%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC009+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 : n014.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 01:04:16 PM UTC 2026
% Result : Theorem 0.13s 0.49s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 17 unt; 1 def)
% Number of atoms : 148 ( 57 equ)
% Maximal formula atoms : 23 ( 4 avg)
% Number of connectives : 185 ( 71 ~; 58 |; 44 &)
% ( 1 <=>; 11 =>; 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 : 60 ( 0 sgn 36 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
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)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X4,X5),X6) = X1
& app(X4,X6) = X0 ) ) )
| ! [X7] :
( ssList(X7)
=> ( app(X2,X7) != X3
| ~ strictorderedP(X2)
| ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X7
& ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(X11,cons(X10,nil)) = X2
& lt(X10,X8) ) ) ) ) ) )
| ( 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
| ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X4,X5),X6) = X1
& app(X4,X6) = X0 ) ) )
| ! [X7] :
( ssList(X7)
=> ( app(X2,X7) != X3
| ~ strictorderedP(X2)
| ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X7
& ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(X11,cons(X10,nil)) = X2
& lt(X10,X8) ) ) ) ) ) )
| ( nil != X3
& nil = X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f201,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X1
| app(X4,X6) != X0 ) ) )
& ? [X7] :
( app(X2,X7) = X3
& strictorderedP(X2)
& ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != X7
| ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X10,nil)) != X2
| ~ lt(X10,X8) ) ) ) )
& ssList(X7) )
& ( 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
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X1
| app(X4,X6) != X0 ) ) )
& ? [X7] :
( app(X2,X7) = X3
& strictorderedP(X2)
& ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != X7
| ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X10,nil)) != X2
| ~ lt(X10,X8) ) ) ) )
& ssList(X7) )
& ( nil = X3
| nil != X2 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f306,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f397,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f412,plain,
! [X6,X4,X5] :
( app(X4,X6) != sK47
| app(app(X4,X5),X6) != sK48
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f222]) ).
fof(f413,plain,
ssList(sK51),
inference(cnf_transformation,[],[f222]) ).
fof(f415,plain,
sK50 = app(sK49,sK51),
inference(cnf_transformation,[],[f222]) ).
fof(f417,plain,
ssList(sK50),
inference(cnf_transformation,[],[f222]) ).
fof(f418,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f419,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f420,plain,
ssList(sK49),
inference(cnf_transformation,[],[f222]) ).
fof(f425,plain,
! [X6,X4,X5] :
( app(app(X4,X5),X6) != sK50
| app(X4,X6) != sK49
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f412,f418,f419]) ).
fof(f612,definition,
( spl52_4
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl52_4])],[avatar_definition]) ).
fof(f613,plain,
( ssList(nil)
| ~ spl52_4 ),
inference(avatar_component_clause,[],[f612]) ).
fof(f641,plain,
spl52_4,
inference(avatar_split_clause,[],[f306,f612]) ).
fof(f642,plain,
! [X0] :
( sK50 != app(sK50,X0)
| sK49 != app(sK49,X0)
| ~ ssList(X0)
| ~ ssList(sK51)
| ~ ssList(sK49) ),
inference(superposition,[],[f425,f415]) ).
fof(f643,plain,
! [X0] :
( sK50 != app(sK50,X0)
| sK49 != app(sK49,X0)
| ~ ssList(X0)
| ~ ssList(sK49) ),
inference(forward_subsumption_resolution,[],[f642,f413]) ).
fof(f644,plain,
! [X0] :
( sK50 != app(sK50,X0)
| sK49 != app(sK49,X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f643,f420]) ).
fof(f672,plain,
sK49 = app(sK49,nil),
inference(resolution,[],[f397,f420]) ).
fof(f673,plain,
sK50 = app(sK50,nil),
inference(resolution,[],[f397,f417]) ).
fof(f703,plain,
( sK50 != sK50
| sK49 != app(sK49,nil)
| ~ ssList(nil) ),
inference(superposition,[],[f644,f673]) ).
fof(f705,plain,
( sK49 != app(sK49,nil)
| ~ ssList(nil) ),
inference(trivial_inequality_removal,[],[f703]) ).
fof(f707,plain,
~ ssList(nil),
inference(forward_subsumption_resolution,[],[f705,f672]) ).
fof(f709,plain,
( $false
| ~ spl52_4 ),
inference(forward_subsumption_resolution,[],[f707,f613]) ).
fof(f710,plain,
~ spl52_4,
inference(avatar_contradiction_clause,[],[f709]) ).
cnf(s10,plain,
spl52_4,
inference(sat_conversion,[],[f641]) ).
cnf(s12,plain,
~ spl52_4,
inference(sat_conversion,[],[f710]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s10,s12]) ).
fof(f711,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC009+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n014.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 07:25:16 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.43 Running first-order model finding
% 0.13/0.43 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
% 0.13/0.49 % (1607466)Will run a generic schedule for satisfiability detection.
% 0.13/0.49 % (1607476)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=28649703:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.49 % (1607472)% WARNING: option uhcvi not known.
% 0.13/0.49 % (1607471)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4160031534_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.49 % (1607472)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2873078531:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.49 % (1607473)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=314975951:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.49 % (1607474)dis+10_1_sil=32000:sp=arity:random_seed=3936079161:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.49 % (1607475)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=426029409:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.49 % (1607477)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4266310571:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.49 % (1607472) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1607466-1607472"...
% 0.13/0.49 % (1607472)...printing done.
% 0.13/0.49 % (1607474) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1607466-1607474"...
% 0.13/0.49 % (1607477) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1607466-1607477"...
% 0.13/0.49 % (1607472)Refutation found. Thanks to Tanya!
% 0.13/0.49 % SZS status Theorem for theBenchmark
% 0.13/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.49 % (1607472)------------------------------
% 0.13/0.49 % (1607472)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.49 % (1607472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.49 % (1607472)CaDiCaL version: 2.1.3
% 0.13/0.49 % (1607472)Termination reason: Refutation
% 0.13/0.49 % (1607472)Time elapsed: 0.010 s
% 0.13/0.49 % (1607472)Peak memory usage: 13 MB
% 0.13/0.49 % (1607472)Instructions burned: 14 (million)
% 0.13/0.49 % (1607466)Success in time 0.052 s
% 0.13/0.49 % Vampire exiting
%------------------------------------------------------------------------------