%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP325-1 : 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 : n019.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 10:17:29 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.47s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 52
% Syntax : Number of formulae : 290 ( 21 unt; 21 def)
% Number of atoms : 874 ( 303 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1073 ( 489 ~; 563 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 22 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 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_c9,sk_c10) = sk_c8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c8 = inverse(sk_c9) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f12]) ).
fof(f24,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c9 = inverse(sk_c1)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = inverse(sk_c9) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f30]) ).
fof(f42,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c9 = multiply(sk_c10,sk_c3)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c9 = multiply(sk_c10,sk_c3)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c9 = multiply(sk_c10,sk_c3)
| sk_c8 = inverse(sk_c9) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c9 = multiply(sk_c10,sk_c3)
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c9 = multiply(sk_c10,sk_c3)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c9 = multiply(sk_c10,sk_c3)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f52]) ).
fof(f60,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c3
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c3 = multiply(sk_c2,sk_c10)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c3
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c3 = multiply(sk_c2,sk_c10)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c3
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c3 = multiply(sk_c2,sk_c10)
| sk_c8 = inverse(sk_c9) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c3
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c3 = multiply(sk_c2,sk_c10)
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c3
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c3 = multiply(sk_c2,sk_c10)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c3
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c3 = multiply(sk_c2,sk_c10)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f70]) ).
fof(f78,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f79,plain,
( sk_c10 = inverse(sk_c2)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f78]) ).
fof(f80,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f81,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f80]) ).
fof(f82,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f83,plain,
( sk_c10 = inverse(sk_c2)
| sk_c8 = inverse(sk_c9) ),
inference(reorient_equations,[],[f82]) ).
fof(f84,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f85,plain,
( sk_c10 = inverse(sk_c2)
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f84]) ).
fof(f86,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f87,plain,
( sk_c10 = inverse(sk_c2)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f86]) ).
fof(f88,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f89,plain,
( sk_c10 = inverse(sk_c2)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f88]) ).
fof(f96,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( multiply(sk_c9,sk_c10) != sk_c8
| multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c9
| multiply(sk_c10,X1) != sk_c9
| multiply(X2,sk_c10) != X1
| inverse(X2) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| inverse(X3) != sk_c10
| inverse(sk_c9) != sk_c8
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(X4) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| inverse(X5) != X6
| inverse(X6) != sk_c10
| multiply(X5,sk_c10) != X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_47) ).
fof(f97,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( multiply(sk_c9,sk_c10) != sk_c8
| sk_c10 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c9 != multiply(sk_c10,X1)
| multiply(X2,sk_c10) != X1
| sk_c10 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c8 != inverse(sk_c9)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c9 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8)
| inverse(X5) != X6
| sk_c10 != inverse(X6)
| multiply(X5,sk_c10) != X6 ),
inference(reorient_equations,[],[f96]) ).
fof(f98,plain,
! [X2,X3,X0,X6,X4,X5] :
( multiply(sk_c9,sk_c10) != sk_c8
| sk_c10 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c9 != multiply(sk_c10,multiply(X2,sk_c10))
| sk_c10 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c8 != inverse(sk_c9)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c9 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8)
| inverse(X5) != X6
| sk_c10 != inverse(X6)
| multiply(X5,sk_c10) != X6 ),
inference(equality_resolution,[],[f97]) ).
fof(f99,plain,
! [X2,X3,X0,X4,X5] :
( multiply(sk_c9,sk_c10) != sk_c8
| sk_c10 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c9 != multiply(sk_c10,multiply(X2,sk_c10))
| sk_c10 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c8 != inverse(sk_c9)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c9 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8)
| sk_c10 != inverse(inverse(X5))
| inverse(X5) != multiply(X5,sk_c10) ),
inference(equality_resolution,[],[f98]) ).
