%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC004-1 : 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 : n001.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 01:04:14 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 25
% Syntax : Number of formulae : 101 ( 21 unt; 11 def)
% Number of atoms : 278 ( 32 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 305 ( 128 ~; 166 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 12 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f11,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause11) ).
fof(f86,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ssList(cons(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
fof(f101,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X1,X0)
| X1 = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
fof(f102,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X1,X0)
| X0 = X1 ),
inference(reorient_equations,[],[f101]) ).
fof(f119,axiom,
! [X0,X1] :
( cons(X0,nil) != X1
| ~ ssItem(X0)
| ~ ssList(X1)
| singletonP(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause116) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f216,negated_conjecture,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X0,X1),X2) != sk2
| app(X0,X2) != sk1
| ~ neq(X1,nil)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
fof(f217,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
fof(f218,negated_conjecture,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
fof(f219,negated_conjecture,
( ssList(sk7)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
fof(f220,negated_conjecture,
( app(app(sk6,cons(sk5,nil)),sk7) = sk4
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_19) ).
fof(f221,plain,
( sk4 = app(app(sk6,cons(sk5,nil)),sk7)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f220]) ).
fof(f222,negated_conjecture,
( app(sk6,sk7) = sk3
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_20) ).
fof(f223,plain,
( sk3 = app(sk6,sk7)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f222]) ).
fof(f226,plain,
( neq(sk4,nil)
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f206,f204,f204]) ).
fof(f234,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X0,X1),X2) != sk4
| app(X0,X2) != sk3
| ~ neq(X1,nil)
| ~ neq(sk4,nil) ),
inference(definition_unfolding,[],[f216,f204,f205]) ).
fof(f242,plain,
! [X0] :
( ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| singletonP(cons(X0,nil)) ),
inference(equality_resolution,[],[f119]) ).
fof(f263,plain,
~ ssList(nil),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f339,plain,
! [X0,X1] :
( ~ ssList(cons(X0,X1))
| ssList(X1)
| ssItem(X0) ),
inference(consistent_polarity_flipping,[],[f86]) ).
fof(f353,plain,
! [X0,X1] :
( neq(X1,X0)
| ssList(X1)
| ssList(X0)
| X0 = X1 ),
inference(consistent_polarity_flipping,[],[f102]) ).
fof(f369,plain,
! [X0] :
( singletonP(cons(X0,nil))
| ssList(cons(X0,nil))
| ssItem(X0) ),
inference(consistent_polarity_flipping,[],[f242]) ).
fof(f447,plain,
! [X2,X0,X1] :
( ssList(X0)
| ssList(X1)
| ssList(X2)
| app(app(X0,X1),X2) != sk4
| app(X0,X2) != sk3
| ~ neq(X1,nil)
| ~ neq(sk4,nil) ),
inference(consistent_polarity_flipping,[],[f234]) ).
fof(f448,plain,
( ~ ssItem(sk5)
| ~ neq(sk4,nil) ),
inference(consistent_polarity_flipping,[],[f217]) ).
fof(f449,plain,
( ~ ssList(sk6)
| ~ neq(sk4,nil) ),
inference(consistent_polarity_flipping,[],[f218]) ).
fof(f450,plain,
( ~ ssList(sk7)
| ~ neq(sk4,nil) ),
inference(consistent_polarity_flipping,[],[f219]) ).
fof(f451,plain,
neq(sk4,nil),
inference(duplicate_literal_removal,[],[f226]) ).
fof(f459,definition,
( spl0_1
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f463,definition,
( spl0_2
<=> sk3 = app(sk6,sk7) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f465,plain,
( sk3 = app(sk6,sk7)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f463]) ).
fof(f466,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f223,f463,f459]) ).
fof(f468,definition,
( spl0_3
<=> sk4 = app(app(sk6,cons(sk5,nil)),sk7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f470,plain,
( sk4 = app(app(sk6,cons(sk5,nil)),sk7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f471,plain,
( ~ spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f221,f468,f459]) ).
fof(f473,definition,
( spl0_4
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f475,plain,
( ~ ssList(sk7)
| spl0_4 ),
inference(avatar_component_clause,[],[f473]) ).
fof(f476,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f450,f473,f459]) ).
