%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP363-1 : 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 : n001.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 10:17:36 AM UTC 2026
% Result : Unsatisfiable 0.16s 5.70s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 43
% Syntax : Number of formulae : 298 ( 20 unt; 15 def)
% Number of atoms : 1031 ( 289 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1388 ( 655 ~; 718 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 52 !; 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_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c6 = multiply(sk_c7,sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c4 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c6) = 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_c6)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c5 = inverse(sk_c6)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c5 = inverse(sk_c6)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c5 = inverse(sk_c6)
| sk_c6 = multiply(sk_c7,sk_c4) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c5 = inverse(sk_c6)
| sk_c4 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c6) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c5 = inverse(sk_c6)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| sk_c6 = multiply(sk_c7,sk_c4) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| sk_c4 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = inverse(sk_c1)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = inverse(sk_c1)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = multiply(sk_c7,sk_c4) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c6 = inverse(sk_c1)
| sk_c4 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c5) != sk_c7
| inverse(sk_c6) != sk_c5
| multiply(X0,sk_c6) != sk_c5
| inverse(X0) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c6
| multiply(sk_c7,X2) != sk_c6
| multiply(X3,sk_c7) != X2
| inverse(X3) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c5) != sk_c7
| sk_c5 != inverse(sk_c6)
| sk_c5 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| sk_c6 != multiply(sk_c7,X2)
| multiply(X3,sk_c7) != X2
| sk_c7 != inverse(X3) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,plain,
! [X3,X0,X1] :
( multiply(sk_c6,sk_c5) != sk_c7
| sk_c5 != inverse(sk_c6)
| sk_c5 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| sk_c6 != multiply(sk_c7,multiply(X3,sk_c7))
| sk_c7 != inverse(X3) ),
inference(equality_resolution,[],[f54]) ).
fof(f57,definition,
( spl0_1
<=> ! [X3] :
( sk_c6 != multiply(sk_c7,multiply(X3,sk_c7))
| sk_c7 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f58,plain,
( ! [X3] :
( sk_c6 != multiply(sk_c7,multiply(X3,sk_c7))
| sk_c7 != inverse(X3) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f60,definition,
( spl0_2
<=> ! [X1] :
( sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f61,plain,
( ! [X1] :
( sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,definition,
( spl0_3
<=> sk_c5 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f64,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f65,plain,
( sk_c5 != multiply(sk_c6,sk_c7)
| spl0_3 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f67,definition,
( spl0_4
<=> ! [X0] :
( sk_c5 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f68,plain,
( ! [X0] :
( sk_c5 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f70,definition,
( spl0_5
<=> sk_c5 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f71,plain,
( sk_c5 = inverse(sk_c6)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f72,plain,
( sk_c5 != inverse(sk_c6)
| spl0_5 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f74,definition,
( spl0_6
<=> multiply(sk_c6,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f75,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( multiply(sk_c6,sk_c5) != sk_c7
| spl0_6 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f55,f74,f70,f67,f63,f60,f57]) ).
fof(f79,definition,
( spl0_7
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f81,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f83,definition,
( spl0_8
<=> sk_c6 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f84,plain,
( sk_c6 != inverse(sk_c1)
| spl0_8 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f85,plain,
( sk_c6 = inverse(sk_c1)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f52,f83,f79]) ).
fof(f88,definition,
( spl0_9
<=> sk_c4 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f90,plain,
( sk_c4 = multiply(sk_c3,sk_c7)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f50,f83,f88]) ).
fof(f93,definition,
( spl0_10
<=> sk_c6 = multiply(sk_c7,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f95,plain,
( sk_c6 = multiply(sk_c7,sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f48,f83,f93]) ).
fof(f98,definition,
( spl0_11
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f100,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f46,f83,f98]) ).
fof(f103,definition,
( spl0_12
<=> sk_c7 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f105,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f106,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f44,f83,f103]) ).
fof(f107,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f42,f83,f63]) ).
fof(f109,definition,
( spl0_13
<=> sk_c5 = multiply(sk_c1,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f111,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f40,f109,f79]) ).
fof(f113,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f38,f109,f88]) ).
fof(f114,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f36,f109,f93]) ).
fof(f115,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f34,f109,f98]) ).
fof(f116,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f32,f109,f103]) ).
fof(f117,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f30,f109,f63]) ).
fof(f118,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f28,f70,f79]) ).
fof(f119,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f26,f70,f88]) ).
fof(f120,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f24,f70,f93]) ).
fof(f121,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f22,f70,f98]) ).
fof(f122,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f20,f70,f103]) ).
fof(f123,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f18,f70,f63]) ).
