%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG012-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 09:20:04 AM UTC 2026
% Result : Unsatisfiable 1.83s 0.61s
% Output : Refutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 24
% Syntax : Number of formulae : 171 ( 24 unt; 14 def)
% Number of atoms : 591 ( 1 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 855 ( 435 ~; 406 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 15 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 188 ( 0 sgn 188 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : f(X0,f(X1,X2)) = f(f(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_is_associative) ).
fof(f2,axiom,
! [X0] :
( d2(X0)
| d1(X0)
| c(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_union) ).
fof(f3,axiom,
! [X0] :
( ~ d1(X0)
| ~ c(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_exclusive_c_d1) ).
fof(f4,axiom,
! [X0] :
( ~ d2(X0)
| ~ c(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_exclusive_c_d2) ).
fof(f6,axiom,
c(a1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition_c_not_empty) ).
fof(f7,axiom,
d1(a2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition_d1_not_empty) ).
fof(f8,axiom,
d2(a3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition_d2_not_empty) ).
fof(f9,negated_conjecture,
! [X0,X1] :
( d2(f(X0,X1))
| d1(f(X0,X1))
| ~ c(X0)
| ~ c(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_1) ).
fof(f10,negated_conjecture,
! [X0,X1] :
( c(f(X0,X1))
| ~ d1(X0)
| ~ d1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_2) ).
fof(f11,negated_conjecture,
! [X0,X1] :
( c(f(X0,X1))
| ~ d2(X0)
| ~ d2(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_3) ).
fof(f13,plain,
! [X0,X1] :
( ~ c(f(X0,X1))
| d1(f(X0,X1))
| ~ c(X0)
| ~ c(X1) ),
inference(resolution,[],[f4,f9]) ).
fof(f15,plain,
! [X0,X1] :
( ~ c(f(X0,X1))
| ~ c(X0)
| ~ c(X1) ),
inference(forward_subsumption_resolution,[],[f13,f3]) ).
fof(f23,plain,
! [X2,X0,X1] :
( ~ c(f(X0,f(X1,X2)))
| ~ c(f(X0,X1))
| ~ c(X2) ),
inference(superposition,[],[f15,f1]) ).
fof(f25,plain,
! [X2,X0,X1] :
( c(f(X0,f(X1,X2)))
| ~ d2(f(X0,X1))
| ~ d2(X2) ),
inference(superposition,[],[f11,f1]) ).
fof(f26,plain,
! [X2,X0,X1] :
( c(f(X0,f(X1,X2)))
| ~ d1(f(X0,X1))
| ~ d1(X2) ),
inference(superposition,[],[f10,f1]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ d2(f(X0,X1))
| ~ d2(X2)
| ~ c(X0)
| ~ c(f(X1,X2)) ),
inference(resolution,[],[f25,f15]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ d1(f(X0,X1))
| ~ d1(X2)
| ~ c(X0)
| ~ c(f(X1,X2)) ),
inference(resolution,[],[f26,f15]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ d2(f(X1,X2))
| ~ c(X2)
| ~ d2(X0)
| ~ c(f(X0,X1)) ),
inference(resolution,[],[f23,f11]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ d1(f(X1,X2))
| ~ c(X2)
| ~ d1(X0)
| ~ c(f(X0,X1)) ),
inference(resolution,[],[f23,f10]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ d2(X0)
| ~ c(X1)
| ~ c(f(X2,X0))
| d1(f(X1,X2))
| ~ c(X1)
| ~ c(X2) ),
inference(resolution,[],[f29,f9]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ c(f(X2,X0))
| ~ c(X1)
| ~ d2(X0)
| d1(f(X1,X2))
| c(f(X1,X2)) ),
inference(resolution,[],[f29,f2]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ c(f(X2,X0))
| ~ c(X1)
| ~ d2(X0)
| d1(f(X1,X2))
| ~ c(X2) ),
inference(duplicate_literal_removal,[],[f44]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( ~ d1(f(X0,f(X1,X2)))
| ~ d1(X3)
| ~ c(f(X0,X1))
| ~ c(f(X2,X3)) ),
inference(superposition,[],[f33,f1]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ c(f(X1,X2))
| ~ d2(X1)
| ~ c(X0)
| d1(f(X2,X0))
| c(f(X2,X0)) ),
inference(resolution,[],[f39,f2]) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( ~ d1(f(X0,f(X1,X2)))
| ~ c(X2)
| ~ d1(X3)
| ~ c(f(X3,f(X0,X1))) ),
inference(superposition,[],[f40,f1]) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( ~ d2(f(X1,X2))
| ~ c(X0)
| d1(f(X0,X3))
| ~ c(X3)
| ~ d1(f(X3,X1))
| ~ d1(X2) ),
inference(resolution,[],[f47,f26]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ c(X0)
| ~ d2(X1)
| d1(f(X0,X2))
| c(f(X0,X2))
| ~ d2(X2)
| ~ d2(X1) ),
inference(resolution,[],[f45,f11]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ c(X0)
| ~ d2(X1)
| d1(f(X0,X2))
| c(f(X0,X2))
| ~ d2(X2) ),
inference(duplicate_literal_removal,[],[f101]) ).
