%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP352-1 : 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 : n003.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 10:13:43 AM UTC 2026
% Result : Unsatisfiable 2.30s 1.16s
% Output : Refutation 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 44
% Syntax : Number of formulae : 274 ( 18 unt; 17 def)
% Number of atoms : 804 ( 246 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 999 ( 469 ~; 513 |; 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 : 39 ( 0 sgn 39 !; 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_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c7 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| 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(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(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_c6,sk_c5) != sk_c7
| 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_c6,sk_c5) != sk_c7
| 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_c6,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f75,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( multiply(sk_c6,sk_c5) != sk_c7
| spl0_6 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[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(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(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(f132,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f74,f93]) ).
fof(f133,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f74,f98]) ).
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(f136,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_11 ),
inference(superposition,[],[f3,f100]) ).
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(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(f148,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c3,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f136]) ).
fof(f149,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c3,X0)) = X0
| ~ spl0_11 ),
inference(forward_demodulation,[],[f148,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(f187,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_3 ),
inference(superposition,[],[f145,f65]) ).
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_c3 = multiply(inverse(sk_c7),identity)
| ~ spl0_11 ),
inference(superposition,[],[f145,f136]) ).
fof(f192,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_10 ),
inference(superposition,[],[f145,f95]) ).
fof(f201,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f192,f100]) ).
fof(f202,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(f203,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f187,f164]) ).
fof(f205,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f202,f145]) ).
fof(f206,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f203,f3]) ).
fof(f215,plain,
( sk_c6 = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f205,f201]) ).
fof(f247,plain,
( sk_c3 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f191,f206]) ).
fof(f248,plain,
( identity = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f247,f3]) ).
fof(f249,plain,
( sk_c7 = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f248,f206]) ).
fof(f250,plain,
( sk_c6 = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f249,f215]) ).
fof(f259,plain,
( ! [X0] : multiply(sk_c3,X0) = X0
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f149,f205]) ).
fof(f260,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f259,f250]) ).
fof(f270,plain,
( sk_c5 != sk_c7
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f76,f260]) ).
fof(f278,plain,
( sk_c6 != sk_c5
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f270,f215]) ).
fof(f287,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f278,f164]) ).
fof(f288,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f287]) ).
fof(f293,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(f298,plain,
( sk_c6 != sk_c7
| sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f293,f100]) ).
fof(f300,plain,
( sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f298,f215]) ).
fof(f302,plain,
( sk_c6 != sk_c7
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f300,f95]) ).
fof(f305,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f302,f215]) ).
fof(f306,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f305]) ).
fof(f315,plain,
( sk_c6 = multiply(inverse(sk_c2),sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f145,f106]) ).
fof(f317,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f315,f85]) ).
fof(f327,plain,
( sk_c6 != sk_c6
| sk_c5 != multiply(sk_c2,sk_c6)
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f69,f85]) ).
fof(f329,plain,
( sk_c5 != multiply(sk_c2,sk_c6)
| ~ spl0_4
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f327]) ).
fof(f335,definition,
( spl0_16
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f336,plain,
( sk_c6 = sk_c7
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f339,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f329,f106]) ).
fof(f340,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f339]) ).
fof(f343,definition,
( spl0_17
<=> sk_c5 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f344,plain,
( sk_c5 = sk_c7
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f345,plain,
( sk_c5 != sk_c7
| spl0_17 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f351,plain,
( sk_c6 != sk_c7
| sk_c7 != multiply(sk_c3,sk_c6)
| ~ spl0_1
| ~ spl0_11 ),
inference(superposition,[],[f59,f100]) ).
fof(f352,plain,
( sk_c6 != sk_c6
| sk_c7 != multiply(sk_c2,sk_c6)
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[],[f59,f85]) ).
fof(f354,plain,
( sk_c7 != multiply(sk_c2,sk_c6)
| ~ spl0_1
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f352]) ).
fof(f356,definition,
( spl0_18
<=> sk_c7 = multiply(sk_c1,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f357,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f356]) ).
fof(f358,plain,
( sk_c7 != multiply(sk_c1,sk_c6)
| spl0_18 ),
inference(avatar_component_clause,[],[f356]) ).
fof(f360,plain,
( sk_c5 != sk_c7
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f354,f106]) ).
