%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n012.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 10:17:34 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.37s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 49
% Syntax : Number of formulae : 292 ( 24 unt; 20 def)
% Number of atoms : 897 ( 261 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1148 ( 543 ~; 585 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_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(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_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_c7 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) )
| ~ 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 != multiply(X2,sk_c6)
| sk_c7 != inverse(X2) )
| ~ 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_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ 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] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(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(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(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(f139,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
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(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(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(f203,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f187,f164]) ).
fof(f206,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f203,f3]) ).
fof(f214,plain,
( sk_c6 = multiply(identity,identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f201,f206]) ).
fof(f215,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f214,f1]) ).
fof(f216,plain,
( sk_c5 = multiply(identity,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f65,f215]) ).
fof(f217,plain,
( sk_c7 != multiply(identity,sk_c5)
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f76,f215]) ).
fof(f220,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f135,f215]) ).
fof(f231,plain,
( identity = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f220,f1]) ).
fof(f234,plain,
( sk_c5 != sk_c7
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f217,f1]) ).
fof(f235,plain,
( sk_c5 = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f216,f1]) ).
fof(f239,plain,
( identity != sk_c5
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f234,f206]) ).
fof(f240,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f235,f206]) ).
fof(f244,plain,
( identity != sk_c6
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f239,f164]) ).
fof(f245,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f244,f215]) ).
fof(f246,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f245]) ).
fof(f247,plain,
( ! [X1] :
( sk_c5 != multiply(X1,identity)
| sk_c6 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f69,f215]) ).
fof(f249,plain,
( ! [X1] :
( sk_c6 != multiply(X1,identity)
| sk_c6 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f247,f164]) ).
fof(f251,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| sk_c6 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f249,f215]) ).
fof(f253,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f251,f215]) ).
fof(f254,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f253,f1]) ).
fof(f258,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f254]) ).
fof(f273,plain,
( sk_c6 = inverse(identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f81,f231]) ).
fof(f274,plain,
( identity = inverse(identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f273,f215]) ).
fof(f279,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f274,f258]) ).
fof(f280,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f279]) ).
fof(f292,plain,
( sk_c6 = multiply(inverse(sk_c2),sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f145,f106]) ).
fof(f294,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f292,f85]) ).
fof(f295,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_14 ),
inference(superposition,[],[f145,f124]) ).
fof(f297,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f295,f115]) ).
fof(f303,plain,
( sk_c5 != sk_c5
| sk_c6 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_12 ),
inference(superposition,[],[f69,f106]) ).
fof(f304,plain,
( sk_c6 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f303]) ).
fof(f305,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f304,f85]) ).
fof(f306,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f305]) ).
fof(f313,definition,
( spl0_16
<=> identity = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f314,plain,
( identity = sk_c5
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f327,definition,
( spl0_19
<=> sk_c5 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f329,plain,
( sk_c5 != sk_c7
| spl0_19 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f331,definition,
( spl0_20
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f332,plain,
( sk_c6 = sk_c7
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f343,plain,
( sk_c7 != sk_c7
| sk_c6 != inverse(sk_c3)
| ~ spl0_1
| ~ spl0_10 ),
inference(superposition,[],[f59,f95]) ).
fof(f344,plain,
( sk_c7 != sk_c7
| sk_c6 != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_9 ),
inference(superposition,[],[f59,f90]) ).
fof(f345,plain,
( sk_c5 != sk_c7
| sk_c6 != inverse(sk_c2)
| ~ spl0_1
| ~ spl0_12 ),
inference(superposition,[],[f59,f106]) ).
fof(f347,plain,
( sk_c6 != inverse(sk_c3)
| ~ spl0_1
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f343]) ).
fof(f348,plain,
( sk_c5 != sk_c7
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f345,f85]) ).
fof(f349,plain,
( sk_c6 != sk_c7
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f347,f100]) ).
fof(f351,definition,
( spl0_21
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f352,plain,
( identity = sk_c7
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f356,plain,
( ~ spl0_19
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f348,f104,f83,f58,f327]) ).