fof(f110,definition,
( spl0_1
<=> ! [X1] : ~ d2(X1) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f111,plain,
( ! [X1] : ~ d2(X1)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,definition,
( spl0_2
<=> ! [X2,X0] :
( ~ c(X0)
| ~ d2(X2)
| c(f(X0,X2))
| d1(f(X0,X2)) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f114,plain,
( ! [X2,X0] :
( d1(f(X0,X2))
| ~ d2(X2)
| c(f(X0,X2))
| ~ c(X0) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f115,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f108,f113,f110]) ).
fof(f117,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f111,f8]) ).
fof(f119,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f117]) ).
fof(f225,definition,
( spl0_11
<=> ! [X2,X1] :
( ~ c(X1)
| ~ c(X2)
| d1(f(X2,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f226,plain,
( ! [X2,X1] :
( d1(f(X2,X1))
| ~ c(X2)
| ~ c(X1) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f238,plain,
( ! [X2,X0,X1] :
( ~ d1(X0)
| ~ c(X1)
| ~ c(f(X2,X0))
| ~ c(X1)
| ~ c(X2) )
| ~ spl0_11 ),
inference(resolution,[],[f33,f226]) ).
fof(f242,plain,
( ! [X2,X0,X1] :
( ~ d1(X0)
| ~ c(X1)
| ~ c(f(X2,X0))
| ~ c(X2) )
| ~ spl0_11 ),
inference(duplicate_literal_removal,[],[f238]) ).
fof(f244,definition,
( spl0_12
<=> ! [X1] : ~ c(X1) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f245,plain,
( ! [X1] : ~ c(X1)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f247,definition,
( spl0_13
<=> ! [X2,X0] :
( ~ d1(X0)
| ~ c(X2)
| ~ c(f(X2,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f248,plain,
( ! [X2,X0] :
( ~ c(f(X2,X0))
| ~ c(X2)
| ~ d1(X0) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f249,plain,
( spl0_12
| spl0_13
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f242,f225,f247,f244]) ).
fof(f254,plain,
( $false
| ~ spl0_12 ),
inference(resolution,[],[f245,f6]) ).
fof(f255,plain,
~ spl0_12,
inference(avatar_contradiction_clause,[],[f254]) ).
fof(f302,plain,
( ! [X2,X0,X1] :
( ~ c(X0)
| ~ d1(X1)
| ~ c(f(X1,X2))
| ~ c(X2)
| ~ c(X0) )
| ~ spl0_11 ),
inference(resolution,[],[f40,f226]) ).
fof(f304,plain,
( ! [X2,X0,X1] :
( ~ c(X0)
| ~ d1(X1)
| ~ c(f(X1,X2))
| ~ c(X2) )
| ~ spl0_11 ),
inference(duplicate_literal_removal,[],[f302]) ).
fof(f306,definition,
( spl0_16
<=> ! [X2,X1] :
( ~ d1(X1)
| ~ c(X2)
| ~ c(f(X1,X2)) ) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f307,plain,
( ! [X2,X1] :
( ~ c(f(X1,X2))
| ~ c(X2)
| ~ d1(X1) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f308,plain,
( spl0_16
| spl0_12
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f304,f225,f244,f306]) ).