fof(f101,definition,
( spl0_1
<=> ! [X5] :
( sk_c10 != inverse(inverse(X5))
| inverse(X5) != multiply(X5,sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f102,plain,
( ! [X5] :
( sk_c10 != inverse(inverse(X5))
| inverse(X5) != multiply(X5,sk_c10) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,definition,
( spl0_2
<=> ! [X4] :
( sk_c9 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f105,plain,
( ! [X4] :
( sk_c9 != multiply(X4,sk_c8)
| sk_c9 != inverse(X4) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,definition,
( spl0_3
<=> sk_c9 = multiply(sk_c10,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f108,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f109,plain,
( sk_c9 != multiply(sk_c10,sk_c8)
| spl0_3 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f111,definition,
( spl0_4
<=> sk_c8 = inverse(sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f112,plain,
( sk_c8 = inverse(sk_c9)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f113,plain,
( sk_c8 != inverse(sk_c9)
| spl0_4 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f115,definition,
( spl0_5
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f116,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,definition,
( spl0_6
<=> ! [X2] :
( sk_c9 != multiply(sk_c10,multiply(X2,sk_c10))
| sk_c10 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f119,plain,
( ! [X2] :
( sk_c9 != multiply(sk_c10,multiply(X2,sk_c10))
| sk_c10 != inverse(X2) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,definition,
( spl0_7
<=> ! [X0] :
( sk_c10 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f122,plain,
( ! [X0] :
( sk_c10 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9 )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,definition,
( spl0_8
<=> multiply(sk_c9,sk_c10) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f125,plain,
( multiply(sk_c9,sk_c10) = sk_c8
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f99,f124,f121,f118,f115,f111,f107,f104,f101]) ).
fof(f133,definition,
( spl0_10
<=> sk_c10 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f135,plain,
( sk_c10 = inverse(sk_c2)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f148,definition,
( spl0_13
<=> sk_c9 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f150,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f151,plain,
( spl0_13
| spl0_10 ),
inference(avatar_split_clause,[],[f89,f133,f148]) ).
fof(f153,definition,
( spl0_14
<=> sk_c9 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f155,plain,
( sk_c9 = inverse(sk_c5)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f156,plain,
( spl0_14
| spl0_10 ),
inference(avatar_split_clause,[],[f87,f133,f153]) ).
fof(f157,plain,
( spl0_3
| spl0_10 ),
inference(avatar_split_clause,[],[f85,f133,f107]) ).
fof(f158,plain,
( spl0_4
| spl0_10 ),
inference(avatar_split_clause,[],[f83,f133,f111]) ).
fof(f160,definition,
( spl0_15
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f162,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f163,plain,
( spl0_15
| spl0_10 ),
inference(avatar_split_clause,[],[f81,f133,f160]) ).
fof(f165,definition,
( spl0_16
<=> sk_c9 = multiply(sk_c4,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f167,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f168,plain,
( spl0_16
| spl0_10 ),
inference(avatar_split_clause,[],[f79,f133,f165]) ).
fof(f170,definition,
( spl0_17
<=> sk_c3 = multiply(sk_c2,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f172,plain,
( sk_c3 = multiply(sk_c2,sk_c10)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f176,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f71,f170,f148]) ).
fof(f177,plain,
( spl0_14
| spl0_17 ),
inference(avatar_split_clause,[],[f69,f170,f153]) ).
fof(f178,plain,
( spl0_3
| spl0_17 ),
inference(avatar_split_clause,[],[f67,f170,f107]) ).
fof(f179,plain,
( spl0_4
| spl0_17 ),
inference(avatar_split_clause,[],[f65,f170,f111]) ).
fof(f180,plain,
( spl0_15
| spl0_17 ),
inference(avatar_split_clause,[],[f63,f170,f160]) ).
fof(f181,plain,
( spl0_16
| spl0_17 ),
inference(avatar_split_clause,[],[f61,f170,f165]) ).
fof(f183,definition,
( spl0_18
<=> sk_c9 = multiply(sk_c10,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f185,plain,
( sk_c9 = multiply(sk_c10,sk_c3)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f189,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f53,f183,f148]) ).
fof(f190,plain,
( spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f51,f183,f153]) ).
fof(f191,plain,
( spl0_3
| spl0_18 ),
inference(avatar_split_clause,[],[f49,f183,f107]) ).
fof(f192,plain,
( spl0_4
| spl0_18 ),
inference(avatar_split_clause,[],[f47,f183,f111]) ).
fof(f193,plain,
( spl0_15
| spl0_18 ),
inference(avatar_split_clause,[],[f45,f183,f160]) ).
fof(f194,plain,
( spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f43,f183,f165]) ).
fof(f196,definition,
( spl0_19
<=> sk_c9 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f198,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f204,plain,
( spl0_3
| spl0_19 ),
inference(avatar_split_clause,[],[f31,f196,f107]) ).
