%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC086+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 01:04:36 PM UTC 2026
% Result : Theorem 0.15s 0.45s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 73 ( 16 unt; 6 def)
% Number of atoms : 235 ( 35 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 274 ( 112 ~; 105 |; 39 &)
% ( 8 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 33 ( 0 sgn 23 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) )
| ( ( nil != X3
| nil != X2 )
& ( ~ neq(X2,nil)
| ~ segmentP(X3,X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) )
| ( ( nil != X3
| nil != X2 )
& ( ~ neq(X2,nil)
| ~ segmentP(X3,X2) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f172,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f176,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) )
& ( ( nil = X3
& nil = X2 )
| ( neq(X2,nil)
& segmentP(X3,X2) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) )
& ( ( nil = X3
& nil = X2 )
| ( neq(X2,nil)
& segmentP(X3,X2) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f285,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f176]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& neq(sK54,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK54,X4)
| ~ segmentP(sK53,X4) )
& ( ( nil = sK56
& nil = sK55 )
| ( neq(sK55,nil)
& segmentP(sK56,sK55) ) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56)],[f222]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f440,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f444,plain,
! [X0] :
( segmentP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f498,plain,
ssList(sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( nil = sK55
| segmentP(sK56,sK55) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( nil = sK55
| neq(sK55,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( nil = sK56
| segmentP(sK56,sK55) ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
( nil = sK56
| neq(sK55,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK54,X4)
| ~ segmentP(sK53,X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
neq(sK54,nil),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
neq(sK56,nil),
inference(definition_unfolding,[],[f505,f507]) ).
fof(f509,plain,
! [X4] :
( ~ segmentP(sK56,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| ~ segmentP(sK55,X4) ),
inference(definition_unfolding,[],[f504,f507,f506]) ).
fof(f531,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f444]) ).
fof(f547,definition,
( spl57_1
<=> segmentP(sK56,sK55) ),
introduced(definition,[new_symbols(definition,[spl57_1])],[avatar_definition]) ).
fof(f549,plain,
( segmentP(sK56,sK55)
| ~ spl57_1 ),
inference(avatar_component_clause,[],[f547]) ).
fof(f551,definition,
( spl57_2
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl57_2])],[avatar_definition]) ).
fof(f553,plain,
( nil = sK55
| ~ spl57_2 ),
inference(avatar_component_clause,[],[f551]) ).
fof(f554,plain,
( spl57_1
| spl57_2 ),
inference(avatar_split_clause,[],[f500,f551,f547]) ).
fof(f556,definition,
( spl57_3
<=> neq(sK55,nil) ),
introduced(definition,[new_symbols(definition,[spl57_3])],[avatar_definition]) ).
fof(f558,plain,
( neq(sK55,nil)
| ~ spl57_3 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f559,plain,
( spl57_3
| spl57_2 ),
inference(avatar_split_clause,[],[f501,f551,f556]) ).
fof(f561,definition,
( spl57_4
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl57_4])],[avatar_definition]) ).
fof(f563,plain,
( nil = sK56
| ~ spl57_4 ),
inference(avatar_component_clause,[],[f561]) ).
fof(f564,plain,
( spl57_1
| spl57_4 ),
inference(avatar_split_clause,[],[f502,f561,f547]) ).
fof(f565,plain,
( spl57_3
| spl57_4 ),
inference(avatar_split_clause,[],[f503,f561,f556]) ).
fof(f567,definition,
( spl57_5
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl57_5])],[avatar_definition]) ).
fof(f568,plain,
( ssList(nil)
| ~ spl57_5 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f586,definition,
( spl57_9
<=> segmentP(nil,nil) ),
introduced(definition,[new_symbols(definition,[spl57_9])],[avatar_definition]) ).
fof(f588,plain,
( segmentP(nil,nil)
| ~ spl57_9 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f589,plain,
( ~ spl57_5
| spl57_9 ),
inference(avatar_split_clause,[],[f531,f586,f567]) ).
fof(f600,plain,
spl57_5,
inference(avatar_split_clause,[],[f389,f567]) ).
fof(f603,plain,
( neq(nil,nil)
| ~ spl57_4 ),
inference(superposition,[],[f508,f563]) ).
fof(f606,plain,
( ! [X4] :
( ~ segmentP(nil,X4)
| ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK55,X4) )
| ~ spl57_4 ),
inference(forward_demodulation,[],[f509,f563]) ).
fof(f607,plain,
( ! [X4] :
( ~ segmentP(nil,X4)
| ~ segmentP(nil,X4)
| ~ ssList(X4)
| ~ neq(X4,nil) )
| ~ spl57_2
| ~ spl57_4 ),
inference(forward_demodulation,[],[f606,f553]) ).
fof(f608,plain,
( ! [X4] :
( ~ segmentP(nil,X4)
| ~ ssList(X4)
| ~ neq(X4,nil) )
| ~ spl57_2
| ~ spl57_4 ),
inference(duplicate_literal_removal,[],[f607]) ).
