%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC277+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 01:03:15 PM UTC 2026
% Result : Theorem 2.07s 0.86s
% Output : Refutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 81 ( 21 unt; 6 def)
% Number of atoms : 237 ( 39 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 258 ( 102 ~; 95 |; 36 &)
% ( 12 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 7 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/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
fof(f65,axiom,
! [X0] :
( ssItem(X0)
=> totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax65) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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/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)
| 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(f540,definition,
( spl57_1
<=> neq(sK56,nil) ),
introduced(definition,[new_symbols(definition,[spl57_1])],[avatar_definition]) ).
fof(f542,plain,
( ~ neq(sK56,nil)
| spl57_1 ),
inference(avatar_component_clause,[],[f540]) ).
fof(f544,definition,
( spl57_2
<=> singletonP(sK55) ),
introduced(definition,[new_symbols(definition,[spl57_2])],[avatar_definition]) ).
fof(f546,plain,
( singletonP(sK55)
| ~ spl57_2 ),
inference(avatar_component_clause,[],[f544]) ).
fof(f547,plain,
( ~ spl57_1
| spl57_2 ),
inference(avatar_split_clause,[],[f500,f544,f540]) ).
fof(f549,definition,
( spl57_3
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl57_3])],[avatar_definition]) ).
fof(f550,plain,
( ssList(nil)
| ~ spl57_3 ),
inference(avatar_component_clause,[],[f549]) ).
fof(f563,definition,
( spl57_6
<=> ! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl57_6])],[avatar_definition]) ).
fof(f564,plain,
( ! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl57_6 ),
inference(avatar_component_clause,[],[f563]) ).
fof(f566,plain,
spl57_6,
inference(avatar_split_clause,[],[f451,f563]) ).
fof(f582,plain,
spl57_3,
inference(avatar_split_clause,[],[f389,f549]) ).
fof(f583,plain,
~ totalorderedP(sK55),
inference(superposition,[],[f501,f503]) ).
fof(f621,definition,
( spl57_12
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl57_12])],[avatar_definition]) ).
fof(f623,plain,
( nil = sK56
| ~ spl57_12 ),
inference(avatar_component_clause,[],[f621]) ).
fof(f625,plain,
( nil = sK56
| ~ ssList(nil)
| ~ ssList(sK56)
| spl57_1 ),
inference(resolution,[],[f387,f542]) ).
fof(f630,plain,
( nil = sK56
| ~ ssList(sK56)
| spl57_1
| ~ spl57_3 ),
inference(forward_subsumption_resolution,[],[f625,f550]) ).
fof(f631,plain,
( nil = sK56
| spl57_1
| ~ spl57_3 ),
inference(forward_subsumption_resolution,[],[f630,f499]) ).
fof(f632,plain,
( spl57_12
| spl57_1
| ~ spl57_3 ),
inference(avatar_split_clause,[],[f631,f549,f540,f621]) ).
fof(f635,plain,
( segmentP(nil,sK55)
| ~ spl57_12 ),
inference(superposition,[],[f502,f623]) ).
fof(f646,plain,
( nil = sK55
| ~ ssList(sK55)
| ~ spl57_12 ),
inference(resolution,[],[f635,f443]) ).
fof(f647,plain,
( nil = sK55
| ~ spl57_12 ),
inference(forward_subsumption_resolution,[],[f646,f498]) ).
fof(f651,plain,
( ~ totalorderedP(nil)
| ~ spl57_12 ),
inference(superposition,[],[f583,f647]) ).
fof(f655,plain,
( $false
| ~ spl57_12 ),
inference(forward_subsumption_resolution,[],[f651,f452]) ).
fof(f656,plain,
~ spl57_12,
inference(avatar_contradiction_clause,[],[f655]) ).
fof(f657,plain,
( sK55 = cons(sK10(sK55),nil)
| ~ ssList(sK55)
| ~ spl57_2 ),
inference(resolution,[],[f546,f306]) ).
fof(f658,plain,
( sK55 = cons(sK10(sK55),nil)
| ~ spl57_2 ),
inference(forward_subsumption_resolution,[],[f657,f498]) ).
fof(f668,plain,
( totalorderedP(sK55)
| ~ ssItem(sK10(sK55))
| ~ spl57_2
| ~ spl57_6 ),
inference(superposition,[],[f564,f658]) ).
fof(f680,plain,
( ~ ssItem(sK10(sK55))
| ~ spl57_2
| ~ spl57_6 ),
inference(forward_subsumption_resolution,[],[f668,f583]) ).
fof(f682,definition,
( spl57_13
<=> ssItem(sK10(sK55)) ),
introduced(definition,[new_symbols(definition,[spl57_13])],[avatar_definition]) ).
fof(f684,plain,
( ~ ssItem(sK10(sK55))
| spl57_13 ),
inference(avatar_component_clause,[],[f682]) ).
fof(f736,plain,
( ~ spl57_13
| ~ spl57_2
| ~ spl57_6 ),
inference(avatar_split_clause,[],[f680,f563,f544,f682]) ).
fof(f737,plain,
( ~ singletonP(sK55)
| ~ ssList(sK55)
| spl57_13 ),
inference(resolution,[],[f684,f307]) ).