fof(f205,plain,
( spl0_4
| spl0_19 ),
inference(avatar_split_clause,[],[f29,f196,f111]) ).
fof(f206,plain,
( spl0_15
| spl0_19 ),
inference(avatar_split_clause,[],[f27,f196,f160]) ).
fof(f207,plain,
( spl0_16
| spl0_19 ),
inference(avatar_split_clause,[],[f25,f196,f165]) ).
fof(f209,definition,
( spl0_20
<=> sk_c10 = multiply(sk_c1,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f211,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f217,plain,
( spl0_3
| spl0_20 ),
inference(avatar_split_clause,[],[f13,f209,f107]) ).
fof(f218,plain,
( spl0_4
| spl0_20 ),
inference(avatar_split_clause,[],[f11,f209,f111]) ).
fof(f219,plain,
( spl0_15
| spl0_20 ),
inference(avatar_split_clause,[],[f9,f209,f160]) ).
fof(f220,plain,
( spl0_16
| spl0_20 ),
inference(avatar_split_clause,[],[f7,f209,f165]) ).
fof(f221,plain,
spl0_8,
inference(avatar_split_clause,[],[f5,f124]) ).
fof(f228,plain,
( sk_c9 != sk_c8
| sk_c9 != inverse(identity)
| ~ spl0_2 ),
inference(superposition,[],[f105,f1]) ).
fof(f230,definition,
( spl0_21
<=> sk_c9 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f234,definition,
( spl0_22
<=> sk_c9 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f235,plain,
( sk_c9 = sk_c8
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f236,plain,
( sk_c9 != sk_c8
| spl0_22 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f237,plain,
( ~ spl0_21
| ~ spl0_22
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f228,f104,f234,f230]) ).
fof(f239,plain,
( identity = multiply(sk_c9,sk_c1)
| ~ spl0_19 ),
inference(superposition,[],[f3,f198]) ).
fof(f241,plain,
( identity = multiply(sk_c9,sk_c5)
| ~ spl0_14 ),
inference(superposition,[],[f3,f155]) ).
fof(f251,definition,
( spl0_24
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f252,plain,
( identity = sk_c9
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f253,plain,
( identity != sk_c9
| spl0_24 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f257,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f266,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f257,f1]) ).
fof(f304,definition,
( spl0_26
<=> sk_c9 = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f305,plain,
( sk_c9 = sk_c10
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f416,plain,
( sk_c10 = multiply(inverse(sk_c9),sk_c8)
| ~ spl0_8 ),
inference(superposition,[],[f266,f125]) ).
fof(f430,plain,
( sk_c9 = multiply(inverse(sk_c1),sk_c10)
| ~ spl0_20 ),
inference(superposition,[],[f266,f211]) ).
fof(f432,plain,
( sk_c10 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_16 ),
inference(superposition,[],[f266,f167]) ).
fof(f437,plain,
( sk_c10 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_17 ),
inference(superposition,[],[f266,f172]) ).
fof(f444,plain,
( sk_c10 = multiply(sk_c10,sk_c3)
| ~ spl0_10
| ~ spl0_17 ),
inference(forward_demodulation,[],[f437,f135]) ).
fof(f449,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f432,f162]) ).
fof(f451,plain,
( sk_c9 = multiply(sk_c9,sk_c10)
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f430,f198]) ).
fof(f459,plain,
( sk_c9 = sk_c10
| ~ spl0_10
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f444,f185]) ).
fof(f461,plain,
( spl0_26
| ~ spl0_10
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f459,f183,f170,f133,f304]) ).
fof(f483,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_19
| ~ spl0_20
| ~ spl0_26 ),
inference(forward_demodulation,[],[f451,f305]) ).
fof(f510,plain,
( sk_c8 = inverse(identity)
| ~ spl0_4
| ~ spl0_24 ),
inference(superposition,[],[f112,f252]) ).
fof(f511,plain,
( sk_c8 = multiply(identity,sk_c10)
| ~ spl0_8
| ~ spl0_24 ),
inference(superposition,[],[f125,f252]) ).
fof(f514,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_19
| ~ spl0_24 ),
inference(superposition,[],[f239,f252]) ).
fof(f515,plain,
( identity = multiply(identity,sk_c5)
| ~ spl0_14
| ~ spl0_24 ),
inference(superposition,[],[f241,f252]) ).