fof(f609,plain,
( ~ ssList(nil)
| ~ neq(nil,nil)
| ~ spl57_2
| ~ spl57_4
| ~ spl57_9 ),
inference(resolution,[],[f588,f608]) ).
fof(f610,plain,
( ~ neq(nil,nil)
| ~ spl57_2
| ~ spl57_4
| ~ spl57_5
| ~ spl57_9 ),
inference(forward_subsumption_resolution,[],[f609,f568]) ).
fof(f611,plain,
( $false
| ~ spl57_2
| ~ spl57_4
| ~ spl57_5
| ~ spl57_9 ),
inference(forward_subsumption_resolution,[],[f610,f603]) ).
fof(f612,plain,
( ~ spl57_2
| ~ spl57_4
| ~ spl57_5
| ~ spl57_9 ),
inference(avatar_contradiction_clause,[],[f611]) ).
fof(f621,plain,
( ~ neq(sK55,nil)
| ~ ssList(sK55)
| ~ segmentP(sK55,sK55)
| ~ spl57_1 ),
inference(resolution,[],[f509,f549]) ).
fof(f622,plain,
( ~ ssList(sK55)
| ~ segmentP(sK55,sK55)
| ~ spl57_1
| ~ spl57_3 ),
inference(forward_subsumption_resolution,[],[f621,f558]) ).
fof(f623,plain,
( ~ segmentP(sK55,sK55)
| ~ spl57_1
| ~ spl57_3 ),
inference(forward_subsumption_resolution,[],[f622,f498]) ).
fof(f661,plain,
( ~ ssList(sK55)
| ~ spl57_1
| ~ spl57_3 ),
inference(resolution,[],[f440,f623]) ).
fof(f663,plain,
( $false
| ~ spl57_1
| ~ spl57_3 ),
inference(forward_subsumption_resolution,[],[f661,f498]) ).
fof(f664,plain,
( ~ spl57_1
| ~ spl57_3 ),
inference(avatar_contradiction_clause,[],[f663]) ).
cnf(s1,plain,
( spl57_1
| spl57_2 ),
inference(sat_conversion,[],[f554]) ).
cnf(s2,plain,
( spl57_2
| spl57_3 ),
inference(sat_conversion,[],[f559]) ).
cnf(s3,plain,
( spl57_1
| spl57_4 ),
inference(sat_conversion,[],[f564]) ).
cnf(s4,plain,
( spl57_3
| spl57_4 ),
inference(sat_conversion,[],[f565]) ).
cnf(s10,plain,
( ~ spl57_5
| spl57_9 ),
inference(sat_conversion,[],[f589]) ).
cnf(s13,plain,
spl57_5,
inference(sat_conversion,[],[f600]) ).
cnf(s16,plain,
( ~ spl57_2
| ~ spl57_4
| ~ spl57_5
| ~ spl57_9 ),
inference(sat_conversion,[],[f612]) ).
cnf(s18,plain,
( ~ spl57_1
| ~ spl57_3 ),
inference(sat_conversion,[],[f664]) ).
cnf(s21,plain,
spl57_9,
inference(rat,[],[s10,s13]) ).
cnf(s23,plain,
spl57_1,
inference(rat,[],[s16,s1,s3,s13,s21]) ).
cnf(s24,plain,
~ spl57_3,
inference(rat,[],[s18,s23]) ).
cnf(s25,plain,
spl57_4,
inference(rat,[],[s4,s24]) ).
cnf(s26,plain,
spl57_2,
inference(rat,[],[s2,s24]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s16,s21,s13,s25,s26]) ).
fof(f667,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC086+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n015.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 07:52:01 UTC 2026
% 0.15/0.37 % CPUTime :
% 0.15/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.40 Running first-order model finding
% 0.15/0.40 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
% 0.15/0.45 % (2456671)Will run a generic schedule for satisfiability detection.
% 0.15/0.45 % (2456679)dis+10_1_sil=32000:sp=arity:random_seed=1538381592:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.45 % (2456679) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2456671-2456679"...
% 0.15/0.45 % (2456679)...printing done.
% 0.15/0.45 % (2456679)Refutation found. Thanks to Tanya!
% 0.15/0.45 % SZS status Theorem for theBenchmark
% 0.15/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.45 % (2456679)------------------------------
% 0.15/0.45 % (2456679)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.45 % (2456679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.45 % (2456679)CaDiCaL version: 2.1.3
% 0.15/0.45 % (2456679)Termination reason: Refutation
% 0.15/0.45 % (2456679)Time elapsed: 0.005 s
% 0.15/0.45 % (2456679)Peak memory usage: 12 MB
% 0.15/0.45 % (2456679)Instructions burned: 12 (million)
% 0.15/0.45 % (2456671)Success in time 0.038 s
% 0.15/0.45 % Vampire exiting
%------------------------------------------------------------------------------