%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP288-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:13:33 AM UTC 2026
% Result : Unsatisfiable 2.62s 1.29s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 44
% Syntax : Number of formulae : 279 ( 24 unt; 17 def)
% Number of atoms : 799 ( 243 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 984 ( 464 ~; 503 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c7 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c7 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c6 = inverse(sk_c2)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(sk_c7,sk_c6) != sk_c5
| multiply(X0,sk_c7) != sk_c6
| inverse(X0) != sk_c7
| multiply(X1,sk_c6) != sk_c5
| inverse(X1) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X2) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| multiply(X3,sk_c6) != sk_c7
| inverse(X3) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( multiply(sk_c7,sk_c6) != sk_c5
| sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6)
| sk_c7 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) ),
inference(reorient_equations,[],[f55]) ).
fof(f58,definition,
( spl0_1
<=> ! [X3] :
( sk_c7 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f59,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c7 != multiply(X3,sk_c6) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f62,plain,
( ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f64,definition,
( spl0_3
<=> sk_c5 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f65,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f66,plain,
( sk_c5 != multiply(sk_c6,sk_c7)
| spl0_3 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f68,definition,
( spl0_4
<=> ! [X1] :
( sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f69,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c5 != multiply(X1,sk_c6) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,definition,
( spl0_5
<=> ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f72,plain,
( ! [X0] :
( inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,definition,
( spl0_6
<=> multiply(sk_c7,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f75,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( multiply(sk_c7,sk_c6) != sk_c5
| spl0_6 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f56,f74,f71,f68,f64,f61,f58]) ).
fof(f79,definition,
( spl0_7
<=> sk_c6 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f81,plain,
( sk_c6 = inverse(sk_c4)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f83,definition,
( spl0_8
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f85,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f54,f83,f79]) ).
fof(f88,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c4,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f90,plain,
( sk_c7 = multiply(sk_c4,sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f52,f83,f88]) ).
fof(f93,definition,
( spl0_10
<=> sk_c7 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f95,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f50,f83,f93]) ).
fof(f98,definition,
( spl0_11
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f100,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f48,f83,f98]) ).
fof(f102,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f46,f83,f64]) ).
fof(f104,definition,
( spl0_12
<=> sk_c5 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f106,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f44,f104,f79]) ).
fof(f108,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f42,f104,f88]) ).
fof(f109,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f40,f104,f93]) ).
fof(f110,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f38,f104,f98]) ).
fof(f111,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f36,f104,f64]) ).
fof(f113,definition,
( spl0_13
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f115,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f34,f113,f79]) ).
fof(f117,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f32,f113,f88]) ).
fof(f118,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f30,f113,f93]) ).
fof(f119,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f28,f113,f98]) ).
fof(f120,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f26,f113,f64]) ).
fof(f122,definition,
( spl0_14
<=> sk_c6 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f124,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f24,f122,f79]) ).
fof(f126,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f22,f122,f88]) ).
fof(f127,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f20,f122,f93]) ).
fof(f128,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f18,f122,f98]) ).
fof(f129,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f16,f122,f64]) ).
fof(f130,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f74,f79]) ).
fof(f131,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f74,f88]) ).
fof(f134,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f74,f64]) ).
fof(f135,plain,
( identity = multiply(sk_c6,sk_c4)
| ~ spl0_7 ),
inference(superposition,[],[f3,f81]) ).
fof(f139,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f140,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(sk_c5,X0)
| ~ spl0_3 ),
inference(superposition,[],[f4,f65]) ).
fof(f141,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c4,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f135]) ).
fof(f142,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c6,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f95]) ).
fof(f144,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c4,X0)) = X0
| ~ spl0_7 ),
inference(forward_demodulation,[],[f141,f1]) ).
fof(f145,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f139,f1]) ).
fof(f154,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f144,f90]) ).
fof(f164,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f154,f65]) ).
fof(f166,plain,
( multiply(sk_c3,sk_c6) = multiply(sk_c7,sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f142,f154]) ).
fof(f168,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f166,f95]) ).
fof(f189,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(inverse(sk_c6),multiply(sk_c5,X0))
| ~ spl0_3 ),
inference(superposition,[],[f145,f140]) ).
fof(f191,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_10 ),
inference(superposition,[],[f145,f95]) ).
fof(f200,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f191,f100]) ).
fof(f201,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(inverse(sk_c6),multiply(sk_c6,X0))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f189,f164]) ).