fof(f442,plain,
! [X2,X0,X1] :
( ~ d2(X0)
| ~ c(X1)
| d1(f(X2,X1))
| c(f(X2,X1))
| ~ d2(X0)
| ~ d2(X2) ),
inference(resolution,[],[f50,f11]) ).
fof(f448,plain,
! [X2,X0,X1] :
( ~ d2(X0)
| ~ c(X1)
| d1(f(X2,X1))
| c(f(X2,X1))
| ~ d2(X2) ),
inference(duplicate_literal_removal,[],[f442]) ).
fof(f454,definition,
( spl0_17
<=> ! [X2,X1] :
( ~ c(X1)
| ~ d2(X2)
| c(f(X2,X1))
| d1(f(X2,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f455,plain,
( ! [X2,X1] :
( d1(f(X2,X1))
| ~ d2(X2)
| c(f(X2,X1))
| ~ c(X1) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f454]) ).
fof(f456,plain,
( spl0_17
| spl0_1 ),
inference(avatar_split_clause,[],[f448,f110,f454]) ).
fof(f534,plain,
( ! [X2,X0,X1] :
( ~ d1(f(X1,X2))
| ~ c(X0)
| ~ d1(f(X0,X1))
| ~ d1(X2) )
| ~ spl0_13 ),
inference(resolution,[],[f248,f26]) ).
fof(f546,plain,
( ! [X2,X0,X1] :
( ~ d1(f(X0,X1))
| ~ c(X2)
| ~ c(f(X0,f(X1,X2))) )
| ~ spl0_16 ),
inference(superposition,[],[f307,f1]) ).
fof(f587,plain,
( ! [X2,X0,X1] :
( ~ c(X0)
| ~ c(f(X1,f(X2,X0)))
| ~ d2(X1)
| c(f(X1,X2))
| ~ c(X2) )
| ~ spl0_16
| ~ spl0_17 ),
inference(resolution,[],[f546,f455]) ).
fof(f592,plain,
( ! [X2,X0,X1] :
( ~ d2(X1)
| ~ c(f(X1,f(X2,X0)))
| ~ c(X0)
| ~ c(X2) )
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f587,f23]) ).
fof(f620,plain,
( ! [X0,X1] :
( ~ c(f(a3,f(X0,X1)))
| ~ c(X1)
| ~ c(X0) )
| ~ spl0_16
| ~ spl0_17 ),
inference(resolution,[],[f592,f8]) ).
fof(f631,plain,
( ! [X0,X1] :
( ~ c(X0)
| ~ c(X1)
| ~ d2(a3)
| ~ d2(f(X1,X0)) )
| ~ spl0_16
| ~ spl0_17 ),
inference(resolution,[],[f620,f11]) ).
fof(f633,plain,
( ! [X0,X1] :
( ~ d2(f(X1,X0))
| ~ c(X1)
| ~ c(X0) )
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f631,f8]) ).
fof(f634,plain,
( ! [X0,X1] :
( ~ c(X0)
| ~ c(X1)
| d1(f(X0,X1))
| ~ c(X0)
| ~ c(X1) )
| ~ spl0_16
| ~ spl0_17 ),
inference(resolution,[],[f633,f9]) ).
fof(f638,plain,
( ! [X0,X1] :
( ~ c(X1)
| ~ c(X0)
| d1(f(X0,X1)) )
| ~ spl0_16
| ~ spl0_17 ),
inference(duplicate_literal_removal,[],[f634]) ).
fof(f646,plain,
( ! [X0] :
( ~ c(X0)
| d1(f(X0,a1)) )
| ~ spl0_16
| ~ spl0_17 ),
inference(resolution,[],[f638,f6]) ).
fof(f648,plain,
( ! [X0,X1] :
( d1(f(f(X0,X1),a1))
| ~ d2(X0)
| ~ d2(X1) )
| ~ spl0_16
| ~ spl0_17 ),
inference(resolution,[],[f646,f11]) ).
fof(f658,plain,
( ! [X0,X1] :
( ~ d2(X1)
| ~ d2(X0)
| d1(f(X0,f(X1,a1))) )
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f648,f1]) ).
fof(f699,plain,
( ! [X0] :
( ~ d2(X0)
| d1(f(X0,f(a3,a1))) )
| ~ spl0_16
| ~ spl0_17 ),
inference(resolution,[],[f658,f8]) ).