fof(f361,plain,
( sk_c6 != sk_c7
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f351,f95]) ).
fof(f362,plain,
( ~ spl0_17
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f360,f104,f83,f58,f343]) ).
fof(f363,plain,
( ~ spl0_16
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f361,f98,f93,f58,f335]) ).
fof(f365,plain,
( sk_c6 = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f75,f317]) ).
fof(f368,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f145,f317]) ).
fof(f370,plain,
( identity = sk_c5
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f368,f3]) ).
fof(f377,plain,
( spl0_16
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f365,f104,f83,f74,f335]) ).
fof(f378,plain,
( sk_c7 != sk_c7
| sk_c6 != multiply(sk_c3,sk_c7)
| ~ spl0_5
| ~ spl0_11 ),
inference(superposition,[],[f72,f100]) ).
fof(f380,plain,
( sk_c7 != sk_c7
| sk_c6 != multiply(sk_c1,sk_c7)
| ~ spl0_5
| ~ spl0_13 ),
inference(superposition,[],[f72,f115]) ).
fof(f381,plain,
( sk_c6 != multiply(sk_c1,sk_c7)
| ~ spl0_5
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f380]) ).
fof(f382,plain,
( sk_c6 != multiply(sk_c3,sk_c7)
| ~ spl0_5
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f378]) ).
fof(f383,plain,
( $false
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f381,f124]) ).
fof(f384,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f383]) ).
fof(f391,plain,
( sk_c6 = multiply(sk_c1,sk_c6)
| ~ spl0_14
| ~ spl0_16 ),
inference(superposition,[],[f124,f336]) ).
fof(f396,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_16 ),
inference(forward_demodulation,[],[f62,f336]) ).
fof(f397,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| sk_c6 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_16 ),
inference(forward_demodulation,[],[f396,f336]) ).
fof(f399,plain,
( sk_c6 != sk_c7
| sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_2
| ~ spl0_11
| ~ spl0_16 ),
inference(superposition,[],[f397,f100]) ).
fof(f401,plain,
( sk_c6 != sk_c7
| sk_c6 != multiply(sk_c1,sk_c6)
| ~ spl0_2
| ~ spl0_13
| ~ spl0_16 ),
inference(superposition,[],[f397,f115]) ).
fof(f403,plain,
( sk_c6 != multiply(sk_c1,sk_c6)
| ~ spl0_2
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f401,f336]) ).
fof(f405,plain,
( sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_2
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f399,f336]) ).
fof(f406,plain,
( sk_c6 != sk_c7
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_demodulation,[],[f405,f95]) ).
fof(f407,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f406,f336]) ).
fof(f408,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f407]) ).
fof(f420,plain,
( $false
| ~ spl0_2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f391,f403]) ).
fof(f421,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f420]) ).
fof(f427,plain,
( sk_c6 != multiply(sk_c1,sk_c6)
| ~ spl0_16
| spl0_18 ),
inference(forward_demodulation,[],[f358,f336]) ).
fof(f434,plain,
( $false
| ~ spl0_14
| ~ spl0_16
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f391,f427]) ).
fof(f435,plain,
( ~ spl0_14
| ~ spl0_16
| spl0_18 ),
inference(avatar_contradiction_clause,[],[f434]) ).
fof(f436,plain,
( spl0_16
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f215,f98,f93,f88,f79,f64,f335]) ).
fof(f446,plain,
( sk_c5 != multiply(sk_c6,sk_c6)
| spl0_3
| ~ spl0_16 ),
inference(forward_demodulation,[],[f66,f336]) ).
fof(f451,plain,
( sk_c6 = multiply(sk_c1,sk_c6)
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f357,f336]) ).
fof(f457,plain,
( sk_c6 = sk_c5
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f344,f336]) ).
fof(f458,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_16
| ~ spl0_18 ),
inference(superposition,[],[f145,f451]) ).
fof(f460,plain,
( sk_c6 = multiply(sk_c7,sk_c6)
| ~ spl0_13
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f458,f115]) ).
fof(f461,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_13
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f460,f336]) ).
fof(f500,plain,
( sk_c7 = multiply(sk_c6,sk_c6)
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f75,f457]) ).