fof(f204,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f201,f145]) ).
fof(f214,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f204,f200]) ).
fof(f217,plain,
( sk_c6 != sk_c5
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f76,f204]) ).
fof(f222,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f217,f164]) ).
fof(f223,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f222]) ).
fof(f225,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c6) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f69,f164]) ).
fof(f238,plain,
( sk_c7 != sk_c6
| sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f225,f100]) ).
fof(f240,plain,
( sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f238,f214]) ).
fof(f242,plain,
( sk_c7 != sk_c6
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f240,f95]) ).
fof(f245,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f242,f214]) ).
fof(f246,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f245]) ).
fof(f254,plain,
( sk_c6 = multiply(inverse(sk_c2),sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f145,f106]) ).
fof(f256,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f254,f85]) ).
fof(f257,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_14 ),
inference(superposition,[],[f145,f124]) ).
fof(f259,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f257,f115]) ).
fof(f266,plain,
( sk_c6 != sk_c6
| sk_c5 != multiply(sk_c2,sk_c6)
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f69,f85]) ).
fof(f268,plain,
( sk_c5 != multiply(sk_c2,sk_c6)
| ~ spl0_4
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f266]) ).
fof(f274,definition,
( spl0_16
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f275,plain,
( sk_c7 = sk_c6
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f278,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f268,f106]) ).
fof(f279,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f278]) ).
fof(f282,definition,
( spl0_17
<=> sk_c7 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f283,plain,
( sk_c7 = sk_c5
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f290,plain,
( sk_c7 != sk_c6
| sk_c7 != multiply(sk_c3,sk_c6)
| ~ spl0_1
| ~ spl0_11 ),
inference(superposition,[],[f59,f100]) ).
fof(f291,plain,
( sk_c6 != sk_c6
| sk_c7 != multiply(sk_c2,sk_c6)
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[],[f59,f85]) ).
fof(f293,plain,
( sk_c7 != multiply(sk_c2,sk_c6)
| ~ spl0_1
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f291]) ).
fof(f295,definition,
( spl0_18
<=> sk_c7 = multiply(sk_c1,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f296,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f297,plain,
( sk_c7 != multiply(sk_c1,sk_c6)
| spl0_18 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f299,plain,
( sk_c7 != sk_c5
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f293,f106]) ).
fof(f300,plain,
( sk_c7 != sk_c6
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f290,f95]) ).
fof(f301,plain,
( ~ spl0_17
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f299,f104,f83,f58,f282]) ).
fof(f302,plain,
( ~ spl0_16
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f300,f98,f93,f58,f274]) ).
fof(f305,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f145,f256]) ).
fof(f307,plain,
( identity = sk_c5
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f305,f3]) ).
fof(f333,plain,
( sk_c7 = sk_c5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f75,f259]) ).
fof(f335,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f145,f259]) ).
fof(f337,plain,
( identity = sk_c6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f335,f3]) ).
fof(f343,plain,
( spl0_17
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f333,f122,f113,f74,f282]) ).
fof(f346,plain,
( sk_c7 != sk_c7
| sk_c6 != multiply(sk_c1,sk_c7)
| ~ spl0_5
| ~ spl0_13 ),
inference(superposition,[],[f72,f115]) ).
fof(f347,plain,
( sk_c6 != multiply(sk_c1,sk_c7)
| ~ spl0_5
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f346]) ).
fof(f349,plain,
( $false
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f347,f124]) ).
fof(f350,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f349]) ).
fof(f352,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c3,sk_c6)
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f62,f100]) ).
fof(f356,plain,
( sk_c7 != multiply(sk_c3,sk_c6)
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f352]) ).
fof(f358,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f356,f95]) ).
fof(f359,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f358]) ).
fof(f363,plain,
( sk_c7 = sk_c6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f168,f200]) ).
fof(f378,plain,
( spl0_16
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f214,f98,f93,f88,f79,f64,f274]) ).
fof(f379,plain,
( spl0_16
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f363,f98,f93,f88,f79,f274]) ).
fof(f382,plain,
( sk_c6 = multiply(sk_c1,sk_c6)
| ~ spl0_14
| ~ spl0_16 ),
inference(superposition,[],[f124,f275]) ).
fof(f413,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c6 != multiply(X0,sk_c7) )
| ~ spl0_5
| ~ spl0_16 ),
inference(forward_demodulation,[],[f72,f275]) ).
