%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP337-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:17:31 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.48s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 39
% Syntax : Number of formulae : 273 ( 21 unt; 14 def)
% Number of atoms : 906 ( 277 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1229 ( 596 ~; 619 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 53 !; 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(f11,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f15]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f27]) ).
fof(f35,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c2,sk_c3)
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(reorient_equations,[],[f41]) ).
fof(f47,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = multiply(sk_c2,sk_c3)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = multiply(sk_c2,sk_c3)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c7 = multiply(sk_c2,sk_c3)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c3 = inverse(sk_c2)
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(reorient_equations,[],[f53]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c3 = inverse(sk_c2)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c3 = inverse(sk_c2)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c3 = inverse(sk_c2)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f63]) ).
fof(f71,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| inverse(X0) != sk_c8
| multiply(X0,sk_c7) != sk_c8
| multiply(X1,X2) != sk_c7
| inverse(X1) != X2
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(X3) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c7)
| multiply(X1,X2) != sk_c7
| inverse(X1) != X2
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != multiply(sk_c7,sk_c6)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3)
| sk_c6 != inverse(sk_c8)
| sk_c7 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,plain,
! [X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c7)
| sk_c7 != multiply(X1,inverse(X1))
| sk_c7 != multiply(inverse(X1),sk_c8)
| sk_c8 != multiply(sk_c7,sk_c6)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3)
| sk_c6 != inverse(sk_c8)
| sk_c7 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) ),
inference(equality_resolution,[],[f78]) ).
fof(f81,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f82,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,definition,
( spl0_2
<=> sk_c6 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f85,plain,
( sk_c6 = inverse(sk_c8)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f86,plain,
( sk_c6 != inverse(sk_c8)
| spl0_2 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f88,definition,
( spl0_3
<=> ! [X3] :
( sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f89,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,definition,
( spl0_4
<=> sk_c8 = multiply(sk_c7,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f92,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f93,plain,
( sk_c8 != multiply(sk_c7,sk_c6)
| spl0_4 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f95,definition,
( spl0_5
<=> ! [X1] :
( sk_c7 != multiply(X1,inverse(X1))
| sk_c7 != multiply(inverse(X1),sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f96,plain,
( ! [X1] :
( sk_c7 != multiply(inverse(X1),sk_c8)
| sk_c7 != multiply(X1,inverse(X1)) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,definition,
( spl0_6
<=> ! [X0] :
( inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f99,plain,
( ! [X0] :
( inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c7) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,definition,
( spl0_7
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f102,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f103,plain,
( multiply(sk_c7,sk_c8) != sk_c6
| spl0_7 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f79,f101,f98,f95,f91,f88,f84,f81]) ).
fof(f106,definition,
( spl0_8
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f108,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f110,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f112,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f76,f110,f106]) ).
fof(f115,definition,
( spl0_10
<=> sk_c7 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f117,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f74,f110,f115]) ).
fof(f119,plain,
( spl0_2
| spl0_9 ),
inference(avatar_split_clause,[],[f72,f110,f84]) ).
fof(f132,definition,
( spl0_13
<=> sk_c3 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f134,plain,
( sk_c3 = inverse(sk_c2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f135,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f64,f132,f106]) ).
fof(f136,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f62,f132,f115]) ).
fof(f137,plain,
( spl0_2
| spl0_13 ),
inference(avatar_split_clause,[],[f60,f132,f84]) ).
fof(f140,plain,
( spl0_4
| spl0_13 ),
inference(avatar_split_clause,[],[f54,f132,f91]) ).
fof(f142,definition,
( spl0_14
<=> sk_c7 = multiply(sk_c2,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f144,plain,
( sk_c7 = multiply(sk_c2,sk_c3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f145,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f52,f142,f106]) ).
fof(f146,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f50,f142,f115]) ).
fof(f147,plain,
( spl0_2
| spl0_14 ),
inference(avatar_split_clause,[],[f48,f142,f84]) ).
fof(f150,plain,
( spl0_4
| spl0_14 ),
inference(avatar_split_clause,[],[f42,f142,f91]) ).
fof(f152,definition,
( spl0_15
<=> sk_c8 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f154,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f40,f152,f106]) ).
fof(f156,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f38,f152,f115]) ).
fof(f157,plain,
( spl0_2
| spl0_15 ),
inference(avatar_split_clause,[],[f36,f152,f84]) ).
fof(f162,definition,
( spl0_16
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f164,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f165,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f28,f162,f106]) ).
