%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC408+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 : n008.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 01:03:51 PM UTC 2026
% Result : Theorem 2.06s 0.90s
% Output : Refutation 2.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 26 ( 13 unt; 0 def)
% Number of atoms : 107 ( 18 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 125 ( 44 ~; 35 |; 31 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 35 ( 25 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X1,X0)
| memberP(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X3) != X2
| X1 != X3
| X0 != X2
| ! [X4] :
( ssItem(X4)
=> ( ~ memberP(X1,X4)
| memberP(X0,X4) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X3) != X2
| X1 != X3
| X0 != X2
| ! [X4] :
( ssItem(X4)
=> ( ~ memberP(X1,X4)
| memberP(X0,X4) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( app(X3,X3) = X2
& X1 = X3
& X0 = X2
& ? [X4] :
( memberP(X1,X4)
& ~ memberP(X0,X4)
& ssItem(X4) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( app(X3,X3) = X2
& X1 = X3
& X0 = X2
& ? [X4] :
( memberP(X1,X4)
& ~ memberP(X0,X4)
& ssItem(X4) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f113,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(app(X1,X2),X0)
<=> ( memberP(X1,X0)
| memberP(X2,X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f115,plain,
( sK2 = app(sK3,sK3)
& sK1 = sK3
& sK0 = sK2
& memberP(sK1,sK4)
& ~ memberP(sK0,sK4)
& ssItem(sK4)
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f99]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X1,X0)
& ~ memberP(X2,X0) ) )
& ( memberP(X1,X0)
| memberP(X2,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f113]) ).
fof(f122,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X1,X0)
& ~ memberP(X2,X0) ) )
& ( memberP(X1,X0)
| memberP(X2,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f121]) ).
fof(f127,plain,
ssList(sK1),
inference(cnf_transformation,[],[f115]) ).
fof(f130,plain,
ssItem(sK4),
inference(cnf_transformation,[],[f115]) ).
fof(f131,plain,
~ memberP(sK0,sK4),
inference(cnf_transformation,[],[f115]) ).
fof(f132,plain,
memberP(sK1,sK4),
inference(cnf_transformation,[],[f115]) ).
fof(f133,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f115]) ).
fof(f134,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f115]) ).
fof(f135,plain,
sK2 = app(sK3,sK3),
inference(cnf_transformation,[],[f115]) ).
fof(f156,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f161,plain,
memberP(sK3,sK4),
inference(definition_unfolding,[],[f132,f134]) ).
fof(f162,plain,
~ memberP(sK2,sK4),
inference(definition_unfolding,[],[f131,f133]) ).
fof(f163,plain,
ssList(sK3),
inference(definition_unfolding,[],[f127,f134]) ).
fof(f177,plain,
~ memberP(app(sK3,sK3),sK4),
inference(superposition,[],[f162,f135]) ).
fof(f196,plain,
( ~ memberP(sK3,sK4)
| ~ ssList(sK3)
| ~ ssList(sK3)
| ~ ssItem(sK4) ),
inference(resolution,[],[f177,f156]) ).
fof(f199,plain,
( ~ memberP(sK3,sK4)
| ~ ssList(sK3)
| ~ ssItem(sK4) ),
inference(duplicate_literal_removal,[],[f196]) ).
fof(f201,plain,
( ~ ssList(sK3)
| ~ ssItem(sK4) ),
inference(forward_subsumption_resolution,[],[f199,f161]) ).
fof(f203,plain,
~ ssItem(sK4),
inference(forward_subsumption_resolution,[],[f201,f163]) ).
fof(f205,plain,
$false,
inference(forward_subsumption_resolution,[],[f203,f130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC408+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n008.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 09:32:10 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 2.06/0.90 % (2124241)Detected formulas, will run a generic FOF schedule.
% 2.06/0.90 % (2124252)dis-21_1_sil=8000:lcm=predicate:random_seed=3484095407: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)
% 2.06/0.90 % (2124252)Instruction limit reached!
% 2.06/0.90 % (2124252)------------------------------
% 2.06/0.90 % (2124252)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.06/0.90 % (2124252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/0.90 % (2124252)CaDiCaL version: 2.1.3
% 2.06/0.90 % (2124252)Termination reason: Instruction limit
% 2.06/0.90 % (2124252)Termination phase: Saturation
% 2.06/0.90 % (2124252)Time elapsed: 0.039 s
% 2.06/0.90 % (2124252)Peak memory usage: 91 MB
% 2.06/0.90 % (2124252)Instructions burned: 132 (million)
% 2.06/0.90 % (2124249)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3785962245:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.06/0.90 % (2124250)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3209693737:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.06/0.90 % (2124246)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=4014613280:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.06/0.90 % (2124251)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3642583186:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.06/0.90 % (2124248)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=1030499147:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.06/0.90 % (2124247)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=3898278578:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.06/0.90 % (2124249)First to succeed.
% 2.06/0.90 % (2124250)Also succeeded, but the first one will report.
% 2.06/0.90 % (2124249)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2124241"
% 2.06/0.90 % (2124260)lrs+10_1_sil=8000:sp=occurrence:random_seed=878958924:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.06/0.90 % (2124260)Also succeeded, but the first one will report.
% 2.06/0.90 % (2124251)Instruction limit reached!
% 2.06/0.90 % (2124251)------------------------------
% 2.06/0.90 % (2124251)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.06/0.90 % (2124251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/0.90 % (2124251)CaDiCaL version: 2.1.3
% 2.06/0.90 % (2124251)Termination reason: Instruction limit
% 2.06/0.90 % (2124251)Termination phase: Saturation
% 2.06/0.90 % (2124251)Time elapsed: 0.092 s
% 2.06/0.90 % (2124251)Peak memory usage: 90 MB
% 2.06/0.90 % (2124251)Instructions burned: 140 (million)
% 2.06/0.90 % (2124262)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4083738616:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.06/0.90 % (2124262)Also succeeded, but the first one will report.
% 2.06/0.90 % (2124249)Refutation found. Thanks to Tanya!
% 2.06/0.90 % SZS status Theorem for theBenchmark
% 2.06/0.90 % SZS output start Proof for theBenchmark
% See solution above
% 2.06/0.90 % (2124249)------------------------------
% 2.06/0.90 % (2124249)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.06/0.90 % (2124249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/0.90 % (2124249)CaDiCaL version: 2.1.3
% 2.06/0.90 % (2124249)Termination reason: Refutation
% 2.06/0.90 % (2124249)Time elapsed: 0.003 s
% 2.06/0.90 % (2124249)Peak memory usage: 89 MB
% 2.06/0.90 % (2124249)Instructions burned: 3 (million)
% 2.06/0.90 % (2124249)------------------------------
% 2.06/0.90 % (2124249)------------------------------
% 2.06/0.90 % (2124241)Success in time 0.392 s
% 2.06/0.90 % Vampire exiting
%------------------------------------------------------------------------------