fof(f527,plain,
( identity = sk_c5
| ~ spl0_14
| ~ spl0_24 ),
inference(forward_demodulation,[],[f515,f1]) ).
fof(f528,plain,
( identity = sk_c1
| ~ spl0_19
| ~ spl0_24 ),
inference(forward_demodulation,[],[f514,f1]) ).
fof(f530,plain,
( sk_c10 = sk_c8
| ~ spl0_8
| ~ spl0_24 ),
inference(forward_demodulation,[],[f511,f1]) ).
fof(f534,plain,
( sk_c9 = sk_c8
| ~ spl0_8
| ~ spl0_24
| ~ spl0_26 ),
inference(forward_demodulation,[],[f530,f305]) ).
fof(f537,plain,
( $false
| ~ spl0_8
| spl0_22
| ~ spl0_24
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f534,f236]) ).
fof(f538,plain,
( ~ spl0_8
| spl0_22
| ~ spl0_24
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f537]) ).
fof(f541,plain,
( sk_c8 != inverse(identity)
| spl0_4
| ~ spl0_24 ),
inference(forward_demodulation,[],[f113,f252]) ).
fof(f607,plain,
( sk_c9 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_19
| ~ spl0_20
| ~ spl0_26 ),
inference(superposition,[],[f266,f483]) ).
fof(f609,plain,
( identity = sk_c9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_26 ),
inference(forward_demodulation,[],[f607,f3]) ).
fof(f617,plain,
( sk_c9 != inverse(identity)
| spl0_4
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f541,f235]) ).
fof(f621,plain,
( sk_c9 = sk_c10
| ~ spl0_8
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f530,f235]) ).
fof(f622,plain,
( spl0_24
| ~ spl0_19
| ~ spl0_20
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f609,f304,f209,f196,f251]) ).
fof(f623,plain,
( ~ spl0_21
| spl0_4
| ~ spl0_22
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f617,f251,f234,f111,f230]) ).
fof(f624,plain,
( sk_c9 != multiply(sk_c10,sk_c9)
| spl0_3
| ~ spl0_22 ),
inference(forward_demodulation,[],[f109,f235]) ).
fof(f625,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_4
| ~ spl0_22 ),
inference(forward_demodulation,[],[f112,f235]) ).
fof(f626,plain,
( sk_c9 = inverse(identity)
| ~ spl0_4
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f510,f235]) ).
fof(f629,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| spl0_3
| ~ spl0_22
| ~ spl0_26 ),
inference(forward_demodulation,[],[f624,f305]) ).
fof(f630,plain,
( spl0_21
| ~ spl0_4
| ~ spl0_22
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f626,f251,f234,f111,f230]) ).
fof(f632,plain,
( $false
| spl0_3
| ~ spl0_19
| ~ spl0_20
| ~ spl0_22
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f629,f483]) ).
fof(f633,plain,
( spl0_3
| ~ spl0_19
| ~ spl0_20
| ~ spl0_22
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f632]) ).
fof(f666,plain,
( identity = inverse(identity)
| ~ spl0_4
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f625,f252]) ).
fof(f680,plain,
( sk_c9 = inverse(identity)
| ~ spl0_19
| ~ spl0_24 ),
inference(superposition,[],[f198,f528]) ).
fof(f762,plain,
( ! [X3] :
( identity != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_5
| ~ spl0_24 ),
inference(forward_demodulation,[],[f116,f252]) ).
fof(f767,plain,
( sk_c10 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_8
| ~ spl0_22 ),
inference(forward_demodulation,[],[f416,f235]) ).
fof(f772,plain,
( identity = sk_c10
| ~ spl0_8
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f621,f252]) ).
fof(f784,plain,
( identity = sk_c10
| ~ spl0_8
| ~ spl0_22 ),
inference(forward_demodulation,[],[f767,f3]) ).
fof(f792,plain,
( identity = multiply(sk_c10,sk_c4)
| ~ spl0_15 ),
inference(superposition,[],[f3,f162]) ).
fof(f819,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_5
| ~ spl0_8
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f762,f772]) ).
fof(f820,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_5
| ~ spl0_8
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f819,f772]) ).
fof(f823,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_5
| ~ spl0_8
| ~ spl0_22
| ~ spl0_24 ),
inference(superposition,[],[f820,f3]) ).
fof(f824,plain,
( identity != inverse(inverse(identity))
| ~ spl0_5
| ~ spl0_8
| ~ spl0_22
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f823]) ).
