%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP278-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 10:13:31 AM UTC 2026
% Result : Unsatisfiable 2.74s 1.30s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 37
% Syntax : Number of formulae : 256 ( 20 unt; 13 def)
% Number of atoms : 889 ( 236 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 1213 ( 580 ~; 620 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 14 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( multiply(sk_c1,sk_c6) = sk_c5
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( multiply(sk_c1,sk_c6) = sk_c5
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( multiply(sk_c1,sk_c6) = sk_c5
| sk_c5 = inverse(sk_c3) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c3,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( multiply(sk_c1,sk_c6) = sk_c5
| sk_c5 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c6 = inverse(sk_c1)
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c3) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c6 = inverse(sk_c1)
| sk_c5 = inverse(sk_c3) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c3,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c6 = inverse(sk_c1)
| sk_c5 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c5 = inverse(sk_c4)
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c5 = inverse(sk_c4)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c5 = inverse(sk_c4)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c3) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c5 = inverse(sk_c4)
| sk_c5 = inverse(sk_c3) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c3,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c5 = inverse(sk_c4)
| sk_c5 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c6,sk_c4) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c5 = multiply(sk_c6,sk_c4)
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c6,sk_c4) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c5 = multiply(sk_c6,sk_c4)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c6,sk_c4) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c5 = multiply(sk_c6,sk_c4)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( multiply(sk_c6,sk_c4) = sk_c5
| inverse(sk_c3) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c5 = multiply(sk_c6,sk_c4)
| sk_c5 = inverse(sk_c3) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c6,sk_c4) = sk_c5
| multiply(sk_c3,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c5 = multiply(sk_c6,sk_c4)
| sk_c5 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
! [X2,X0,X1] :
( multiply(X0,sk_c6) != sk_c5
| inverse(X0) != sk_c6
| inverse(sk_c4) != sk_c5
| multiply(sk_c6,sk_c4) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c4
| inverse(X1) != sk_c6
| multiply(X1,sk_c5) != sk_c6
| inverse(X2) != sk_c5
| multiply(X2,sk_c4) != sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
! [X2,X0,X1] :
( sk_c5 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6
| sk_c5 != inverse(sk_c4)
| sk_c5 != multiply(sk_c6,sk_c4)
| multiply(sk_c5,sk_c6) != sk_c4
| sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5)
| sk_c5 != inverse(X2)
| sk_c5 != multiply(X2,sk_c4) ),
inference(reorient_equations,[],[f44]) ).
fof(f47,definition,
( spl0_1
<=> ! [X2] :
( sk_c5 != inverse(X2)
| sk_c5 != multiply(X2,sk_c4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f48,plain,
( ! [X2] :
( sk_c5 != inverse(X2)
| sk_c5 != multiply(X2,sk_c4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,definition,
( spl0_2
<=> ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f51,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f53,definition,
( spl0_3
<=> multiply(sk_c5,sk_c6) = sk_c4 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f54,plain,
( multiply(sk_c5,sk_c6) = sk_c4
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f55,plain,
( multiply(sk_c5,sk_c6) != sk_c4
| spl0_3 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f57,definition,
( spl0_4
<=> sk_c5 = multiply(sk_c6,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f58,plain,
( sk_c5 = multiply(sk_c6,sk_c4)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f61,definition,
( spl0_5
<=> sk_c5 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f62,plain,
( sk_c5 = inverse(sk_c4)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f63,plain,
( sk_c5 != inverse(sk_c4)
| spl0_5 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f65,definition,
( spl0_6
<=> ! [X0] :
( sk_c5 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f66,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c5 != multiply(X0,sk_c6) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f67,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f45,f65,f61,f57,f53,f50,f47]) ).
fof(f69,definition,
( spl0_7
<=> sk_c5 = multiply(sk_c3,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f71,plain,
( sk_c5 = multiply(sk_c3,sk_c4)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,plain,
( spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f43,f57,f69]) ).
fof(f74,definition,
( spl0_8
<=> sk_c5 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f76,plain,
( sk_c5 = inverse(sk_c3)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,plain,
( spl0_8
| spl0_4 ),
inference(avatar_split_clause,[],[f41,f57,f74]) ).
