%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC348+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 01:03:34 PM UTC 2026
% Result : Theorem 2.55s 1.05s
% Output : Refutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 13 unt; 0 def)
% Number of atoms : 178 ( 37 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 202 ( 74 ~; 71 |; 38 &)
% ( 6 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 36 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
fof(f68,axiom,
! [X0] :
( ssItem(X0)
=> strictorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax68) ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69) ).
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)
& strictorderedP(X0) ) ) ) ) ) ),
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)
| ( ~ singletonP(X2)
& neq(X3,nil) )
| ( segmentP(X1,X0)
& strictorderedP(X0) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& segmentP(X3,X2)
& ( singletonP(X2)
| ~ neq(X3,nil) )
& ( ~ segmentP(X1,X0)
| ~ strictorderedP(X0) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& segmentP(X3,X2)
& ( singletonP(X2)
| ~ neq(X3,nil) )
& ( ~ segmentP(X1,X0)
| ~ strictorderedP(X0) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f102,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f103,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f114,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f157,plain,
( sK1 = sK3
& sK0 = sK2
& segmentP(sK3,sK2)
& ( singletonP(sK2)
| ~ neq(sK3,nil) )
& ( ~ segmentP(sK1,sK0)
| ~ strictorderedP(sK0) )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f99]) ).
fof(f158,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f100]) ).
fof(f160,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,[],[f102]) ).
fof(f161,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != X0 ) )
& ( ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X0 )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f160]) ).
fof(f162,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != X0 ) )
& ( ( ssItem(sK4(X0))
& cons(sK4(X0),nil) = X0 )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0))],[f161]) ).
fof(f163,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f103]) ).
fof(f181,plain,
ssList(sK2),
inference(cnf_transformation,[],[f157]) ).
fof(f182,plain,
ssList(sK3),
inference(cnf_transformation,[],[f157]) ).
fof(f183,plain,
( ~ segmentP(sK1,sK0)
| ~ strictorderedP(sK0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f184,plain,
( ~ neq(sK3,nil)
| singletonP(sK2) ),
inference(cnf_transformation,[],[f157]) ).
fof(f185,plain,
segmentP(sK3,sK2),
inference(cnf_transformation,[],[f157]) ).
fof(f186,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f157]) ).
fof(f187,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f157]) ).
fof(f189,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f192,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f194,plain,
! [X0] :
( cons(sK4(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f162]) ).
fof(f195,plain,
! [X0] :
( ssItem(sK4(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f162]) ).
fof(f197,plain,
! [X0] :
( ~ segmentP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f163]) ).
fof(f213,plain,
strictorderedP(nil),
inference(cnf_transformation,[],[f69]) ).
fof(f214,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f261,plain,
( ~ segmentP(sK3,sK2)
| ~ strictorderedP(sK2) ),
inference(definition_unfolding,[],[f183,f187,f186,f186]) ).
fof(f279,plain,
~ strictorderedP(sK2),
inference(forward_subsumption_resolution,[],[f261,f185]) ).
fof(f288,plain,
( nil = sK3
| ~ ssList(nil)
| ~ ssList(sK3)
| singletonP(sK2) ),
inference(resolution,[],[f189,f184]) ).
fof(f293,plain,
( nil = sK3
| ~ ssList(sK3)
| singletonP(sK2) ),
inference(forward_subsumption_resolution,[],[f288,f192]) ).
fof(f294,plain,
( nil = sK3
| singletonP(sK2) ),
inference(forward_subsumption_resolution,[],[f293,f182]) ).
fof(f298,plain,
! [X0] :
( ~ segmentP(sK3,X0)
| sK3 = X0
| ~ ssList(X0)
| singletonP(sK2) ),
inference(superposition,[],[f197,f294]) ).
fof(f300,plain,
( strictorderedP(sK3)
| singletonP(sK2) ),
inference(superposition,[],[f213,f294]) ).
fof(f311,plain,
! [X0] :
( strictorderedP(X0)
| ~ ssItem(sK4(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(superposition,[],[f214,f194]) ).
