%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP328-1 : 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 : n008.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 10:17:30 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.46s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 44
% Syntax : Number of formulae : 316 ( 26 unt; 13 def)
% Number of atoms : 1154 ( 321 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1587 ( 749 ~; 825 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 14 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 78 !; 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_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = inverse(sk_c1)
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f39]) ).
fof(f43,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f49]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = inverse(sk_c2)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f59]) ).
fof(f63,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c7
| multiply(sk_c8,X1) != sk_c7
| multiply(X2,sk_c8) != X1
| inverse(X2) != sk_c8
| multiply(sk_c7,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,X3) != sk_c7
| multiply(X4,sk_c8) != X3
| inverse(X4) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(sk_c8,X1)
| multiply(X2,sk_c8) != X1
| sk_c8 != inverse(X2)
| sk_c8 != multiply(sk_c7,sk_c6)
| sk_c6 != inverse(sk_c8)
| sk_c7 != multiply(sk_c8,X3)
| multiply(X4,sk_c8) != X3
| sk_c8 != inverse(X4) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X0,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2)
| sk_c8 != multiply(sk_c7,sk_c6)
| sk_c6 != inverse(sk_c8)
| sk_c7 != multiply(sk_c8,X3)
| multiply(X4,sk_c8) != X3
| sk_c8 != inverse(X4) ),
inference(equality_resolution,[],[f66]) ).
fof(f68,plain,
! [X2,X0,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2)
| sk_c8 != multiply(sk_c7,sk_c6)
| sk_c6 != inverse(sk_c8)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) ),
inference(equality_resolution,[],[f67]) ).
fof(f70,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f71,plain,
( ! [X4] :
( sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,definition,
( spl0_2
<=> sk_c6 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f74,plain,
( sk_c6 = inverse(sk_c8)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f75,plain,
( sk_c6 != inverse(sk_c8)
| spl0_2 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f77,definition,
( spl0_3
<=> sk_c8 = multiply(sk_c7,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f78,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f79,plain,
( sk_c8 != multiply(sk_c7,sk_c6)
| spl0_3 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f81,definition,
( spl0_4
<=> ! [X0] :
( sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f82,plain,
( ! [X0] :
( sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,definition,
( spl0_5
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f85,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f86,plain,
( multiply(sk_c7,sk_c8) != sk_c6
| spl0_5 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_1
| spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f68,f84,f81,f70,f77,f73,f70]) ).
fof(f89,definition,
( spl0_6
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f91,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f93,definition,
( spl0_7
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f95,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f64,f93,f89]) ).
fof(f98,definition,
( spl0_8
<=> sk_c5 = multiply(sk_c4,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f99,plain,
( sk_c5 != multiply(sk_c4,sk_c8)
| spl0_8 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f100,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f103,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c8,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f105,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f106,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f60,f93,f103]) ).
fof(f107,plain,
( spl0_2
| spl0_7 ),
inference(avatar_split_clause,[],[f58,f93,f73]) ).
fof(f108,plain,
( spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f56,f93,f77]) ).
fof(f110,definition,
( spl0_10
<=> sk_c3 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f112,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,plain,
( spl0_6
| spl0_10 ),
inference(avatar_split_clause,[],[f54,f110,f89]) ).
fof(f115,plain,
( spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f50,f110,f103]) ).
fof(f116,plain,
( spl0_2
| spl0_10 ),
inference(avatar_split_clause,[],[f48,f110,f73]) ).
fof(f117,plain,
( spl0_3
| spl0_10 ),
inference(avatar_split_clause,[],[f46,f110,f77]) ).
fof(f119,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c8,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f121,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,plain,
( spl0_6
| spl0_11 ),
inference(avatar_split_clause,[],[f44,f119,f89]) ).
fof(f124,plain,
( spl0_9
| spl0_11 ),
inference(avatar_split_clause,[],[f40,f119,f103]) ).
fof(f125,plain,
( spl0_2
| spl0_11 ),
inference(avatar_split_clause,[],[f38,f119,f73]) ).