fof(f79,definition,
( spl0_9
<=> sk_c6 = multiply(sk_c2,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f81,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,plain,
( spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f39,f57,f79]) ).
fof(f84,definition,
( spl0_10
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f86,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f37,f57,f84]) ).
fof(f88,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f35,f57,f53]) ).
fof(f89,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f33,f61,f69]) ).
fof(f90,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f31,f61,f74]) ).
fof(f91,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f29,f61,f79]) ).
fof(f92,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f27,f61,f84]) ).
fof(f93,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f25,f61,f53]) ).
fof(f95,definition,
( spl0_11
<=> sk_c6 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f97,plain,
( sk_c6 = inverse(sk_c1)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,plain,
( spl0_7
| spl0_11 ),
inference(avatar_split_clause,[],[f23,f95,f69]) ).
fof(f99,plain,
( spl0_8
| spl0_11 ),
inference(avatar_split_clause,[],[f21,f95,f74]) ).
fof(f100,plain,
( spl0_9
| spl0_11 ),
inference(avatar_split_clause,[],[f19,f95,f79]) ).
fof(f101,plain,
( spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f17,f95,f84]) ).
fof(f102,plain,
( spl0_3
| spl0_11 ),
inference(avatar_split_clause,[],[f15,f95,f53]) ).
fof(f104,definition,
( spl0_12
<=> multiply(sk_c1,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f106,plain,
( multiply(sk_c1,sk_c6) = sk_c5
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f13,f104,f69]) ).
fof(f108,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f11,f104,f74]) ).
fof(f109,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f9,f104,f79]) ).
fof(f110,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f7,f104,f84]) ).
fof(f111,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f5,f104,f53]) ).
fof(f112,plain,
( identity = multiply(sk_c5,sk_c3)
| ~ spl0_8 ),
inference(superposition,[],[f3,f76]) ).
fof(f113,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_10 ),
inference(superposition,[],[f3,f86]) ).
fof(f116,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f117,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c6,X0)) = multiply(sk_c4,X0)
| ~ spl0_3 ),
inference(superposition,[],[f4,f54]) ).
fof(f118,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c5,multiply(sk_c3,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f112]) ).
fof(f119,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c2,multiply(sk_c5,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f81]) ).
fof(f121,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c3,X0)) = X0
| ~ spl0_8 ),
inference(forward_demodulation,[],[f118,f1]) ).
fof(f122,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f116,f1]) ).
fof(f131,plain,
( sk_c4 = multiply(sk_c5,sk_c5)
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f121,f71]) ).
fof(f134,plain,
( multiply(sk_c6,sk_c6) = multiply(sk_c2,sk_c4)
| ~ spl0_3
| ~ spl0_9 ),
inference(superposition,[],[f119,f54]) ).
fof(f158,plain,
( sk_c2 = multiply(inverse(sk_c6),identity)
| ~ spl0_10 ),
inference(superposition,[],[f122,f113]) ).
fof(f162,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c4)
| ~ spl0_3 ),
inference(superposition,[],[f122,f54]) ).
fof(f165,plain,
( sk_c5 = multiply(inverse(sk_c2),sk_c6)
| ~ spl0_9 ),
inference(superposition,[],[f122,f81]) ).
fof(f174,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f165,f86]) ).
fof(f175,plain,
( multiply(sk_c5,sk_c5) = multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f117,f174]) ).
fof(f178,plain,
( sk_c4 = multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f175,f131]) ).
fof(f185,plain,
( sk_c6 = multiply(inverse(sk_c4),sk_c4)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f122,f178]) ).
fof(f187,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f185,f3]) ).
fof(f193,plain,
( sk_c2 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f158,f187]) ).
fof(f195,plain,
( identity = sk_c2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f193,f3]) ).
fof(f196,plain,
( sk_c6 = sk_c2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f195,f187]) ).
fof(f201,plain,
( identity = multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f113,f196]) ).
fof(f203,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f86,f196]) ).
fof(f204,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f201,f174]) ).
fof(f206,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f204,f187]) ).
fof(f214,plain,
( multiply(sk_c6,sk_c4) = multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f134,f196]) ).
fof(f215,plain,
( sk_c5 = multiply(sk_c6,sk_c4)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f214,f174]) ).
fof(f218,plain,
( spl0_4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f215,f84,f79,f74,f69,f53,f57]) ).