fof(f357,plain,
( ~ spl0_20
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f349,f98,f93,f58,f331]) ).
fof(f372,plain,
( sk_c6 = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f75,f294]) ).
fof(f375,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f145,f294]) ).
fof(f377,plain,
( identity = sk_c5
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f375,f3]) ).
fof(f384,plain,
( spl0_16
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f377,f104,f83,f313]) ).
fof(f385,plain,
( spl0_20
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f372,f104,f83,f74,f331]) ).
fof(f389,plain,
( sk_c7 != sk_c7
| sk_c7 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f62,f95]) ).
fof(f391,plain,
( sk_c5 != sk_c7
| sk_c7 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[],[f62,f106]) ).
fof(f393,plain,
( sk_c7 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f389]) ).
fof(f394,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f393,f100]) ).
fof(f395,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f394]) ).
fof(f408,plain,
( sk_c6 != sk_c5
| sk_c7 != inverse(sk_c6)
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f72,f65]) ).
fof(f410,plain,
( sk_c6 != sk_c6
| sk_c7 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_14 ),
inference(superposition,[],[f72,f124]) ).
fof(f415,plain,
( identity != sk_c6
| sk_c7 != inverse(sk_c6)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_16 ),
inference(forward_demodulation,[],[f408,f314]) ).
fof(f421,definition,
( spl0_24
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f422,plain,
( identity = sk_c6
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f431,plain,
( identity != multiply(sk_c6,sk_c7)
| spl0_3
| ~ spl0_16 ),
inference(forward_demodulation,[],[f66,f314]) ).
fof(f436,plain,
( sk_c6 != sk_c5
| spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f329,f332]) ).
fof(f439,plain,
( identity != sk_c6
| ~ spl0_16
| spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f436,f314]) ).
fof(f440,plain,
( ~ spl0_24
| ~ spl0_16
| spl0_19
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f439,f331,f327,f313,f421]) ).
fof(f441,plain,
( identity != multiply(sk_c6,sk_c6)
| spl0_3
| ~ spl0_16
| ~ spl0_20 ),
inference(forward_demodulation,[],[f431,f332]) ).
fof(f442,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f297,f332]) ).
fof(f491,plain,
( identity != sk_c6
| spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_20 ),
inference(superposition,[],[f441,f442]) ).
fof(f496,plain,
( sk_c6 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20 ),
inference(superposition,[],[f145,f442]) ).
fof(f498,plain,
( identity = sk_c6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f496,f3]) ).
fof(f506,plain,
( ~ spl0_24
| spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f491,f331,f313,f122,f113,f64,f421]) ).
fof(f507,plain,
( spl0_24
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f498,f331,f122,f113,f421]) ).
fof(f515,plain,
( sk_c6 != sk_c5
| sk_c7 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_12
| ~ spl0_20 ),
inference(forward_demodulation,[],[f391,f332]) ).
fof(f523,plain,
( identity != sk_c6
| sk_c7 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_12
| ~ spl0_16
| ~ spl0_20 ),
inference(forward_demodulation,[],[f515,f314]) ).
fof(f528,plain,
( sk_c6 != sk_c7
| identity != sk_c6
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_16
| ~ spl0_20 ),
inference(forward_demodulation,[],[f523,f85]) ).
fof(f530,plain,
( identity != sk_c6
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_16
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f528,f332]) ).
fof(f532,plain,
( ~ spl0_24
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_16
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f530,f331,f313,f104,f83,f61,f421]) ).
fof(f534,plain,
( sk_c6 != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f344]) ).
fof(f538,plain,
( ~ spl0_7
| ~ spl0_1
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f534,f88,f58,f79]) ).
fof(f542,plain,
( spl0_24
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f215,f98,f93,f88,f79,f64,f421]) ).
fof(f544,plain,
( spl0_21
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f206,f88,f79,f64,f351]) ).
fof(f551,plain,
( sk_c7 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f410]) ).
