%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC292+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 01:03:19 PM UTC 2026
% Result : Theorem 2.62s 0.82s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 66 ( 20 unt; 7 def)
% Number of atoms : 193 ( 42 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 207 ( 80 ~; 70 |; 35 &)
% ( 9 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 8 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 23 !; 10 ?)
% 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(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
| strictorderedP(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
| strictorderedP(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(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f182,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ~ strictorderedP(X0)
& ( nil = X2
| nil != X3 )
& ( ? [X4] :
( cons(X4,nil) = X2
& memberP(X3,X4)
& ssItem(X4) )
| ~ neq(X3,nil) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ~ strictorderedP(X0)
& ( nil = X2
| nil != X3 )
& ( ? [X4] :
( cons(X4,nil) = X2
& memberP(X3,X4)
& ssItem(X4) )
| ~ neq(X3,nil) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f273,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& ~ strictorderedP(sK53)
& ( nil = sK55
| nil != sK56 )
& ( ( sK55 = cons(sK57,nil)
& memberP(sK56,sK57)
& ssItem(sK57) )
| ~ neq(sK56,nil) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57)],[f222]) ).
fof(f387,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f458,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f182]) ).
fof(f459,plain,
strictorderedP(nil),
inference(cnf_transformation,[],[f69]) ).
fof(f499,plain,
ssList(sK56),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( ssItem(sK57)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( sK55 = cons(sK57,nil)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
( nil = sK55
| nil != sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
~ strictorderedP(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f542,definition,
( spl58_1
<=> neq(sK56,nil) ),
introduced(definition,[new_symbols(definition,[spl58_1])],[avatar_definition]) ).
fof(f544,plain,
( ~ neq(sK56,nil)
| spl58_1 ),
inference(avatar_component_clause,[],[f542]) ).
fof(f546,definition,
( spl58_2
<=> ssItem(sK57) ),
introduced(definition,[new_symbols(definition,[spl58_2])],[avatar_definition]) ).
fof(f548,plain,
( ssItem(sK57)
| ~ spl58_2 ),
inference(avatar_component_clause,[],[f546]) ).
fof(f549,plain,
( ~ spl58_1
| spl58_2 ),
inference(avatar_split_clause,[],[f500,f546,f542]) ).
fof(f556,definition,
( spl58_4
<=> sK55 = cons(sK57,nil) ),
introduced(definition,[new_symbols(definition,[spl58_4])],[avatar_definition]) ).
fof(f558,plain,
( sK55 = cons(sK57,nil)
| ~ spl58_4 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f559,plain,
( ~ spl58_1
| spl58_4 ),
inference(avatar_split_clause,[],[f502,f556,f542]) ).
fof(f561,definition,
( spl58_5
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl58_5])],[avatar_definition]) ).
fof(f565,definition,
( spl58_6
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl58_6])],[avatar_definition]) ).
fof(f567,plain,
( nil = sK55
| ~ spl58_6 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f568,plain,
( ~ spl58_5
| spl58_6 ),
inference(avatar_split_clause,[],[f503,f565,f561]) ).
fof(f570,definition,
( spl58_7
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl58_7])],[avatar_definition]) ).
fof(f571,plain,
( ssList(nil)
| ~ spl58_7 ),
inference(avatar_component_clause,[],[f570]) ).
fof(f579,definition,
( spl58_9
<=> ! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl58_9])],[avatar_definition]) ).
fof(f580,plain,
( ! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl58_9 ),
inference(avatar_component_clause,[],[f579]) ).
fof(f582,plain,
spl58_9,
inference(avatar_split_clause,[],[f458,f579]) ).
fof(f603,plain,
spl58_7,
inference(avatar_split_clause,[],[f389,f570]) ).
fof(f604,plain,
~ strictorderedP(sK55),
inference(superposition,[],[f504,f505]) ).
fof(f643,plain,
( nil = sK56
| ~ ssList(nil)
| ~ ssList(sK56)
| spl58_1 ),
inference(resolution,[],[f387,f544]) ).
fof(f652,plain,
( nil = sK56
| ~ ssList(sK56)
| spl58_1
| ~ spl58_7 ),
inference(forward_subsumption_resolution,[],[f643,f571]) ).
fof(f653,plain,
( nil = sK56
| spl58_1
| ~ spl58_7 ),
inference(forward_subsumption_resolution,[],[f652,f499]) ).
fof(f654,plain,
( spl58_5
| spl58_1
| ~ spl58_7 ),
inference(avatar_split_clause,[],[f653,f570,f542,f561]) ).
fof(f659,plain,
( ~ strictorderedP(nil)
| ~ spl58_6 ),
inference(superposition,[],[f604,f567]) ).
fof(f661,plain,
( $false
| ~ spl58_6 ),
inference(forward_subsumption_resolution,[],[f659,f459]) ).
fof(f662,plain,
~ spl58_6,
inference(avatar_contradiction_clause,[],[f661]) ).
