%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC332+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 01:05:35 PM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 91 ( 21 unt; 8 def)
% Number of atoms : 264 ( 42 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 287 ( 114 ~; 108 |; 38 &)
% ( 14 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 9 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 33 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(f73,axiom,
! [X0] :
( ssItem(X0)
=> equalelemsP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax73) ).
fof(f74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax74) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ segmentP(X3,X2)
| ( ~ singletonP(X2)
& neq(X3,nil) )
| ( segmentP(X1,X0)
& equalelemsP(X0) ) ) ) ) ) ),
file('/export/starexec/sandbox2/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)
| ( ~ singletonP(X2)
& neq(X3,nil) )
| ( segmentP(X1,X0)
& equalelemsP(X0) ) ) ) ) ) ),
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(f185,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& segmentP(X3,X2)
& ( singletonP(X2)
| ~ neq(X3,nil) )
& ( ~ segmentP(X1,X0)
| ~ equalelemsP(X0) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& segmentP(X3,X2)
& ( singletonP(X2)
| ~ neq(X3,nil) )
& ( ~ segmentP(X1,X0)
| ~ equalelemsP(X0) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f237,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != X0 ) )
& ( ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f100]) ).
fof(f238,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != X0 ) )
& ( ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X0 )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f237]) ).
fof(f239,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != X0 ) )
& ( ( ssItem(sK10(X0))
& cons(sK10(X0),nil) = X0 )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0))],[f238]) ).
fof(f273,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f285,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f176]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& segmentP(sK56,sK55)
& ( singletonP(sK55)
| ~ neq(sK56,nil) )
& ( ~ segmentP(sK54,sK53)
| ~ equalelemsP(sK53) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56)],[f222]) ).
fof(f306,plain,
! [X0] :
( ~ singletonP(X0)
| cons(sK10(X0),nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f239]) ).
fof(f307,plain,
! [X0] :
( ssItem(sK10(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f239]) ).
fof(f387,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f443,plain,
! [X0] :
( ~ segmentP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f467,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f185]) ).
fof(f468,plain,
equalelemsP(nil),
inference(cnf_transformation,[],[f74]) ).
fof(f498,plain,
ssList(sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f499,plain,
ssList(sK56),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( ~ segmentP(sK54,sK53)
| ~ equalelemsP(sK53) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( singletonP(sK55)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
segmentP(sK56,sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
( ~ segmentP(sK56,sK55)
| ~ equalelemsP(sK55) ),
inference(definition_unfolding,[],[f500,f504,f503,f503]) ).
fof(f543,definition,
( spl57_1
<=> equalelemsP(sK55) ),
introduced(definition,[new_symbols(definition,[spl57_1])],[avatar_definition]) ).
fof(f545,plain,
( ~ equalelemsP(sK55)
| spl57_1 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f547,definition,
( spl57_2
<=> segmentP(sK56,sK55) ),
introduced(definition,[new_symbols(definition,[spl57_2])],[avatar_definition]) ).
fof(f548,plain,
( segmentP(sK56,sK55)
| ~ spl57_2 ),
inference(avatar_component_clause,[],[f547]) ).
fof(f550,plain,
( ~ spl57_1
| ~ spl57_2 ),
inference(avatar_split_clause,[],[f505,f547,f543]) ).
fof(f552,definition,
( spl57_3
<=> neq(sK56,nil) ),
introduced(definition,[new_symbols(definition,[spl57_3])],[avatar_definition]) ).
fof(f554,plain,
( ~ neq(sK56,nil)
| spl57_3 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f556,definition,
( spl57_4
<=> singletonP(sK55) ),
introduced(definition,[new_symbols(definition,[spl57_4])],[avatar_definition]) ).
fof(f558,plain,
( singletonP(sK55)
| ~ spl57_4 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f559,plain,
( ~ spl57_3
| spl57_4 ),
inference(avatar_split_clause,[],[f501,f556,f552]) ).
fof(f560,plain,
spl57_2,
inference(avatar_split_clause,[],[f502,f547]) ).