fof(f166,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f26,f162,f115]) ).
fof(f167,plain,
( spl0_2
| spl0_16 ),
inference(avatar_split_clause,[],[f24,f162,f84]) ).
fof(f171,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f16,f101,f106]) ).
fof(f172,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f14,f101,f115]) ).
fof(f173,plain,
( spl0_2
| spl0_7 ),
inference(avatar_split_clause,[],[f12,f101,f84]) ).
fof(f176,plain,
( spl0_4
| spl0_7 ),
inference(avatar_split_clause,[],[f6,f101,f91]) ).
fof(f177,plain,
( identity = multiply(sk_c6,sk_c8)
| ~ spl0_2 ),
inference(superposition,[],[f3,f85]) ).
fof(f178,plain,
( identity = multiply(sk_c6,sk_c5)
| ~ spl0_8 ),
inference(superposition,[],[f3,f108]) ).
fof(f181,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f187,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f181,f1]) ).
fof(f238,plain,
( sk_c8 = multiply(inverse(sk_c6),identity)
| ~ spl0_2 ),
inference(superposition,[],[f187,f177]) ).
fof(f240,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c7)
| ~ spl0_10 ),
inference(superposition,[],[f187,f117]) ).
fof(f242,plain,
( sk_c5 = multiply(inverse(sk_c6),identity)
| ~ spl0_8 ),
inference(superposition,[],[f187,f178]) ).
fof(f246,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f240,f108]) ).
fof(f252,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f187,f246]) ).
fof(f254,plain,
( identity = sk_c7
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f252,f3]) ).
fof(f267,plain,
( sk_c6 != multiply(identity,sk_c8)
| spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f103,f254]) ).
fof(f268,plain,
( sk_c8 = multiply(identity,sk_c6)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f92,f254]) ).
fof(f269,plain,
( sk_c8 = sk_c6
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f268,f1]) ).
fof(f270,plain,
( sk_c8 != sk_c6
| spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f267,f1]) ).
fof(f276,plain,
( sk_c8 = sk_c5
| ~ spl0_2
| ~ spl0_8 ),
inference(forward_demodulation,[],[f242,f238]) ).
fof(f321,plain,
( $false
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f270,f269]) ).
fof(f322,plain,
( ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f321]) ).
fof(f323,plain,
( ! [X1] :
( identity != multiply(X1,inverse(X1))
| sk_c7 != multiply(inverse(X1),sk_c8) )
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f96,f254]) ).
fof(f325,plain,
( ! [X1] :
( identity != multiply(inverse(X1),sk_c8)
| identity != multiply(X1,inverse(X1)) )
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f323,f254]) ).
fof(f328,plain,
( identity != multiply(sk_c6,sk_c8)
| identity != multiply(sk_c5,sk_c6)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f325,f108]) ).
fof(f336,plain,
( identity != multiply(sk_c5,sk_c6)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f328,f177]) ).
fof(f341,plain,
( identity != sk_c7
| ~ spl0_2
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f336,f117]) ).
fof(f352,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f341,f254]) ).
fof(f353,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f352]) ).
fof(f361,plain,
( identity = multiply(sk_c3,sk_c2)
| ~ spl0_13 ),
inference(superposition,[],[f3,f134]) ).
fof(f363,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_16 ),
inference(superposition,[],[f3,f164]) ).
fof(f433,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c8,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f112]) ).
fof(f434,plain,
( sk_c3 = multiply(inverse(sk_c2),sk_c7)
| ~ spl0_14 ),
inference(superposition,[],[f187,f144]) ).
fof(f435,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c2,multiply(sk_c3,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f144]) ).
fof(f436,plain,
( sk_c3 = multiply(sk_c3,sk_c7)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f434,f134]) ).
fof(f446,plain,
( sk_c7 != multiply(sk_c3,sk_c8)
| sk_c7 != multiply(sk_c2,sk_c3)
| ~ spl0_5
| ~ spl0_13 ),
inference(superposition,[],[f96,f134]) ).
fof(f449,plain,
( sk_c7 != multiply(sk_c2,sk_c3)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f446,f112]) ).
fof(f452,plain,
( $false
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f449,f144]) ).
fof(f453,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f452]) ).
fof(f455,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_15 ),
inference(superposition,[],[f187,f154]) ).
fof(f456,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c1,multiply(sk_c7,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f154]) ).
fof(f457,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f455,f164]) ).