fof(f126,plain,
( spl0_3
| spl0_11 ),
inference(avatar_split_clause,[],[f36,f119,f77]) ).
fof(f128,definition,
( spl0_12
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f130,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f131,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f34,f128,f89]) ).
fof(f132,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f32,f128,f98]) ).
fof(f133,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f30,f128,f103]) ).
fof(f134,plain,
( spl0_2
| spl0_12 ),
inference(avatar_split_clause,[],[f28,f128,f73]) ).
fof(f135,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f26,f128,f77]) ).
fof(f137,definition,
( spl0_13
<=> sk_c8 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f139,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f140,plain,
( spl0_6
| spl0_13 ),
inference(avatar_split_clause,[],[f24,f137,f89]) ).
fof(f141,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f22,f137,f98]) ).
fof(f142,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f20,f137,f103]) ).
fof(f143,plain,
( spl0_2
| spl0_13 ),
inference(avatar_split_clause,[],[f18,f137,f73]) ).
fof(f144,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f16,f137,f77]) ).
fof(f145,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f14,f84,f89]) ).
fof(f146,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f12,f84,f98]) ).
fof(f147,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f10,f84,f103]) ).
fof(f148,plain,
( spl0_2
| spl0_5 ),
inference(avatar_split_clause,[],[f8,f84,f73]) ).
fof(f149,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f6,f84,f77]) ).
fof(f150,plain,
( identity = multiply(sk_c6,sk_c8)
| ~ spl0_2 ),
inference(superposition,[],[f3,f74]) ).
fof(f151,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_6 ),
inference(superposition,[],[f3,f91]) ).
fof(f154,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f155,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c6,X0)) = multiply(sk_c8,X0)
| ~ spl0_3 ),
inference(superposition,[],[f4,f78]) ).
fof(f156,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c5,X0)) = multiply(sk_c7,X0)
| ~ spl0_9 ),
inference(superposition,[],[f4,f105]) ).
fof(f157,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c8,X0))
| ~ spl0_2 ),
inference(superposition,[],[f4,f150]) ).
fof(f159,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c8,X0)) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f157,f1]) ).
fof(f160,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f154,f1]) ).
fof(f163,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c4,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f151]) ).
fof(f164,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c4,X0)) = X0
| ~ spl0_6 ),
inference(forward_demodulation,[],[f163,f1]) ).
fof(f165,plain,
( multiply(sk_c8,sk_c8) = multiply(sk_c7,identity)
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f155,f150]) ).
fof(f170,plain,
( sk_c4 = multiply(sk_c6,identity)
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f159,f151]) ).
fof(f174,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c7,X0))
| ~ spl0_2
| ~ spl0_9 ),
inference(superposition,[],[f159,f156]) ).
fof(f187,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(sk_c6,multiply(identity,X0))
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f4,f170]) ).
fof(f188,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c4,X0)
| ~ spl0_2
| ~ spl0_6 ),
inference(forward_demodulation,[],[f187,f1]) ).
fof(f192,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[],[f160,f4]) ).
fof(f193,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f160,f3]) ).
fof(f194,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f160,f160]) ).
fof(f195,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c8)
| ~ spl0_3 ),
inference(superposition,[],[f160,f78]) ).
fof(f196,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(inverse(sk_c7),multiply(sk_c8,X0))
| ~ spl0_3 ),
inference(superposition,[],[f160,f155]) ).
fof(f201,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(inverse(sk_c6),X0)
| ~ spl0_2 ),
inference(superposition,[],[f160,f159]) ).
fof(f203,plain,
( sk_c8 = multiply(inverse(sk_c6),identity)
| ~ spl0_2 ),
inference(superposition,[],[f160,f150]) ).
fof(f204,plain,
( sk_c8 = multiply(inverse(sk_c4),sk_c5)
| ~ spl0_8 ),
inference(superposition,[],[f160,f100]) ).
fof(f209,plain,
( sk_c8 = multiply(sk_c8,sk_c5)
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f204,f91]) ).
fof(f214,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f193,f194]) ).
fof(f216,plain,
( sk_c7 = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f105,f209]) ).