fof(f826,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f824,f666]) ).
fof(f829,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f826,f666]) ).
fof(f830,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_22
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f829]) ).
fof(f860,plain,
( ! [X5] :
( identity != inverse(inverse(X5))
| inverse(X5) != multiply(X5,sk_c10) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f102,f772]) ).
fof(f861,plain,
( ! [X5] :
( inverse(X5) != multiply(X5,identity)
| identity != inverse(inverse(X5)) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f860,f772]) ).
fof(f864,plain,
( identity != inverse(inverse(identity))
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_8
| ~ spl0_22
| ~ spl0_24 ),
inference(superposition,[],[f861,f3]) ).
fof(f865,plain,
( identity != inverse(identity)
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f864,f666]) ).
fof(f867,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f865,f666]) ).
fof(f869,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f867,f666]) ).
fof(f872,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f869,f666]) ).
fof(f873,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f872,f666]) ).
fof(f874,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_22
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f873]) ).
fof(f916,plain,
( ! [X0] :
( identity != multiply(X0,sk_c9)
| inverse(X0) != sk_c9 )
| ~ spl0_7
| ~ spl0_8
| ~ spl0_22 ),
inference(forward_demodulation,[],[f122,f784]) ).
fof(f925,plain,
( identity != identity
| sk_c9 != inverse(inverse(sk_c9))
| ~ spl0_7
| ~ spl0_8
| ~ spl0_22 ),
inference(superposition,[],[f916,f3]) ).
fof(f928,plain,
( sk_c9 != inverse(inverse(sk_c9))
| ~ spl0_7
| ~ spl0_8
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f925]) ).
fof(f930,plain,
( sk_c9 != inverse(sk_c9)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_22 ),
inference(forward_demodulation,[],[f928,f625]) ).
fof(f933,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f930,f625]) ).
fof(f934,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f933]) ).
fof(f959,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_8
| ~ spl0_15
| ~ spl0_22 ),
inference(forward_demodulation,[],[f792,f784]) ).
fof(f960,plain,
( identity = sk_c4
| ~ spl0_8
| ~ spl0_15
| ~ spl0_22 ),
inference(forward_demodulation,[],[f959,f1]) ).
fof(f963,plain,
( sk_c9 = multiply(identity,sk_c10)
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(superposition,[],[f167,f960]) ).
fof(f964,plain,
( sk_c9 = sk_c10
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f963,f1]) ).
fof(f967,plain,
( identity = sk_c9
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f964,f784]) ).
fof(f969,plain,
( $false
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22
| spl0_24 ),
inference(forward_subsumption_resolution,[],[f967,f253]) ).
fof(f970,plain,
( ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22
| spl0_24 ),
inference(avatar_contradiction_clause,[],[f969]) ).
fof(f1020,plain,
( sk_c9 != multiply(sk_c10,sk_c8)
| sk_c10 != inverse(sk_c9)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f119,f125]) ).
fof(f1025,plain,
( sk_c10 != inverse(sk_c9)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f1020,f108]) ).
fof(f1044,plain,
( sk_c10 != sk_c8
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f1025,f112]) ).
fof(f1076,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f266,f449]) ).
fof(f1078,plain,
( identity = sk_c9
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1076,f3]) ).
fof(f1105,plain,
( spl0_24
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f1078,f165,f160,f251]) ).
fof(f1107,plain,
( spl0_21
| ~ spl0_19
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f680,f251,f196,f230]) ).
fof(f1124,plain,
( identity = multiply(sk_c5,sk_c8)
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f150,f252]) ).
fof(f1151,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f530,f1044]) ).
fof(f1152,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f1151]) ).
fof(f1175,plain,
( identity = multiply(sk_c5,sk_c10)
| ~ spl0_8
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1124,f530]) ).
fof(f1176,plain,
( identity = multiply(identity,sk_c10)
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1175,f527]) ).
fof(f1177,plain,
( identity = sk_c10
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1176,f1]) ).
fof(f1178,plain,
( sk_c9 = multiply(identity,sk_c8)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_24 ),
inference(superposition,[],[f108,f1177]) ).
fof(f1198,plain,
( sk_c9 = sk_c8
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1178,f1]) ).
fof(f1203,plain,
( $false
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| spl0_22
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f1198,f236]) ).
fof(f1204,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| spl0_22
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f1203]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f127]) ).