fof(f556,plain,
( ~ spl0_13
| ~ spl0_5
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f551,f122,f71,f113]) ).
fof(f602,plain,
( spl0_16
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f240,f98,f93,f88,f79,f64,f313]) ).
fof(f626,definition,
( spl0_26
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f641,plain,
( sk_c7 != inverse(sk_c6)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_16
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f415,f422]) ).
fof(f653,plain,
( sk_c7 != inverse(identity)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_16
| ~ spl0_24 ),
inference(forward_demodulation,[],[f641,f422]) ).
fof(f661,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_16
| ~ spl0_21
| ~ spl0_24 ),
inference(forward_demodulation,[],[f653,f352]) ).
fof(f663,plain,
( ~ spl0_26
| ~ spl0_3
| ~ spl0_5
| ~ spl0_16
| ~ spl0_21
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f661,f421,f351,f313,f71,f64,f626]) ).
fof(f673,plain,
( sk_c6 = inverse(identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f81,f231]) ).
fof(f678,plain,
( identity = inverse(identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_24 ),
inference(forward_demodulation,[],[f673,f422]) ).
fof(f681,plain,
( spl0_26
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f678,f421,f98,f93,f88,f79,f64,f626]) ).
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(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,[],[f246]) ).
cnf(s28,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f280]) ).
cnf(s29,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(sat_conversion,[],[f306]) ).
cnf(s35,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_19 ),
inference(sat_conversion,[],[f356]) ).
cnf(s36,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_20 ),
inference(sat_conversion,[],[f357]) ).
cnf(s39,plain,
( ~ spl0_8
| ~ spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f384]) ).
cnf(s40,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| spl0_20 ),
inference(sat_conversion,[],[f385]) ).
cnf(s42,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f395]) ).
cnf(s49,plain,
( ~ spl0_16
| spl0_19
| ~ spl0_20
| ~ spl0_24 ),
inference(sat_conversion,[],[f440]) ).
cnf(s51,plain,
( spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_20
| ~ spl0_24 ),
inference(sat_conversion,[],[f506]) ).
cnf(s52,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| spl0_24 ),
inference(sat_conversion,[],[f507]) ).
cnf(s58,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_16
| ~ spl0_20
| ~ spl0_24 ),
inference(sat_conversion,[],[f532]) ).
cnf(s62,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f538]) ).
cnf(s64,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_24 ),
inference(sat_conversion,[],[f542]) ).
cnf(s66,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| spl0_21 ),
inference(sat_conversion,[],[f544]) ).
cnf(s75,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f556]) ).
cnf(s84,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f602]) ).
cnf(s99,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_16
| ~ spl0_21
| ~ spl0_24
| ~ spl0_26 ),
inference(sat_conversion,[],[f663]) ).
cnf(s101,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_24
| spl0_26 ),
inference(sat_conversion,[],[f681]) ).
cnf(s102,plain,
spl0_3,
inference(rat,[],[s51,s52,s39,s40,s6,s11,s16,s21,s26]) ).
cnf(s103,plain,
spl0_6,
inference(rat,[],[s27,s22,s23,s24,s25,s102]) ).
cnf(s104,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_9
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s99,s101,s64,s84,s66,s102]) ).
cnf(s105,plain,
( spl0_11
| ~ spl0_5 ),
inference(rat,[],[s75,s15,s20]) ).
cnf(s106,plain,
( spl0_10
| ~ spl0_5 ),
inference(rat,[],[s75,s14,s19]) ).
cnf(s107,plain,
( spl0_9
| ~ spl0_5 ),
inference(rat,[],[s75,s13,s18]) ).
cnf(s108,plain,
( ~ spl0_9
| ~ spl0_5
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s75,s12,s17,s104]) ).
cnf(s109,plain,
~ spl0_5,
inference(rat,[],[s108,s107,s106,s105]) ).
cnf(s110,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s29,s5,s10]) ).
cnf(s111,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s29,s4,s9]) ).
