%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC106-1 : 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 : n006.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 01:02:28 PM UTC 2026
% Result : Unsatisfiable 3.65s 1.49s
% Output : Refutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 21
% Syntax : Number of formulae : 73 ( 16 unt; 7 def)
% Number of atoms : 180 ( 21 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 207 ( 100 ~; 100 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f98,axiom,
! [X0,X1] :
( cons(X0,X1) != nil
| ~ ssItem(X0)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause98) ).
fof(f99,plain,
! [X0,X1] :
( nil != cons(X0,X1)
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(reorient_equations,[],[f98]) ).
fof(f101,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X1,X0)
| X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause100) ).
fof(f102,plain,
! [X0,X1] :
( neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1 ),
inference(reorient_equations,[],[f101]) ).
fof(f154,axiom,
! [X2,X0,X1] :
( app(X0,X1) != X2
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| rearsegP(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause143) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f215,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f216,negated_conjecture,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f217,negated_conjecture,
( cons(sk5,nil) = sk3
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f218,plain,
( sk3 = cons(sk5,nil)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f217]) ).
fof(f219,negated_conjecture,
( app(sk6,cons(sk5,nil)) = sk4
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
fof(f220,plain,
( sk4 = app(sk6,cons(sk5,nil))
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f219]) ).
fof(f221,negated_conjecture,
( ~ neq(sk1,nil)
| ~ rearsegP(sk2,sk1)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
fof(f224,plain,
( neq(sk4,nil)
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f206,f204,f204]) ).
fof(f231,plain,
( ~ neq(sk3,nil)
| ~ rearsegP(sk4,sk3)
| ~ neq(sk4,nil) ),
inference(definition_unfolding,[],[f221,f205,f204,f205]) ).
fof(f236,plain,
! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X0) ),
inference(equality_resolution,[],[f154]) ).
fof(f241,plain,
neq(sk4,nil),
inference(duplicate_literal_removal,[],[f224]) ).
fof(f243,definition,
( spl0_1
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f247,definition,
( spl0_2
<=> rearsegP(sk4,sk3) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f249,plain,
( ~ rearsegP(sk4,sk3)
| spl0_2 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f251,definition,
( spl0_3
<=> neq(sk3,nil) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f253,plain,
( ~ neq(sk3,nil)
| spl0_3 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f254,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f231,f251,f247,f243]) ).
fof(f256,definition,
( spl0_4
<=> sk4 = app(sk6,cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f258,plain,
( sk4 = app(sk6,cons(sk5,nil))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f259,plain,
( ~ spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f220,f256,f243]) ).
fof(f261,definition,
( spl0_5
<=> sk3 = cons(sk5,nil) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f263,plain,
( sk3 = cons(sk5,nil)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f264,plain,
( ~ spl0_1
| spl0_5 ),
inference(avatar_split_clause,[],[f218,f261,f243]) ).
fof(f266,definition,
( spl0_6
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f268,plain,
( ssList(sk6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f269,plain,
( ~ spl0_1
| spl0_6 ),
inference(avatar_split_clause,[],[f216,f266,f243]) ).
fof(f271,definition,
( spl0_7
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f273,plain,
( ssItem(sk5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f274,plain,
( ~ spl0_1
| spl0_7 ),
inference(avatar_split_clause,[],[f215,f271,f243]) ).
fof(f280,plain,
spl0_1,
inference(avatar_split_clause,[],[f241,f243]) ).
fof(f305,plain,
( nil != sk3
| ~ ssItem(sk5)
| ~ ssList(nil)
| ~ spl0_5 ),
inference(superposition,[],[f99,f263]) ).
fof(f306,plain,
( nil != sk3
| ~ ssList(nil)
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f305,f273]) ).
fof(f307,plain,
( nil != sk3
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f306,f8]) ).
fof(f366,plain,
( rearsegP(sk4,cons(sk5,nil))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk4)
| ~ ssList(sk6)
| ~ spl0_4 ),
inference(superposition,[],[f236,f258]) ).
fof(f378,plain,
( rearsegP(sk4,cons(sk5,nil))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6)
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f366,f203]) ).
fof(f381,plain,
( rearsegP(sk4,cons(sk5,nil))
| ~ ssList(cons(sk5,nil))
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f378,f268]) ).
fof(f383,plain,
( rearsegP(sk4,sk3)
| ~ ssList(cons(sk5,nil))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f381,f263]) ).
fof(f386,plain,
( ~ ssList(cons(sk5,nil))
| spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f383,f249]) ).
