%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC294+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 : n008.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 01:05:26 PM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 69 ( 20 unt; 5 def)
% Number of atoms : 173 ( 25 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 181 ( 77 ~; 70 |; 12 &)
% ( 11 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 26 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(f68,axiom,
! [X0] :
( ssItem(X0)
=> strictorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax68) ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax69) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ~ segmentP(X3,X2)
| strictorderedP(X0)
| ( ~ singletonP(X2)
& neq(X3,nil) ) ) ) ) ),
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
| ~ segmentP(X3,X2)
| strictorderedP(X0)
| ( ~ singletonP(X2)
& neq(X3,nil) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f100,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f176,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f182,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& segmentP(X3,X2)
& ~ strictorderedP(X0)
& ( singletonP(X2)
| ~ neq(X3,nil) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f231,plain,
! [X0] :
( ~ singletonP(X0)
| cons(sK4(X0),nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f232,plain,
! [X0] :
( ~ singletonP(X0)
| ssItem(sK4(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f302,plain,
! [X0,X1] :
( neq(X0,X1)
| ~ ssList(X1)
| X0 = X1
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f305,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f360,plain,
! [X0] :
( ~ segmentP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f176]) ).
fof(f373,plain,
! [X0] :
( ~ ssItem(X0)
| strictorderedP(cons(X0,nil)) ),
inference(cnf_transformation,[],[f182]) ).
fof(f374,plain,
strictorderedP(nil),
inference(cnf_transformation,[],[f69]) ).
fof(f410,plain,
( ~ neq(sK50,nil)
| singletonP(sK49) ),
inference(cnf_transformation,[],[f221]) ).
fof(f411,plain,
~ strictorderedP(sK47),
inference(cnf_transformation,[],[f221]) ).
fof(f412,plain,
segmentP(sK50,sK49),
inference(cnf_transformation,[],[f221]) ).
fof(f413,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f221]) ).
fof(f415,plain,
ssList(sK50),
inference(cnf_transformation,[],[f221]) ).
fof(f416,plain,
ssList(sK49),
inference(cnf_transformation,[],[f221]) ).
fof(f421,plain,
~ strictorderedP(sK49),
inference(definition_unfolding,[],[f411,f413]) ).
fof(f453,definition,
( spl51_1
<=> singletonP(sK49) ),
introduced(definition,[new_symbols(definition,[spl51_1])],[avatar_definition]) ).
fof(f455,plain,
( singletonP(sK49)
| ~ spl51_1 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f457,definition,
( spl51_2
<=> neq(sK50,nil) ),
introduced(definition,[new_symbols(definition,[spl51_2])],[avatar_definition]) ).
fof(f459,plain,
( ~ neq(sK50,nil)
| spl51_2 ),
inference(avatar_component_clause,[],[f457]) ).
fof(f460,plain,
( spl51_1
| ~ spl51_2 ),
inference(avatar_split_clause,[],[f410,f457,f453]) ).
fof(f462,definition,
( spl51_3
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl51_3])],[avatar_definition]) ).
fof(f463,plain,
( ssList(nil)
| ~ spl51_3 ),
inference(avatar_component_clause,[],[f462]) ).
fof(f466,definition,
( spl51_4
<=> ! [X0] :
( ~ ssItem(X0)
| strictorderedP(cons(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[spl51_4])],[avatar_definition]) ).
fof(f467,plain,
( ! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl51_4 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f469,plain,
spl51_4,
inference(avatar_split_clause,[],[f373,f466]) ).
fof(f490,plain,
spl51_3,
inference(avatar_split_clause,[],[f305,f462]) ).
fof(f682,definition,
( spl51_10
<=> nil = sK50 ),
introduced(definition,[new_symbols(definition,[spl51_10])],[avatar_definition]) ).
fof(f684,plain,
( nil = sK50
| ~ spl51_10 ),
inference(avatar_component_clause,[],[f682]) ).
fof(f690,plain,
( ~ ssList(nil)
| nil = sK50
| ~ ssList(sK50)
| spl51_2 ),
inference(resolution,[],[f302,f459]) ).
fof(f691,plain,
( nil = sK50
| ~ ssList(sK50)
| spl51_2
| ~ spl51_3 ),
inference(forward_subsumption_resolution,[],[f690,f463]) ).
fof(f692,plain,
( nil = sK50
| spl51_2
| ~ spl51_3 ),
inference(forward_subsumption_resolution,[],[f691,f415]) ).
fof(f693,plain,
( spl51_10
| spl51_2
| ~ spl51_3 ),
inference(avatar_split_clause,[],[f692,f462,f457,f682]) ).