fof(f738,plain,
( ~ ssList(sK55)
| ~ spl57_2
| spl57_13 ),
inference(forward_subsumption_resolution,[],[f737,f546]) ).
fof(f739,plain,
( $false
| ~ spl57_2
| spl57_13 ),
inference(forward_subsumption_resolution,[],[f738,f498]) ).
fof(f740,plain,
( ~ spl57_2
| spl57_13 ),
inference(avatar_contradiction_clause,[],[f739]) ).
cnf(s1,plain,
( ~ spl57_1
| spl57_2 ),
inference(sat_conversion,[],[f547]) ).
cnf(s6,plain,
spl57_6,
inference(sat_conversion,[],[f566]) ).
cnf(s10,plain,
spl57_3,
inference(sat_conversion,[],[f582]) ).
cnf(s12,plain,
( spl57_1
| ~ spl57_3
| spl57_12 ),
inference(sat_conversion,[],[f632]) ).
cnf(s14,plain,
~ spl57_12,
inference(sat_conversion,[],[f656]) ).
cnf(s26,plain,
( ~ spl57_2
| ~ spl57_6
| ~ spl57_13 ),
inference(sat_conversion,[],[f736]) ).
cnf(s27,plain,
( ~ spl57_2
| spl57_13 ),
inference(sat_conversion,[],[f740]) ).
cnf(s28,plain,
( spl57_1
| ~ spl57_3 ),
inference(rat,[],[s12,s14]) ).
cnf(s30,plain,
spl57_1,
inference(rat,[],[s28,s10]) ).
cnf(s35,plain,
spl57_2,
inference(rat,[],[s1,s30]) ).
cnf(s36,plain,
spl57_13,
inference(rat,[],[s27,s35]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s26,s6,s36,s35]) ).
fof(f741,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC277+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.15 % Computer : n012.cluster.edu
% 0.09/0.15 % Model : x86_64 x86_64
% 0.09/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.15 % Memory : 8046.5625MB
% 0.09/0.15 % OS : Linux 6.8.0-71-generic
% 0.09/0.15 % CPULimit : 300
% 0.09/0.15 % WCLimit : 300
% 0.09/0.15 % DateTime : Mon Sep 28 08:50:04 UTC 2026
% 0.09/0.15 % CPUTime :
% 0.09/0.15 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 Running first-order theorem proving
% 0.09/0.17 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.07/0.86 % (3241058)Detected formulas, will run a generic FOF schedule.
% 2.07/0.86 % (3241068)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2751338452:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.07/0.86 % (3241068)First to succeed.
% 2.07/0.86 % (3241068)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3241058"
% 2.07/0.86 % (3241065)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=662773293:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.07/0.86 % (3241066)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3438611585:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.07/0.86 % (3241064)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3778172511:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.07/0.86 % (3241067)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=667515904:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.07/0.86 % (3241063)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=4035695011:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.07/0.86 % (3241067)Also succeeded, but the first one will report.
% 2.07/0.86 % (3241069)dis-21_1_sil=8000:lcm=predicate:random_seed=3048503574:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.07/0.86 % (3241066)Instruction limit reached!
% 2.07/0.86 % (3241066)------------------------------
% 2.07/0.86 % (3241066)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.07/0.86 % (3241066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.86 % (3241066)CaDiCaL version: 2.1.3
% 2.07/0.86 % (3241066)Termination reason: Instruction limit
% 2.07/0.86 % (3241066)Termination phase: Saturation
% 2.07/0.86 % (3241066)Time elapsed: 0.058 s
% 2.07/0.86 % (3241066)Peak memory usage: 89 MB
% 2.07/0.86 % (3241066)Instructions burned: 110 (million)
% 2.07/0.86 % (3241069)Instruction limit reached!
% 2.07/0.86 % (3241069)------------------------------
% 2.07/0.86 % (3241069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.07/0.86 % (3241069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.86 % (3241069)CaDiCaL version: 2.1.3
% 2.07/0.86 % (3241069)Termination reason: Instruction limit
% 2.07/0.86 % (3241069)Termination phase: Saturation
% 2.07/0.86 % (3241069)Time elapsed: 0.068 s
% 2.07/0.86 % (3241069)Peak memory usage: 90 MB
% 2.07/0.86 % (3241069)Instructions burned: 129 (million)
% 2.07/0.86 % (3241068)Refutation found. Thanks to Tanya!
% 2.07/0.86 % SZS status Theorem for theBenchmark
% 2.07/0.86 % SZS output start Proof for theBenchmark
% See solution above
% 2.79/1.00 % (3241068)------------------------------
% 2.79/1.00 % (3241068)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.00 % (3241068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.00 % (3241068)CaDiCaL version: 2.1.3
% 2.79/1.00 % (3241068)Termination reason: Refutation
% 2.79/1.00 % (3241068)Time elapsed: 0.008 s
% 2.79/1.00 % (3241068)Peak memory usage: 90 MB
% 2.79/1.00 % (3241068)Instructions burned: 17 (million)
% 2.79/1.00 % (3241068)------------------------------
% 2.79/1.00 % (3241068)------------------------------
% 2.79/1.00 % (3241058)Success in time 0.344 s
% 2.79/1.00 % Vampire exiting
%------------------------------------------------------------------------------