fof(f705,plain,
( d1(f(a3,f(a3,a1)))
| ~ spl0_16
| ~ spl0_17 ),
inference(resolution,[],[f699,f8]) ).
fof(f711,plain,
( ! [X0] :
( ~ c(a1)
| ~ d1(X0)
| ~ c(f(X0,f(a3,a3))) )
| ~ spl0_16
| ~ spl0_17 ),
inference(resolution,[],[f705,f53]) ).
fof(f715,plain,
( ! [X0] :
( ~ c(f(a3,a1))
| ~ d1(X0)
| ~ c(f(X0,a3)) )
| ~ spl0_16
| ~ spl0_17 ),
inference(resolution,[],[f705,f40]) ).
fof(f717,plain,
( ! [X0] :
( ~ c(X0)
| ~ d1(f(X0,a3))
| ~ d1(f(a3,a1)) )
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(resolution,[],[f705,f534]) ).
fof(f726,definition,
( spl0_20
<=> ! [X0] :
( ~ d1(X0)
| ~ c(f(X0,a3)) ) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f727,plain,
( ! [X0] :
( ~ c(f(X0,a3))
| ~ d1(X0) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f726]) ).
fof(f729,definition,
( spl0_21
<=> d1(f(a3,a1)) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f731,plain,
( ~ d1(f(a3,a1))
| spl0_21 ),
inference(avatar_component_clause,[],[f729]) ).
fof(f735,definition,
( spl0_22
<=> ! [X0] :
( ~ c(X0)
| ~ d1(f(X0,a3)) ) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f736,plain,
( ! [X0] :
( ~ d1(f(X0,a3))
| ~ c(X0) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f735]) ).
fof(f737,plain,
( ~ spl0_21
| spl0_22
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f717,f454,f306,f247,f735,f729]) ).
fof(f739,definition,
( spl0_23
<=> c(f(a3,a1)) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f741,plain,
( ~ c(f(a3,a1))
| spl0_23 ),
inference(avatar_component_clause,[],[f739]) ).
fof(f742,plain,
( spl0_20
| ~ spl0_23
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f715,f454,f306,f739,f726]) ).
fof(f744,definition,
( spl0_24
<=> c(f(a3,a3)) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f745,plain,
( c(f(a3,a3))
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f744]) ).
fof(f746,plain,
( ~ c(f(a3,a3))
| spl0_24 ),
inference(avatar_component_clause,[],[f744]) ).
fof(f751,plain,
( ! [X0] :
( ~ c(f(X0,f(a3,a3)))
| ~ d1(X0) )
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f711,f6]) ).
fof(f759,plain,
( ! [X0] :
( ~ c(X0)
| ~ d2(a3)
| c(f(X0,a3))
| ~ c(X0) )
| ~ spl0_2
| ~ spl0_22 ),
inference(resolution,[],[f736,f114]) ).
fof(f761,plain,
( ! [X0] :
( ~ c(X0)
| ~ d2(a3)
| c(f(X0,a3)) )
| ~ spl0_2
| ~ spl0_22 ),
inference(duplicate_literal_removal,[],[f759]) ).
fof(f762,plain,
( ! [X0] :
( ~ c(X0)
| c(f(X0,a3)) )
| ~ spl0_2
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f761,f8]) ).
fof(f778,plain,
( c(f(a1,a3))
| ~ spl0_2
| ~ spl0_22 ),
inference(resolution,[],[f762,f6]) ).
fof(f801,plain,
( c(f(f(a1,a3),a3))
| ~ spl0_2
| ~ spl0_22 ),
inference(resolution,[],[f778,f762]) ).
fof(f805,plain,
( c(f(a1,f(a3,a3)))
| ~ spl0_2
| ~ spl0_22 ),
inference(forward_demodulation,[],[f801,f1]) ).
fof(f810,plain,
( ~ c(a1)
| ~ c(f(a3,a3))
| ~ spl0_2
| ~ spl0_22 ),
inference(resolution,[],[f805,f15]) ).
fof(f824,plain,
( ~ c(f(a3,a3))
| ~ spl0_2
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f810,f6]) ).
