%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC112-1 : 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 : n010.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 01:02:30 PM UTC 2026
% Result : Unsatisfiable 5.43s 1.73s
% Output : Refutation 5.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 21
% Syntax : Number of formulae : 75 ( 16 unt; 5 def)
% Number of atoms : 189 ( 27 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 220 ( 106 ~; 109 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f56,axiom,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause56) ).
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(f118,axiom,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause115) ).
fof(f134,axiom,
! [X0,X1] :
( ~ segmentP(X0,X1)
| ~ segmentP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause127) ).
fof(f135,plain,
! [X0,X1] :
( ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1 ),
inference(reorient_equations,[],[f134]) ).
fof(f187,axiom,
! [X2,X3,X0,X1] :
( app(app(X0,X1),X2) != X3
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| segmentP(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause173) ).
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,
ssList(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
app(app(sk5,sk3),sk6) = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f209,plain,
sk4 = app(app(sk5,sk3),sk6),
inference(reorient_equations,[],[f208]) ).
fof(f215,negated_conjecture,
( nil = sk4
| nil != sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f217,negated_conjecture,
( nil = sk2
| ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f218,negated_conjecture,
( nil != sk1
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f223,plain,
( nil = sk4
| ~ neq(sk3,nil)
| ~ segmentP(sk4,sk3) ),
inference(definition_unfolding,[],[f217,f204,f205,f204,f205]) ).
fof(f224,plain,
( nil != sk3
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f218,f205,f204]) ).
fof(f232,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f118]) ).
fof(f233,plain,
! [X2,X0,X1] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X2) ),
inference(equality_resolution,[],[f187]) ).
fof(f235,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f232]) ).
fof(f240,definition,
( spl0_1
<=> segmentP(sk4,sk3) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f241,plain,
( segmentP(sk4,sk3)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f242,plain,
( ~ segmentP(sk4,sk3)
| spl0_1 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f244,definition,
( spl0_2
<=> neq(sk3,nil) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f246,plain,
( ~ neq(sk3,nil)
| spl0_2 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f248,definition,
( spl0_3
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f250,plain,
( nil != sk3
| spl0_3 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f253,definition,
( spl0_4
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f255,plain,
( neq(sk4,nil)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f256,plain,
( spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f224,f248,f253]) ).
fof(f258,definition,
( spl0_5
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f260,plain,
( nil = sk4
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f261,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_5 ),
inference(avatar_split_clause,[],[f223,f258,f244,f240]) ).
fof(f263,plain,
( ~ spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f215,f258,f248]) ).
fof(f394,plain,
( ~ ssList(sk3)
| ~ ssList(nil)
| nil = sk3
| spl0_2 ),
inference(resolution,[],[f246,f102]) ).
fof(f395,plain,
( ~ ssList(nil)
| nil = sk3
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f394,f202]) ).
fof(f397,plain,
( nil = sk3
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f395,f8]) ).
fof(f407,plain,
( $false
| spl0_2
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f397,f250]) ).
fof(f408,plain,
( spl0_2
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f407]) ).
fof(f429,plain,
( segmentP(nil,sk3)
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_demodulation,[],[f241,f260]) ).
fof(f438,plain,
( neq(nil,nil)
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f255,f260]) ).
fof(f442,plain,
( ~ segmentP(sk3,nil)
| ~ ssList(sk3)
| ~ ssList(nil)
| nil = sk3
| ~ spl0_1
| ~ spl0_5 ),
inference(resolution,[],[f429,f135]) ).
fof(f443,plain,
( ~ ssList(sk3)
| ~ ssList(nil)
| nil = sk3
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f442,f56]) ).
fof(f445,plain,
( ~ ssList(nil)
| nil = sk3
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f443,f202]) ).
fof(f448,plain,
( nil = sk3
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f445,f8]) ).
fof(f449,plain,
( $false
| ~ spl0_1
| spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f448,f250]) ).
fof(f450,plain,
( ~ spl0_1
| spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f449]) ).
fof(f477,plain,
( ~ ssList(nil)
| ~ spl0_4
| ~ spl0_5 ),
inference(resolution,[],[f438,f235]) ).
fof(f478,plain,
( $false
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f477,f8]) ).
fof(f479,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f478]) ).
fof(f775,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk5)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(sk6) ),
inference(superposition,[],[f233,f209]) ).