fof(f478,definition,
( spl0_5
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f480,plain,
( ~ ssList(sk6)
| spl0_5 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f481,plain,
( ~ spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f449,f478,f459]) ).
fof(f483,definition,
( spl0_6
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f485,plain,
( ~ ssItem(sk5)
| spl0_6 ),
inference(avatar_component_clause,[],[f483]) ).
fof(f486,plain,
( ~ spl0_1
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f448,f483,f459]) ).
fof(f488,definition,
( spl0_7
<=> ! [X2,X0,X1] :
( ssList(X0)
| ~ neq(X1,nil)
| app(X0,X2) != sk3
| app(app(X0,X1),X2) != sk4
| ssList(X2)
| ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f489,plain,
( ! [X2,X0,X1] :
( app(app(X0,X1),X2) != sk4
| ~ neq(X1,nil)
| app(X0,X2) != sk3
| ssList(X0)
| ssList(X2)
| ssList(X1) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f488]) ).
fof(f490,plain,
( ~ spl0_1
| spl0_7 ),
inference(avatar_split_clause,[],[f447,f488,f459]) ).
fof(f497,plain,
spl0_1,
inference(avatar_split_clause,[],[f451,f459]) ).
fof(f503,definition,
( spl0_9
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f504,plain,
( ~ ssList(nil)
| spl0_9 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f539,plain,
~ spl0_9,
inference(avatar_split_clause,[],[f263,f503]) ).
fof(f542,plain,
( sk4 != sk4
| ~ neq(cons(sk5,nil),nil)
| sk3 != app(sk6,sk7)
| ssList(sk6)
| ssList(sk7)
| ssList(cons(sk5,nil))
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f489,f470]) ).
fof(f543,plain,
( ~ neq(cons(sk5,nil),nil)
| sk3 != app(sk6,sk7)
| ssList(sk6)
| ssList(sk7)
| ssList(cons(sk5,nil))
| ~ spl0_3
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f542]) ).
fof(f544,plain,
( ~ neq(cons(sk5,nil),nil)
| ssList(sk6)
| ssList(sk7)
| ssList(cons(sk5,nil))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f543,f465]) ).
fof(f547,plain,
( ~ neq(cons(sk5,nil),nil)
| ssList(sk7)
| ssList(cons(sk5,nil))
| ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f544,f480]) ).
fof(f561,plain,
( ~ neq(cons(sk5,nil),nil)
| ssList(cons(sk5,nil))
| ~ spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f547,f475]) ).
fof(f567,definition,
( spl0_21
<=> ssList(cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f568,plain,
( ~ ssList(cons(sk5,nil))
| spl0_21 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f569,plain,
( ssList(cons(sk5,nil))
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f571,definition,
( spl0_22
<=> neq(cons(sk5,nil),nil) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f573,plain,
( ~ neq(cons(sk5,nil),nil)
| spl0_22 ),
inference(avatar_component_clause,[],[f571]) ).
fof(f574,plain,
( spl0_21
| ~ spl0_22
| ~ spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f561,f488,f478,f473,f468,f463,f571,f567]) ).
fof(f823,definition,
( spl0_27
<=> nil = cons(sk5,nil) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f825,plain,
( nil = cons(sk5,nil)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f823]) ).
fof(f881,plain,
( ssList(nil)
| ssItem(sk5)
| ~ spl0_21 ),
inference(resolution,[],[f569,f339]) ).
fof(f882,plain,
( ssItem(sk5)
| spl0_9
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f881,f504]) ).
fof(f883,plain,
( $false
| spl0_6
| spl0_9
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f882,f485]) ).
fof(f884,plain,
( spl0_6
| spl0_9
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f883]) ).
fof(f898,plain,
( ssList(cons(sk5,nil))
| ssList(nil)
| nil = cons(sk5,nil)
| spl0_22 ),
inference(resolution,[],[f573,f353]) ).
fof(f899,plain,
( ssList(nil)
| nil = cons(sk5,nil)
| spl0_21
| spl0_22 ),
inference(forward_subsumption_resolution,[],[f898,f568]) ).
fof(f901,plain,
( nil = cons(sk5,nil)
| spl0_9
| spl0_21
| spl0_22 ),
inference(forward_subsumption_resolution,[],[f899,f504]) ).