fof(f501,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f500,f336]) ).
fof(f503,plain,
( sk_c6 != sk_c5
| spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f446,f501]) ).
fof(f511,plain,
( $false
| spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f503,f457]) ).
fof(f512,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f511]) ).
fof(f515,plain,
( sk_c6 != sk_c5
| ~ spl0_16
| spl0_17 ),
inference(forward_demodulation,[],[f345,f336]) ).
fof(f564,plain,
( sk_c6 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_13
| ~ spl0_16
| ~ spl0_18 ),
inference(superposition,[],[f145,f461]) ).
fof(f566,plain,
( identity = sk_c6
| ~ spl0_13
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f564,f3]) ).
fof(f586,plain,
( sk_c6 = sk_c5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_18 ),
inference(superposition,[],[f566,f370]) ).
fof(f591,plain,
( $false
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f586,f515]) ).
fof(f592,plain,
( ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f591]) ).
fof(f604,plain,
( sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_demodulation,[],[f382,f336]) ).
fof(f618,plain,
( sk_c6 != sk_c7
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_demodulation,[],[f604,f95]) ).
fof(f623,plain,
( $false
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f618,f336]) ).
fof(f624,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f623]) ).
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(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(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(s24,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f132]) ).
cnf(s25,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f133]) ).
cnf(s26,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f134]) ).
cnf(s27,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f288]) ).
cnf(s29,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f306]) ).
cnf(s31,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(sat_conversion,[],[f340]) ).
cnf(s34,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(sat_conversion,[],[f362]) ).
cnf(s35,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(sat_conversion,[],[f363]) ).
cnf(s38,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f377]) ).
cnf(s40,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f384]) ).
cnf(s42,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(sat_conversion,[],[f408]) ).
cnf(s43,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(sat_conversion,[],[f421]) ).
cnf(s44,plain,
( ~ spl0_14
| ~ spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f435]) ).
cnf(s45,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f436]) ).
cnf(s53,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f512]) ).
cnf(s55,plain,
( ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f592]) ).
cnf(s57,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(sat_conversion,[],[f624]) ).
cnf(s58,plain,
spl0_3,
inference(rat,[],[s53,s55,s44,s38,s6,s11,s16,s21,s26]) ).
cnf(s59,plain,
spl0_6,
inference(rat,[],[s27,s22,s23,s24,s25,s58]) ).
cnf(s61,plain,
( spl0_11
| ~ spl0_5 ),
inference(rat,[],[s40,s15,s20]) ).
cnf(s62,plain,
( spl0_10
| ~ spl0_5 ),
inference(rat,[],[s40,s14,s19]) ).
cnf(s63,plain,
( spl0_9
| spl0_16 ),
inference(rat,[],[s38,s3,s8,s59]) ).
cnf(s64,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_5 ),
inference(rat,[],[s40,s12,s17,s45,s63,s57,s58]) ).
cnf(s65,plain,
~ spl0_5,
inference(rat,[],[s64,s62,s61]) ).
cnf(s66,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s31,s5,s10]) ).
cnf(s67,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s31,s4,s9]) ).
cnf(s68,plain,
( spl0_9
| ~ spl0_4 ),
inference(rat,[],[s31,s3,s8]) ).
cnf(s69,plain,
( ~ spl0_9
| ~ spl0_11
| ~ spl0_4
| ~ spl0_10 ),
inference(rat,[],[s31,s2,s7,s29,s58]) ).
cnf(s70,plain,
~ spl0_4,
inference(rat,[],[s69,s68,s67,s66]) ).
cnf(s72,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s38,s43,s5,s10,s15,s20,s59]) ).
cnf(s73,plain,
( spl0_10
| ~ spl0_2 ),
inference(rat,[],[s38,s43,s4,s9,s14,s19,s59]) ).
cnf(s74,plain,
( spl0_16
| ~ spl0_10
| ~ spl0_9
| ~ spl0_11 ),
inference(rat,[],[s38,s2,s7,s45,s58,s59]) ).
cnf(s75,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s74,s63,s42]) ).
cnf(s76,plain,
~ spl0_2,
inference(rat,[],[s75,s73,s72]) ).
cnf(s77,plain,
spl0_1,
inference(rat,[],[s1,s59,s65,s58,s70,s76]) ).
