%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC275+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 : n004.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 01:03:14 PM UTC 2026
% Result : Theorem 3.63s 1.30s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 14 unt; 0 def)
% Number of atoms : 108 ( 35 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 121 ( 46 ~; 39 |; 25 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 21 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
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(f65,axiom,
! [X0] :
( ssItem(X0)
=> totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax65) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| totalorderedP(X0)
| ( nil != X2
& nil = X3 )
| ( ! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != X2
| ~ memberP(X3,X4) )
& 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
| totalorderedP(X0)
| ( nil != X2
& nil = X3 )
| ( ! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != X2
| ~ memberP(X3,X4) )
& neq(X3,nil) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ~ totalorderedP(X0)
& ( nil = X2
| nil != X3 )
& ( ? [X4] :
( ssItem(X4)
& cons(X4,nil) = X2
& memberP(X3,X4) )
| ~ neq(X3,nil) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f113,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f139,plain,
( ssList(sK3)
& sK1 = sK3
& sK0 = sK2
& ~ totalorderedP(sK0)
& ( nil = sK2
| nil != sK3 )
& ( ( ssItem(sK4)
& sK2 = cons(sK4,nil)
& memberP(sK3,sK4) )
| ~ neq(sK3,nil) )
& 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)],[f98]) ).
fof(f142,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f106]) ).
fof(f163,plain,
( sK2 = cons(sK4,nil)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f139]) ).
fof(f164,plain,
( ~ neq(sK3,nil)
| ssItem(sK4) ),
inference(cnf_transformation,[],[f139]) ).
fof(f165,plain,
( nil != sK3
| nil = sK2 ),
inference(cnf_transformation,[],[f139]) ).
fof(f166,plain,
~ totalorderedP(sK0),
inference(cnf_transformation,[],[f139]) ).
fof(f167,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f139]) ).
fof(f169,plain,
ssList(sK3),
inference(cnf_transformation,[],[f139]) ).
fof(f182,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f185,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f202,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f203,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f231,plain,
~ totalorderedP(sK2),
inference(definition_unfolding,[],[f166,f167]) ).
fof(f247,plain,
( totalorderedP(sK2)
| ~ ssItem(sK4)
| ~ neq(sK3,nil) ),
inference(superposition,[],[f203,f163]) ).
fof(f248,plain,
( totalorderedP(sK2)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f247,f164]) ).
fof(f249,plain,
~ neq(sK3,nil),
inference(forward_subsumption_resolution,[],[f248,f231]) ).
fof(f258,plain,
( nil = sK3
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(resolution,[],[f182,f249]) ).
fof(f265,plain,
( nil = sK3
| ~ ssList(sK3) ),
inference(forward_subsumption_resolution,[],[f258,f185]) ).
fof(f267,plain,
nil = sK3,
inference(forward_subsumption_resolution,[],[f265,f169]) ).
fof(f270,plain,
( sK3 != sK3
| sK2 = sK3 ),
inference(superposition,[],[f165,f267]) ).
fof(f273,plain,
totalorderedP(sK3),
inference(superposition,[],[f202,f267]) ).
fof(f278,plain,
sK2 = sK3,
inference(trivial_inequality_removal,[],[f270]) ).
fof(f294,plain,
totalorderedP(sK2),
inference(superposition,[],[f273,f278]) ).
fof(f296,plain,
$false,
inference(forward_subsumption_resolution,[],[f294,f231]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC275+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n004.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
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 08:49:07 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 3.63/1.30 % (215237)Detected formulas, will run a generic FOF schedule.
% 3.63/1.30 % (215242)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=3531777096:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.63/1.30 % (215247)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3225159203:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.63/1.30 % (215243)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=4193591364:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.63/1.30 % (215244)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=87654010:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.63/1.30 % (215246)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2383676859:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.63/1.30 % (215245)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=907622833:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.63/1.30 % (215248)dis-21_1_sil=8000:lcm=predicate:random_seed=1867518730: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)
% 3.63/1.30 % (215246)First to succeed.
% 3.63/1.30 % (215245)Also succeeded, but the first one will report.
% 3.63/1.30 % (215246)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-215237"
% 3.63/1.30 % (215247)Also succeeded, but the first one will report.
% 3.63/1.30 % (215248)Instruction limit reached!
% 3.63/1.30 % (215248)------------------------------
% 3.63/1.30 % (215248)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.30 % (215248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.30 % (215248)CaDiCaL version: 2.1.3
% 3.63/1.30 % (215248)Termination reason: Instruction limit
% 3.63/1.30 % (215248)Termination phase: Saturation
% 3.63/1.30 % (215248)Time elapsed: 0.075 s
% 3.63/1.30 % (215248)Peak memory usage: 90 MB
% 3.63/1.30 % (215248)Instructions burned: 129 (million)
% 3.63/1.30 % (215256)lrs+10_1_sil=8000:sp=occurrence:random_seed=3563291038:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.63/1.30 % (215246)Refutation found. Thanks to Tanya!
% 3.63/1.30 % SZS status Theorem for theBenchmark
% 3.63/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.30 % (215246)------------------------------
% 3.63/1.30 % (215246)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.30 % (215246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.30 % (215246)CaDiCaL version: 2.1.3
% 3.63/1.30 % (215246)Termination reason: Refutation
% 3.63/1.30 % (215246)Time elapsed: 0.005 s
% 3.63/1.30 % (215246)Peak memory usage: 88 MB
% 3.63/1.30 % (215246)Instructions burned: 5 (million)
% 3.63/1.30 % (215246)------------------------------
% 3.63/1.30 % (215246)------------------------------
% 3.63/1.30 % (215237)Success in time 0.436 s
% 3.63/1.30 % Vampire exiting
%------------------------------------------------------------------------------