%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC252-1 : 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 : n016.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 01:03:09 PM UTC 2026
% Result : Unsatisfiable 3.73s 1.31s
% Output : Refutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 52 ( 13 unt; 3 def)
% Number of atoms : 153 ( 31 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 201 ( 100 ~; 98 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 33 ( 0 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f71,axiom,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).
fof(f73,axiom,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause73) ).
fof(f74,axiom,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause74) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
nil != sk1,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f222,negated_conjecture,
( cons(sk6,nil) = sk3
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
fof(f223,plain,
( sk3 = cons(sk6,nil)
| nil = sk3 ),
inference(reorient_equations,[],[f222]) ).
fof(f227,plain,
nil != sk3,
inference(definition_unfolding,[],[f206,f205]) ).
fof(f228,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(f229,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(f242,definition,
( spl0_1
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f251,definition,
( spl0_3
<=> sk3 = cons(sk6,nil) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f253,plain,
( sk3 = cons(sk6,nil)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f254,plain,
( spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f223,f251,f242]) ).
fof(f262,definition,
( spl0_5
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f264,plain,
( ssItem(sk6)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f265,plain,
( spl0_1
| spl0_5 ),
inference(avatar_split_clause,[],[f218,f262,f242]) ).
fof(f267,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f227,f242]) ).
fof(f268,plain,
( ! [X0,X1] :
( sk3 != app(app(X0,sk3),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(sk6)
| ssItem(sk5(X1,X0,sk6)) )
| ~ spl0_3 ),
inference(superposition,[],[f228,f253]) ).
fof(f269,plain,
( ! [X0,X1] :
( sk3 != app(app(X0,sk3),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ssItem(sk5(X1,X0,sk6)) )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f268,f264]) ).
fof(f270,plain,
( ! [X0,X1] :
( sk3 != app(app(X0,sk3),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(sk6)
| memberP(X0,sk5(X1,X0,sk6)) )
| ~ spl0_3 ),
inference(superposition,[],[f229,f253]) ).
fof(f271,plain,
( ! [X0,X1] :
( sk3 != app(app(X0,sk3),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| memberP(X0,sk5(X1,X0,sk6)) )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f270,f264]) ).
fof(f278,plain,
sk3 = app(sk3,nil),
inference(resolution,[],[f73,f202]) ).
fof(f281,plain,
sk3 = app(nil,sk3),
inference(resolution,[],[f74,f202]) ).
fof(f294,plain,
( ! [X0] :
( sk3 != app(sk3,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| memberP(nil,sk5(X0,nil,sk6)) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f271,f281]) ).
fof(f295,plain,
( ! [X0] :
( sk3 != app(sk3,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ssItem(sk5(X0,nil,sk6)) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f269,f281]) ).
fof(f297,plain,
( ! [X0] :
( sk3 != app(sk3,X0)
| ~ ssList(X0)
| ssItem(sk5(X0,nil,sk6)) )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f295,f8]) ).
fof(f298,plain,
( ! [X0] :
( sk3 != app(sk3,X0)
| ~ ssList(X0)
| memberP(nil,sk5(X0,nil,sk6)) )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f294,f8]) ).
fof(f305,plain,
( sk3 != sk3
| ~ ssList(nil)
| ssItem(sk5(nil,nil,sk6))
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f297,f278]) ).
fof(f306,plain,
( ~ ssList(nil)
| ssItem(sk5(nil,nil,sk6))
| ~ spl0_3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f305]) ).
fof(f307,plain,
( ssItem(sk5(nil,nil,sk6))
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f306,f8]) ).
fof(f311,plain,
( sk3 != sk3
| ~ ssList(nil)
| memberP(nil,sk5(nil,nil,sk6))
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f298,f278]) ).
fof(f312,plain,
( ~ ssList(nil)
| memberP(nil,sk5(nil,nil,sk6))
| ~ spl0_3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f311]) ).
fof(f313,plain,
( memberP(nil,sk5(nil,nil,sk6))
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f312,f8]) ).
fof(f316,plain,
( ~ ssItem(sk5(nil,nil,sk6))
| ~ spl0_3
| ~ spl0_5 ),
inference(resolution,[],[f313,f71]) ).
fof(f317,plain,
( $false
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f316,f307]) ).
fof(f318,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f317]) ).
cnf(s2,plain,
( spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f254]) ).
cnf(s5,plain,
( spl0_1
| spl0_5 ),
inference(sat_conversion,[],[f265]) ).
cnf(s7,plain,
~ spl0_1,
inference(sat_conversion,[],[f267]) ).
cnf(s8,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(sat_conversion,[],[f318]) ).
cnf(s9,plain,
spl0_5,
inference(rat,[],[s5,s7]) ).
cnf(s10,plain,
~ spl0_3,
inference(rat,[],[s8,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s2,s10,s7]) ).
fof(f319,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC252-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n016.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 08:46:18 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 3.73/1.31 % (3484340)Input is clausal, will run a generic CNF schedule.
% 3.73/1.31 % (3484345)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=2086955229:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.73/1.31 % (3484346)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3630023076:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.73/1.31 % (3484347)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2090712325:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.73/1.31 % (3484350)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=934082386:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.73/1.31 % (3484349)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4132386762:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.73/1.31 % (3484348)lrs+10_1_sil=8000:sp=occurrence:random_seed=179746877:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.73/1.31 % (3484348)First to succeed.
% 3.73/1.31 % (3484349)Also succeeded, but the first one will report.
% 3.73/1.31 % (3484348)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3484340"
% 3.73/1.31 % (3484350)Also succeeded, but the first one will report.
% 3.73/1.31 % (3484351)dis-21_1_sil=8000:lcm=predicate:random_seed=1968159861: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)
% 3.73/1.31 % (3484351)Instruction limit reached!
% 3.73/1.31 % (3484351)------------------------------
% 3.73/1.31 % (3484351)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.31 % (3484351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.31 % (3484351)CaDiCaL version: 2.1.3
% 3.73/1.31 % (3484351)Termination reason: Instruction limit
% 3.73/1.31 % (3484351)Termination phase: Saturation
% 3.73/1.31 % (3484351)Time elapsed: 0.055 s
% 3.73/1.31 % (3484351)Peak memory usage: 89 MB
% 3.73/1.31 % (3484351)Instructions burned: 119 (million)
% 3.73/1.31 % (3484359)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3223963507:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.73/1.31 % (3484359)Also succeeded, but the first one will report.
% 3.73/1.31 % (3484348)Refutation found. Thanks to Tanya!
% 3.73/1.31 % SZS status Unsatisfiable for theBenchmark
% 3.73/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 3.73/1.31 % (3484348)------------------------------
% 3.73/1.31 % (3484348)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.32 % (3484348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.32 % (3484348)CaDiCaL version: 2.1.3
% 3.73/1.32 % (3484348)Termination reason: Refutation
% 3.73/1.32 % (3484348)Time elapsed: 0.006 s
% 3.73/1.32 % (3484348)Peak memory usage: 89 MB
% 3.73/1.32 % (3484348)Instructions burned: 7 (million)
% 3.73/1.32 % (3484348)------------------------------
% 3.73/1.32 % (3484348)------------------------------
% 3.73/1.32 % (3484340)Success in time 0.436 s
% 3.73/1.32 % Vampire exiting
%------------------------------------------------------------------------------