fof(f458,plain,
( sk_c7 = multiply(inverse(sk_c3),sk_c3)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f187,f436]) ).
fof(f460,plain,
( identity = sk_c7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f458,f3]) ).
fof(f469,plain,
( sk_c6 = multiply(identity,sk_c8)
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f102,f460]) ).
fof(f476,plain,
( sk_c8 = sk_c6
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f469,f1]) ).
fof(f478,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c3,multiply(sk_c8,X0))
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f433,f460]) ).
fof(f479,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c8,X0)) = X0
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f478,f1]) ).
fof(f488,plain,
( sk_c1 = multiply(sk_c3,identity)
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(superposition,[],[f479,f363]) ).
fof(f492,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c2,multiply(sk_c3,X0))
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f435,f460]) ).
fof(f493,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c3,X0)) = X0
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f492,f1]) ).
fof(f494,plain,
( identity = multiply(sk_c8,sk_c8)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f457,f460]) ).
fof(f497,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f493,f112]) ).
fof(f498,plain,
( sk_c2 = multiply(sk_c2,identity)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f493,f361]) ).
fof(f502,plain,
( sk_c8 = multiply(sk_c2,identity)
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f497,f460]) ).
fof(f507,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c1,multiply(identity,X0))
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f456,f460]) ).
fof(f508,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c1,X0)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f507,f1]) ).
fof(f511,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f154,f508]) ).
fof(f516,plain,
( sk_c8 = multiply(sk_c8,identity)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f511,f460]) ).
fof(f523,plain,
( sk_c8 = multiply(sk_c3,identity)
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f479,f494]) ).
fof(f533,plain,
( sk_c8 = sk_c2
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f502,f498]) ).
fof(f539,plain,
( inverse(sk_c8) = sk_c3
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f134,f533]) ).
fof(f595,plain,
( sk_c8 = sk_c1
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f488,f523]) ).
fof(f600,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f164,f595]) ).
fof(f610,plain,
( sk_c8 != multiply(sk_c7,sk_c8)
| spl0_4
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f93,f476]) ).
fof(f612,plain,
( sk_c8 != sk_c6
| spl0_4
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f610,f102]) ).
fof(f613,plain,
( $false
| spl0_4
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f612,f476]) ).
fof(f614,plain,
( spl0_4
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f613]) ).
fof(f615,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c6 != inverse(X4) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f82,f476]) ).
fof(f617,plain,
( ! [X4] :
( identity != multiply(X4,sk_c8)
| sk_c6 != inverse(X4) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f615,f460]) ).
fof(f619,plain,
( ! [X4] :
( identity != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f617,f476]) ).
fof(f642,plain,
( identity != multiply(sk_c8,sk_c8)
| sk_c8 != inverse(sk_c1)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f619,f508]) ).
fof(f646,plain,
( sk_c8 != inverse(sk_c1)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f642,f494]) ).
fof(f657,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f646,f164]) ).
fof(f658,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f657]) ).
fof(f667,plain,
( ! [X3] :
( identity != multiply(X3,sk_c8)
| sk_c8 != inverse(X3) )
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f89,f460]) ).
fof(f673,plain,
( identity != multiply(sk_c8,sk_c8)
| sk_c8 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f667,f508]) ).
fof(f677,plain,
( sk_c8 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f673,f494]) ).
fof(f684,plain,
( $false
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f677,f164]) ).
fof(f685,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f684]) ).
fof(f694,plain,
( ! [X0] :
( sk_c8 != multiply(X0,identity)
| inverse(X0) != sk_c8 )
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f99,f460]) ).
fof(f701,plain,
( sk_c8 != multiply(sk_c8,identity)
| sk_c8 != inverse(sk_c1)
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f694,f508]) ).
fof(f706,plain,
( sk_c8 != inverse(sk_c1)
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f701,f516]) ).
fof(f718,plain,
( $false
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f706,f164]) ).
fof(f719,plain,
( ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f718]) ).
fof(f727,plain,
( sk_c6 != sk_c3
| spl0_2
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f86,f539]) ).
fof(f731,plain,
( sk_c8 != sk_c3
| spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f727,f476]) ).
fof(f742,plain,
( sk_c8 = sk_c3
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f600,f539]) ).
fof(f748,plain,
( $false
| spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f742,f731]) ).
fof(f749,plain,
( spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f748]) ).
fof(f764,plain,
( sk_c8 = multiply(identity,sk_c6)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f92,f254]) ).