fof(f236,plain,
( sk_c5 = multiply(sk_c5,sk_c4)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f58,f206]) ).
fof(f239,plain,
( sk_c4 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f122,f236]) ).
fof(f241,plain,
( identity = sk_c4
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f239,f3]) ).
fof(f243,plain,
( sk_c6 = sk_c4
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f241,f187]) ).
fof(f245,plain,
( sk_c5 = sk_c4
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f243,f206]) ).
fof(f248,plain,
( sk_c5 != inverse(sk_c5)
| ~ spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f63,f245]) ).
fof(f297,plain,
( sk_c5 = inverse(sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f203,f206]) ).
fof(f298,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f297,f248]) ).
fof(f299,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f298]) ).
fof(f300,plain,
( ! [X2] :
( sk_c5 != inverse(X2)
| sk_c5 != multiply(X2,sk_c5) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f48,f245]) ).
fof(f313,plain,
( sk_c6 != sk_c5
| sk_c5 != multiply(sk_c2,sk_c5)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f300,f86]) ).
fof(f319,plain,
( sk_c5 != multiply(sk_c2,sk_c5)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f313,f206]) ).
fof(f321,plain,
( sk_c6 != sk_c5
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f319,f81]) ).
fof(f324,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f321,f206]) ).
fof(f325,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f324]) ).
fof(f326,plain,
( ! [X1] :
( sk_c5 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f51,f206]) ).
fof(f327,plain,
( ! [X1] :
( sk_c5 != inverse(X1)
| sk_c5 != multiply(X1,sk_c5) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f326,f206]) ).
fof(f329,plain,
( sk_c6 != sk_c5
| sk_c5 != multiply(sk_c2,sk_c5)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f327,f86]) ).
fof(f335,plain,
( sk_c5 != multiply(sk_c2,sk_c5)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f329,f206]) ).
fof(f337,plain,
( sk_c6 != sk_c5
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f335,f81]) ).
fof(f340,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f337,f206]) ).
fof(f341,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f340]) ).
fof(f342,plain,
( ! [X0] :
( sk_c5 != multiply(X0,sk_c5)
| inverse(X0) != sk_c6 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f66,f206]) ).
fof(f343,plain,
( ! [X0] :
( inverse(X0) != sk_c5
| sk_c5 != multiply(X0,sk_c5) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f342,f206]) ).
fof(f374,plain,
( sk_c6 != sk_c5
| sk_c5 != multiply(sk_c2,sk_c5)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f343,f86]) ).
fof(f380,plain,
( sk_c5 != multiply(sk_c2,sk_c5)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f374,f206]) ).
fof(f382,plain,
( sk_c6 != sk_c5
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f380,f81]) ).
fof(f385,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f382,f206]) ).
fof(f386,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f385]) ).
fof(f388,plain,
( identity = multiply(sk_c5,sk_c4)
| ~ spl0_5 ),
inference(superposition,[],[f3,f62]) ).
fof(f390,plain,
( identity = multiply(sk_c6,sk_c1)
| ~ spl0_11 ),
inference(superposition,[],[f3,f97]) ).
fof(f392,plain,
( sk_c4 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_4 ),
inference(superposition,[],[f122,f58]) ).
fof(f395,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f122,f106]) ).
fof(f396,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c1,multiply(sk_c6,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f106]) ).
fof(f397,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f395,f97]) ).
fof(f398,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c1,sk_c5)
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f51,f97]) ).
fof(f403,plain,
( sk_c6 != multiply(sk_c1,sk_c5)
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f398]) ).
fof(f409,definition,
( spl0_14
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f410,plain,
( sk_c6 = sk_c5
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f411,plain,
( sk_c6 != sk_c5
| spl0_14 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f418,plain,
( sk_c4 = multiply(inverse(sk_c5),identity)
| ~ spl0_5 ),
inference(superposition,[],[f122,f388]) ).
fof(f422,plain,
( sk_c1 = multiply(inverse(sk_c6),identity)
| ~ spl0_11 ),
inference(superposition,[],[f122,f390]) ).
fof(f446,plain,
( multiply(sk_c5,sk_c4) = multiply(sk_c1,sk_c5)
| ~ spl0_4
| ~ spl0_12 ),
inference(superposition,[],[f396,f58]) ).