fof(f836,plain,
( ~ d2(a3)
| ~ d2(a3)
| ~ spl0_2
| ~ spl0_22 ),
inference(resolution,[],[f824,f11]) ).
fof(f837,plain,
( ~ d2(a3)
| ~ spl0_2
| ~ spl0_22 ),
inference(duplicate_literal_removal,[],[f836]) ).
fof(f839,plain,
( $false
| ~ spl0_2
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f837,f8]) ).
fof(f840,plain,
( ~ spl0_2
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f839]) ).
fof(f841,plain,
( ~ d2(a3)
| c(f(a3,a1))
| ~ c(a1)
| ~ spl0_17
| spl0_21 ),
inference(resolution,[],[f731,f455]) ).
fof(f843,plain,
( c(f(a3,a1))
| ~ c(a1)
| ~ spl0_17
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f841,f8]) ).
fof(f844,plain,
( c(f(a3,a1))
| ~ spl0_17
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f843,f6]) ).
fof(f897,plain,
( ! [X0] :
( ~ d1(X0)
| ~ d2(f(X0,a3))
| ~ d2(a3) )
| ~ spl0_16
| ~ spl0_17 ),
inference(resolution,[],[f751,f25]) ).
fof(f902,plain,
( ! [X0] :
( ~ d2(f(X0,a3))
| ~ d1(X0) )
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f897,f8]) ).
fof(f904,plain,
( ! [X0] :
( ~ d1(X0)
| d1(f(X0,a3))
| c(f(X0,a3)) )
| ~ spl0_16
| ~ spl0_17 ),
inference(resolution,[],[f902,f2]) ).
fof(f906,plain,
( ! [X0] :
( ~ d1(X0)
| d1(f(X0,a3)) )
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f904,f727]) ).
fof(f907,plain,
( d1(f(a2,a3))
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20 ),
inference(resolution,[],[f906,f7]) ).
fof(f927,plain,
( d1(f(f(a2,a3),a3))
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20 ),
inference(resolution,[],[f907,f906]) ).
fof(f933,plain,
( d1(f(a2,f(a3,a3)))
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[],[f927,f1]) ).
fof(f1001,plain,
( ! [X0] :
( ~ c(f(a3,a3))
| ~ d1(X0)
| ~ c(f(X0,a2)) )
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20 ),
inference(resolution,[],[f933,f40]) ).
fof(f1018,definition,
( spl0_30
<=> ! [X0] :
( ~ d1(X0)
| ~ c(f(X0,a2)) ) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f1019,plain,
( ! [X0] :
( ~ c(f(X0,a2))
| ~ d1(X0) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f1018]) ).
fof(f1020,plain,
( spl0_30
| ~ spl0_24
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f1001,f726,f454,f306,f744,f1018]) ).
fof(f1024,plain,
( ! [X0] :
( ~ d1(X0)
| ~ d1(X0)
| ~ d1(a2) )
| ~ spl0_30 ),
inference(resolution,[],[f1019,f10]) ).
fof(f1027,plain,
( ! [X0] :
( ~ d1(X0)
| ~ d1(a2) )
| ~ spl0_30 ),
inference(duplicate_literal_removal,[],[f1024]) ).
fof(f1028,plain,
( ! [X0] : ~ d1(X0)
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f1027,f7]) ).
fof(f1029,plain,
( $false
| ~ spl0_30 ),
inference(resolution,[],[f1028,f7]) ).
fof(f1044,plain,
~ spl0_30,
inference(avatar_contradiction_clause,[],[f1029]) ).
fof(f1060,plain,
( ~ d2(a3)
| ~ d2(a3)
| spl0_24 ),
inference(resolution,[],[f746,f11]) ).
fof(f1061,plain,
( ~ d2(a3)
| spl0_24 ),
inference(duplicate_literal_removal,[],[f1060]) ).
fof(f1062,plain,
( $false
| spl0_24 ),
inference(forward_subsumption_resolution,[],[f1061,f8]) ).
fof(f1063,plain,
spl0_24,
inference(avatar_contradiction_clause,[],[f1062]) ).
fof(f1064,plain,
( $false
| ~ spl0_17
| spl0_21
| spl0_23 ),
inference(forward_subsumption_resolution,[],[f741,f844]) ).