fof(f124,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f74,f79]) ).
fof(f125,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f74,f88]) ).
fof(f126,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f74,f93]) ).
fof(f127,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f74,f98]) ).
fof(f128,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f74,f103]) ).
fof(f129,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f74,f63]) ).
fof(f130,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_7 ),
inference(superposition,[],[f3,f81]) ).
fof(f131,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_11 ),
inference(superposition,[],[f3,f100]) ).
fof(f133,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f135,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c6,X0)) = multiply(sk_c7,X0)
| ~ spl0_12 ),
inference(superposition,[],[f4,f105]) ).
fof(f137,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c7,X0)) = multiply(sk_c4,X0)
| ~ spl0_9 ),
inference(superposition,[],[f4,f90]) ).
fof(f140,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f133,f1]) ).
fof(f142,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c3,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f130]) ).
fof(f143,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c3,X0)) = X0
| ~ spl0_7 ),
inference(forward_demodulation,[],[f142,f1]) ).
fof(f146,plain,
( sk_c7 = multiply(sk_c7,sk_c4)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f143,f90]) ).
fof(f149,plain,
( sk_c6 = sk_c7
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f146,f95]) ).
fof(f151,plain,
( multiply(sk_c7,sk_c2) = multiply(sk_c2,identity)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f135,f131]) ).
fof(f154,plain,
( multiply(sk_c6,sk_c2) = multiply(sk_c2,identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f151,f149]) ).
fof(f157,plain,
( identity = multiply(sk_c2,identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f154,f131]) ).
fof(f162,plain,
( sk_c6 = multiply(sk_c6,sk_c4)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f95,f149]) ).
fof(f163,plain,
( sk_c4 = multiply(sk_c3,sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f90,f149]) ).
fof(f164,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f64,f149]) ).
fof(f176,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c2,multiply(identity,X0))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f4,f157]) ).
fof(f177,plain,
( ! [X0] : multiply(sk_c2,X0) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f176,f1]) ).
fof(f180,plain,
( multiply(sk_c3,sk_c6) = multiply(sk_c4,sk_c4)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f137,f95]) ).
fof(f186,plain,
( sk_c4 = multiply(sk_c4,sk_c4)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f180,f163]) ).
fof(f203,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f140,f3]) ).
fof(f205,plain,
( identity = multiply(inverse(sk_c2),identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f140,f157]) ).
fof(f211,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f140,f140]) ).
fof(f212,plain,
( sk_c6 = multiply(inverse(sk_c2),sk_c7)
| ~ spl0_12 ),
inference(superposition,[],[f140,f105]) ).
fof(f215,plain,
( sk_c2 = multiply(inverse(sk_c6),identity)
| ~ spl0_11 ),
inference(superposition,[],[f140,f131]) ).
fof(f218,plain,
( sk_c4 = multiply(inverse(sk_c4),sk_c4)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f140,f186]) ).
fof(f219,plain,
( sk_c3 = multiply(inverse(sk_c7),identity)
| ~ spl0_7 ),
inference(superposition,[],[f140,f130]) ).
fof(f222,plain,
( sk_c3 = multiply(inverse(sk_c6),identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f219,f149]) ).
fof(f223,plain,
( identity = sk_c4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f218,f3]) ).
fof(f228,plain,
( sk_c6 = multiply(inverse(sk_c2),sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(forward_demodulation,[],[f212,f149]) ).
fof(f234,plain,
( identity = multiply(sk_c6,identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f205,f100]) ).
fof(f235,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f203,f211]) ).
fof(f236,plain,
( sk_c2 = sk_c3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f222,f215]) ).
fof(f239,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f228,f100]) ).
fof(f244,plain,
( sk_c4 = multiply(sk_c6,sk_c4)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f234,f223]) ).
fof(f245,plain,
( ! [X0] : multiply(X0,sk_c4) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f235,f223]) ).
fof(f247,plain,
( sk_c6 = sk_c4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f244,f162]) ).
fof(f250,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c2,X0)) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f143,f236]) ).
fof(f257,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f250,f177]) ).
fof(f260,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f257,f149]) ).
fof(f263,plain,
( multiply(sk_c2,sk_c6) = multiply(sk_c7,sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f135,f239]) ).
fof(f267,plain,
( multiply(sk_c2,sk_c6) = multiply(sk_c6,sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f263,f149]) ).
fof(f268,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f267,f164]) ).
fof(f269,plain,
( sk_c5 = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f268,f105]) ).
fof(f270,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f269,f149]) ).
fof(f286,plain,
( ! [X0] : multiply(X0,sk_c6) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f245,f247]) ).
