%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC239-1 : 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 : n019.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 01:03:05 PM UTC 2026
% Result : Unsatisfiable 2.72s 1.05s
% Output : Refutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 52 ( 11 unt; 3 def)
% Number of atoms : 163 ( 33 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 225 ( 114 ~; 108 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 37 ( 0 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f71,axiom,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
fof(f73,axiom,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause73) ).
fof(f74,axiom,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause74) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
nil != sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,cons(X0,nil)),X2) != sk1
| ssItem(sk5(X2,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| sk1 != app(app(X1,cons(X0,nil)),X2)
| ssItem(sk5(X2,X1,X0)) ),
inference(reorient_equations,[],[f207]) ).
fof(f209,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,cons(X0,nil)),X2) != sk1
| memberP(X1,sk5(X2,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f210,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| sk1 != app(app(X1,cons(X0,nil)),X2)
| memberP(X1,sk5(X2,X1,X0)) ),
inference(reorient_equations,[],[f209]) ).
fof(f218,negated_conjecture,
( ssItem(sk6)
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
fof(f223,negated_conjecture,
( cons(sk6,nil) = sk3
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
fof(f224,plain,
( sk3 = cons(sk6,nil)
| nil = sk3 ),
inference(reorient_equations,[],[f223]) ).
fof(f229,plain,
nil != sk3,
inference(definition_unfolding,[],[f206,f205]) ).
fof(f230,plain,
! [X2,X0,X1] :
( sk3 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X0)
| ssItem(sk5(X2,X1,X0)) ),
inference(definition_unfolding,[],[f208,f205]) ).
fof(f231,plain,
! [X2,X0,X1] :
( sk3 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X0)
| memberP(X1,sk5(X2,X1,X0)) ),
inference(definition_unfolding,[],[f210,f205]) ).
fof(f251,definition,
( spl0_3
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f252,plain,
( nil = sk3
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f262,definition,
( spl0_6
<=> sk3 = cons(sk6,nil) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f263,plain,
( sk3 = cons(sk6,nil)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f264,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f224,f262,f251]) ).
fof(f272,definition,
( spl0_8
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f273,plain,
( ssItem(sk6)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f274,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f218,f272,f251]) ).
fof(f276,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f252,f229]) ).
fof(f277,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f276]) ).
fof(f282,plain,
( ! [X0,X1] :
( sk3 != app(app(X0,sk3),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(sk6)
| ssItem(sk5(X1,X0,sk6)) )
| ~ spl0_6 ),
inference(superposition,[],[f230,f263]) ).
fof(f283,plain,
( ! [X0,X1] :
( sk3 != app(app(X0,sk3),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ssItem(sk5(X1,X0,sk6)) )
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f282,f273]) ).
fof(f287,plain,
( ! [X0,X1] :
( sk3 != app(app(X0,sk3),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(sk6)
| memberP(X0,sk5(X1,X0,sk6)) )
| ~ spl0_6 ),
inference(superposition,[],[f231,f263]) ).
fof(f288,plain,
( ! [X0,X1] :
( sk3 != app(app(X0,sk3),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| memberP(X0,sk5(X1,X0,sk6)) )
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f287,f273]) ).
fof(f326,plain,
( ! [X0] :
( sk3 != app(sk3,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| memberP(nil,sk5(X0,nil,sk6))
| ~ ssList(sk3) )
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f288,f74]) ).
fof(f327,plain,
( ! [X0] :
( sk3 != app(sk3,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ssItem(sk5(X0,nil,sk6))
| ~ ssList(sk3) )
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f283,f74]) ).
fof(f328,plain,
( ! [X0] :
( sk3 != app(sk3,X0)
| ~ ssList(X0)
| ssItem(sk5(X0,nil,sk6))
| ~ ssList(sk3) )
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f327,f8]) ).
fof(f329,plain,
( ! [X0] :
( sk3 != app(sk3,X0)
| ~ ssList(X0)
| memberP(nil,sk5(X0,nil,sk6))
| ~ ssList(sk3) )
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f326,f8]) ).
fof(f338,plain,
( ! [X0] :
( ssItem(sk5(X0,nil,sk6))
| ~ ssList(X0)
| sk3 != app(sk3,X0) )
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f328,f202]) ).
