%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC277+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 : n003.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 01:05:22 PM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 85 ( 22 unt; 7 def)
% Number of atoms : 242 ( 41 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 261 ( 104 ~; 95 |; 36 &)
% ( 13 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 8 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 35 !; 12 ?)
% 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(f65,axiom,
! [X0] :
( ssItem(X0)
=> totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax65) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax66) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ segmentP(X3,X2)
| totalorderedP(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)
| totalorderedP(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(f180,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& segmentP(X3,X2)
& ~ totalorderedP(X0)
& ( singletonP(X2)
| ~ neq(X3,nil) )
& 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)
& ~ totalorderedP(X0)
& ( singletonP(X2)
| ~ neq(X3,nil) )
& 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)
& ~ totalorderedP(sK53)
& ( singletonP(sK55)
| ~ neq(sK56,nil) )
& 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(f451,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f452,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f498,plain,
ssList(sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f499,plain,
ssList(sK56),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( singletonP(sK55)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
~ totalorderedP(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
segmentP(sK56,sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
~ totalorderedP(sK55),
inference(definition_unfolding,[],[f501,f503]) ).
fof(f543,definition,
( spl57_1
<=> neq(sK56,nil) ),
introduced(definition,[new_symbols(definition,[spl57_1])],[avatar_definition]) ).
fof(f545,plain,
( ~ neq(sK56,nil)
| spl57_1 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f547,definition,
( spl57_2
<=> singletonP(sK55) ),
introduced(definition,[new_symbols(definition,[spl57_2])],[avatar_definition]) ).
fof(f549,plain,
( singletonP(sK55)
| ~ spl57_2 ),
inference(avatar_component_clause,[],[f547]) ).
fof(f550,plain,
( ~ spl57_1
| spl57_2 ),
inference(avatar_split_clause,[],[f500,f547,f543]) ).
fof(f552,definition,
( spl57_3
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl57_3])],[avatar_definition]) ).
fof(f553,plain,
( ssList(nil)
| ~ spl57_3 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f566,definition,
( spl57_6
<=> ! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl57_6])],[avatar_definition]) ).
fof(f567,plain,
( ! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl57_6 ),
inference(avatar_component_clause,[],[f566]) ).
fof(f569,plain,
spl57_6,
inference(avatar_split_clause,[],[f451,f566]) ).
fof(f585,plain,
spl57_3,
inference(avatar_split_clause,[],[f389,f552]) ).
fof(f965,definition,
( spl57_28
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl57_28])],[avatar_definition]) ).
fof(f967,plain,
( nil = sK56
| ~ spl57_28 ),
inference(avatar_component_clause,[],[f965]) ).
fof(f971,plain,
( nil = sK56
| ~ ssList(nil)
| ~ ssList(sK56)
| spl57_1 ),
inference(resolution,[],[f387,f545]) ).
fof(f976,plain,
( nil = sK56
| ~ ssList(sK56)
| spl57_1
| ~ spl57_3 ),
inference(forward_subsumption_resolution,[],[f971,f553]) ).
fof(f977,plain,
( nil = sK56
| spl57_1
| ~ spl57_3 ),
inference(forward_subsumption_resolution,[],[f976,f499]) ).
fof(f978,plain,
( spl57_28
| spl57_1
| ~ spl57_3 ),
inference(avatar_split_clause,[],[f977,f552,f543,f965]) ).
fof(f979,plain,
( sK55 = cons(sK10(sK55),nil)
| ~ ssList(sK55)
| ~ spl57_2 ),
inference(resolution,[],[f549,f306]) ).
fof(f980,plain,
( sK55 = cons(sK10(sK55),nil)
| ~ spl57_2 ),
inference(forward_subsumption_resolution,[],[f979,f498]) ).
fof(f987,plain,
( totalorderedP(sK55)
| ~ ssItem(sK10(sK55))
| ~ spl57_2
| ~ spl57_6 ),
inference(superposition,[],[f567,f980]) ).
fof(f995,plain,
( ~ ssItem(sK10(sK55))
| ~ spl57_2
| ~ spl57_6 ),
inference(forward_subsumption_resolution,[],[f987,f505]) ).
fof(f997,definition,
( spl57_29
<=> ssItem(sK10(sK55)) ),
introduced(definition,[new_symbols(definition,[spl57_29])],[avatar_definition]) ).
fof(f999,plain,
( ~ ssItem(sK10(sK55))
| spl57_29 ),
inference(avatar_component_clause,[],[f997]) ).
fof(f1014,definition,
( spl57_32
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl57_32])],[avatar_definition]) ).
fof(f1015,plain,
( nil = sK55
| ~ spl57_32 ),
inference(avatar_component_clause,[],[f1014]) ).