fof(f293,plain,
( identity = inverse(sk_c4)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f3,f245]) ).
fof(f298,plain,
( sk_c4 = multiply(sk_c7,sk_c3)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f143,f245]) ).
fof(f303,plain,
( sk_c4 = multiply(sk_c7,sk_c2)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f298,f236]) ).
fof(f308,plain,
( identity = inverse(sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f293,f247]) ).
fof(f310,plain,
( sk_c4 = multiply(sk_c6,sk_c2)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f303,f149]) ).
fof(f311,plain,
( sk_c4 = inverse(sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f308,f223]) ).
fof(f313,plain,
( sk_c2 = sk_c4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f310,f260]) ).
fof(f314,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f311,f247]) ).
fof(f316,plain,
( sk_c6 = sk_c2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f313,f247]) ).
fof(f372,plain,
( sk_c6 != sk_c5
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f72,f314]) ).
fof(f377,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f372,f270]) ).
fof(f378,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f377]) ).
fof(f384,plain,
( sk_c6 != multiply(sk_c6,sk_c5)
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f76,f149]) ).
fof(f385,plain,
( sk_c6 != sk_c5
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f384,f260]) ).
fof(f386,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f385,f270]) ).
fof(f387,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f386]) ).
fof(f390,plain,
( sk_c5 = sk_c1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f111,f286]) ).
fof(f405,plain,
( sk_c2 = multiply(sk_c5,identity)
| ~ spl0_5
| ~ spl0_11 ),
inference(superposition,[],[f215,f71]) ).
fof(f406,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c6,X0)) = X0
| ~ spl0_5 ),
inference(superposition,[],[f140,f71]) ).
fof(f407,plain,
( identity = multiply(sk_c5,sk_c6)
| ~ spl0_5 ),
inference(superposition,[],[f3,f71]) ).
fof(f408,plain,
( sk_c5 = sk_c2
| ~ spl0_5
| ~ spl0_11 ),
inference(forward_demodulation,[],[f405,f235]) ).
fof(f410,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f105,f408]) ).
fof(f424,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c7)
| ~ spl0_6 ),
inference(superposition,[],[f140,f75]) ).
fof(f437,plain,
( sk_c6 = multiply(inverse(sk_c5),identity)
| ~ spl0_5 ),
inference(superposition,[],[f140,f407]) ).
fof(f440,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_5 ),
inference(forward_demodulation,[],[f437,f235]) ).
fof(f529,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f424,f71]) ).
fof(f536,plain,
( identity = multiply(sk_c6,sk_c5)
| ~ spl0_5 ),
inference(superposition,[],[f3,f440]) ).
fof(f537,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f536,f75]) ).
fof(f538,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f1,f537]) ).
fof(f539,plain,
( identity != sk_c5
| sk_c6 != inverse(sk_c5)
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f68,f407]) ).
fof(f540,plain,
( sk_c5 != sk_c5
| sk_c6 != inverse(sk_c1)
| ~ spl0_4
| ~ spl0_13 ),
inference(superposition,[],[f68,f111]) ).
fof(f544,plain,
( sk_c6 != inverse(sk_c1)
| ~ spl0_4
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f540]) ).
fof(f547,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f544,f85]) ).
fof(f548,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f547]) ).
fof(f549,plain,
( identity != sk_c5
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f539,f440]) ).
fof(f552,definition,
( spl0_14
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f553,plain,
( sk_c6 = sk_c5
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f554,plain,
( sk_c6 != sk_c5
| spl0_14 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f560,plain,
( sk_c5 != sk_c7
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f549,f537]) ).
fof(f573,plain,
( sk_c6 = sk_c3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f236,f316]) ).
fof(f580,plain,
( sk_c6 != inverse(sk_c5)
| ~ spl0_7
| spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f84,f390]) ).
fof(f588,plain,
( sk_c5 = sk_c7
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f410,f286]) ).
fof(f603,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f580,f440]) ).
fof(f604,plain,
( ~ spl0_5
| ~ spl0_7
| spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f603]) ).
fof(f610,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f588,f560]) ).
fof(f611,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f610]) ).
fof(f678,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f58,f538]) ).
fof(f679,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c6)
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f678,f149]) ).
fof(f680,plain,
( ! [X3] :
( sk_c6 != X3
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f679,f286]) ).
fof(f681,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != X3 )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f680,f149]) ).
fof(f686,plain,
( sk_c6 != sk_c7
| sk_c6 != sk_c3
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f681,f81]) ).
fof(f689,plain,
( sk_c6 != sk_c3
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f686,f149]) ).
fof(f694,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f689,f573]) ).
fof(f695,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f694]) ).