fof(f453,plain,
( identity = multiply(sk_c1,sk_c5)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12 ),
inference(forward_demodulation,[],[f446,f388]) ).
fof(f465,plain,
( multiply(sk_c5,sk_c6) = multiply(sk_c4,sk_c5)
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f117,f397]) ).
fof(f466,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f122,f397]) ).
fof(f468,plain,
( identity = sk_c5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f466,f3]) ).
fof(f469,plain,
( sk_c4 = multiply(sk_c4,sk_c5)
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f465,f54]) ).
fof(f552,plain,
( sk_c6 != sk_c6
| multiply(sk_c1,sk_c6) != sk_c5
| ~ spl0_6
| ~ spl0_11 ),
inference(superposition,[],[f66,f97]) ).
fof(f556,plain,
( multiply(sk_c1,sk_c6) != sk_c5
| ~ spl0_6
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f552]) ).
fof(f562,plain,
( $false
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f556,f106]) ).
fof(f563,plain,
( ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f562]) ).
fof(f592,plain,
( sk_c5 = multiply(sk_c1,sk_c5)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f453,f468]) ).
fof(f593,plain,
( sk_c6 != sk_c5
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f403,f592]) ).
fof(f609,plain,
( sk_c4 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f418,f468]) ).
fof(f610,plain,
( identity = sk_c4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f609,f3]) ).
fof(f611,plain,
( sk_c5 = sk_c4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f610,f468]) ).
fof(f613,plain,
( sk_c5 = inverse(sk_c5)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f62,f611]) ).
fof(f616,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f162,f611]) ).
fof(f623,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f616,f3]) ).
fof(f624,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f623,f468]) ).
fof(f629,plain,
( ~ spl0_14
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f593,f104,f95,f61,f57,f50,f409]) ).
fof(f631,plain,
( spl0_14
| ~ spl0_3
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f624,f104,f95,f61,f53,f409]) ).
fof(f632,plain,
( ! [X2] :
( sk_c5 != inverse(X2)
| sk_c5 != multiply(X2,sk_c5) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f48,f611]) ).
fof(f637,plain,
( sk_c5 != sk_c5
| sk_c5 != multiply(sk_c4,sk_c5)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f632,f62]) ).
fof(f639,plain,
( sk_c5 != multiply(sk_c4,sk_c5)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f637]) ).
fof(f641,plain,
( sk_c5 != sk_c4
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f639,f469]) ).
fof(f643,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f641,f611]) ).
fof(f644,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f643]) ).
fof(f646,plain,
( sk_c5 != multiply(sk_c5,sk_c6)
| spl0_3
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f55,f611]) ).
fof(f666,plain,
( sk_c5 != multiply(sk_c5,sk_c5)
| spl0_3
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14 ),
inference(forward_demodulation,[],[f646,f410]) ).
fof(f677,plain,
( identity = multiply(sk_c5,sk_c5)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f3,f613]) ).
fof(f678,plain,
( sk_c5 = multiply(sk_c5,sk_c5)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f677,f468]) ).
fof(f679,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f678,f666]) ).
fof(f680,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f679]) ).
fof(f686,plain,
( sk_c1 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f422,f468]) ).
fof(f687,plain,
( sk_c1 = sk_c4
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f686,f392]) ).
fof(f688,plain,
( sk_c1 = sk_c5
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f687,f611]) ).
fof(f691,plain,
( identity = multiply(sk_c6,sk_c5)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f390,f688]) ).
fof(f697,plain,
( identity = sk_c6
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f691,f397]) ).
fof(f700,plain,
( sk_c6 = sk_c5
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f697,f468]) ).
fof(f701,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| spl0_14 ),
inference(forward_subsumption_resolution,[],[f700,f411]) ).
fof(f702,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| spl0_14 ),
inference(avatar_contradiction_clause,[],[f701]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f67]) ).
cnf(s2,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f72]) ).
cnf(s3,plain,
( spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f77]) ).
cnf(s4,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f82]) ).
cnf(s5,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f87]) ).
cnf(s6,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f88]) ).
cnf(s7,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f89]) ).
cnf(s8,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f90]) ).
cnf(s9,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f91]) ).
cnf(s10,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f92]) ).