fof(f414,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c6 != multiply(X0,sk_c6) )
| ~ spl0_5
| ~ spl0_16 ),
inference(forward_demodulation,[],[f413,f275]) ).
fof(f415,plain,
( sk_c7 != sk_c6
| sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_16 ),
inference(superposition,[],[f414,f100]) ).
fof(f421,plain,
( sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f415,f275]) ).
fof(f424,plain,
( sk_c7 != sk_c6
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_demodulation,[],[f421,f95]) ).
fof(f425,plain,
( $false
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f424,f275]) ).
fof(f426,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f425]) ).
fof(f428,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_16 ),
inference(forward_demodulation,[],[f62,f275]) ).
fof(f433,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f106,f283]) ).
fof(f441,plain,
( identity = sk_c7
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f307,f283]) ).
fof(f445,plain,
( sk_c6 != multiply(sk_c1,sk_c6)
| ~ spl0_16
| spl0_18 ),
inference(forward_demodulation,[],[f297,f275]) ).
fof(f450,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| sk_c6 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_16 ),
inference(forward_demodulation,[],[f428,f275]) ).
fof(f452,plain,
( sk_c6 = multiply(sk_c2,sk_c6)
| ~ spl0_12
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f433,f275]) ).
fof(f462,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17 ),
inference(superposition,[],[f283,f164]) ).
fof(f470,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c4,sk_c6)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_16 ),
inference(superposition,[],[f450,f81]) ).
fof(f471,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c2,sk_c6)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_16 ),
inference(superposition,[],[f450,f85]) ).
fof(f474,plain,
( sk_c6 != multiply(sk_c2,sk_c6)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f471]) ).
fof(f475,plain,
( sk_c6 != multiply(sk_c4,sk_c6)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f470]) ).
fof(f476,plain,
( $false
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f474,f452]) ).
fof(f477,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f476]) ).
fof(f478,plain,
( sk_c7 != sk_c6
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_16 ),
inference(forward_demodulation,[],[f475,f90]) ).
fof(f479,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f478,f275]) ).
fof(f480,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f479]) ).
fof(f487,plain,
( spl0_16
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f462,f282,f88,f79,f64,f274]) ).
fof(f488,plain,
( sk_c7 != multiply(sk_c6,sk_c7)
| spl0_3
| ~ spl0_17 ),
inference(forward_demodulation,[],[f66,f283]) ).
fof(f493,plain,
( sk_c7 = sk_c6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f441,f337]) ).
fof(f497,plain,
( spl0_16
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f493,f282,f122,f113,f104,f83,f274]) ).
fof(f514,plain,
( sk_c6 != multiply(sk_c6,sk_c6)
| spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f488,f275]) ).
fof(f521,plain,
( $false
| ~ spl0_14
| ~ spl0_16
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f382,f445]) ).
fof(f522,plain,
( ~ spl0_14
| ~ spl0_16
| spl0_18 ),
inference(avatar_contradiction_clause,[],[f521]) ).
fof(f523,plain,
( sk_c6 = multiply(sk_c1,sk_c6)
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f296,f275]) ).
fof(f524,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_16
| ~ spl0_18 ),
inference(superposition,[],[f145,f523]) ).
fof(f526,plain,
( sk_c6 = multiply(sk_c7,sk_c6)
| ~ spl0_13
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f524,f115]) ).
fof(f527,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_13
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f526,f275]) ).
fof(f528,plain,
( $false
| spl0_3
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f527,f514]) ).
fof(f529,plain,
( spl0_3
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f528]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f77]) ).
cnf(s2,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f86]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f91]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f96]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f101]) ).
cnf(s6,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f102]) ).
cnf(s7,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f107]) ).
cnf(s8,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f108]) ).
cnf(s9,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f109]) ).
cnf(s10,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f110]) ).
cnf(s11,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f111]) ).
cnf(s12,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f116]) ).
cnf(s13,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f117]) ).
cnf(s14,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f118]) ).
cnf(s15,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f119]) ).
cnf(s16,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f120]) ).
cnf(s17,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f125]) ).
cnf(s18,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f126]) ).
cnf(s19,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f127]) ).
cnf(s20,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f128]) ).
cnf(s21,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f129]) ).
cnf(s22,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f130]) ).
cnf(s23,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f131]) ).
cnf(s26,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f134]) ).
cnf(s27,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f223]) ).
cnf(s29,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f246]) ).
