%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC023+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 : n005.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 01:04:20 PM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 86 ( 17 unt; 8 def)
% Number of atoms : 275 ( 39 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 306 ( 117 ~; 123 |; 45 &)
% ( 10 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 34 ( 0 sgn 22 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f46,axiom,
! [X0] :
( ssList(X0)
=> ( frontsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax46) ).
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)
& frontsegP(X1,X4)
& frontsegP(X0,X4) )
| ( ! [X5] :
( ssList(X5)
=> ( ~ neq(X5,nil)
| ~ frontsegP(X3,X5)
| ~ frontsegP(X2,X5) ) )
& ( nil != X3
| nil != 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)
& frontsegP(X1,X4)
& frontsegP(X0,X4) )
| ( ! [X5] :
( ssList(X5)
=> ( ~ neq(X5,nil)
| ~ frontsegP(X3,X5)
| ~ frontsegP(X2,X5) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f158,plain,
! [X0] :
( ( frontsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ frontsegP(X1,X4)
| ~ frontsegP(X0,X4) )
& ( ? [X5] :
( neq(X5,nil)
& frontsegP(X3,X5)
& frontsegP(X2,X5)
& ssList(X5) )
| ( nil = X3
& nil = 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)
| ~ frontsegP(X1,X4)
| ~ frontsegP(X0,X4) )
& ( ? [X5] :
( neq(X5,nil)
& frontsegP(X3,X5)
& frontsegP(X2,X5)
& ssList(X5) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f283,plain,
! [X0] :
( ( ( frontsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ frontsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f158]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& neq(sK54,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ frontsegP(sK54,X4)
| ~ frontsegP(sK53,X4) )
& ( ( neq(sK57,nil)
& frontsegP(sK56,sK57)
& frontsegP(sK55,sK57)
& ssList(sK57) )
| ( nil = sK56
& nil = sK55 ) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X5,sK57)],[f222]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f430,plain,
! [X0] :
( frontsegP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f283]) ).
fof(f500,plain,
( ssList(sK57)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( ssList(sK57)
| nil = sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( frontsegP(sK55,sK57)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
( frontsegP(sK55,sK57)
| nil = sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( frontsegP(sK56,sK57)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
( frontsegP(sK56,sK57)
| nil = sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
( neq(sK57,nil)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
( neq(sK57,nil)
| nil = sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ frontsegP(sK54,X4)
| ~ frontsegP(sK53,X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
neq(sK54,nil),
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f512,plain,
neq(sK56,nil),
inference(definition_unfolding,[],[f509,f511]) ).
fof(f513,plain,
! [X4] :
( ~ frontsegP(sK56,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| ~ frontsegP(sK55,X4) ),
inference(definition_unfolding,[],[f508,f511,f510]) ).
fof(f533,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f430]) ).
fof(f551,definition,
( spl58_1
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl58_1])],[avatar_definition]) ).
fof(f553,plain,
( nil = sK55
| ~ spl58_1 ),
inference(avatar_component_clause,[],[f551]) ).
fof(f555,definition,
( spl58_2
<=> ssList(sK57) ),
introduced(definition,[new_symbols(definition,[spl58_2])],[avatar_definition]) ).
fof(f557,plain,
( ssList(sK57)
| ~ spl58_2 ),
inference(avatar_component_clause,[],[f555]) ).
fof(f558,plain,
( spl58_1
| spl58_2 ),
inference(avatar_split_clause,[],[f500,f555,f551]) ).
fof(f560,definition,
( spl58_3
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl58_3])],[avatar_definition]) ).
fof(f562,plain,
( nil = sK56
| ~ spl58_3 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f563,plain,
( spl58_3
| spl58_2 ),
inference(avatar_split_clause,[],[f501,f555,f560]) ).
fof(f565,definition,
( spl58_4
<=> frontsegP(sK55,sK57) ),
introduced(definition,[new_symbols(definition,[spl58_4])],[avatar_definition]) ).
fof(f567,plain,
( frontsegP(sK55,sK57)
| ~ spl58_4 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f568,plain,
( spl58_1
| spl58_4 ),
inference(avatar_split_clause,[],[f502,f565,f551]) ).