cnf(s11,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f93]) ).
cnf(s12,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f98]) ).
cnf(s13,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f99]) ).
cnf(s14,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f100]) ).
cnf(s15,plain,
( spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f101]) ).
cnf(s16,plain,
( spl0_3
| spl0_11 ),
inference(sat_conversion,[],[f102]) ).
cnf(s17,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f107]) ).
cnf(s18,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f108]) ).
cnf(s19,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f109]) ).
cnf(s20,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f110]) ).
cnf(s21,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f111]) ).
cnf(s23,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f218]) ).
cnf(s24,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f299]) ).
cnf(s27,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f325]) ).
cnf(s30,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f341]) ).
cnf(s33,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f386]) ).
cnf(s44,plain,
( ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f563]) ).
cnf(s48,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14 ),
inference(sat_conversion,[],[f629]) ).
cnf(s50,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f631]) ).
cnf(s54,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f644]) ).
cnf(s56,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14 ),
inference(sat_conversion,[],[f680]) ).
cnf(s59,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f702]) ).
cnf(s60,plain,
spl0_3,
inference(rat,[],[s56,s59,s6,s11,s16,s21]) ).
cnf(s61,plain,
( spl0_7
| ~ spl0_6 ),
inference(rat,[],[s44,s12,s17]) ).
cnf(s62,plain,
( spl0_12
| ~ spl0_6 ),
inference(rat,[],[s33,s18,s19,s20,s61,s60]) ).
cnf(s63,plain,
~ spl0_6,
inference(rat,[],[s33,s13,s14,s15,s44,s62,s61,s60]) ).
cnf(s64,plain,
( ~ spl0_4
| spl0_2
| spl0_1 ),
inference(rat,[],[s24,s7,s8,s9,s10,s1,s63,s60]) ).
cnf(s65,plain,
spl0_4,
inference(rat,[],[s23,s2,s3,s4,s5,s60]) ).
cnf(s66,plain,
( spl0_10
| ~ spl0_5
| ~ spl0_2 ),
inference(rat,[],[s48,s50,s15,s20,s65,s60]) ).
cnf(s67,plain,
( spl0_9
| ~ spl0_5
| ~ spl0_2 ),
inference(rat,[],[s48,s50,s14,s19,s65,s60]) ).
cnf(s68,plain,
( spl0_8
| ~ spl0_5
| ~ spl0_2 ),
inference(rat,[],[s48,s50,s13,s18,s65,s60]) ).
cnf(s69,plain,
( ~ spl0_5
| ~ spl0_2 ),
inference(rat,[],[s48,s50,s12,s17,s30,s68,s67,s66,s60,s65]) ).
cnf(s70,plain,
spl0_5,
inference(rat,[],[s24,s7,s8,s9,s10,s60,s65]) ).
cnf(s71,plain,
~ spl0_2,
inference(rat,[],[s69,s70]) ).
cnf(s72,plain,
spl0_1,
inference(rat,[],[s64,s65,s71]) ).
cnf(s73,plain,
spl0_10,
inference(rat,[],[s54,s15,s20,s72,s60,s70]) ).
cnf(s74,plain,
spl0_9,
inference(rat,[],[s54,s14,s19,s72,s60,s70]) ).
cnf(s75,plain,
spl0_8,
inference(rat,[],[s54,s13,s18,s72,s60,s70]) ).
cnf(s76,plain,
~ spl0_7,
inference(rat,[],[s27,s74,s72,s65,s60,s73,s75]) ).
cnf(s77,plain,
spl0_12,
inference(rat,[],[s17,s76]) ).
cnf(s78,plain,
spl0_11,
inference(rat,[],[s12,s76]) ).
cnf(s79,plain,
$false,
inference(rat,[],[s54,s70,s60,s72,s77,s78]) ).
fof(f703,plain,
$false,
inference(avatar_sat_refutation,[],[s79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP278-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:49:17 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.74/1.30 % (2381321)Input is clausal, will run a generic CNF schedule.