fof(f562,definition,
( spl57_5
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl57_5])],[avatar_definition]) ).
fof(f563,plain,
( ssList(nil)
| ~ spl57_5 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f595,plain,
spl57_5,
inference(avatar_split_clause,[],[f389,f562]) ).
fof(f975,definition,
( spl57_30
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl57_30])],[avatar_definition]) ).
fof(f977,plain,
( nil = sK56
| ~ spl57_30 ),
inference(avatar_component_clause,[],[f975]) ).
fof(f981,plain,
( nil = sK56
| ~ ssList(nil)
| ~ ssList(sK56)
| spl57_3 ),
inference(resolution,[],[f387,f554]) ).
fof(f986,plain,
( nil = sK56
| ~ ssList(sK56)
| spl57_3
| ~ spl57_5 ),
inference(forward_subsumption_resolution,[],[f981,f563]) ).
fof(f987,plain,
( nil = sK56
| spl57_3
| ~ spl57_5 ),
inference(forward_subsumption_resolution,[],[f986,f499]) ).
fof(f988,plain,
( spl57_30
| spl57_3
| ~ spl57_5 ),
inference(avatar_split_clause,[],[f987,f562,f552,f975]) ).
fof(f989,plain,
( sK55 = cons(sK10(sK55),nil)
| ~ ssList(sK55)
| ~ spl57_4 ),
inference(resolution,[],[f558,f306]) ).
fof(f990,plain,
( sK55 = cons(sK10(sK55),nil)
| ~ spl57_4 ),
inference(forward_subsumption_resolution,[],[f989,f498]) ).
fof(f995,plain,
( equalelemsP(sK55)
| ~ ssItem(sK10(sK55))
| ~ spl57_4 ),
inference(superposition,[],[f467,f990]) ).
fof(f1006,definition,
( spl57_31
<=> ssItem(sK10(sK55)) ),
introduced(definition,[new_symbols(definition,[spl57_31])],[avatar_definition]) ).
fof(f1008,plain,
( ~ ssItem(sK10(sK55))
| spl57_31 ),
inference(avatar_component_clause,[],[f1006]) ).
fof(f1019,plain,
( ~ ssItem(sK10(sK55))
| spl57_1
| ~ spl57_4 ),
inference(forward_subsumption_resolution,[],[f995,f545]) ).
fof(f1024,definition,
( spl57_34
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl57_34])],[avatar_definition]) ).
fof(f1025,plain,
( nil = sK55
| ~ spl57_34 ),
inference(avatar_component_clause,[],[f1024]) ).
fof(f1034,plain,
( ~ spl57_31
| spl57_1
| ~ spl57_4 ),
inference(avatar_split_clause,[],[f1019,f556,f543,f1006]) ).
fof(f1066,plain,
( ~ singletonP(sK55)
| ~ ssList(sK55)
| spl57_31 ),
inference(resolution,[],[f1008,f307]) ).
fof(f1070,plain,
( ~ singletonP(sK55)
| spl57_31 ),
inference(forward_subsumption_resolution,[],[f1066,f498]) ).
fof(f1071,plain,
( ~ spl57_4
| spl57_31 ),
inference(avatar_split_clause,[],[f1070,f1006,f556]) ).
fof(f1105,plain,
( segmentP(nil,sK55)
| ~ spl57_2
| ~ spl57_30 ),
inference(superposition,[],[f548,f977]) ).
fof(f1152,plain,
( nil = sK55
| ~ ssList(sK55)
| ~ spl57_2
| ~ spl57_30 ),
inference(resolution,[],[f1105,f443]) ).
fof(f1153,plain,
( nil = sK55
| ~ spl57_2
| ~ spl57_30 ),
inference(forward_subsumption_resolution,[],[f1152,f498]) ).
fof(f1154,plain,
( spl57_34
| ~ spl57_2
| ~ spl57_30 ),
inference(avatar_split_clause,[],[f1153,f975,f547,f1024]) ).