fof(f1024,plain,
( ~ spl57_29
| ~ spl57_2
| ~ spl57_6 ),
inference(avatar_split_clause,[],[f995,f566,f547,f997]) ).
fof(f1056,plain,
( ~ singletonP(sK55)
| ~ ssList(sK55)
| spl57_29 ),
inference(resolution,[],[f999,f307]) ).
fof(f1060,plain,
( ~ singletonP(sK55)
| spl57_29 ),
inference(forward_subsumption_resolution,[],[f1056,f498]) ).
fof(f1061,plain,
( ~ spl57_2
| spl57_29 ),
inference(avatar_split_clause,[],[f1060,f997,f547]) ).
fof(f1095,plain,
( segmentP(nil,sK55)
| ~ spl57_28 ),
inference(superposition,[],[f502,f967]) ).
fof(f1142,plain,
( nil = sK55
| ~ ssList(sK55)
| ~ spl57_28 ),
inference(resolution,[],[f1095,f443]) ).
fof(f1143,plain,
( nil = sK55
| ~ spl57_28 ),
inference(forward_subsumption_resolution,[],[f1142,f498]) ).
fof(f1144,plain,
( spl57_32
| ~ spl57_28 ),
inference(avatar_split_clause,[],[f1143,f965,f1014]) ).
fof(f1147,plain,
( ~ totalorderedP(nil)
| ~ spl57_32 ),
inference(superposition,[],[f505,f1015]) ).
fof(f1175,plain,
( $false
| ~ spl57_32 ),
inference(forward_subsumption_resolution,[],[f1147,f452]) ).
fof(f1176,plain,
~ spl57_32,
inference(avatar_contradiction_clause,[],[f1175]) ).
cnf(s1,plain,
( ~ spl57_1
| spl57_2 ),
inference(sat_conversion,[],[f550]) ).
cnf(s6,plain,
spl57_6,
inference(sat_conversion,[],[f569]) ).
cnf(s10,plain,
spl57_3,
inference(sat_conversion,[],[f585]) ).
cnf(s26,plain,
( spl57_1
| ~ spl57_3
| spl57_28 ),
inference(sat_conversion,[],[f978]) ).
cnf(s32,plain,
( ~ spl57_2
| ~ spl57_6
| ~ spl57_29 ),
inference(sat_conversion,[],[f1024]) ).
cnf(s38,plain,
( ~ spl57_2
| spl57_29 ),
inference(sat_conversion,[],[f1061]) ).
cnf(s47,plain,
( ~ spl57_28
| spl57_32 ),
inference(sat_conversion,[],[f1144]) ).
cnf(s54,plain,
~ spl57_32,
inference(sat_conversion,[],[f1176]) ).
cnf(s55,plain,
~ spl57_28,
inference(rat,[],[s47,s54]) ).
cnf(s56,plain,
( spl57_1
| ~ spl57_3 ),
inference(rat,[],[s26,s55]) ).
cnf(s58,plain,
spl57_1,
inference(rat,[],[s56,s10]) ).
cnf(s63,plain,
spl57_2,
inference(rat,[],[s1,s58]) ).
cnf(s64,plain,
spl57_29,
inference(rat,[],[s38,s63]) ).
cnf(s68,plain,
$false,
inference(rat,[],[s32,s6,s64,s63]) ).
fof(f1178,plain,
$false,
inference(avatar_sat_refutation,[],[s68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC277+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 08:52:12 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.22/0.27 % (1439387)Will run a generic schedule for satisfiability detection.
% 0.22/0.27 % (1439395)dis+10_1_sil=32000:sp=arity:random_seed=2747583076:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.27 % (1439393)% WARNING: option uhcvi not known.
% 0.22/0.27 % (1439392)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2944702591_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.27 % (1439393)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2807764854:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.27 % (1439394)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1196722751:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.27 % (1439396)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2172304066:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.27 % (1439397)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=753631571:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.27 % (1439398)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1823470915:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.27 % (1439395) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1439387-1439395"...
% 0.22/0.27 % (1439395)...printing done.
% 0.22/0.27 % (1439395)Refutation found. Thanks to Tanya!
% 0.22/0.27 % SZS status Theorem for theBenchmark
% 0.22/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.27 % (1439395)------------------------------
% 0.22/0.27 % (1439395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.27 % (1439395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.27 % (1439395)CaDiCaL version: 2.1.3
% 0.22/0.27 % (1439395)Termination reason: Refutation
% 0.22/0.27 % (1439395)Time elapsed: 0.009 s
% 0.22/0.27 % (1439395)Peak memory usage: 13 MB
% 0.22/0.27 % (1439395)Instructions burned: 27 (million)
% 0.22/0.27 % (1439387)Success in time 0.04 s
% 0.22/0.27 % Vampire exiting
%------------------------------------------------------------------------------