fof(f765,plain,
( sk_c8 = sk_c6
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f764,f1]) ).
fof(f766,plain,
( sk_c7 = multiply(sk_c5,sk_c8)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f117,f765]) ).
fof(f767,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f766,f276]) ).
fof(f768,plain,
( identity = multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f767,f254]) ).
fof(f774,plain,
( sk_c8 = multiply(inverse(sk_c8),identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f187,f768]) ).
fof(f777,plain,
( sk_c8 = multiply(sk_c6,identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f774,f85]) ).
fof(f779,plain,
( sk_c8 = multiply(sk_c8,identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f777,f765]) ).
fof(f791,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c6 != inverse(X4) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f82,f765]) ).
fof(f792,plain,
( ! [X4] :
( identity != multiply(X4,sk_c8)
| sk_c6 != inverse(X4) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f791,f254]) ).
fof(f793,plain,
( ! [X4] :
( identity != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f792,f765]) ).
fof(f808,plain,
( identity != identity
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f793,f3]) ).
fof(f810,plain,
( sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f808]) ).
fof(f813,plain,
( sk_c8 != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f810,f85]) ).
fof(f820,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f813,f765]) ).
fof(f824,plain,
( sk_c8 != sk_c6
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f820,f85]) ).
fof(f826,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f824,f765]) ).
fof(f827,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f826]) ).
fof(f828,plain,
( ! [X3] :
( identity != multiply(X3,sk_c8)
| sk_c8 != inverse(X3) )
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f89,f254]) ).
fof(f836,plain,
( identity != identity
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f828,f3]) ).
fof(f838,plain,
( sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f836]) ).
fof(f841,plain,
( sk_c8 != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f838,f85]) ).
fof(f848,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f841,f765]) ).
fof(f852,plain,
( sk_c8 != sk_c6
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f848,f85]) ).
fof(f854,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f852,f765]) ).
fof(f855,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f854]) ).
fof(f856,plain,
( ! [X0] :
( sk_c8 != multiply(X0,identity)
| inverse(X0) != sk_c8 )
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f99,f254]) ).
fof(f884,plain,
( sk_c8 != sk_c8
| sk_c8 != inverse(sk_c8)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f856,f779]) ).
fof(f887,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f884]) ).
fof(f888,plain,
( sk_c8 != sk_c6
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f887,f85]) ).
fof(f890,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f888,f765]) ).
fof(f891,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f890]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f104]) ).
cnf(s2,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f113]) ).
cnf(s3,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f118]) ).
cnf(s4,plain,
( spl0_2
| spl0_9 ),
inference(sat_conversion,[],[f119]) ).
cnf(s8,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f135]) ).
cnf(s9,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f136]) ).
cnf(s10,plain,
( spl0_2
| spl0_13 ),
inference(sat_conversion,[],[f137]) ).
cnf(s13,plain,
( spl0_4
| spl0_13 ),
inference(sat_conversion,[],[f140]) ).
cnf(s14,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f145]) ).
cnf(s15,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f146]) ).
cnf(s16,plain,
( spl0_2
| spl0_14 ),
inference(sat_conversion,[],[f147]) ).
cnf(s19,plain,
( spl0_4
| spl0_14 ),
inference(sat_conversion,[],[f150]) ).
cnf(s20,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f155]) ).
cnf(s21,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f156]) ).
cnf(s22,plain,
( spl0_2
| spl0_15 ),
inference(sat_conversion,[],[f157]) ).
cnf(s26,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f165]) ).
cnf(s27,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f166]) ).
cnf(s28,plain,
( spl0_2
| spl0_16 ),
inference(sat_conversion,[],[f167]) ).
cnf(s32,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f171]) ).
cnf(s33,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f172]) ).
cnf(s34,plain,
( spl0_2
| spl0_7 ),
inference(sat_conversion,[],[f173]) ).
cnf(s37,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f176]) ).
cnf(s38,plain,
( ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(sat_conversion,[],[f322]) ).
cnf(s40,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10 ),
inference(sat_conversion,[],[f353]) ).
cnf(s42,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f453]) ).
cnf(s45,plain,
( spl0_4
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f614]) ).
cnf(s48,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f658]) ).
cnf(s54,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f685]) ).
cnf(s61,plain,
( ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f719]) ).
cnf(s66,plain,
( spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f749]) ).
cnf(s71,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(sat_conversion,[],[f827]) ).
cnf(s76,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(sat_conversion,[],[f855]) ).