cnf(s78,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_9 ),
inference(rat,[],[s74,s35,s77]) ).
cnf(s79,plain,
spl0_11,
inference(rat,[],[s55,s44,s34,s38,s5,s10,s15,s20,s77,s59]) ).
cnf(s80,plain,
spl0_10,
inference(rat,[],[s55,s44,s34,s38,s4,s9,s14,s19,s77,s59]) ).
cnf(s81,plain,
~ spl0_9,
inference(rat,[],[s78,s79,s80]) ).
cnf(s82,plain,
~ spl0_16,
inference(rat,[],[s35,s79,s77,s80]) ).
cnf(s87,plain,
$false,
inference(rat,[],[s63,s82,s81]) ).
fof(f625,plain,
$false,
inference(avatar_sat_refutation,[],[s87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP352-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n003.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 09:57:10 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 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
% 2.30/1.16 % (263384)Input is clausal, will run a generic CNF schedule.
% 2.30/1.16 % (263394)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3939879560:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.30/1.16 % (263394)First to succeed.
% 2.30/1.16 % (263394)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-263384"
% 2.30/1.16 % (263391)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1666548861:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.30/1.16 % (263389)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=1992506799:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.30/1.16 % (263390)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1773458908:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.30/1.16 % (263393)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=520671647:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.30/1.16 % (263392)lrs+10_1_sil=8000:sp=occurrence:random_seed=2883399767:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.30/1.16 % (263392)Refutation not found, incomplete strategy
% 2.30/1.16 % (263392)------------------------------
% 2.30/1.16 % (263392)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.30/1.16 % (263392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/1.16 % (263392)CaDiCaL version: 2.1.3
% 2.30/1.16 % (263392)Termination reason: Refutation not found, incomplete strategy
% 2.30/1.16 % (263392)Time elapsed: 0.003 s
% 2.30/1.16 % (263392)Peak memory usage: 88 MB
% 2.30/1.16 % (263392)Instructions burned: 3 (million)
% 2.30/1.16 % (263395)dis-21_1_sil=8000:lcm=predicate:random_seed=1227580189: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)
% 2.30/1.16 % (263395)Refutation not found, incomplete strategy
% 2.30/1.16 % (263395)------------------------------
% 2.30/1.16 % (263395)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.30/1.16 % (263395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/1.16 % (263395)CaDiCaL version: 2.1.3
% 2.30/1.16 % (263395)Termination reason: Refutation not found, incomplete strategy
% 2.30/1.16 % (263395)Time elapsed: 0.002 s
% 2.30/1.16 % (263395)Peak memory usage: 88 MB
% 2.30/1.16 % (263395)Instructions burned: 1 (million)
% 2.30/1.16 % (263393)Instruction limit reached!
% 2.30/1.16 % (263393)------------------------------
% 2.30/1.16 % (263393)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.30/1.16 % (263393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/1.16 % (263393)CaDiCaL version: 2.1.3
% 2.30/1.16 % (263393)Termination reason: Instruction limit
% 2.30/1.16 % (263393)Termination phase: Saturation
% 2.30/1.16 % (263393)Time elapsed: 0.068 s
% 2.30/1.16 % (263393)Peak memory usage: 88 MB
% 2.30/1.16 % (263393)Instructions burned: 116 (million)
% 2.30/1.16 % (263394)Refutation found. Thanks to Tanya!
% 2.30/1.16 % SZS status Unsatisfiable for theBenchmark
% 2.30/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.61/1.25 % (263394)------------------------------
% 2.61/1.25 % (263394)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/1.25 % (263394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/1.25 % (263394)CaDiCaL version: 2.1.3
% 2.61/1.25 % (263394)Termination reason: Refutation
% 2.61/1.25 % (263394)Time elapsed: 0.009 s
% 2.61/1.25 % (263394)Peak memory usage: 89 MB
% 2.61/1.25 % (263394)Instructions burned: 23 (million)
% 2.61/1.25 % (263394)------------------------------
% 2.61/1.25 % (263394)------------------------------
% 2.61/1.25 % (263384)Success in time 0.297 s
% 2.61/1.25 % Vampire exiting
%------------------------------------------------------------------------------