fof(f317,plain,
! [X0] :
( strictorderedP(X0)
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f311,f195]) ).
fof(f345,plain,
( sK2 = sK3
| ~ ssList(sK2)
| singletonP(sK2) ),
inference(resolution,[],[f298,f185]) ).
fof(f351,plain,
( sK2 = sK3
| singletonP(sK2) ),
inference(forward_subsumption_resolution,[],[f345,f181]) ).
fof(f355,plain,
( ~ strictorderedP(sK3)
| singletonP(sK2) ),
inference(superposition,[],[f279,f351]) ).
fof(f358,plain,
singletonP(sK2),
inference(forward_subsumption_resolution,[],[f355,f300]) ).
fof(f363,plain,
( ~ singletonP(sK2)
| ~ ssList(sK2) ),
inference(resolution,[],[f317,f279]) ).
fof(f364,plain,
~ ssList(sK2),
inference(forward_subsumption_resolution,[],[f363,f358]) ).
fof(f365,plain,
$false,
inference(forward_subsumption_resolution,[],[f364,f181]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC348+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n015.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Mon Sep 28 09:15:31 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running first-order theorem proving
% 0.10/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.55/1.05 % (2492863)Detected formulas, will run a generic FOF schedule.
% 2.55/1.05 % (2492959)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2379050778:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.55/1.05 % (2492959)First to succeed.
% 2.55/1.05 % (2492959)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2492863"
% 2.55/1.05 % (2492956)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=3050598355:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.55/1.05 % (2492957)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4173902384:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.55/1.05 % (2492955)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=3634057773:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.55/1.05 % (2492954)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=441620567:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.55/1.05 % (2492960)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1527335462:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.55/1.05 % (2492961)dis-21_1_sil=8000:lcm=predicate:random_seed=1355696494: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)
% 2.55/1.05 % (2492960)Also succeeded, but the first one will report.
% 2.55/1.05 % (2492957)Instruction limit reached!
% 2.55/1.05 % (2492957)------------------------------
% 2.55/1.05 % (2492957)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.05 % (2492957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.05 % (2492957)CaDiCaL version: 2.1.3
% 2.55/1.05 % (2492957)Termination reason: Instruction limit
% 2.55/1.05 % (2492957)Termination phase: Saturation
% 2.55/1.05 % (2492957)Time elapsed: 0.068 s
% 2.55/1.05 % (2492957)Peak memory usage: 89 MB
% 2.55/1.05 % (2492957)Instructions burned: 110 (million)
% 2.55/1.05 % (2492961)Instruction limit reached!
% 2.55/1.05 % (2492961)------------------------------
% 2.55/1.05 % (2492961)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.05 % (2492961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.05 % (2492961)CaDiCaL version: 2.1.3
% 2.55/1.05 % (2492961)Termination reason: Instruction limit
% 2.55/1.05 % (2492961)Termination phase: Saturation
% 2.55/1.05 % (2492961)Time elapsed: 0.074 s
% 2.55/1.05 % (2492961)Peak memory usage: 90 MB
% 2.55/1.05 % (2492961)Instructions burned: 129 (million)
% 2.55/1.05 % (2492959)Refutation found. Thanks to Tanya!
% 2.55/1.05 % SZS status Theorem for theBenchmark
% 2.55/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 2.55/1.05 % (2492959)------------------------------
% 2.55/1.05 % (2492959)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.05 % (2492959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.05 % (2492959)CaDiCaL version: 2.1.3
% 2.55/1.05 % (2492959)Termination reason: Refutation
% 2.55/1.05 % (2492959)Time elapsed: 0.003 s
% 2.55/1.05 % (2492959)Peak memory usage: 88 MB
% 2.55/1.05 % (2492959)Instructions burned: 7 (million)
% 2.55/1.05 % (2492959)------------------------------
% 2.55/1.05 % (2492959)------------------------------
% 2.55/1.05 % (2492863)Success in time 0.274 s
% 2.55/1.05 % Vampire exiting
%------------------------------------------------------------------------------