fof(f1065,plain,
( ~ spl0_17
| spl0_21
| spl0_23 ),
inference(avatar_contradiction_clause,[],[f1064]) ).
fof(f2906,plain,
! [X2,X3,X0,X1] :
( ~ c(X0)
| d1(f(X0,X1))
| ~ c(X1)
| ~ d1(f(X1,X2))
| ~ d1(X3)
| d1(f(X2,X3))
| c(f(X2,X3)) ),
inference(resolution,[],[f56,f2]) ).
fof(f2908,plain,
! [X2,X3,X0,X1] :
( ~ d1(f(X1,X2))
| d1(f(X0,X1))
| ~ c(X1)
| ~ c(X0)
| ~ d1(X3)
| d1(f(X2,X3)) ),
inference(forward_subsumption_resolution,[],[f2906,f33]) ).
fof(f2952,plain,
( ! [X2,X3,X0,X1] :
( d1(f(X0,X1))
| ~ c(X1)
| ~ c(X0)
| ~ d1(X2)
| d1(f(X3,X2))
| ~ d2(X3)
| c(f(X1,X3))
| ~ c(X1) )
| ~ spl0_2 ),
inference(resolution,[],[f2908,f114]) ).
fof(f2954,plain,
( ! [X2,X3,X0,X1] :
( d1(f(X0,X1))
| ~ c(X1)
| ~ c(X0)
| ~ d1(X2)
| d1(f(X3,X2))
| ~ d2(X3)
| c(f(X1,X3)) )
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f2952]) ).
fof(f2955,plain,
( ! [X2,X3,X0,X1] :
( d1(f(X0,X1))
| ~ c(X1)
| ~ c(X0)
| ~ d1(X2)
| d1(f(X3,X2))
| ~ d2(X3) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f2954,f47]) ).
fof(f2959,definition,
( spl0_50
<=> ! [X2,X3] :
( ~ d1(X2)
| ~ d2(X3)
| d1(f(X3,X2)) ) ),
introduced(definition,[new_symbols(definition,[spl0_50])],[avatar_definition]) ).
fof(f2960,plain,
( ! [X2,X3] :
( ~ d2(X3)
| ~ d1(X2)
| d1(f(X3,X2)) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f2959]) ).
fof(f2961,plain,
( spl0_50
| spl0_11
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f2955,f113,f225,f2959]) ).
fof(f3225,plain,
( ! [X0] :
( ~ d1(X0)
| d1(f(a3,X0)) )
| ~ spl0_50 ),
inference(resolution,[],[f2960,f8]) ).
fof(f3231,plain,
( d1(f(a3,a2))
| ~ spl0_50 ),
inference(resolution,[],[f3225,f7]) ).
fof(f3247,plain,
( d1(f(a3,f(a3,a2)))
| ~ spl0_50 ),
inference(resolution,[],[f3231,f3225]) ).
fof(f3252,plain,
( ! [X0] :
( ~ d1(X0)
| ~ c(f(a3,a3))
| ~ c(f(a2,X0)) )
| ~ spl0_50 ),
inference(resolution,[],[f3247,f48]) ).
fof(f3272,plain,
( ! [X0] :
( ~ c(f(a2,X0))
| ~ d1(X0) )
| ~ spl0_24
| ~ spl0_50 ),
inference(forward_subsumption_resolution,[],[f3252,f745]) ).
fof(f3280,plain,
( ! [X0] :
( ~ d1(X0)
| ~ d1(a2)
| ~ d1(X0) )
| ~ spl0_24
| ~ spl0_50 ),
inference(resolution,[],[f3272,f10]) ).
fof(f3286,plain,
( ! [X0] :
( ~ d1(X0)
| ~ d1(a2) )
| ~ spl0_24
| ~ spl0_50 ),
inference(duplicate_literal_removal,[],[f3280]) ).
fof(f3287,plain,
( ! [X0] : ~ d1(X0)
| ~ spl0_24
| ~ spl0_50 ),
inference(forward_subsumption_resolution,[],[f3286,f7]) ).
fof(f3288,plain,
( $false
| ~ spl0_24
| ~ spl0_50 ),
inference(resolution,[],[f3287,f7]) ).