cnf(s112,plain,
( spl0_9
| ~ spl0_4 ),
inference(rat,[],[s29,s3,s8]) ).
cnf(s113,plain,
( ~ spl0_9
| ~ spl0_11
| ~ spl0_4
| ~ spl0_10 ),
inference(rat,[],[s29,s2,s7,s28,s102]) ).
cnf(s114,plain,
~ spl0_4,
inference(rat,[],[s113,s112,s111,s110]) ).
cnf(s115,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s58,s52,s39,s40,s5,s10,s15,s20,s103]) ).
cnf(s116,plain,
( ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s58,s52,s39,s40,s4,s9,s14,s19,s42,s103]) ).
cnf(s117,plain,
~ spl0_2,
inference(rat,[],[s116,s115]) ).
cnf(s118,plain,
spl0_1,
inference(rat,[],[s1,s103,s109,s102,s114,s117]) ).
cnf(s119,plain,
( spl0_9
| spl0_20 ),
inference(rat,[],[s40,s3,s8,s103]) ).
cnf(s120,plain,
spl0_20,
inference(rat,[],[s40,s2,s7,s62,s119,s103,s118]) ).
cnf(s122,plain,
spl0_11,
inference(rat,[],[s49,s35,s39,s52,s5,s10,s15,s20,s120,s118]) ).
cnf(s123,plain,
~ spl0_10,
inference(rat,[],[s36,s118,s120,s122]) ).
cnf(s124,plain,
spl0_14,
inference(rat,[],[s19,s123]) ).
cnf(s125,plain,
spl0_13,
inference(rat,[],[s14,s123]) ).
cnf(s126,plain,
spl0_12,
inference(rat,[],[s9,s123]) ).
cnf(s127,plain,
spl0_8,
inference(rat,[],[s4,s123]) ).
cnf(s128,plain,
spl0_24,
inference(rat,[],[s52,s120,s124,s125]) ).
cnf(s129,plain,
spl0_16,
inference(rat,[],[s39,s127,s126]) ).
cnf(s130,plain,
~ spl0_19,
inference(rat,[],[s35,s118,s126,s127]) ).
cnf(s132,plain,
$false,
inference(rat,[],[s49,s128,s120,s129,s130]) ).
fof(f682,plain,
$false,
inference(avatar_sat_refutation,[],[s132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP352-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sun Sep 27 09:55:05 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.33 Running first-order model finding
% 0.07/0.33 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.37 % (2128653)Will run a generic schedule for satisfiability detection.
% 0.07/0.37 % (2128659)% WARNING: option uhcvi not known.
% 0.07/0.37 % (2128658)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3017108101_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.37 % (2128661)dis+10_1_sil=32000:sp=arity:random_seed=903009651:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.37 % (2128660)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1717221367:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.37 % (2128659)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2646239530:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.37 % (2128662)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1110997815:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.37 % (2128663)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1430380227:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.37 % (2128664)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3628448030:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.37 % TRYING [1]
% 0.07/0.37 % TRYING [2]
% 0.07/0.37 % TRYING [3]
% 0.07/0.37 % TRYING [4]
% 0.07/0.37 % (2128661) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2128653-2128661"...
% 0.07/0.37 % (2128662) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2128653-2128662"...
% 0.07/0.37 % (2128661)...printing done.
% 0.07/0.37 % TRYING [5]
% 0.07/0.37 % (2128661)Refutation found. Thanks to Tanya!
% 0.07/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.37 % (2128661)------------------------------
% 0.07/0.37 % (2128661)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.37 % (2128661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.37 % (2128661)CaDiCaL version: 2.1.3
% 0.07/0.37 % (2128661)Termination reason: Refutation
% 0.07/0.37 % (2128661)Time elapsed: 0.008 s
% 0.07/0.37 % (2128661)Peak memory usage: 12 MB
% 0.07/0.37 % (2128661)Instructions burned: 23 (million)
% 0.07/0.37 % (2128653)Success in time 0.036 s
% 0.07/0.37 % Vampire exiting
%------------------------------------------------------------------------------