fof(f704,plain,
( sk_c6 = multiply(sk_c1,sk_c6)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f111,f553]) ).
fof(f733,plain,
( identity = multiply(sk_c6,sk_c1)
| ~ spl0_8 ),
inference(superposition,[],[f3,f85]) ).
fof(f793,plain,
( sk_c7 = multiply(sk_c6,sk_c1)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f733,f537]) ).
fof(f803,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c1,multiply(sk_c6,X0))
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f4,f704]) ).
fof(f805,plain,
( sk_c1 = multiply(inverse(sk_c6),sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f140,f793]) ).
fof(f808,plain,
( sk_c1 = multiply(sk_c5,sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f805,f71]) ).
fof(f809,plain,
( sk_c5 = sk_c1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f808,f529]) ).
fof(f810,plain,
( sk_c6 = sk_c1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14 ),
inference(forward_demodulation,[],[f809,f553]) ).
fof(f812,plain,
( sk_c6 != sk_c5
| sk_c7 != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f678,f64]) ).
fof(f818,plain,
( sk_c7 != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f812,f553]) ).
fof(f824,definition,
( spl0_17
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f826,plain,
( sk_c6 != sk_c7
| spl0_17 ),
inference(avatar_component_clause,[],[f824]) ).
fof(f833,plain,
( sk_c5 != sk_c7
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_demodulation,[],[f818,f71]) ).
fof(f834,plain,
( sk_c6 != sk_c7
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_demodulation,[],[f833,f553]) ).
fof(f835,plain,
( ~ spl0_17
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f834,f552,f74,f70,f63,f57,f824]) ).
fof(f860,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14 ),
inference(superposition,[],[f529,f553]) ).
fof(f896,plain,
( sk_c7 = multiply(sk_c1,sk_c7)
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f803,f75]) ).
fof(f905,plain,
( sk_c7 = multiply(sk_c6,sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f896,f810]) ).
fof(f911,plain,
( sk_c6 = sk_c7
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f905,f860]) ).
fof(f915,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f911,f826]) ).
fof(f916,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| spl0_17 ),
inference(avatar_contradiction_clause,[],[f915]) ).
fof(f925,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c1,multiply(sk_c6,X0))
| ~ spl0_13 ),
inference(superposition,[],[f4,f111]) ).
fof(f926,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c5,multiply(sk_c6,X0))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f925,f809]) ).
fof(f928,plain,
( ! [X0] : multiply(sk_c5,X0) = X0
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f926,f406]) ).
fof(f929,plain,
( sk_c5 = multiply(sk_c5,sk_c6)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f111,f809]) ).
fof(f932,plain,
( sk_c6 = sk_c5
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f929,f928]) ).
fof(f933,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| spl0_14 ),
inference(forward_subsumption_resolution,[],[f932,f554]) ).
fof(f934,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| spl0_14 ),
inference(avatar_contradiction_clause,[],[f933]) ).
fof(f947,plain,
( identity != sk_c7
| sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_2 ),
inference(superposition,[],[f61,f3]) ).
fof(f951,plain,
( sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f947,f537]) ).
fof(f955,plain,
( sk_c6 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f951,f71]) ).
fof(f960,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f955,f440]) ).
fof(f961,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f960]) ).
fof(f967,plain,
( sk_c6 != sk_c5
| spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_demodulation,[],[f65,f860]) ).
fof(f968,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f967,f553]) ).
fof(f969,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f968]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f77]) ).
cnf(s2,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f86]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f91]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f96]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f101]) ).
cnf(s6,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f106]) ).
cnf(s7,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f107]) ).
cnf(s8,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f112]) ).
cnf(s9,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f113]) ).
cnf(s10,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f114]) ).
cnf(s11,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f115]) ).
cnf(s12,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f116]) ).
cnf(s13,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f117]) ).
cnf(s14,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f118]) ).
cnf(s15,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f119]) ).
cnf(s16,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f120]) ).
cnf(s17,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f121]) ).
cnf(s18,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f122]) ).
cnf(s19,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f123]) ).
cnf(s20,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f124]) ).
cnf(s21,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f125]) ).
cnf(s22,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f126]) ).
cnf(s23,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f127]) ).
cnf(s24,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f128]) ).
cnf(s25,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f129]) ).
cnf(s26,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f378]) ).
cnf(s27,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f387]) ).
cnf(s36,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_13 ),
inference(sat_conversion,[],[f548]) ).
cnf(s43,plain,
( ~ spl0_5
| ~ spl0_7
| spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f604]) ).
cnf(s45,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f611]) ).
cnf(s53,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f695]) ).