fof(f226,plain,
( sk_c6 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f195,f216]) ).
fof(f229,plain,
( sk_c6 != multiply(sk_c8,sk_c8)
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f86,f216]) ).
fof(f231,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f226,f3]) ).
fof(f250,plain,
( sk_c8 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f203,f231]) ).
fof(f251,plain,
( sk_c4 = multiply(sk_c6,sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f170,f231]) ).
fof(f252,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f1,f231]) ).
fof(f253,plain,
( sk_c6 = sk_c4
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f251,f252]) ).
fof(f254,plain,
( identity = sk_c8
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f250,f3]) ).
fof(f256,plain,
( multiply(sk_c7,sk_c6) = multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f165,f231]) ).
fof(f263,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f256,f78]) ).
fof(f289,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c6,X0)) = X0
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f164,f253]) ).
fof(f292,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f289,f252]) ).
fof(f325,plain,
( sk_c8 = sk_c6
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f231,f254]) ).
fof(f442,plain,
( ! [X0] : multiply(X0,sk_c8) = X0
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f214,f254]) ).
fof(f454,plain,
identity = inverse(identity),
inference(superposition,[],[f3,f214]) ).
fof(f456,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f165,f214]) ).
fof(f540,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[],[f214,f194]) ).
fof(f541,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f540,f214]) ).
fof(f1093,plain,
( multiply(sk_c6,sk_c8) = multiply(sk_c5,sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_9 ),
inference(superposition,[],[f174,f78]) ).
fof(f1095,plain,
( multiply(sk_c5,identity) = multiply(sk_c6,multiply(sk_c8,sk_c8))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_9 ),
inference(superposition,[],[f174,f165]) ).
fof(f1112,plain,
( sk_c8 = multiply(sk_c5,identity)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1095,f159]) ).
fof(f1190,plain,
( sk_c8 != sk_c6
| ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f229,f263]) ).
fof(f1203,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f1190,f325]) ).
fof(f1204,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f1203]) ).
fof(f1207,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f71,f292]) ).
fof(f1209,plain,
( ! [X4] :
( sk_c7 != X4
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1207,f442]) ).
fof(f1211,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c8 != X4 )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1209,f216]) ).
fof(f1214,plain,
( sk_c8 != sk_c6
| sk_c8 != sk_c8
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f1211,f74]) ).
fof(f1219,plain,
( sk_c8 != sk_c6
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f1214]) ).
fof(f1227,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f1219,f325]) ).
fof(f1228,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f1227]) ).
fof(f1229,plain,
( ! [X0] :
( sk_c8 != multiply(X0,sk_c8)
| inverse(X0) != sk_c7 )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f82,f216]) ).
fof(f1230,plain,
( ! [X0] :
( sk_c8 != X0
| inverse(X0) != sk_c7 )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1229,f442]) ).
fof(f1231,plain,
( ! [X0] :
( inverse(X0) != sk_c8
| sk_c8 != X0 )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1230,f216]) ).
fof(f1282,plain,
( sk_c8 != sk_c6
| sk_c8 != sk_c8
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f1231,f74]) ).
fof(f1287,plain,
( sk_c8 != sk_c6
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f1282]) ).
fof(f1295,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f1287,f325]) ).
fof(f1296,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f1295]) ).
fof(f1297,plain,
( sk_c5 != multiply(sk_c6,sk_c8)
| ~ spl0_2
| ~ spl0_6
| spl0_8 ),
inference(forward_demodulation,[],[f99,f188]) ).
fof(f1331,plain,
( identity = multiply(sk_c5,sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1093,f150]) ).
fof(f1332,plain,
( sk_c8 = sk_c5
| ~ spl0_2
| ~ spl0_3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1112,f214]) ).
fof(f1334,plain,
( identity != sk_c5
| ~ spl0_2
| ~ spl0_6
| spl0_8 ),
inference(forward_demodulation,[],[f1297,f150]) ).
fof(f1343,plain,
( identity != sk_c8
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1334,f1332]) ).