cnf(s31,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(sat_conversion,[],[f279]) ).
cnf(s34,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(sat_conversion,[],[f301]) ).
cnf(s35,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(sat_conversion,[],[f302]) ).
cnf(s38,plain,
( ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f343]) ).
cnf(s40,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f350]) ).
cnf(s42,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f359]) ).
cnf(s48,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f378]) ).
cnf(s50,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f379]) ).
cnf(s53,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(sat_conversion,[],[f426]) ).
cnf(s54,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f477]) ).
cnf(s55,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_16 ),
inference(sat_conversion,[],[f480]) ).
cnf(s60,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f487]) ).
cnf(s63,plain,
( ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f497]) ).
cnf(s65,plain,
( ~ spl0_14
| ~ spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f522]) ).
cnf(s66,plain,
( spl0_3
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f529]) ).
cnf(s67,plain,
spl0_3,
inference(rat,[],[s65,s66,s63,s38,s6,s11,s16,s21,s26]) ).
cnf(s68,plain,
spl0_6,
inference(rat,[],[s27,s22,s23,s67]) ).
cnf(s69,plain,
( spl0_11
| ~ spl0_5 ),
inference(rat,[],[s40,s15,s20]) ).
cnf(s70,plain,
( spl0_10
| ~ spl0_5 ),
inference(rat,[],[s40,s14,s19]) ).
cnf(s71,plain,
( spl0_9
| ~ spl0_5 ),
inference(rat,[],[s40,s13,s18]) ).
cnf(s72,plain,
( ~ spl0_10
| ~ spl0_5
| ~ spl0_11 ),
inference(rat,[],[s40,s12,s17,s50,s71,s53]) ).
cnf(s73,plain,
~ spl0_5,
inference(rat,[],[s72,s70,s69]) ).
cnf(s74,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s31,s5,s10]) ).
cnf(s75,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s31,s4,s9]) ).
cnf(s76,plain,
( spl0_9
| ~ spl0_4 ),
inference(rat,[],[s31,s3,s8]) ).
cnf(s77,plain,
( ~ spl0_9
| ~ spl0_11
| ~ spl0_4
| ~ spl0_10 ),
inference(rat,[],[s31,s2,s7,s29,s67]) ).
cnf(s78,plain,
~ spl0_4,
inference(rat,[],[s77,s76,s75,s74]) ).
cnf(s79,plain,
( spl0_11
| spl0_17 ),
inference(rat,[],[s38,s15,s20,s68]) ).
cnf(s80,plain,
( spl0_17
| ~ spl0_2 ),
inference(rat,[],[s38,s14,s19,s42,s79,s68]) ).
cnf(s81,plain,
( ~ spl0_9
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s60,s55,s80,s67]) ).
cnf(s82,plain,
( spl0_9
| ~ spl0_2 ),
inference(rat,[],[s54,s63,s3,s8,s13,s18,s80]) ).
cnf(s83,plain,
~ spl0_2,
inference(rat,[],[s54,s63,s2,s7,s12,s17,s81,s82,s80]) ).
cnf(s84,plain,
spl0_1,
inference(rat,[],[s1,s73,s68,s67,s78,s83]) ).
cnf(s85,plain,
spl0_11,
inference(rat,[],[s34,s79,s5,s10,s84]) ).
cnf(s87,plain,
spl0_10,
inference(rat,[],[s34,s38,s4,s9,s14,s19,s84,s68]) ).
cnf(s88,plain,
~ spl0_16,
inference(rat,[],[s35,s84,s85,s87]) ).
cnf(s89,plain,
spl0_9,
inference(rat,[],[s63,s38,s3,s8,s13,s18,s88,s68]) ).
cnf(s90,plain,
~ spl0_7,
inference(rat,[],[s48,s85,s89,s87,s67,s88]) ).
cnf(s91,plain,
spl0_14,
inference(rat,[],[s17,s90]) ).
cnf(s92,plain,
spl0_13,
inference(rat,[],[s12,s90]) ).
cnf(s93,plain,
spl0_12,
inference(rat,[],[s7,s90]) ).
cnf(s94,plain,
spl0_8,
inference(rat,[],[s2,s90]) ).
cnf(s95,plain,
spl0_17,
inference(rat,[],[s38,s91,s68,s92]) ).
cnf(s96,plain,
$false,
inference(rat,[],[s63,s88,s92,s91,s94,s95,s93]) ).
fof(f530,plain,
$false,
inference(avatar_sat_refutation,[],[s96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP288-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n001.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 09:52:15 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.62/1.29 % (3312727)Input is clausal, will run a generic CNF schedule.