cnf(s5,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f151]) ).
cnf(s6,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f156]) ).
cnf(s7,plain,
( spl0_3
| spl0_10 ),
inference(sat_conversion,[],[f157]) ).
cnf(s8,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f158]) ).
cnf(s9,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f163]) ).
cnf(s10,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f168]) ).
cnf(s14,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f176]) ).
cnf(s15,plain,
( spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f177]) ).
cnf(s16,plain,
( spl0_3
| spl0_17 ),
inference(sat_conversion,[],[f178]) ).
cnf(s17,plain,
( spl0_4
| spl0_17 ),
inference(sat_conversion,[],[f179]) ).
cnf(s18,plain,
( spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f180]) ).
cnf(s19,plain,
( spl0_16
| spl0_17 ),
inference(sat_conversion,[],[f181]) ).
cnf(s23,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f189]) ).
cnf(s24,plain,
( spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f190]) ).
cnf(s25,plain,
( spl0_3
| spl0_18 ),
inference(sat_conversion,[],[f191]) ).
cnf(s26,plain,
( spl0_4
| spl0_18 ),
inference(sat_conversion,[],[f192]) ).
cnf(s27,plain,
( spl0_15
| spl0_18 ),
inference(sat_conversion,[],[f193]) ).
cnf(s28,plain,
( spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f194]) ).
cnf(s34,plain,
( spl0_3
| spl0_19 ),
inference(sat_conversion,[],[f204]) ).
cnf(s35,plain,
( spl0_4
| spl0_19 ),
inference(sat_conversion,[],[f205]) ).
cnf(s36,plain,
( spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f206]) ).
cnf(s37,plain,
( spl0_16
| spl0_19 ),
inference(sat_conversion,[],[f207]) ).
cnf(s43,plain,
( spl0_3
| spl0_20 ),
inference(sat_conversion,[],[f217]) ).
cnf(s44,plain,
( spl0_4
| spl0_20 ),
inference(sat_conversion,[],[f218]) ).
cnf(s45,plain,
( spl0_15
| spl0_20 ),
inference(sat_conversion,[],[f219]) ).
cnf(s46,plain,
( spl0_16
| spl0_20 ),
inference(sat_conversion,[],[f220]) ).
cnf(s47,plain,
spl0_8,
inference(sat_conversion,[],[f221]) ).
cnf(s49,plain,
( ~ spl0_2
| ~ spl0_21
| ~ spl0_22 ),
inference(sat_conversion,[],[f237]) ).
cnf(s53,plain,
( ~ spl0_10
| ~ spl0_17
| ~ spl0_18
| spl0_26 ),
inference(sat_conversion,[],[f461]) ).
cnf(s59,plain,
( ~ spl0_8
| spl0_22
| ~ spl0_24
| ~ spl0_26 ),
inference(sat_conversion,[],[f538]) ).
cnf(s65,plain,
( ~ spl0_19
| ~ spl0_20
| spl0_24
| ~ spl0_26 ),
inference(sat_conversion,[],[f622]) ).
cnf(s66,plain,
( spl0_4
| ~ spl0_21
| ~ spl0_22
| ~ spl0_24 ),
inference(sat_conversion,[],[f623]) ).
cnf(s67,plain,
( ~ spl0_4
| spl0_21
| ~ spl0_22
| ~ spl0_24 ),
inference(sat_conversion,[],[f630]) ).
cnf(s68,plain,
( spl0_3
| ~ spl0_19
| ~ spl0_20
| ~ spl0_22
| ~ spl0_26 ),
inference(sat_conversion,[],[f633]) ).
cnf(s78,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_22
| ~ spl0_24 ),
inference(sat_conversion,[],[f830]) ).
cnf(s84,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_22
| ~ spl0_24 ),
inference(sat_conversion,[],[f874]) ).
cnf(s86,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_22 ),
inference(sat_conversion,[],[f934]) ).
cnf(s88,plain,
( ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22
| spl0_24 ),
inference(sat_conversion,[],[f970]) ).
cnf(s104,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_24 ),
inference(sat_conversion,[],[f1105]) ).
cnf(s105,plain,
( ~ spl0_19
| spl0_21
| ~ spl0_24 ),
inference(sat_conversion,[],[f1107]) ).
cnf(s108,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_24 ),
inference(sat_conversion,[],[f1152]) ).