fof(f1347,plain,
( inverse(sk_c8) = sk_c2
| ~ spl0_7 ),
inference(superposition,[],[f541,f95]) ).
fof(f1348,plain,
( sk_c6 = sk_c2
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1347,f74]) ).
fof(f1356,plain,
( sk_c1 = inverse(sk_c7)
| ~ spl0_12 ),
inference(superposition,[],[f541,f130]) ).
fof(f1359,plain,
( multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c8)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9 ),
inference(superposition,[],[f174,f85]) ).
fof(f1366,plain,
( multiply(sk_c8,sk_c8) = multiply(sk_c6,sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1359,f1332]) ).
fof(f1368,plain,
( sk_c7 = multiply(sk_c6,sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1366,f456]) ).
fof(f1375,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c8,X0)) = multiply(sk_c3,X0)
| ~ spl0_10 ),
inference(superposition,[],[f4,f112]) ).
fof(f1376,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c8,X0)) = multiply(sk_c3,X0)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f1375,f1348]) ).
fof(f1380,plain,
( ! [X0] : multiply(sk_c3,X0) = X0
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f1376,f159]) ).
fof(f1392,plain,
( ! [X0] : multiply(inverse(sk_c7),multiply(sk_c8,multiply(sk_c3,X0))) = X0
| ~ spl0_11 ),
inference(superposition,[],[f192,f121]) ).
fof(f1394,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c3,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f121]) ).
fof(f1395,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c7,X0)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1394,f1380]) ).
fof(f1397,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c3,X0)) = X0
| ~ spl0_3
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1392,f196]) ).
fof(f1402,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1397,f1380]) ).
fof(f1409,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_13 ),
inference(superposition,[],[f160,f139]) ).
fof(f1410,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c1,multiply(sk_c7,X0))
| ~ spl0_13 ),
inference(superposition,[],[f4,f139]) ).
fof(f1411,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c1,multiply(sk_c8,X0))
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1410,f1395]) ).
fof(f1412,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1409,f130]) ).
fof(f1414,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1412,f1395]) ).
fof(f1416,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c1,multiply(sk_c8,X0))
| ~ spl0_3
| ~ spl0_12 ),
inference(superposition,[],[f196,f1356]) ).
fof(f1418,plain,
( identity = multiply(sk_c1,sk_c7)
| ~ spl0_12 ),
inference(superposition,[],[f3,f1356]) ).
fof(f1423,plain,
( identity = sk_c8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1418,f139]) ).
fof(f1424,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c8,X0)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1416,f1411]) ).
fof(f1425,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1423,f1343]) ).
fof(f1426,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f1425]) ).
fof(f1427,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1424,f1402]) ).
fof(f1438,plain,
( sk_c8 = multiply(sk_c8,sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f78,f1395]) ).
fof(f1441,plain,
( sk_c7 = sk_c6
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1368,f1402]) ).
fof(f1442,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1331,f1423]) ).
fof(f1444,plain,
( sk_c8 = sk_c6
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1438,f1427]) ).
fof(f1447,plain,
( sk_c8 = multiply(sk_c5,sk_c7)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1442,f1441]) ).
fof(f1449,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1447,f1332]) ).
fof(f1450,plain,
( sk_c7 = sk_c8
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1449,f1427]) ).
fof(f1451,plain,
( identity = multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f150,f1444]) ).
fof(f1463,plain,
( identity = sk_c7
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1451,f1414]) ).
fof(f1477,plain,
( identity != sk_c8
| sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_4 ),
inference(superposition,[],[f82,f3]) ).
fof(f1490,plain,
( sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1477,f1423]) ).
fof(f1497,plain,
( $false
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1490,f541]) ).
fof(f1498,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f1497]) ).
fof(f1513,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f71,f1427]) ).
fof(f1514,plain,
( ! [X4] :
( sk_c8 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1513,f1450]) ).
fof(f1545,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| sk_c8 != inverse(inverse(sk_c6))
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f1514,f201]) ).
fof(f1554,plain,
( sk_c8 != inverse(inverse(sk_c6))
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1545,f1427]) ).