fof(f668,plain,
( strictorderedP(sK55)
| ~ ssItem(sK57)
| ~ spl58_4
| ~ spl58_9 ),
inference(superposition,[],[f580,f558]) ).
fof(f676,plain,
( ~ ssItem(sK57)
| ~ spl58_4
| ~ spl58_9 ),
inference(forward_subsumption_resolution,[],[f668,f604]) ).
fof(f683,plain,
( $false
| ~ spl58_2
| ~ spl58_4
| ~ spl58_9 ),
inference(forward_subsumption_resolution,[],[f676,f548]) ).
fof(f684,plain,
( ~ spl58_2
| ~ spl58_4
| ~ spl58_9 ),
inference(avatar_contradiction_clause,[],[f683]) ).
cnf(s1,plain,
( ~ spl58_1
| spl58_2 ),
inference(sat_conversion,[],[f549]) ).
cnf(s3,plain,
( ~ spl58_1
| spl58_4 ),
inference(sat_conversion,[],[f559]) ).
cnf(s4,plain,
( ~ spl58_5
| spl58_6 ),
inference(sat_conversion,[],[f568]) ).
cnf(s7,plain,
spl58_9,
inference(sat_conversion,[],[f582]) ).
cnf(s13,plain,
spl58_7,
inference(sat_conversion,[],[f603]) ).
cnf(s16,plain,
( spl58_1
| spl58_5
| ~ spl58_7 ),
inference(sat_conversion,[],[f654]) ).
cnf(s18,plain,
~ spl58_6,
inference(sat_conversion,[],[f662]) ).
cnf(s19,plain,
( ~ spl58_2
| ~ spl58_4
| ~ spl58_9 ),
inference(sat_conversion,[],[f684]) ).
cnf(s24,plain,
~ spl58_5,
inference(rat,[],[s4,s18]) ).
cnf(s25,plain,
spl58_1,
inference(rat,[],[s16,s13,s24]) ).
cnf(s26,plain,
spl58_4,
inference(rat,[],[s3,s25]) ).
cnf(s27,plain,
~ spl58_2,
inference(rat,[],[s19,s7,s26]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s1,s27,s25]) ).
fof(f685,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC292+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.16 % Computer : n002.cluster.edu
% 0.07/0.16 % Model : x86_64 x86_64
% 0.07/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.16 % Memory : 8046.5625MB
% 0.07/0.16 % OS : Linux 6.8.0-71-generic
% 0.07/0.16 % CPULimit : 300
% 0.07/0.16 % WCLimit : 300
% 0.07/0.16 % DateTime : Mon Sep 28 08:57:52 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running first-order theorem proving
% 0.07/0.20 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
% 2.62/0.82 % (221142)Detected formulas, will run a generic FOF schedule.
% 2.62/0.82 % (221152)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=649771055:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.62/0.82 % (221149)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=1979965416:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.62/0.82 % (221151)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3269100264:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.62/0.82 % (221147)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=996311390:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.62/0.82 % (221153)dis-21_1_sil=8000:lcm=predicate:random_seed=1450970318: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)
% 2.62/0.82 % (221150)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2950736202:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.62/0.82 % (221148)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=689524646:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.62/0.82 % (221152)First to succeed.
% 2.62/0.82 % (221151)Also succeeded, but the first one will report.
% 2.62/0.82 % (221152)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-221142"
% 2.62/0.82 % (221150)Also succeeded, but the first one will report.
% 2.62/0.82 % (221153)Instruction limit reached!
% 2.62/0.82 % (221153)------------------------------
% 2.62/0.82 % (221153)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/0.82 % (221153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.82 % (221153)CaDiCaL version: 2.1.3
% 2.62/0.82 % (221153)Termination reason: Instruction limit
% 2.62/0.82 % (221153)Termination phase: Saturation
% 2.62/0.82 % (221153)Time elapsed: 0.074 s
% 2.62/0.82 % (221153)Peak memory usage: 91 MB
% 2.62/0.82 % (221153)Instructions burned: 129 (million)
% 2.62/0.82 % (221152)Refutation found. Thanks to Tanya!
% 2.62/0.82 % SZS status Theorem for theBenchmark
% 2.62/0.82 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/0.82 % (221152)------------------------------
% 2.62/0.82 % (221152)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/0.82 % (221152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.82 % (221152)CaDiCaL version: 2.1.3
% 2.62/0.82 % (221152)Termination reason: Refutation
% 2.62/0.82 % (221152)Time elapsed: 0.007 s
% 2.62/0.82 % (221152)Peak memory usage: 90 MB
% 2.62/0.82 % (221152)Instructions burned: 16 (million)
% 2.62/0.82 % (221152)------------------------------
% 2.62/0.82 % (221152)------------------------------
% 2.62/0.82 % (221142)Success in time 0.327 s
% 2.62/0.82 % Vampire exiting
%------------------------------------------------------------------------------