fof(f569,plain,
( spl58_3
| spl58_4 ),
inference(avatar_split_clause,[],[f503,f565,f560]) ).
fof(f571,definition,
( spl58_5
<=> frontsegP(sK56,sK57) ),
introduced(definition,[new_symbols(definition,[spl58_5])],[avatar_definition]) ).
fof(f573,plain,
( frontsegP(sK56,sK57)
| ~ spl58_5 ),
inference(avatar_component_clause,[],[f571]) ).
fof(f574,plain,
( spl58_1
| spl58_5 ),
inference(avatar_split_clause,[],[f504,f571,f551]) ).
fof(f575,plain,
( spl58_3
| spl58_5 ),
inference(avatar_split_clause,[],[f505,f571,f560]) ).
fof(f577,definition,
( spl58_6
<=> neq(sK57,nil) ),
introduced(definition,[new_symbols(definition,[spl58_6])],[avatar_definition]) ).
fof(f579,plain,
( neq(sK57,nil)
| ~ spl58_6 ),
inference(avatar_component_clause,[],[f577]) ).
fof(f580,plain,
( spl58_1
| spl58_6 ),
inference(avatar_split_clause,[],[f506,f577,f551]) ).
fof(f581,plain,
( spl58_3
| spl58_6 ),
inference(avatar_split_clause,[],[f507,f577,f560]) ).
fof(f583,definition,
( spl58_7
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl58_7])],[avatar_definition]) ).
fof(f584,plain,
( ssList(nil)
| ~ spl58_7 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f612,definition,
( spl58_13
<=> frontsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[spl58_13])],[avatar_definition]) ).
fof(f614,plain,
( frontsegP(nil,nil)
| ~ spl58_13 ),
inference(avatar_component_clause,[],[f612]) ).
fof(f615,plain,
( ~ spl58_7
| spl58_13 ),
inference(avatar_split_clause,[],[f533,f612,f583]) ).
fof(f616,plain,
spl58_7,
inference(avatar_split_clause,[],[f389,f583]) ).
fof(f617,plain,
( ~ neq(sK57,nil)
| ~ ssList(sK57)
| ~ frontsegP(sK55,sK57)
| ~ spl58_5 ),
inference(resolution,[],[f513,f573]) ).
fof(f618,plain,
( ~ ssList(sK57)
| ~ frontsegP(sK55,sK57)
| ~ spl58_5
| ~ spl58_6 ),
inference(forward_subsumption_resolution,[],[f617,f579]) ).
fof(f619,plain,
( ~ frontsegP(sK55,sK57)
| ~ spl58_2
| ~ spl58_5
| ~ spl58_6 ),
inference(forward_subsumption_resolution,[],[f618,f557]) ).
fof(f620,plain,
( $false
| ~ spl58_2
| ~ spl58_4
| ~ spl58_5
| ~ spl58_6 ),
inference(forward_subsumption_resolution,[],[f619,f567]) ).
fof(f621,plain,
( ~ spl58_2
| ~ spl58_4
| ~ spl58_5
| ~ spl58_6 ),
inference(avatar_contradiction_clause,[],[f620]) ).
fof(f625,plain,
( ! [X0] :
( ~ frontsegP(nil,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| ~ frontsegP(sK55,X0) )
| ~ spl58_3 ),
inference(superposition,[],[f513,f562]) ).
fof(f626,plain,
( neq(nil,nil)
| ~ spl58_3 ),
inference(superposition,[],[f512,f562]) ).
fof(f629,plain,
( ! [X0] :
( ~ frontsegP(nil,X0)
| ~ frontsegP(nil,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) )
| ~ spl58_1
| ~ spl58_3 ),
inference(forward_demodulation,[],[f625,f553]) ).
fof(f630,plain,
( ! [X0] :
( ~ frontsegP(nil,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) )
| ~ spl58_1
| ~ spl58_3 ),
inference(duplicate_literal_removal,[],[f629]) ).
fof(f636,plain,
( ~ neq(nil,nil)
| ~ ssList(nil)
| ~ spl58_1
| ~ spl58_3
| ~ spl58_13 ),
inference(resolution,[],[f614,f630]) ).