% 2.74/1.30 % (2381329)lrs+10_1_sil=8000:sp=occurrence:random_seed=2714980479:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.74/1.30 % (2381329)Refutation not found, incomplete strategy
% 2.74/1.30 % (2381329)------------------------------
% 2.74/1.30 % (2381329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.30 % (2381329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.30 % (2381329)CaDiCaL version: 2.1.3
% 2.74/1.30 % (2381329)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.30 % (2381329)Time elapsed: 0.002 s
% 2.74/1.30 % (2381329)Peak memory usage: 88 MB
% 2.74/1.30 % (2381329)Instructions burned: 2 (million)
% 2.74/1.30 % (2381328)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=448029952:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.74/1.30 % (2381331)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2774218890:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.74/1.30 % (2381332)dis-21_1_sil=8000:lcm=predicate:random_seed=2719633882: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)
% 2.74/1.30 % (2381326)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=3903389836:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.74/1.30 % (2381327)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3085250380:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.74/1.30 % (2381332)Refutation not found, incomplete strategy
% 2.74/1.30 % (2381332)------------------------------
% 2.74/1.30 % (2381332)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.30 % (2381332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.30 % (2381332)CaDiCaL version: 2.1.3
% 2.74/1.30 % (2381332)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.30 % (2381332)Time elapsed: 0.002 s
% 2.74/1.30 % (2381332)Peak memory usage: 88 MB
% 2.74/1.30 % (2381332)Instructions burned: 1 (million)
% 2.74/1.30 % (2381330)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2815409420:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.74/1.30 % (2381331)First to succeed.
% 2.74/1.30 % (2381331)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2381321"
% 2.74/1.30 % (2381330)Instruction limit reached!
% 2.74/1.30 % (2381330)------------------------------
% 2.74/1.30 % (2381330)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.30 % (2381330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.30 % (2381330)CaDiCaL version: 2.1.3
% 2.74/1.30 % (2381330)Termination reason: Instruction limit
% 2.74/1.30 % (2381330)Termination phase: Saturation
% 2.74/1.30 % (2381330)Time elapsed: 0.070 s
% 2.74/1.30 % (2381330)Peak memory usage: 89 MB
% 2.74/1.30 % (2381330)Instructions burned: 115 (million)
% 2.74/1.30 % (2381329)------------------------------
% 2.74/1.30 % (2381329)------------------------------
% 2.74/1.30 % (2381340)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=1563488385:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.74/1.30 % (2381341)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1903855008:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 2.74/1.30 % (2381341)Refutation not found, incomplete strategy
% 2.74/1.30 % (2381341)------------------------------
% 2.74/1.30 % (2381341)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.30 % (2381341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.30 % (2381341)CaDiCaL version: 2.1.3
% 2.74/1.30 % (2381341)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.30 % (2381341)Time elapsed: 0.001 s
% 2.74/1.30 % (2381341)Peak memory usage: 88 MB
% 2.74/1.30 % (2381341)Instructions burned: 2 (million)
% 2.74/1.30 % (2381332)------------------------------
% 2.74/1.30 % (2381332)------------------------------
% 2.74/1.30 % (2381340)Refutation not found, incomplete strategy
% 2.74/1.30 % (2381340)------------------------------
% 2.74/1.30 % (2381340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.30 % (2381340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.30 % (2381340)CaDiCaL version: 2.1.3
% 2.74/1.30 % (2381340)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.30 % (2381340)Time elapsed: 0.005 s
% 2.74/1.30 % (2381340)Peak memory usage: 88 MB
% 2.74/1.30 % (2381340)Instructions burned: 7 (million)
% 2.74/1.30 % (2381331)Refutation found. Thanks to Tanya!
% 2.74/1.30 % SZS status Unsatisfiable for theBenchmark
% 2.74/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.39 % (2381331)------------------------------
% 3.63/1.39 % (2381331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.39 % (2381331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.39 % (2381331)CaDiCaL version: 2.1.3
% 3.63/1.39 % (2381331)Termination reason: Refutation
% 3.63/1.39 % (2381331)Time elapsed: 0.017 s
% 3.63/1.39 % (2381331)Peak memory usage: 89 MB
% 3.63/1.39 % (2381331)Instructions burned: 24 (million)
% 3.63/1.39 % (2381331)------------------------------
% 3.63/1.39 % (2381331)------------------------------
% 3.63/1.39 % (2381321)Success in time 0.451 s
% 3.63/1.39 % Vampire exiting
%------------------------------------------------------------------------------