cnf(s112,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| spl0_22
| ~ spl0_24 ),
inference(sat_conversion,[],[f1204]) ).
cnf(s113,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| spl0_7 ),
inference(rat,[],[s1,s47]) ).
cnf(s114,plain,
spl0_3,
inference(rat,[],[s59,s68,s65,s53,s7,s16,s25,s34,s43,s47]) ).
cnf(s115,plain,
spl0_4,
inference(rat,[],[s66,s105,s59,s65,s53,s8,s17,s26,s35,s44,s47]) ).
cnf(s117,plain,
( spl0_20
| spl0_24 ),
inference(rat,[],[s104,s45,s46]) ).
cnf(s118,plain,
( ~ spl0_20
| spl0_24
| ~ spl0_26 ),
inference(rat,[],[s104,s36,s37,s65]) ).
cnf(s119,plain,
( ~ spl0_26
| spl0_22 ),
inference(rat,[],[s118,s117,s59,s47]) ).
cnf(s120,plain,
( spl0_18
| spl0_22 ),
inference(rat,[],[s112,s104,s23,s24,s27,s28,s47,s114]) ).
cnf(s121,plain,
( spl0_17
| spl0_22 ),
inference(rat,[],[s112,s104,s14,s15,s18,s19,s47,s114]) ).
cnf(s122,plain,
spl0_22,
inference(rat,[],[s112,s104,s5,s6,s9,s10,s53,s121,s120,s119,s47,s114]) ).
cnf(s123,plain,
~ spl0_7,
inference(rat,[],[s86,s115,s47,s122]) ).
cnf(s124,plain,
( spl0_16
| spl0_26 ),
inference(rat,[],[s53,s10,s19,s28]) ).
cnf(s125,plain,
( ~ spl0_20
| spl0_24 ),
inference(rat,[],[s53,s9,s18,s27,s88,s124,s118,s122,s47]) ).
cnf(s126,plain,
spl0_24,
inference(rat,[],[s125,s117]) ).
cnf(s127,plain,
~ spl0_5,
inference(rat,[],[s78,s126,s115,s47,s122]) ).
cnf(s129,plain,
~ spl0_6,
inference(rat,[],[s108,s115,s47,s114,s126]) ).
cnf(s130,plain,
spl0_21,
inference(rat,[],[s67,s122,s115,s126]) ).
cnf(s132,plain,
~ spl0_2,
inference(rat,[],[s49,s122,s130]) ).
cnf(s133,plain,
~ spl0_1,
inference(rat,[],[s84,s126,s122,s47,s115]) ).
cnf(s134,plain,
$false,
inference(rat,[],[s113,s127,s114,s115,s123,s133,s132,s129]) ).
fof(f1207,plain,
$false,
inference(avatar_sat_refutation,[],[s134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP325-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n019.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 09:51:03 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.42 Running first-order model finding
% 0.15/0.42 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
% 0.15/0.47 % (2846922)Will run a generic schedule for satisfiability detection.
% 0.15/0.47 % (2846930)dis+10_1_sil=32000:sp=arity:random_seed=1388107397:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.47 % (2846928)% WARNING: option uhcvi not known.
% 0.15/0.47 % (2846927)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3992146539_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.47 % (2846928)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3739742978:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.47 % (2846931)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1190606341:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.47 % (2846932)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3342661417:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.47 % (2846933)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1983013920:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.47 % (2846929)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=32894919:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.47 % TRYING [1]
% 0.15/0.47 % (2846930) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2846922-2846930"...
% 0.15/0.47 % TRYING [2]
% 0.15/0.47 % TRYING [3]
% 0.15/0.47 % (2846930)...printing done.
% 0.15/0.47 % (2846930)Refutation found. Thanks to Tanya!
% 0.15/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.48 % (2846930)------------------------------
% 0.15/0.48 % (2846930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.48 % (2846930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.48 % (2846930)CaDiCaL version: 2.1.3
% 0.15/0.48 % (2846930)Termination reason: Refutation
% 0.15/0.48 % (2846930)Time elapsed: 0.014 s
% 0.15/0.48 % (2846930)Peak memory usage: 12 MB
% 0.15/0.48 % (2846930)Instructions burned: 41 (million)
% 0.15/0.48 % (2846922)Success in time 0.048 s
% 0.15/0.48 % Vampire exiting
%------------------------------------------------------------------------------