%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC042+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 : n012.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 01:04:25 PM UTC 2026
% Result : Theorem 0.07s 0.37s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 16 unt; 1 def)
% Number of atoms : 184 ( 87 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 220 ( 78 ~; 70 |; 56 &)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 38 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( nil != X1
| X1 != X3
| X0 != X2
| nil = X0
| ! [X4] :
( ssList(X4)
=> ( app(X2,X4) != X3
| ~ totalorderedP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X2
& leq(X7,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)
=> ( nil != X1
| X1 != X3
| X0 != X2
| nil = X0
| ! [X4] :
( ssList(X4)
=> ( app(X2,X4) != X3
| ~ totalorderedP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X2
& leq(X7,X5) ) ) ) ) ) )
| ( nil != X3
& nil = X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f200,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f201,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil = X1
& X1 = X3
& X0 = X2
& nil != X0
& ? [X4] :
( app(X2,X4) = X3
& totalorderedP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != X2
| ~ leq(X7,X5) ) ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil = X1
& X1 = X3
& X0 = X2
& nil != X0
& ? [X4] :
( app(X2,X4) = X3
& totalorderedP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != X2
| ~ leq(X7,X5) ) ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f292,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X1
| nil != X0 )
& ( ( nil = X1
& nil = X0 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f200]) ).
fof(f293,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X1
| nil != X0 )
& ( ( nil = X1
& nil = X0 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f292]) ).
fof(f296,plain,
( nil = sK54
& sK54 = sK56
& sK53 = sK55
& nil != sK53
& sK56 = app(sK55,sK57)
& totalorderedP(sK55)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != sK57
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != sK55
| ~ leq(X7,X5) ) ) ) )
& 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(X4,sK57)],[f222]) ).
fof(f480,plain,
! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f482,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f201]) ).
fof(f498,plain,
ssList(sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
ssList(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
sK56 = app(sK55,sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
nil != sK53,
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,
nil = sK54,
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
nil = sK56,
inference(definition_unfolding,[],[f508,f507]) ).
fof(f563,plain,
! [X0,X1] :
( app(X0,X1) != sK56
| sK56 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f480,f509,f509]) ).
fof(f565,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,sK56) = X0 ),
inference(definition_unfolding,[],[f482,f509]) ).
fof(f568,plain,
sK55 != sK56,
inference(definition_unfolding,[],[f505,f509,f506]) ).
fof(f645,plain,
sK55 = app(sK55,sK56),
inference(resolution,[],[f565,f498]) ).
fof(f674,definition,
( spl58_9
<=> sK56 = sK57 ),
introduced(definition,[new_symbols(definition,[spl58_9])],[avatar_definition]) ).
fof(f675,plain,
( sK56 != sK57
| spl58_9 ),
inference(avatar_component_clause,[],[f674]) ).
fof(f676,plain,
( sK56 = sK57
| ~ spl58_9 ),
inference(avatar_component_clause,[],[f674]) ).
fof(f681,plain,
( sK56 = app(sK55,sK56)
| ~ spl58_9 ),
inference(superposition,[],[f504,f676]) ).
fof(f683,plain,
( sK55 = sK56
| ~ spl58_9 ),
inference(forward_demodulation,[],[f681,f645]) ).
fof(f684,plain,
( $false
| ~ spl58_9 ),
inference(forward_subsumption_resolution,[],[f683,f568]) ).
fof(f685,plain,
~ spl58_9,
inference(avatar_contradiction_clause,[],[f684]) ).
fof(f717,plain,
( sK56 != sK56
| sK56 = sK57
| ~ ssList(sK57)
| ~ ssList(sK55) ),
inference(superposition,[],[f563,f504]) ).
fof(f720,plain,
( sK56 = sK57
| ~ ssList(sK57)
| ~ ssList(sK55) ),
inference(trivial_inequality_removal,[],[f717]) ).
fof(f721,plain,
( ~ ssList(sK57)
| ~ ssList(sK55)
| spl58_9 ),
inference(forward_subsumption_resolution,[],[f720,f675]) ).
fof(f722,plain,
( ~ ssList(sK55)
| spl58_9 ),
inference(forward_subsumption_resolution,[],[f721,f501]) ).
fof(f723,plain,
( $false
| spl58_9 ),
inference(forward_subsumption_resolution,[],[f722,f498]) ).
fof(f724,plain,
spl58_9,
inference(avatar_contradiction_clause,[],[f723]) ).
cnf(s13,plain,
~ spl58_9,
inference(sat_conversion,[],[f685]) ).
cnf(s15,plain,
spl58_9,
inference(sat_conversion,[],[f724]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s13,s15]) ).
fof(f725,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC042+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Mon Sep 28 07:34:19 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.33 Running first-order model finding
% 0.07/0.33 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
% 0.07/0.37 % (3216355)Will run a generic schedule for satisfiability detection.
% 0.07/0.37 % (3216361)% WARNING: option uhcvi not known.
% 0.07/0.37 % (3216366)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3969987540:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.37 % (3216360)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=124652131_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.37 % (3216361)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3678696002:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.37 % (3216362)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2264521216:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.37 % (3216363)dis+10_1_sil=32000:sp=arity:random_seed=3723840674:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.37 % (3216364)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1686005022:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.37 % (3216365)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3633262208:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.37 % (3216363) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3216355-3216363"...
% 0.07/0.37 % (3216361) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3216355-3216361"...
% 0.07/0.37 % (3216363)...printing done.
% 0.07/0.37 % (3216361)...printing done.
% 0.07/0.37 % (3216363)Refutation found. Thanks to Tanya!
% 0.07/0.37 % SZS status Theorem for theBenchmark
% 0.07/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.37 % (3216363)------------------------------
% 0.07/0.37 % (3216363)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.37 % (3216363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.37 % (3216363)CaDiCaL version: 2.1.3
% 0.07/0.37 % (3216363)Termination reason: Refutation
% 0.07/0.37 % (3216363)Time elapsed: 0.005 s
% 0.07/0.37 % (3216363)Peak memory usage: 13 MB
% 0.07/0.37 % (3216363)Instructions burned: 14 (million)
% 0.07/0.37 % (3216355)Success in time 0.035 s
% 0.07/0.37 % Vampire exiting
%------------------------------------------------------------------------------