%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC381+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 : n007.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 01:03:43 PM UTC 2026
% Result : Theorem 2.71s 1.14s
% Output : Refutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 28 ( 6 unt; 1 def)
% Number of atoms : 146 ( 32 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 180 ( 62 ~; 50 |; 58 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 91 ( 72 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssItem(X4)
& cons(X4,nil) = X0
& memberP(X1,X4) )
| ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X2
| ~ memberP(X3,X5) ) ) )
& ( ~ neq(X1,nil)
| 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
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssItem(X4)
& cons(X4,nil) = X0
& memberP(X1,X4) )
| ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X2
| ~ memberP(X3,X5) ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != X0
| ~ memberP(X1,X4) )
& ? [X5] :
( cons(X5,nil) = X2
& memberP(X3,X5)
& ssItem(X5) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != X0
| ~ memberP(X1,X4) )
& ? [X5] :
( cons(X5,nil) = X2
& memberP(X3,X5)
& ssItem(X5) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f124,definition,
! [X1,X0,X2,X3] :
( ( neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != X0
| ~ memberP(X1,X4) )
& ? [X5] :
( cons(X5,nil) = X2
& memberP(X3,X5)
& ssItem(X5) ) )
| ~ sP0(X1,X0,X2,X3) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f125,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( sP0(X1,X0,X2,X3)
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f99,f124]) ).
fof(f126,plain,
! [X1,X0,X2,X3] :
( ( neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != X0
| ~ memberP(X1,X4) )
& ? [X5] :
( cons(X5,nil) = X2
& memberP(X3,X5)
& ssItem(X5) ) )
| ~ sP0(X1,X0,X2,X3) ),
inference(nnf_transformation,[],[f124]) ).
fof(f127,plain,
! [X0,X1,X2,X3] :
( ( neq(X0,nil)
& ! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != X1
| ~ memberP(X0,X4) )
& ? [X5] :
( cons(X5,nil) = X2
& memberP(X3,X5)
& ssItem(X5) ) )
| ~ sP0(X0,X1,X2,X3) ),
inference(rectify,[],[f126]) ).
fof(f128,plain,
! [X0,X1,X2,X3] :
( ( neq(X0,nil)
& ! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != X1
| ~ memberP(X0,X4) )
& cons(sK1(X2,X3),nil) = X2
& memberP(X3,sK1(X2,X3))
& ssItem(sK1(X2,X3)) )
| ~ sP0(X0,X1,X2,X3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X5,sK1(X2,X3))],[f127]) ).
fof(f129,plain,
( sK3 = sK5
& sK2 = sK4
& ( sP0(sK3,sK2,sK4,sK5)
| ( neq(sK3,nil)
& ~ neq(sK5,nil) ) )
& ssList(sK5)
& ssList(sK4)
& ssList(sK3)
& ssList(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f125]) ).
fof(f143,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssItem(sK1(X2,X3)) ),
inference(cnf_transformation,[],[f128]) ).
fof(f144,plain,
! [X2,X3,X0,X1] :
( memberP(X3,sK1(X2,X3))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f128]) ).
fof(f145,plain,
! [X2,X3,X0,X1] :
( cons(sK1(X2,X3),nil) = X2
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f128]) ).
fof(f146,plain,
! [X2,X3,X0,X1,X4] :
( ~ ssItem(X4)
| cons(X4,nil) != X1
| ~ memberP(X0,X4)
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f128]) ).
fof(f152,plain,
( sP0(sK3,sK2,sK4,sK5)
| ~ neq(sK5,nil) ),
inference(cnf_transformation,[],[f129]) ).
fof(f153,plain,
( sP0(sK3,sK2,sK4,sK5)
| neq(sK3,nil) ),
inference(cnf_transformation,[],[f129]) ).
fof(f154,plain,
sK2 = sK4,
inference(cnf_transformation,[],[f129]) ).
fof(f155,plain,
sK3 = sK5,
inference(cnf_transformation,[],[f129]) ).
fof(f194,plain,
( sP0(sK5,sK4,sK4,sK5)
| neq(sK5,nil) ),
inference(definition_unfolding,[],[f153,f155,f154,f155]) ).
fof(f195,plain,
( sP0(sK5,sK4,sK4,sK5)
| ~ neq(sK5,nil) ),
inference(definition_unfolding,[],[f152,f155,f154]) ).
fof(f198,plain,
! [X2,X3,X0,X4] :
( ~ sP0(X0,cons(X4,nil),X2,X3)
| ~ memberP(X0,X4)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f146]) ).