fof(f339,plain,
( ! [X0] :
( memberP(nil,sk5(X0,nil,sk6))
| ~ ssList(X0)
| sk3 != app(sk3,X0) )
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f329,f202]) ).
fof(f349,plain,
( ! [X0] :
( ~ ssList(X0)
| sk3 != app(sk3,X0)
| ~ ssItem(sk5(X0,nil,sk6)) )
| ~ spl0_6
| ~ spl0_8 ),
inference(resolution,[],[f339,f71]) ).
fof(f350,plain,
( ! [X0] :
( sk3 != app(sk3,X0)
| ~ ssList(X0) )
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f349,f338]) ).
fof(f352,plain,
( sk3 != sk3
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f350,f73]) ).
fof(f353,plain,
( ~ ssList(nil)
| ~ ssList(sk3)
| ~ spl0_6
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f352]) ).
fof(f354,plain,
( ~ ssList(sk3)
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f353,f8]) ).
fof(f355,plain,
( $false
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f354,f202]) ).
fof(f356,plain,
( ~ spl0_6
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f355]) ).
cnf(s4,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f264]) ).
cnf(s8,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f274]) ).
cnf(s10,plain,
~ spl0_3,
inference(sat_conversion,[],[f277]) ).
cnf(s13,plain,
( ~ spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f356]) ).
cnf(s14,plain,
spl0_8,
inference(rat,[],[s8,s10]) ).
cnf(s15,plain,
~ spl0_6,
inference(rat,[],[s13,s14]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s4,s15,s10]) ).
fof(f357,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC239-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.16 % Computer : n019.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Mon Sep 28 08:38:33 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running first-order theorem proving
% 0.08/0.20 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
% 2.72/1.05 % (3855954)Input is clausal, will run a generic CNF schedule.
% 2.72/1.05 % (3855963)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1591214761:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.72/1.05 % (3855963)First to succeed.
% 2.72/1.05 % (3855963)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3855954"
% 2.72/1.05 % (3855960)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=70577272:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.72/1.05 % (3855962)lrs+10_1_sil=8000:sp=occurrence:random_seed=4180336285:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.72/1.05 % (3855964)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3337167676:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.72/1.05 % (3855959)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=1001197042:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.72/1.05 % (3855965)dis-21_1_sil=8000:lcm=predicate:random_seed=1074724098:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.72/1.05 % (3855961)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=794218727:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.72/1.05 % (3855962)Also succeeded, but the first one will report.
% 2.72/1.05 % (3855964)Also succeeded, but the first one will report.
% 2.72/1.05 % (3855965)Instruction limit reached!
% 2.72/1.05 % (3855965)------------------------------
% 2.72/1.05 % (3855965)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.05 % (3855965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.05 % (3855965)CaDiCaL version: 2.1.3
% 2.72/1.05 % (3855965)Termination reason: Instruction limit
% 2.72/1.05 % (3855965)Termination phase: Saturation
% 2.72/1.05 % (3855965)Time elapsed: 0.056 s
% 2.72/1.05 % (3855965)Peak memory usage: 89 MB
% 2.72/1.05 % (3855965)Instructions burned: 119 (million)
% 2.72/1.05 % (3855963)Refutation found. Thanks to Tanya!
% 2.72/1.05 % SZS status Unsatisfiable for theBenchmark
% 2.72/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 2.72/1.05 % (3855963)------------------------------
% 2.72/1.05 % (3855963)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.05 % (3855963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.05 % (3855963)CaDiCaL version: 2.1.3
% 2.72/1.05 % (3855963)Termination reason: Refutation
% 2.72/1.05 % (3855963)Time elapsed: 0.004 s
% 2.72/1.05 % (3855963)Peak memory usage: 90 MB
% 2.72/1.05 % (3855963)Instructions burned: 7 (million)
% 2.72/1.05 % (3855963)------------------------------
% 2.72/1.05 % (3855963)------------------------------
% 2.72/1.05 % (3855954)Success in time 0.314 s
% 2.72/1.05 % Vampire exiting
%------------------------------------------------------------------------------