fof(f1564,plain,
( sk_c8 != sk_c6
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1554,f541]) ).
fof(f1571,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1564,f1444]) ).
fof(f1572,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f1571]) ).
fof(f1577,plain,
( sk_c7 = sk_c8
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1463,f1423]) ).
fof(f1580,plain,
( sk_c7 != sk_c8
| sk_c8 != inverse(identity)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f1513,f1]) ).
fof(f1597,plain,
( sk_c8 != inverse(identity)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1580,f1577]) ).
fof(f1606,plain,
( identity != sk_c8
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1597,f454]) ).
fof(f1616,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1606,f1423]) ).
fof(f1617,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f1616]) ).
fof(f1624,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f1,f1423]) ).
fof(f1626,plain,
( ! [X0] : multiply(X0,sk_c8) = X0
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f214,f1423]) ).
fof(f1629,plain,
( identity = multiply(sk_c2,sk_c8)
| ~ spl0_7 ),
inference(superposition,[],[f3,f1347]) ).
fof(f1634,plain,
( identity = sk_c3
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f1629,f112]) ).
fof(f1635,plain,
( sk_c8 = sk_c3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1634,f1423]) ).
fof(f1638,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c8)
| ~ spl0_3 ),
inference(superposition,[],[f160,f78]) ).
fof(f1641,plain,
( sk_c6 = inverse(sk_c7)
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1638,f1626]) ).
fof(f1645,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f121,f1635]) ).
fof(f1646,plain,
( sk_c7 = sk_c8
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1645,f1624]) ).
fof(f1657,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f85,f1646]) ).
fof(f1661,plain,
( sk_c8 = sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1657,f1624]) ).
fof(f1747,plain,
( sk_c6 = inverse(sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f1641,f1646]) ).
fof(f1760,plain,
( $false
| spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1747,f75]) ).
fof(f1761,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f1760]) ).
fof(f1770,plain,
( sk_c8 != multiply(sk_c7,sk_c8)
| spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f79,f1661]) ).
fof(f1773,plain,
( sk_c8 != sk_c6
| spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1770,f85]) ).
fof(f1776,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1773,f1661]) ).
fof(f1777,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f1776]) ).
cnf(s1,plain,
( spl0_1
| spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f87]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f96]) ).
cnf(s5,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f106]) ).
cnf(s6,plain,
( spl0_2
| spl0_7 ),
inference(sat_conversion,[],[f107]) ).
cnf(s7,plain,
( spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f108]) ).
cnf(s8,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f113]) ).
cnf(s10,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f115]) ).
cnf(s11,plain,
( spl0_2
| spl0_10 ),
inference(sat_conversion,[],[f116]) ).
cnf(s12,plain,
( spl0_3
| spl0_10 ),
inference(sat_conversion,[],[f117]) ).
cnf(s13,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f122]) ).
cnf(s15,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f124]) ).
cnf(s16,plain,
( spl0_2
| spl0_11 ),
inference(sat_conversion,[],[f125]) ).
cnf(s17,plain,
( spl0_3
| spl0_11 ),
inference(sat_conversion,[],[f126]) ).
cnf(s18,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f131]) ).
cnf(s19,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f132]) ).
cnf(s20,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f133]) ).
cnf(s21,plain,
( spl0_2
| spl0_12 ),
inference(sat_conversion,[],[f134]) ).
cnf(s22,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f135]) ).
cnf(s23,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f140]) ).
cnf(s24,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f141]) ).
cnf(s25,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f142]) ).
cnf(s26,plain,
( spl0_2
| spl0_13 ),
inference(sat_conversion,[],[f143]) ).
cnf(s27,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f144]) ).
cnf(s28,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f145]) ).
cnf(s29,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f146]) ).
cnf(s30,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f147]) ).
cnf(s31,plain,
( spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f148]) ).
cnf(s32,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f149]) ).
cnf(s33,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f1204]) ).
cnf(s37,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f1228]) ).
cnf(s41,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f1296]) ).
cnf(s42,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f1426]) ).
cnf(s45,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f1498]) ).