fof(f1156,plain,
( ~ equalelemsP(nil)
| spl57_1
| ~ spl57_34 ),
inference(superposition,[],[f545,f1025]) ).
fof(f1186,plain,
( $false
| spl57_1
| ~ spl57_34 ),
inference(forward_subsumption_resolution,[],[f1156,f468]) ).
fof(f1187,plain,
( spl57_1
| ~ spl57_34 ),
inference(avatar_contradiction_clause,[],[f1186]) ).
cnf(s1,plain,
( ~ spl57_1
| ~ spl57_2 ),
inference(sat_conversion,[],[f550]) ).
cnf(s2,plain,
( ~ spl57_3
| spl57_4 ),
inference(sat_conversion,[],[f559]) ).
cnf(s3,plain,
spl57_2,
inference(sat_conversion,[],[f560]) ).
cnf(s12,plain,
spl57_5,
inference(sat_conversion,[],[f595]) ).
cnf(s28,plain,
( spl57_3
| ~ spl57_5
| spl57_30 ),
inference(sat_conversion,[],[f988]) ).
cnf(s34,plain,
( spl57_1
| ~ spl57_4
| ~ spl57_31 ),
inference(sat_conversion,[],[f1034]) ).
cnf(s40,plain,
( ~ spl57_4
| spl57_31 ),
inference(sat_conversion,[],[f1071]) ).
cnf(s49,plain,
( ~ spl57_2
| ~ spl57_30
| spl57_34 ),
inference(sat_conversion,[],[f1154]) ).
cnf(s56,plain,
( spl57_1
| ~ spl57_34 ),
inference(sat_conversion,[],[f1187]) ).
cnf(s61,plain,
~ spl57_1,
inference(rat,[],[s1,s3]) ).
cnf(s62,plain,
~ spl57_34,
inference(rat,[],[s56,s61]) ).
cnf(s63,plain,
~ spl57_30,
inference(rat,[],[s49,s3,s62]) ).
cnf(s64,plain,
spl57_3,
inference(rat,[],[s28,s12,s63]) ).
cnf(s65,plain,
spl57_4,
inference(rat,[],[s2,s64]) ).
cnf(s66,plain,
spl57_31,
inference(rat,[],[s40,s65]) ).
cnf(s70,plain,
$false,
inference(rat,[],[s34,s61,s66,s65]) ).
fof(f1188,plain,
$false,
inference(avatar_sat_refutation,[],[s70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC332+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 % Computer : n013.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Mon Sep 28 09:08:07 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.31 % (1040508)Will run a generic schedule for satisfiability detection.
% 0.21/0.31 % (1040513)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1484766540_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.31 % (1040514)% WARNING: option uhcvi not known.
% 0.21/0.31 % TRYING [1]
% 0.21/0.31 % (1040516)dis+10_1_sil=32000:sp=arity:random_seed=1729342244:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.31 % (1040514)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2947395200:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.31 % (1040515)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1426348230:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.31 % TRYING [2]
% 0.21/0.31 % (1040517)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1793022242:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.31 % (1040518)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1365685613:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.31 % (1040519)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2060772133:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.31 % TRYING [3]
% 0.21/0.31 % TRYING [4]
% 0.21/0.31 % (1040516) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1040508-1040516"...
% 0.21/0.31 % (1040514) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1040508-1040514"...
% 0.21/0.31 % (1040517) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1040508-1040517"...
% 0.21/0.31 % (1040516)...printing done.
% 0.21/0.31 % (1040514)...printing done.
% 0.21/0.31 % (1040516)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.31 % (1040516)------------------------------
% 0.21/0.31 % (1040516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1040516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1040516)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1040516)Termination reason: Refutation
% 0.21/0.31 % (1040516)Time elapsed: 0.017 s
% 0.21/0.31 % (1040516)Peak memory usage: 13 MB
% 0.21/0.31 % (1040516)Instructions burned: 27 (million)
% 0.21/0.31 % (1040508)Success in time 0.062 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------