% 2.62/1.29 % (3312736)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1991732143:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.62/1.29 % (3312732)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2089374487:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.62/1.29 % (3312735)lrs+10_1_sil=8000:sp=occurrence:random_seed=2002171921:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.62/1.29 % (3312734)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2834862139:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.62/1.29 % (3312733)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=906505269:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.62/1.29 % (3312737)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3346410315:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.62/1.29 % (3312735)Refutation not found, incomplete strategy
% 2.62/1.29 % (3312735)------------------------------
% 2.62/1.29 % (3312735)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.29 % (3312735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.29 % (3312735)CaDiCaL version: 2.1.3
% 2.62/1.29 % (3312735)Termination reason: Refutation not found, incomplete strategy
% 2.62/1.29 % (3312735)Time elapsed: 0.003 s
% 2.62/1.29 % (3312735)Peak memory usage: 88 MB
% 2.62/1.29 % (3312735)Instructions burned: 3 (million)
% 2.62/1.29 % (3312738)dis-21_1_sil=8000:lcm=predicate:random_seed=3846788744:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.62/1.29 % (3312738)Refutation not found, incomplete strategy
% 2.62/1.29 % (3312738)------------------------------
% 2.62/1.29 % (3312738)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.29 % (3312738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.29 % (3312738)CaDiCaL version: 2.1.3
% 2.62/1.29 % (3312738)Termination reason: Refutation not found, incomplete strategy
% 2.62/1.29 % (3312738)Time elapsed: 0.001 s
% 2.62/1.29 % (3312738)Peak memory usage: 88 MB
% 2.62/1.29 % (3312738)Instructions burned: 1 (million)
% 2.62/1.29 % (3312736)Instruction limit reached!
% 2.62/1.29 % (3312736)------------------------------
% 2.62/1.29 % (3312736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.29 % (3312736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.29 % (3312736)CaDiCaL version: 2.1.3
% 2.62/1.29 % (3312736)Termination reason: Instruction limit
% 2.62/1.29 % (3312736)Termination phase: Saturation
% 2.62/1.29 % (3312736)Time elapsed: 0.037 s
% 2.62/1.29 % (3312736)Peak memory usage: 89 MB
% 2.62/1.29 % (3312736)Instructions burned: 117 (million)
% 2.62/1.29 % (3312737)First to succeed.
% 2.62/1.29 % (3312737)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3312727"
% 2.62/1.29 % (3312746)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1514527130:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.62/1.29 % (3312746)Refutation not found, incomplete strategy
% 2.62/1.29 % (3312746)------------------------------
% 2.62/1.29 % (3312746)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.29 % (3312746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.29 % (3312746)CaDiCaL version: 2.1.3
% 2.62/1.29 % (3312746)Termination reason: Refutation not found, incomplete strategy
% 2.62/1.29 % (3312746)Time elapsed: 0.001 s
% 2.62/1.29 % (3312746)Peak memory usage: 88 MB
% 2.62/1.29 % (3312746)Instructions burned: 3 (million)
% 2.62/1.29 % (3312735)------------------------------
% 2.62/1.29 % (3312735)------------------------------
% 2.62/1.29 % (3312738)------------------------------
% 2.62/1.29 % (3312738)------------------------------
% 2.62/1.29 % (3312746)------------------------------
% 2.62/1.29 % (3312746)------------------------------
% 2.62/1.29 % (3312737)Refutation found. Thanks to Tanya!
% 2.62/1.29 % SZS status Unsatisfiable for theBenchmark
% 2.62/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/1.47 % (3312737)------------------------------
% 3.58/1.47 % (3312737)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.47 % (3312737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.47 % (3312737)CaDiCaL version: 2.1.3
% 3.58/1.47 % (3312737)Termination reason: Refutation
% 3.58/1.47 % (3312737)Time elapsed: 0.015 s
% 3.58/1.47 % (3312737)Peak memory usage: 89 MB
% 3.58/1.47 % (3312737)Instructions burned: 20 (million)
% 3.58/1.47 % (3312737)------------------------------
% 3.58/1.47 % (3312737)------------------------------
% 3.58/1.47 % (3312727)Success in time 0.421 s
% 3.58/1.47 % Vampire exiting
%------------------------------------------------------------------------------