58,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f777]) ).
cnf(s66,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_15
| ~ spl0_17
| ~ spl0_20 ),
inference(sat_conversion,[],[f870]) ).
cnf(s68,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_15
| ~ spl0_17
| ~ spl0_20 ),
inference(sat_conversion,[],[f876]) ).
cnf(s70,plain,
spl0_3,
inference(rat,[],[s50,s44,s40,s43,s6,s11,s16,s21,s26]) ).
cnf(s71,plain,
spl0_6,
inference(rat,[],[s28,s22,s23,s24,s25,s70]) ).
cnf(s72,plain,
spl0_5,
inference(rat,[],[s27,s17,s18,s19,s20,s70]) ).
cnf(s73,plain,
( ~ spl0_15
| ~ spl0_9
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s58,s68,s55,s70]) ).
cnf(s74,plain,
( spl0_11
| spl0_15
| ~ spl0_8 ),
inference(rat,[],[s40,s10,s15,s72,s71]) ).
cnf(s75,plain,
( ~ spl0_9
| ~ spl0_8
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s40,s9,s14,s54,s74,s73,s72,s71,s70]) ).
cnf(s76,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s47,s40,s43,s8,s13,s75,s71,s72]) ).
cnf(s77,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s73,s54,s3,s4,s5,s76,s70]) ).
cnf(s78,plain,
~ spl0_4,
inference(rat,[],[s47,s40,s43,s2,s7,s12,s77,s72,s71]) ).
cnf(s79,plain,
( ~ spl0_15
| ~ spl0_9
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s58,s66,s55,s70]) ).
cnf(s80,plain,
( ~ spl0_8
| spl0_15
| ~ spl0_9
| ~ spl0_7 ),
inference(rat,[],[s40,s9,s14,s54,s74,s72,s71,s70]) ).
cnf(s81,plain,
( spl0_15
| ~ spl0_9
| ~ spl0_7 ),
inference(rat,[],[s54,s4,s5,s80,s70]) ).
cnf(s82,plain,
( ~ spl0_9
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s81,s79]) ).
cnf(s83,plain,
( ~ spl0_13
| ~ spl0_12
| ~ spl0_2
| ~ spl0_8 ),
inference(rat,[],[s43,s45,s71,s72]) ).
cnf(s84,plain,
( spl0_9
| ~ spl0_2 ),
inference(rat,[],[s83,s3,s8,s13]) ).
cnf(s85,plain,
( ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s83,s2,s7,s12,s82]) ).
cnf(s86,plain,
~ spl0_2,
inference(rat,[],[s85,s84]) ).
cnf(s87,plain,
spl0_1,
inference(rat,[],[s1,s72,s70,s78,s71,s86]) ).
cnf(s88,plain,
( ~ spl0_16
| ~ spl0_8
| ~ spl0_13
| ~ spl0_12 ),
inference(rat,[],[s33,s44,s71,s72,s87]) ).
cnf(s89,plain,
( ~ spl0_12
| ~ spl0_8
| ~ spl0_13 ),
inference(rat,[],[s88,s43,s71,s72]) ).
cnf(s90,plain,
spl0_9,
inference(rat,[],[s89,s3,s8,s13]) ).
cnf(s91,plain,
~ spl0_7,
inference(rat,[],[s34,s87,s90]) ).
cnf(s92,plain,
spl0_13,
inference(rat,[],[s12,s91]) ).
cnf(s93,plain,
spl0_12,
inference(rat,[],[s7,s91]) ).
cnf(s94,plain,
spl0_8,
inference(rat,[],[s2,s91]) ).
cnf(s95,plain,
$false,
inference(rat,[],[s89,s92,s94,s93]) ).
fof(f888,plain,
$false,
inference(avatar_sat_refutation,[],[s95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP360-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Sun Sep 27 09:55:20 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.33 Running first-order model finding
% 0.07/0.33 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
% 0.07/0.38 % (2129199)Will run a generic schedule for satisfiability detection.
% 0.07/0.38 % (2129212)% WARNING: option uhcvi not known.
% 0.07/0.38 % (2129213)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=101170566:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.38 % (2129215)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3102484850:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.38 % (2129211)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2132388071_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.38 % (2129212)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1758528122:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.38 % (2129214)dis+10_1_sil=32000:sp=arity:random_seed=1331892779:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.38 % (2129216)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1245006821:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.38 % (2129217)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=976558923:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.38 % TRYING [1]
% 0.07/0.38 % TRYING [2]
% 0.07/0.38 % TRYING [3]
% 0.07/0.38 % TRYING [4]
% 0.07/0.38 % (2129214) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2129199-2129214"...
% 0.07/0.38 % TRYING [5]
% 0.07/0.38 % (2129215) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2129199-2129215"...
% 0.07/0.38 % (2129214)...printing done.
% 0.07/0.38 % (2129215)...printing done.
% 0.07/0.38 % (2129216) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2129199-2129216"...
% 0.07/0.38 % (2129214)Refutation found. Thanks to Tanya!
% 0.07/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.38 % (2129214)------------------------------
% 0.07/0.38 % (2129214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.38 % (2129214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.38 % (2129214)CaDiCaL version: 2.1.3
% 0.07/0.38 % (2129214)Termination reason: Refutation
% 0.07/0.38 % (2129214)Time elapsed: 0.010 s
% 0.07/0.38 % (2129214)Peak memory usage: 12 MB
% 0.07/0.38 % (2129214)Instructions burned: 32 (million)
% 0.07/0.38 % (2129199)Success in time 0.043 s
% 0.07/0.38 % Vampire exiting
%------------------------------------------------------------------------------