cnf(s62,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14
| ~ spl0_17 ),
inference(sat_conversion,[],[f835]) ).
cnf(s64,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f916]) ).
cnf(s65,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f934]) ).
cnf(s69,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f961]) ).
cnf(s72,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14 ),
inference(sat_conversion,[],[f969]) ).
cnf(s73,plain,
spl0_3,
inference(rat,[],[s65,s72,s7,s13,s19,s25]) ).
cnf(s74,plain,
spl0_6,
inference(rat,[],[s27,s20,s21,s22,s23,s24,s73]) ).
cnf(s75,plain,
spl0_5,
inference(rat,[],[s26,s14,s15,s16,s17,s18,s73]) ).
cnf(s76,plain,
~ spl0_2,
inference(rat,[],[s69,s74,s75]) ).
cnf(s77,plain,
( spl0_13
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s45,s9,s10,s11,s12,s74,s75]) ).
cnf(s78,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s43,s3,s4,s5,s6,s36,s77,s75]) ).
cnf(s79,plain,
~ spl0_4,
inference(rat,[],[s36,s2,s8,s78]) ).
cnf(s80,plain,
spl0_1,
inference(rat,[],[s1,s74,s73,s76,s75,s79]) ).
cnf(s82,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_8 ),
inference(rat,[],[s62,s64,s80,s75,s74,s73]) ).
cnf(s83,plain,
( ~ spl0_13
| ~ spl0_8 ),
inference(rat,[],[s82,s65,s74,s75]) ).
cnf(s84,plain,
( spl0_13
| ~ spl0_7 ),
inference(rat,[],[s9,s53,s10,s11,s12,s74,s75,s80]) ).
cnf(s85,plain,
~ spl0_7,
inference(rat,[],[s43,s3,s4,s5,s6,s83,s84,s75]) ).
cnf(s86,plain,
spl0_13,
inference(rat,[],[s8,s85]) ).
cnf(s87,plain,
spl0_8,
inference(rat,[],[s2,s85]) ).
cnf(s88,plain,
$false,
inference(rat,[],[s83,s87,s86]) ).
fof(f970,plain,
$false,
inference(avatar_sat_refutation,[],[s88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP363-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/5.60 % Computer : n001.cluster.edu
% 0.12/5.60 % Model : x86_64 x86_64
% 0.12/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.60 % Memory : 8046.5625MB
% 0.12/5.60 % OS : Linux 6.8.0-71-generic
% 0.12/5.60 % CPULimit : 300
% 0.12/5.60 % WCLimit : 300
% 0.12/5.60 % DateTime : Sun Sep 27 10:02:22 UTC 2026
% 0.12/5.60 % CPUTime :
% 0.12/5.60 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/5.63 Running first-order model finding
% 0.12/5.63 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
% 0.16/5.70 % (3317348)Will run a generic schedule for satisfiability detection.
% 0.16/5.70 % (3317359)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4162964511:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/5.70 % (3317354)% WARNING: option uhcvi not known.
% 0.16/5.70 % (3317353)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3943732554_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/5.70 % (3317354)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=299499942:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/5.70 % (3317355)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1684663360:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/5.70 % (3317356)dis+10_1_sil=32000:sp=arity:random_seed=3205562672:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/5.70 % (3317357)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=331195534:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/5.70 % (3317358)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1854354112:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/5.70 % TRYING [1]
% 0.16/5.70 % TRYING [2]
% 0.16/5.70 % TRYING [3]
% 0.16/5.70 % TRYING [4]
% 0.16/5.70 % TRYING [5]
% 0.16/5.70 % (3317357) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3317348-3317357"...
% 0.16/5.70 % (3317356) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3317348-3317356"...
% 0.16/5.70 % (3317358) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3317348-3317358"...
% 0.16/5.70 % (3317356)...printing done.
% 0.16/5.70 % (3317357)...printing done.
% 0.16/5.70 % (3317357)Refutation found. Thanks to Tanya!
% 0.16/5.70 % SZS status Unsatisfiable for theBenchmark
% 0.16/5.70 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/5.70 % (3317357)------------------------------
% 0.16/5.70 % (3317357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/5.70 % (3317357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/5.70 % (3317357)CaDiCaL version: 2.1.3
% 0.16/5.70 % (3317357)Termination reason: Refutation
% 0.16/5.70 % (3317357)Time elapsed: 0.020 s
% 0.16/5.70 % (3317357)Peak memory usage: 12 MB
% 0.16/5.70 % (3317357)Instructions burned: 31 (million)
% 0.16/5.70 % (3317348)Success in time 0.057 s
% 0.16/5.70 % Vampire exiting
%------------------------------------------------------------------------------