cnf(s80,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(sat_conversion,[],[f891]) ).
cnf(s81,plain,
spl0_2,
inference(rat,[],[s66,s4,s10,s16,s22,s28,s34]) ).
cnf(s82,plain,
spl0_4,
inference(rat,[],[s45,s13,s19,s37]) ).
cnf(s83,plain,
spl0_7,
inference(rat,[],[s38,s32,s33,s82]) ).
cnf(s84,plain,
( spl0_10
| ~ spl0_6 ),
inference(rat,[],[s61,s9,s15,s21,s27]) ).
cnf(s85,plain,
( ~ spl0_10
| ~ spl0_6 ),
inference(rat,[],[s61,s8,s14,s20,s26,s80,s82,s81]) ).
cnf(s86,plain,
~ spl0_6,
inference(rat,[],[s85,s84]) ).
cnf(s87,plain,
( spl0_10
| ~ spl0_5 ),
inference(rat,[],[s42,s3,s9,s15]) ).
cnf(s88,plain,
( ~ spl0_10
| ~ spl0_5 ),
inference(rat,[],[s42,s2,s8,s14,s40,s81]) ).
cnf(s89,plain,
~ spl0_5,
inference(rat,[],[s88,s87]) ).
cnf(s90,plain,
( spl0_10
| ~ spl0_3 ),
inference(rat,[],[s54,s9,s15,s21,s27]) ).
cnf(s91,plain,
( ~ spl0_10
| ~ spl0_3 ),
inference(rat,[],[s54,s8,s14,s20,s26,s76,s82,s81]) ).
cnf(s92,plain,
~ spl0_3,
inference(rat,[],[s91,s90]) ).
cnf(s93,plain,
spl0_1,
inference(rat,[],[s1,s83,s86,s82,s81,s89,s92]) ).
cnf(s94,plain,
spl0_10,
inference(rat,[],[s48,s9,s15,s21,s27,s83,s93]) ).
cnf(s95,plain,
~ spl0_8,
inference(rat,[],[s71,s82,s81,s93,s94]) ).
cnf(s96,plain,
spl0_16,
inference(rat,[],[s26,s95]) ).
cnf(s97,plain,
spl0_15,
inference(rat,[],[s20,s95]) ).
cnf(s98,plain,
spl0_14,
inference(rat,[],[s14,s95]) ).
cnf(s99,plain,
spl0_13,
inference(rat,[],[s8,s95]) ).
cnf(s101,plain,
$false,
inference(rat,[],[s48,s96,s97,s93,s83,s98,s99]) ).
fof(f894,plain,
$false,
inference(avatar_sat_refutation,[],[s101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP337-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n017.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:49:35 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.11/0.48 % (2295387)Will run a generic schedule for satisfiability detection.
% 0.11/0.48 % (2295392)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3015991059_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.48 % TRYING [1]
% 0.11/0.48 % TRYING [2]
% 0.11/0.48 % TRYING [3]
% 0.11/0.48 % (2295393)% WARNING: option uhcvi not known.
% 0.11/0.48 % TRYING [4]
% 0.11/0.48 % (2295396)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=533232536:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.48 % (2295393)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1353277733:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.48 % (2295394)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3726737003:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.48 % (2295397)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2284791166:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.48 % (2295395)dis+10_1_sil=32000:sp=arity:random_seed=1181927371:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.48 % TRYING [5]
% 0.11/0.48 % (2295396) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2295387-2295396"...
% 0.11/0.48 % TRYING [6]
% 0.11/0.48 % (2295395) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2295387-2295395"...
% 0.11/0.48 % (2295397) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2295387-2295397"...
% 0.11/0.48 % (2295396)...printing done.
% 0.11/0.48 % (2295395)...printing done.
% 0.11/0.48 % (2295395)Refutation found. Thanks to Tanya!
% 0.11/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.47/0.48 % (2295395)------------------------------
% 0.47/0.48 % (2295395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.48 % (2295395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.48 % (2295395)CaDiCaL version: 2.1.3
% 0.47/0.48 % (2295395)Termination reason: Refutation
% 0.47/0.48 % (2295395)Time elapsed: 0.020 s
% 0.47/0.48 % (2295395)Peak memory usage: 12 MB
% 0.47/0.48 % (2295395)Instructions burned: 32 (million)
% 0.47/0.48 % (2295387)Success in time 0.059 s
% 0.47/0.48 % Vampire exiting
%------------------------------------------------------------------------------