fof(f3303,plain,
( ~ spl0_24
| ~ spl0_50 ),
inference(avatar_contradiction_clause,[],[f3288]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f115]) ).
cnf(s2,plain,
~ spl0_1,
inference(sat_conversion,[],[f119]) ).
cnf(s13,plain,
( ~ spl0_11
| spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f249]) ).
cnf(s14,plain,
~ spl0_12,
inference(sat_conversion,[],[f255]) ).
cnf(s21,plain,
( ~ spl0_11
| spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f308]) ).
cnf(s24,plain,
( spl0_1
| spl0_17 ),
inference(sat_conversion,[],[f456]) ).
cnf(s30,plain,
( ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21
| spl0_22 ),
inference(sat_conversion,[],[f737]) ).
cnf(s31,plain,
( ~ spl0_16
| ~ spl0_17
| spl0_20
| ~ spl0_23 ),
inference(sat_conversion,[],[f742]) ).
cnf(s34,plain,
( ~ spl0_2
| ~ spl0_22 ),
inference(sat_conversion,[],[f840]) ).
cnf(s39,plain,
( ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_24
| spl0_30 ),
inference(sat_conversion,[],[f1020]) ).
cnf(s46,plain,
~ spl0_30,
inference(sat_conversion,[],[f1044]) ).
cnf(s47,plain,
spl0_24,
inference(sat_conversion,[],[f1063]) ).
cnf(s48,plain,
( ~ spl0_17
| spl0_21
| spl0_23 ),
inference(sat_conversion,[],[f1065]) ).
cnf(s107,plain,
( ~ spl0_2
| spl0_11
| spl0_50 ),
inference(sat_conversion,[],[f2961]) ).
cnf(s125,plain,
( ~ spl0_24
| ~ spl0_50 ),
inference(sat_conversion,[],[f3303]) ).
cnf(s127,plain,
~ spl0_50,
inference(rat,[],[s125,s47]) ).
cnf(s128,plain,
( ~ spl0_16
| ~ spl0_17
| ~ spl0_20 ),
inference(rat,[],[s39,s46,s47]) ).
cnf(s130,plain,
( ~ spl0_11
| spl0_13 ),
inference(rat,[],[s13,s14]) ).
cnf(s132,plain,
spl0_17,
inference(rat,[],[s24,s2]) ).
cnf(s134,plain,
spl0_2,
inference(rat,[],[s1,s2]) ).
cnf(s135,plain,
spl0_11,
inference(rat,[],[s107,s127,s134]) ).
cnf(s136,plain,
~ spl0_22,
inference(rat,[],[s34,s134]) ).
cnf(s139,plain,
spl0_16,
inference(rat,[],[s21,s14,s135]) ).
cnf(s140,plain,
spl0_13,
inference(rat,[],[s130,s135]) ).
cnf(s141,plain,
~ spl0_20,
inference(rat,[],[s128,s132,s139]) ).
cnf(s144,plain,
~ spl0_21,
inference(rat,[],[s30,s136,s139,s132,s140]) ).
cnf(s145,plain,
~ spl0_23,
inference(rat,[],[s31,s139,s132,s141]) ).
cnf(s148,plain,
$false,
inference(rat,[],[s48,s132,s145,s144]) ).
fof(f3304,plain,
$false,
inference(avatar_sat_refutation,[],[s148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG012-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.27 % Computer : n010.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Mon Sep 28 19:17:47 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.26/0.31 Running first-order model finding
% 0.26/0.31 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
% 1.83/0.61 % (2230570)Will run a generic schedule for satisfiability detection.
% 1.83/0.61 % (2230575)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4265710941_2999 on theBenchmark for (2999ds/0Mi)
% 1.83/0.61 % TRYING [1]
% 1.83/0.61 % TRYING [2]
% 1.83/0.61 % TRYING [3]
% 1.83/0.61 % TRYING [4]
% 1.83/0.61 % (2230576)% WARNING: option uhcvi not known.
% 1.83/0.61 % TRYING [5]
% 1.83/0.61 % (2230578)dis+10_1_sil=32000:sp=arity:random_seed=129419577:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.83/0.61 % (2230576)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1094952626:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.83/0.61 % (2230577)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2301758717:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.83/0.61 % (2230579)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2405261259:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.83/0.61 % (2230581)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2586998661:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.83/0.61 % (2230580)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3357016795:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.83/0.61 % TRYING [6]
% 1.83/0.61 % (2230578)Instruction limit reached!