fof(f902,plain,
( spl0_27
| spl0_9
| spl0_21
| spl0_22 ),
inference(avatar_split_clause,[],[f901,f571,f567,f503,f823]) ).
fof(f1911,plain,
( singletonP(nil)
| ssList(nil)
| ssItem(sk5)
| ~ spl0_27 ),
inference(superposition,[],[f369,f825]) ).
fof(f1928,plain,
( ssList(nil)
| ssItem(sk5)
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f1911,f11]) ).
fof(f1937,plain,
( ssItem(sk5)
| spl0_9
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f1928,f504]) ).
fof(f1942,plain,
( $false
| spl0_6
| spl0_9
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f1937,f485]) ).
fof(f1943,plain,
( spl0_6
| spl0_9
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f1942]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f466]) ).
cnf(s2,plain,
( ~ spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f471]) ).
cnf(s3,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f476]) ).
cnf(s4,plain,
( ~ spl0_1
| ~ spl0_5 ),
inference(sat_conversion,[],[f481]) ).
cnf(s5,plain,
( ~ spl0_1
| ~ spl0_6 ),
inference(sat_conversion,[],[f486]) ).
cnf(s6,plain,
( ~ spl0_1
| spl0_7 ),
inference(sat_conversion,[],[f490]) ).
cnf(s13,plain,
spl0_1,
inference(sat_conversion,[],[f497]) ).
cnf(s23,plain,
~ spl0_9,
inference(sat_conversion,[],[f539]) ).
cnf(s26,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_7
| spl0_21
| ~ spl0_22 ),
inference(sat_conversion,[],[f574]) ).
cnf(s33,plain,
( spl0_6
| spl0_9
| ~ spl0_21 ),
inference(sat_conversion,[],[f884]) ).
cnf(s38,plain,
( spl0_9
| spl0_21
| spl0_22
| spl0_27 ),
inference(sat_conversion,[],[f902]) ).
cnf(s71,plain,
( spl0_6
| spl0_9
| ~ spl0_27 ),
inference(sat_conversion,[],[f1943]) ).
cnf(s76,plain,
spl0_7,
inference(rat,[],[s6,s13]) ).
cnf(s77,plain,
~ spl0_6,
inference(rat,[],[s5,s13]) ).
cnf(s78,plain,
~ spl0_27,
inference(rat,[],[s71,s23,s77]) ).
cnf(s79,plain,
~ spl0_21,
inference(rat,[],[s33,s23,s77]) ).
cnf(s84,plain,
spl0_22,
inference(rat,[],[s38,s78,s23,s79]) ).
cnf(s85,plain,
~ spl0_5,
inference(rat,[],[s4,s13]) ).
cnf(s86,plain,
~ spl0_4,
inference(rat,[],[s3,s13]) ).
cnf(s87,plain,
spl0_3,
inference(rat,[],[s2,s13]) ).
cnf(s88,plain,
~ spl0_2,
inference(rat,[],[s26,s84,s79,s76,s85,s86,s87]) ).
cnf(s89,plain,
$false,
inference(rat,[],[s1,s88,s13]) ).
fof(f1944,plain,
$false,
inference(avatar_sat_refutation,[],[s89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC004-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n001.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 07:29:48 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.17/0.47 % (185987)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (185993)% WARNING: option uhcvi not known.
% 0.17/0.47 % (185993)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3665945595:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (185992)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=979852040_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (185994)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3981466137:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (185995)dis+10_1_sil=32000:sp=arity:random_seed=2585458111:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (185996)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3785502373:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (185997)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=619427031:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (185998)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4235951520:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % (185993) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-185987-185993"...
% 0.17/0.48 % (185995) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-185987-185995"...
% 0.17/0.48 % TRYING [1]
% 0.17/0.48 % (185993)...printing done.
% 0.17/0.48 % (185993)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (185993)------------------------------
% 0.17/0.48 % (185993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (185993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (185993)CaDiCaL version: 2.1.3
% 0.17/0.48 % (185993)Termination reason: Refutation
% 0.17/0.48 % (185993)Time elapsed: 0.019 s
% 0.17/0.48 % (185993)Peak memory usage: 13 MB
% 0.17/0.48 % (185993)Instructions burned: 54 (million)
% 0.17/0.48 % (185987)Success in time 0.047 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------