%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC332+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 : n002.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 01:03:30 PM UTC 2026
% Result : Theorem 5.64s 1.64s
% Output : Refutation 5.64s
% 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(f73,axiom,
! [X0] :
( ssItem(X0)
=> equalelemsP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73) ).
fof(f74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/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)
& equalelemsP(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)
| ~ equalelemsP(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)
| ~ equalelemsP(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(f113,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f134,plain,
( sK1 = sK3
& sK0 = sK2
& segmentP(sK3,sK2)
& ( singletonP(sK2)
| ~ neq(sK3,nil) )
& ( ~ segmentP(sK1,sK0)
| ~ equalelemsP(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(f135,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f100]) ).
fof(f137,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(f138,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != X0 ) )
& ( ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X0 )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f137]) ).
fof(f139,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))],[f138]) ).
fof(f140,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f103]) ).
fof(f153,plain,
ssList(sK2),
inference(cnf_transformation,[],[f134]) ).
fof(f154,plain,
ssList(sK3),
inference(cnf_transformation,[],[f134]) ).
fof(f155,plain,
( ~ segmentP(sK1,sK0)
| ~ equalelemsP(sK0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f156,plain,
( ~ neq(sK3,nil)
| singletonP(sK2) ),
inference(cnf_transformation,[],[f134]) ).
fof(f157,plain,
segmentP(sK3,sK2),
inference(cnf_transformation,[],[f134]) ).
fof(f158,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f134]) ).
fof(f159,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f134]) ).
fof(f161,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f164,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f166,plain,
! [X0] :
( cons(sK4(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f167,plain,
! [X0] :
( ssItem(sK4(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f169,plain,
! [X0] :
( ~ segmentP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f140]) ).
fof(f180,plain,
equalelemsP(nil),
inference(cnf_transformation,[],[f74]) ).
fof(f181,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f211,plain,
( ~ segmentP(sK3,sK2)
| ~ equalelemsP(sK2) ),
inference(definition_unfolding,[],[f155,f159,f158,f158]) ).
fof(f225,plain,
~ equalelemsP(sK2),
inference(forward_subsumption_resolution,[],[f211,f157]) ).
fof(f234,plain,
( nil = sK3
| ~ ssList(nil)
| ~ ssList(sK3)
| singletonP(sK2) ),
inference(resolution,[],[f161,f156]) ).
fof(f239,plain,
( nil = sK3
| ~ ssList(sK3)
| singletonP(sK2) ),
inference(forward_subsumption_resolution,[],[f234,f164]) ).
fof(f240,plain,
( nil = sK3
| singletonP(sK2) ),
inference(forward_subsumption_resolution,[],[f239,f154]) ).
fof(f244,plain,
! [X0] :
( ~ segmentP(sK3,X0)
| sK3 = X0
| ~ ssList(X0)
| singletonP(sK2) ),
inference(superposition,[],[f169,f240]) ).
fof(f246,plain,
( equalelemsP(sK3)
| singletonP(sK2) ),
inference(superposition,[],[f180,f240]) ).
fof(f257,plain,
! [X0] :
( equalelemsP(X0)
| ~ ssItem(sK4(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(superposition,[],[f181,f166]) ).
fof(f263,plain,
! [X0] :
( equalelemsP(X0)
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f257,f167]) ).
fof(f282,plain,
( sK2 = sK3
| ~ ssList(sK2)
| singletonP(sK2) ),
inference(resolution,[],[f244,f157]) ).
fof(f288,plain,
( sK2 = sK3
| singletonP(sK2) ),
inference(forward_subsumption_resolution,[],[f282,f153]) ).
fof(f295,plain,
( ~ equalelemsP(sK3)
| singletonP(sK2) ),
inference(superposition,[],[f225,f288]) ).
fof(f298,plain,
singletonP(sK2),
inference(forward_subsumption_resolution,[],[f295,f246]) ).
fof(f335,plain,
( ~ singletonP(sK2)
| ~ ssList(sK2) ),
inference(resolution,[],[f263,f225]) ).
fof(f336,plain,
~ ssList(sK2),
inference(forward_subsumption_resolution,[],[f335,f298]) ).
fof(f337,plain,
$false,
inference(forward_subsumption_resolution,[],[f336,f153]) ).
%------------------------------------------------------------------------------
%----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/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n002.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 09:09:52 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 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
% 5.64/1.64 % (226367)Detected formulas, will run a generic FOF schedule.
% 5.64/1.64 % (226499)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=734256416:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.64/1.64 % (226503)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=192322447:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.64/1.64 % (226501)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=4040839412:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.64/1.64 % (226505)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2300426213:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.64/1.64 % (226504)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1478723486:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.64/1.64 % (226502)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=1571985612:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.64/1.64 % (226506)dis-21_1_sil=8000:lcm=predicate:random_seed=3311237469: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)
% 5.64/1.64 % (226504)First to succeed.
% 5.64/1.64 % (226504)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-226367"
% 5.64/1.64 % (226503)Instruction limit reached!
% 5.64/1.64 % (226503)------------------------------
% 5.64/1.64 % (226503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.64 % (226503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.64 % (226503)CaDiCaL version: 2.1.3
% 5.64/1.64 % (226503)Termination reason: Instruction limit
% 5.64/1.64 % (226503)Termination phase: Saturation
% 5.64/1.64 % (226503)Time elapsed: 0.077 s
% 5.64/1.64 % (226503)Peak memory usage: 89 MB
% 5.64/1.64 % (226503)Instructions burned: 109 (million)
% 5.64/1.64 % (226505)Also succeeded, but the first one will report.
% 5.64/1.64 % (226506)Instruction limit reached!
% 5.64/1.64 % (226506)------------------------------
% 5.64/1.64 % (226506)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.64 % (226506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.64 % (226506)CaDiCaL version: 2.1.3
% 5.64/1.64 % (226506)Termination reason: Instruction limit
% 5.64/1.64 % (226506)Termination phase: Saturation
% 5.64/1.64 % (226506)Time elapsed: 0.129 s
% 5.64/1.64 % (226506)Peak memory usage: 90 MB
% 5.64/1.64 % (226506)Instructions burned: 129 (million)
% 5.64/1.64 % (226515)lrs+10_1_sil=8000:sp=occurrence:random_seed=496936271:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.64/1.64 % (226515)Also succeeded, but the first one will report.
% 5.64/1.64 % (226518)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1624319025:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 5.64/1.64 % (226518)Also succeeded, but the first one will report.
% 5.64/1.64 % (226504)Refutation found. Thanks to Tanya!
% 5.64/1.64 % SZS status Theorem for theBenchmark
% 5.64/1.64 % SZS output start Proof for theBenchmark
% See solution above
% 5.64/1.64 % (226504)------------------------------
% 5.64/1.64 % (226504)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.64 % (226504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.64 % (226504)CaDiCaL version: 2.1.3
% 5.64/1.64 % (226504)Termination reason: Refutation
% 5.64/1.64 % (226504)Time elapsed: 0.010 s
% 5.64/1.64 % (226504)Peak memory usage: 88 MB
% 5.64/1.64 % (226504)Instructions burned: 7 (million)
% 5.64/1.64 % (226504)------------------------------
% 5.64/1.64 % (226504)------------------------------
% 5.64/1.64 % (226367)Success in time 0.701 s
% 5.64/1.64 % Vampire exiting
%------------------------------------------------------------------------------