fof(f694,plain,
( segmentP(nil,sK49)
| ~ spl51_10 ),
inference(superposition,[],[f412,f684]) ).
fof(f718,plain,
( nil = sK49
| ~ ssList(sK49)
| ~ spl51_10 ),
inference(resolution,[],[f694,f360]) ).
fof(f719,plain,
( nil = sK49
| ~ spl51_10 ),
inference(forward_subsumption_resolution,[],[f718,f416]) ).
fof(f730,plain,
( ~ strictorderedP(nil)
| ~ spl51_10 ),
inference(superposition,[],[f421,f719]) ).
fof(f762,plain,
( $false
| ~ spl51_10 ),
inference(forward_subsumption_resolution,[],[f730,f374]) ).
fof(f763,plain,
~ spl51_10,
inference(avatar_contradiction_clause,[],[f762]) ).
fof(f765,plain,
( sK49 = cons(sK4(sK49),nil)
| ~ ssList(sK49)
| ~ spl51_1 ),
inference(resolution,[],[f455,f231]) ).
fof(f766,plain,
( ssItem(sK4(sK49))
| ~ ssList(sK49)
| ~ spl51_1 ),
inference(resolution,[],[f455,f232]) ).
fof(f767,plain,
( ssItem(sK4(sK49))
| ~ spl51_1 ),
inference(forward_subsumption_resolution,[],[f766,f416]) ).
fof(f768,plain,
( sK49 = cons(sK4(sK49),nil)
| ~ spl51_1 ),
inference(forward_subsumption_resolution,[],[f765,f416]) ).
fof(f781,plain,
( strictorderedP(sK49)
| ~ ssItem(sK4(sK49))
| ~ spl51_1
| ~ spl51_4 ),
inference(superposition,[],[f467,f768]) ).
fof(f786,plain,
( ~ ssItem(sK4(sK49))
| ~ spl51_1
| ~ spl51_4 ),
inference(forward_subsumption_resolution,[],[f781,f421]) ).
fof(f793,plain,
( $false
| ~ spl51_1
| ~ spl51_4 ),
inference(forward_subsumption_resolution,[],[f786,f767]) ).
fof(f794,plain,
( ~ spl51_1
| ~ spl51_4 ),
inference(avatar_contradiction_clause,[],[f793]) ).
cnf(s1,plain,
( spl51_1
| ~ spl51_2 ),
inference(sat_conversion,[],[f460]) ).
cnf(s3,plain,
spl51_4,
inference(sat_conversion,[],[f469]) ).
cnf(s9,plain,
spl51_3,
inference(sat_conversion,[],[f490]) ).
cnf(s11,plain,
( spl51_2
| ~ spl51_3
| spl51_10 ),
inference(sat_conversion,[],[f693]) ).
cnf(s13,plain,
~ spl51_10,
inference(sat_conversion,[],[f763]) ).
cnf(s14,plain,
( ~ spl51_1
| ~ spl51_4 ),
inference(sat_conversion,[],[f794]) ).
cnf(s15,plain,
( spl51_2
| ~ spl51_3 ),
inference(rat,[],[s11,s13]) ).
cnf(s17,plain,
spl51_2,
inference(rat,[],[s15,s9]) ).
cnf(s21,plain,
~ spl51_1,
inference(rat,[],[s14,s3]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s1,s17,s21]) ).
fof(f795,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC294+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n008.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 08:55:54 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 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
% 0.08/0.25 % (2110279)Will run a generic schedule for satisfiability detection.
% 0.08/0.25 % (2110288)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3752085470:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.25 % (2110285)% WARNING: option uhcvi not known.
% 0.08/0.25 % (2110286)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=509942208:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.25 % (2110287)dis+10_1_sil=32000:sp=arity:random_seed=742817763:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.25 % (2110284)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2780844032_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.25 % (2110289)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4243733246:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.25 % (2110290)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3346989032:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.25 % (2110285)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=509114833:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.25 % (2110288) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2110279-2110288"...
% 0.08/0.25 % (2110288)...printing done.
% 0.08/0.25 % (2110288)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.25 % (2110288)------------------------------
% 0.08/0.25 % (2110288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (2110288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (2110288)CaDiCaL version: 2.1.3
% 0.08/0.25 % (2110288)Termination reason: Refutation
% 0.08/0.25 % (2110288)Time elapsed: 0.011 s
% 0.08/0.25 % (2110288)Peak memory usage: 13 MB
% 0.08/0.25 % (2110288)Instructions burned: 31 (million)
% 0.08/0.25 % (2110279)Success in time 0.042 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------