fof(f209,plain,
sP0(sK5,sK4,sK4,sK5),
inference(forward_subsumption_resolution,[],[f195,f194]) ).
fof(f256,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sP0(X1,X0,X3,X4)
| ~ memberP(X1,sK1(X0,X2))
| ~ ssItem(sK1(X0,X2))
| ~ sP0(X5,X6,X0,X2) ),
inference(superposition,[],[f198,f145]) ).
fof(f257,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sP0(X5,X6,X0,X2)
| ~ memberP(X1,sK1(X0,X2))
| ~ sP0(X1,X0,X3,X4) ),
inference(forward_subsumption_resolution,[],[f256,f143]) ).
fof(f982,plain,
! [X2,X0,X1] :
( ~ sP0(X0,sK4,X1,X2)
| ~ memberP(X0,sK1(sK4,sK5)) ),
inference(resolution,[],[f257,f209]) ).
fof(f985,plain,
~ memberP(sK5,sK1(sK4,sK5)),
inference(resolution,[],[f982,f209]) ).
fof(f989,plain,
! [X0,X1] : ~ sP0(X0,X1,sK4,sK5),
inference(resolution,[],[f985,f144]) ).
fof(f990,plain,
$false,
inference(resolution,[],[f989,f209]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC381+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n007.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 09:20:25 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 2.71/1.14 % (2262298)Detected formulas, will run a generic FOF schedule.
% 2.71/1.14 % (2262307)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2059158626:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.71/1.14 % (2262307)First to succeed.
% 2.71/1.14 % (2262307)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2262298"
% 2.71/1.14 % (2262305)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=40455695:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.71/1.14 % (2262308)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2426256418:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.71/1.14 % (2262303)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=2415648650:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.71/1.14 % (2262304)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=2638167123:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.71/1.14 % (2262309)dis-21_1_sil=8000:lcm=predicate:random_seed=4168653519: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)
% 2.71/1.14 % (2262306)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3890286562:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.71/1.14 % (2262306)Refutation not found, incomplete strategy
% 2.71/1.14 % (2262306)------------------------------
% 2.71/1.14 % (2262306)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.14 % (2262306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.14 % (2262306)CaDiCaL version: 2.1.3
% 2.71/1.14 % (2262306)Termination reason: Refutation not found, incomplete strategy
% 2.71/1.14 % (2262306)Time elapsed: 0.003 s
% 2.71/1.14 % (2262306)Peak memory usage: 88 MB
% 2.71/1.14 % (2262306)Instructions burned: 3 (million)
% 2.71/1.14 % (2262309)Instruction limit reached!
% 2.71/1.14 % (2262309)------------------------------
% 2.71/1.14 % (2262309)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.14 % (2262309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.14 % (2262309)CaDiCaL version: 2.1.3
% 2.71/1.14 % (2262309)Termination reason: Instruction limit
% 2.71/1.14 % (2262309)Termination phase: Saturation
% 2.71/1.14 % (2262309)Time elapsed: 0.072 s
% 2.71/1.14 % (2262309)Peak memory usage: 90 MB
% 2.71/1.14 % (2262309)Instructions burned: 130 (million)
% 2.71/1.14 % (2262308)Instruction limit reached!
% 2.71/1.14 % (2262308)------------------------------
% 2.71/1.14 % (2262308)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.14 % (2262308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.14 % (2262308)CaDiCaL version: 2.1.3
% 2.71/1.14 % (2262308)Termination reason: Instruction limit
% 2.71/1.14 % (2262308)Termination phase: Saturation
% 2.71/1.14 % (2262308)Time elapsed: 0.092 s
% 2.71/1.14 % (2262308)Peak memory usage: 90 MB
% 2.71/1.14 % (2262308)Instructions burned: 139 (million)
% 2.71/1.14 % (2262307)Refutation found. Thanks to Tanya!
% 2.71/1.14 % SZS status Theorem for theBenchmark
% 2.71/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 2.71/1.15 % (2262307)------------------------------
% 2.71/1.15 % (2262307)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.15 % (2262307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.15 % (2262307)CaDiCaL version: 2.1.3
% 2.71/1.15 % (2262307)Termination reason: Refutation
% 2.71/1.15 % (2262307)Time elapsed: 0.009 s
% 2.71/1.15 % (2262307)Peak memory usage: 88 MB
% 2.71/1.15 % (2262307)Instructions burned: 25 (million)
% 2.71/1.15 % (2262307)------------------------------
% 2.71/1.15 % (2262307)------------------------------
% 2.71/1.15 % (2262298)Success in time 0.291 s
% 2.71/1.15 % Vampire exiting
%------------------------------------------------------------------------------