% 1.83/0.61 % (2230578)------------------------------
% 1.83/0.61 % (2230578)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (2230578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (2230578)CaDiCaL version: 2.1.3
% 1.83/0.61 % (2230578)Termination reason: Instruction limit
% 1.83/0.61 % (2230578)Termination phase: Saturation
% 1.83/0.61 % (2230578)Time elapsed: 0.101 s
% 1.83/0.61 % (2230578)Peak memory usage: 11 MB
% 1.83/0.61 % (2230578)Instructions burned: 103 (million)
% 1.83/0.61 % (2230579)Instruction limit reached!
% 1.83/0.61 % (2230579)------------------------------
% 1.83/0.61 % (2230579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (2230579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (2230579)CaDiCaL version: 2.1.3
% 1.83/0.61 % (2230579)Termination reason: Instruction limit
% 1.83/0.61 % (2230579)Termination phase: Saturation
% 1.83/0.61 % (2230579)Time elapsed: 0.103 s
% 1.83/0.61 % (2230579)Peak memory usage: 11 MB
% 1.83/0.61 % (2230579)Instructions burned: 117 (million)
% 1.83/0.61 % (2230590)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3517673856:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.83/0.61 % (2230589)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=214770102:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 1.83/0.61 % (2230580)Instruction limit reached!
% 1.83/0.61 % (2230580)------------------------------
% 1.83/0.61 % (2230580)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (2230580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (2230580)CaDiCaL version: 2.1.3
% 1.83/0.61 % (2230580)Termination reason: Instruction limit
% 1.83/0.61 % (2230580)Termination phase: Saturation
% 1.83/0.61 % (2230580)Time elapsed: 0.122 s
% 1.83/0.61 % (2230580)Peak memory usage: 12 MB
% 1.83/0.61 % (2230580)Instructions burned: 131 (million)
% 1.83/0.61 % TRYING [1]
% 1.83/0.61 % TRYING [2]
% 1.83/0.61 % TRYING [3]
% 1.83/0.61 % TRYING [4]
% 1.83/0.61 % TRYING [5]
% 1.83/0.61 % TRYING [7]
% 1.83/0.61 % (2230593)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1220710158:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.83/0.61 % (2230581)Instruction limit reached!
% 1.83/0.61 % (2230581)------------------------------
% 1.83/0.61 % (2230581)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (2230581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (2230581)CaDiCaL version: 2.1.3
% 1.83/0.61 % (2230581)Termination reason: Instruction limit
% 1.83/0.61 % (2230581)Termination phase: Saturation
% 1.83/0.61 % (2230581)Time elapsed: 0.171 s
% 1.83/0.61 % (2230581)Peak memory usage: 13 MB
% 1.83/0.61 % (2230581)Instructions burned: 159 (million)
% 1.83/0.61 % TRYING [6]
% 1.83/0.61 % (2230595)ott-21_1_sil=16000:fs=off:random_seed=1921951155:i=180:av=off:fsr=off_2997 on theBenchmark for (2997ds/180Mi)
% 1.83/0.61 % (2230593) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2230570-2230593"...
% 1.83/0.61 % (2230593)...printing done.
% 1.83/0.61 % (2230593)Refutation found. Thanks to Tanya!
% 1.83/0.61 % SZS status Unsatisfiable for theBenchmark
% 1.83/0.61 % SZS output start Proof for theBenchmark
% See solution above
% 1.83/0.61 % (2230593)------------------------------
% 1.83/0.61 % (2230593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (2230593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (2230593)CaDiCaL version: 2.1.3
% 1.83/0.61 % (2230593)Termination reason: Refutation
% 1.83/0.61 % (2230593)Time elapsed: 0.087 s
% 1.83/0.61 % (2230593)Peak memory usage: 13 MB
% 1.83/0.61 % (2230593)Instructions burned: 150 (million)
% 1.83/0.61 % (2230570)Success in time 0.286 s
% 1.83/0.61 % Vampire exiting
%------------------------------------------------------------------------------