fof(f387,plain,
( ~ ssList(sk3)
| spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f386,f263]) ).
fof(f388,plain,
( $false
| spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f387,f202]) ).
fof(f389,plain,
( spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f388]) ).
fof(f403,plain,
( ~ ssList(sk3)
| ~ ssList(nil)
| nil = sk3
| spl0_3 ),
inference(resolution,[],[f253,f102]) ).
fof(f404,plain,
( ~ ssList(nil)
| nil = sk3
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f403,f202]) ).
fof(f406,plain,
( nil = sk3
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f404,f8]) ).
fof(f416,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f406,f307]) ).
fof(f417,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f416]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f254]) ).
cnf(s2,plain,
( ~ spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f259]) ).
cnf(s3,plain,
( ~ spl0_1
| spl0_5 ),
inference(sat_conversion,[],[f264]) ).
cnf(s4,plain,
( ~ spl0_1
| spl0_6 ),
inference(sat_conversion,[],[f269]) ).
cnf(s5,plain,
( ~ spl0_1
| spl0_7 ),
inference(sat_conversion,[],[f274]) ).
cnf(s11,plain,
spl0_1,
inference(sat_conversion,[],[f280]) ).
cnf(s15,plain,
( spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f389]) ).
cnf(s18,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(sat_conversion,[],[f417]) ).
cnf(s19,plain,
spl0_7,
inference(rat,[],[s5,s11]) ).
cnf(s20,plain,
spl0_6,
inference(rat,[],[s4,s11]) ).
cnf(s21,plain,
spl0_5,
inference(rat,[],[s3,s11]) ).
cnf(s22,plain,
spl0_3,
inference(rat,[],[s18,s19,s21]) ).
cnf(s23,plain,
spl0_4,
inference(rat,[],[s2,s11]) ).
cnf(s24,plain,
spl0_2,
inference(rat,[],[s15,s20,s21,s23]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s1,s22,s24,s11]) ).
fof(f418,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC106-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n006.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 07:53:40 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 3.65/1.49 % (3810325)Input is clausal, will run a generic CNF schedule.
% 3.65/1.49 % (3810331)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3389548156:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.65/1.49 % (3810332)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3659701006:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.65/1.49 % (3810330)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=3279379295:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.65/1.49 % (3810333)lrs+10_1_sil=8000:sp=occurrence:random_seed=2004397409:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.65/1.49 % (3810334)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2655549312:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.65/1.49 % (3810336)dis-21_1_sil=8000:lcm=predicate:random_seed=1893406695: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)
% 3.65/1.49 % (3810335)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2018970891:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.65/1.49 % (3810333)First to succeed.
% 3.65/1.49 % (3810334)Also succeeded, but the first one will report.
% 3.65/1.49 % (3810333)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3810325"
% 3.65/1.49 % (3810335)Also succeeded, but the first one will report.
% 3.65/1.49 % (3810336)Instruction limit reached!
% 3.65/1.49 % (3810336)------------------------------
% 3.65/1.49 % (3810336)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.49 % (3810336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.49 % (3810336)CaDiCaL version: 2.1.3
% 3.65/1.49 % (3810336)Termination reason: Instruction limit
% 3.65/1.49 % (3810336)Termination phase: Saturation
% 3.65/1.49 % (3810336)Time elapsed: 0.061 s
% 3.65/1.49 % (3810336)Peak memory usage: 89 MB
% 3.65/1.49 % (3810336)Instructions burned: 117 (million)
% 3.65/1.49 % (3810344)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=1000777707:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.65/1.49 % (3810344)Also succeeded, but the first one will report.
% 3.65/1.49 % (3810333)Refutation found. Thanks to Tanya!
% 3.65/1.49 % SZS status Unsatisfiable for theBenchmark
% 3.65/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.65/1.49 % (3810333)------------------------------
% 3.65/1.49 % (3810333)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.49 % (3810333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.49 % (3810333)CaDiCaL version: 2.1.3
% 3.65/1.49 % (3810333)Termination reason: Refutation
% 3.65/1.49 % (3810333)Time elapsed: 0.006 s
% 3.65/1.49 % (3810333)Peak memory usage: 89 MB
% 3.65/1.49 % (3810333)Instructions burned: 7 (million)
% 3.65/1.49 % (3810333)------------------------------
% 3.65/1.49 % (3810333)------------------------------
% 3.65/1.49 % (3810325)Success in time 0.441 s
% 3.65/1.49 % Vampire exiting
%------------------------------------------------------------------------------