fof(f637,plain,
( ~ ssList(nil)
| ~ spl58_1
| ~ spl58_3
| ~ spl58_13 ),
inference(forward_subsumption_resolution,[],[f636,f626]) ).
fof(f638,plain,
( $false
| ~ spl58_1
| ~ spl58_3
| ~ spl58_7
| ~ spl58_13 ),
inference(forward_subsumption_resolution,[],[f637,f584]) ).
fof(f639,plain,
( ~ spl58_1
| ~ spl58_3
| ~ spl58_7
| ~ spl58_13 ),
inference(avatar_contradiction_clause,[],[f638]) ).
cnf(s1,plain,
( spl58_1
| spl58_2 ),
inference(sat_conversion,[],[f558]) ).
cnf(s2,plain,
( spl58_2
| spl58_3 ),
inference(sat_conversion,[],[f563]) ).
cnf(s3,plain,
( spl58_1
| spl58_4 ),
inference(sat_conversion,[],[f568]) ).
cnf(s4,plain,
( spl58_3
| spl58_4 ),
inference(sat_conversion,[],[f569]) ).
cnf(s5,plain,
( spl58_1
| spl58_5 ),
inference(sat_conversion,[],[f574]) ).
cnf(s6,plain,
( spl58_3
| spl58_5 ),
inference(sat_conversion,[],[f575]) ).
cnf(s7,plain,
( spl58_1
| spl58_6 ),
inference(sat_conversion,[],[f580]) ).
cnf(s8,plain,
( spl58_3
| spl58_6 ),
inference(sat_conversion,[],[f581]) ).
cnf(s16,plain,
( ~ spl58_7
| spl58_13 ),
inference(sat_conversion,[],[f615]) ).
cnf(s17,plain,
spl58_7,
inference(sat_conversion,[],[f616]) ).
cnf(s18,plain,
( ~ spl58_2
| ~ spl58_4
| ~ spl58_5
| ~ spl58_6 ),
inference(sat_conversion,[],[f621]) ).
cnf(s22,plain,
( ~ spl58_1
| ~ spl58_3
| ~ spl58_7
| ~ spl58_13 ),
inference(sat_conversion,[],[f639]) ).
cnf(s23,plain,
spl58_13,
inference(rat,[],[s16,s17]) ).
cnf(s27,plain,
spl58_1,
inference(rat,[],[s18,s1,s3,s5,s7]) ).
cnf(s28,plain,
~ spl58_3,
inference(rat,[],[s22,s23,s17,s27]) ).
cnf(s29,plain,
spl58_6,
inference(rat,[],[s8,s28]) ).
cnf(s30,plain,
spl58_5,
inference(rat,[],[s6,s28]) ).
cnf(s31,plain,
spl58_4,
inference(rat,[],[s4,s28]) ).
cnf(s32,plain,
spl58_2,
inference(rat,[],[s2,s28]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s18,s29,s30,s31,s32]) ).
fof(f640,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC023+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n005.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 07:29:17 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 Running first-order model finding
% 0.12/0.40 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
% 0.12/0.45 % (621053)Will run a generic schedule for satisfiability detection.
% 0.12/0.45 % (621061)dis+10_1_sil=32000:sp=arity:random_seed=3740905829:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.45 % (621059)% WARNING: option uhcvi not known.
% 0.12/0.45 % (621061) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-621053-621061"...
% 0.12/0.45 % (621061)...printing done.
% 0.12/0.45 % (621061)Refutation found. Thanks to Tanya!
% 0.12/0.45 % SZS status Theorem for theBenchmark
% 0.12/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.45 % (621061)------------------------------
% 0.12/0.45 % (621061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.45 % (621061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.45 % (621061)CaDiCaL version: 2.1.3
% 0.12/0.45 % (621061)Termination reason: Refutation
% 0.12/0.45 % (621061)Time elapsed: 0.005 s
% 0.12/0.45 % (621061)Peak memory usage: 12 MB
% 0.12/0.45 % (621061)Instructions burned: 11 (million)
% 0.12/0.45 % (621053)Success in time 0.033 s
% 0.12/0.45 % Vampire exiting
%------------------------------------------------------------------------------