fof(f779,plain,
( ~ ssList(sk5)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(sk6)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f775,f242]) ).
fof(f785,plain,
( ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(sk6)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f779,f206]) ).
fof(f791,plain,
( ~ ssList(sk4)
| ~ ssList(sk6)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f785,f202]) ).
fof(f792,plain,
( ~ ssList(sk6)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f791,f203]) ).
fof(f793,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f792,f207]) ).
fof(f794,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f793]) ).
cnf(s2,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f256]) ).
cnf(s3,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f261]) ).
cnf(s5,plain,
( ~ spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f263]) ).
cnf(s12,plain,
( spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f408]) ).
cnf(s19,plain,
( ~ spl0_1
| spl0_3
| ~ spl0_5 ),
inference(sat_conversion,[],[f450]) ).
cnf(s21,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f479]) ).
cnf(s31,plain,
spl0_1,
inference(sat_conversion,[],[f794]) ).
cnf(s34,plain,
( spl0_3
| ~ spl0_5 ),
inference(rat,[],[s19,s31]) ).
cnf(s37,plain,
( ~ spl0_2
| spl0_5 ),
inference(rat,[],[s3,s31]) ).
cnf(s39,plain,
~ spl0_3,
inference(rat,[],[s21,s2,s5]) ).
cnf(s43,plain,
~ spl0_5,
inference(rat,[],[s34,s39]) ).
cnf(s44,plain,
spl0_2,
inference(rat,[],[s12,s39]) ).
cnf(s46,plain,
$false,
inference(rat,[],[s37,s43,s44]) ).
fof(f795,plain,
$false,
inference(avatar_sat_refutation,[],[s46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC112-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n010.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 07:55:32 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 5.43/1.73 % (1755397)Input is clausal, will run a generic CNF schedule.
% 5.43/1.73 % (1755445)dis-21_1_sil=8000:lcm=predicate:random_seed=1961107801: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)
% 5.43/1.73 % (1755439)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=4219237847:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.43/1.73 % (1755444)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3120149593:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.43/1.73 % (1755441)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2178330053:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.43/1.73 % (1755442)lrs+10_1_sil=8000:sp=occurrence:random_seed=4096182880:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.43/1.73 % (1755440)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4237752058:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.43/1.73 % (1755443)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1385592336:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.43/1.73 % (1755442)First to succeed.
% 5.43/1.73 % (1755442)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1755397"
% 5.43/1.73 % (1755445)Instruction limit reached!
% 5.43/1.73 % (1755445)------------------------------
% 5.43/1.73 % (1755445)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.73 % (1755445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.73 % (1755445)CaDiCaL version: 2.1.3
% 5.43/1.73 % (1755445)Termination reason: Instruction limit
% 5.43/1.73 % (1755445)Termination phase: Saturation
% 5.43/1.73 % (1755445)Time elapsed: 0.058 s
% 5.43/1.73 % (1755445)Peak memory usage: 90 MB
% 5.43/1.73 % (1755445)Instructions burned: 119 (million)
% 5.43/1.73 % (1755443)Also succeeded, but the first one will report.
% 5.43/1.73 % (1755444)Also succeeded, but the first one will report.
% 5.43/1.73 % (1755455)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=660500930:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.43/1.73 % (1755455)Also succeeded, but the first one will report.
% 5.43/1.73 % (1755442)Refutation found. Thanks to Tanya!
% 5.43/1.73 % SZS status Unsatisfiable for theBenchmark
% 5.43/1.73 % SZS output start Proof for theBenchmark
% See solution above
% 5.43/1.73 % (1755442)------------------------------
% 5.43/1.73 % (1755442)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.73 % (1755442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.73 % (1755442)CaDiCaL version: 2.1.3
% 5.43/1.73 % (1755442)Termination reason: Refutation
% 5.43/1.73 % (1755442)Time elapsed: 0.022 s
% 5.43/1.73 % (1755442)Peak memory usage: 90 MB
% 5.43/1.73 % (1755442)Instructions burned: 19 (million)
% 5.43/1.73 % (1755442)------------------------------
% 5.43/1.73 % (1755442)------------------------------
% 5.43/1.73 % (1755397)Success in time 0.688 s
% 5.43/1.73 % Vampire exiting
%------------------------------------------------------------------------------