cnf(s55,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f1572]) ).
cnf(s61,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f1617]) ).
cnf(s62,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f1761]) ).
cnf(s63,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f1777]) ).
cnf(s64,plain,
spl0_2,
inference(rat,[],[s62,s63,s6,s11,s16,s21,s26,s31]) ).
cnf(s65,plain,
( spl0_5
| ~ spl0_3 ),
inference(rat,[],[s33,s28,s29,s30,s64]) ).
cnf(s66,plain,
( spl0_9
| ~ spl0_4 ),
inference(rat,[],[s45,s20,s25]) ).
cnf(s67,plain,
( ~ spl0_9
| ~ spl0_6
| ~ spl0_3
| ~ spl0_4 ),
inference(rat,[],[s42,s19,s24,s41,s64]) ).
cnf(s68,plain,
( ~ spl0_9
| ~ spl0_4
| ~ spl0_3 ),
inference(rat,[],[s45,s18,s23,s67]) ).
cnf(s69,plain,
( ~ spl0_5
| ~ spl0_3
| spl0_1 ),
inference(rat,[],[s68,s66,s2,s64]) ).
cnf(s70,plain,
( ~ spl0_3
| spl0_1 ),
inference(rat,[],[s69,s65]) ).
cnf(s71,plain,
spl0_3,
inference(rat,[],[s63,s7,s12,s17,s22,s27,s32]) ).
cnf(s72,plain,
spl0_5,
inference(rat,[],[s65,s71]) ).
cnf(s73,plain,
spl0_1,
inference(rat,[],[s70,s71]) ).
cnf(s75,plain,
spl0_9,
inference(rat,[],[s61,s5,s10,s15,s20,s25,s64,s71,s73]) ).
cnf(s76,plain,
~ spl0_6,
inference(rat,[],[s42,s19,s24,s37,s64,s71,s75,s73]) ).
cnf(s77,plain,
spl0_13,
inference(rat,[],[s23,s76]) ).
cnf(s78,plain,
spl0_12,
inference(rat,[],[s18,s76]) ).
cnf(s79,plain,
spl0_11,
inference(rat,[],[s13,s76]) ).
cnf(s80,plain,
spl0_10,
inference(rat,[],[s8,s76]) ).
cnf(s81,plain,
spl0_7,
inference(rat,[],[s3,s76]) ).
cnf(s82,plain,
$false,
inference(rat,[],[s55,s77,s78,s75,s73,s72,s71,s64,s80,s79,s81]) ).
fof(f1780,plain,
$false,
inference(avatar_sat_refutation,[],[s82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP328-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n008.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 09:52:46 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.15/0.46 % (989609)Will run a generic schedule for satisfiability detection.
% 0.15/0.46 % (989618)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=831315102:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.46 % (989615)% WARNING: option uhcvi not known.
% 0.15/0.46 % (989615)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2508642719:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.46 % (989614)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2470414341_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.46 % (989616)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2823512920:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.46 % (989619)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=344177196:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.46 % (989617)dis+10_1_sil=32000:sp=arity:random_seed=641652054:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.46 % (989620)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1676993762:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.46 % TRYING [1]
% 0.15/0.46 % TRYING [2]
% 0.15/0.46 % TRYING [3]
% 0.15/0.46 % (989618) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-989609-989618"...
% 0.15/0.46 % TRYING [4]
% 0.15/0.46 % (989618)...printing done.
% 0.15/0.46 % (989618)Refutation found. Thanks to Tanya!
% 0.15/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (989618)------------------------------
% 0.15/0.47 % (989618)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.47 % (989618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.47 % (989618)CaDiCaL version: 2.1.3
% 0.15/0.47 % (989618)Termination reason: Refutation
% 0.15/0.47 % (989618)Time elapsed: 0.016 s
% 0.15/0.47 % (989618)Peak memory usage: 13 MB
% 0.15/0.47 % (989618)Instructions burned: 48 (million)
% 0.15/0.47 % (989609)Success in time 0.041 s
% 0.15/0.47 % Vampire exiting
%------------------------------------------------------------------------------