%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC124-1 : 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 : n017.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 01:02:33 PM UTC 2026
% Result : Unsatisfiable 3.92s 1.53s
% Output : Refutation 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 20
% Syntax : Number of formulae : 71 ( 19 unt; 5 def)
% Number of atoms : 155 ( 34 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 158 ( 74 ~; 79 |; 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 : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f73,axiom,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause73) ).
fof(f74,axiom,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause74) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause85) ).
fof(f101,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X1,X0)
| X1 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause100) ).
fof(f102,plain,
! [X0,X1] :
( neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1 ),
inference(reorient_equations,[],[f101]) ).
fof(f123,axiom,
! [X0,X1] :
( app(X0,X1) != nil
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).
fof(f124,plain,
! [X0,X1] :
( nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X1 ),
inference(reorient_equations,[],[f123]) ).
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/sandbox/benchmark/theBenchmark.p',clause173) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
app(sk3,sk5) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f209,plain,
sk4 = app(sk3,sk5),
inference(reorient_equations,[],[f208]) ).
fof(f213,negated_conjecture,
( nil = sk4
| nil != sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f214,negated_conjecture,
( ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f217,plain,
neq(sk4,nil),
inference(definition_unfolding,[],[f206,f204]) ).
fof(f218,plain,
( ~ neq(sk3,nil)
| ~ segmentP(sk4,sk3) ),
inference(definition_unfolding,[],[f214,f205,f204,f205]) ).
fof(f225,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(f231,definition,
( spl0_1
<=> segmentP(sk4,sk3) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f233,plain,
( ~ segmentP(sk4,sk3)
| spl0_1 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f235,definition,
( spl0_2
<=> neq(sk3,nil) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f237,plain,
( ~ neq(sk3,nil)
| spl0_2 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f238,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f218,f235,f231]) ).
fof(f240,definition,
( spl0_3
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f242,plain,
( nil != sk3
| spl0_3 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f244,definition,
( spl0_4
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f246,plain,
( nil = sk4
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f247,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f213,f244,f240]) ).
fof(f249,plain,
sk3 = app(sk3,nil),
inference(resolution,[],[f73,f202]) ).
fof(f253,plain,
sk3 = app(nil,sk3),
inference(resolution,[],[f74,f202]) ).
fof(f293,plain,
( nil != sk4
| ~ ssList(sk5)
| ~ ssList(sk3)
| nil = sk5 ),
inference(superposition,[],[f124,f209]) ).
fof(f316,definition,
( spl0_5
<=> nil = sk5 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f317,plain,
( nil != sk5
| spl0_5 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f318,plain,
( nil = sk5
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f328,plain,
( sk4 = app(sk3,nil)
| ~ spl0_5 ),
inference(superposition,[],[f209,f318]) ).
fof(f330,plain,
( sk3 = sk4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f328,f249]) ).
fof(f334,plain,
( neq(sk3,nil)
| ~ spl0_5 ),
inference(superposition,[],[f217,f330]) ).
fof(f339,plain,
( spl0_2
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f334,f316,f235]) ).
fof(f581,plain,
! [X0] :
( segmentP(app(sk3,X0),sk3)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(app(sk3,X0))
| ~ ssList(X0) ),
inference(superposition,[],[f225,f253]) ).
fof(f594,plain,
! [X0] :
( segmentP(app(sk3,X0),sk3)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f581,f85]) ).
fof(f598,plain,
! [X0] :
( segmentP(app(sk3,X0),sk3)
| ~ ssList(sk3)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f594,f8]) ).
fof(f601,plain,
! [X0] :
( segmentP(app(sk3,X0),sk3)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f598,f202]) ).
fof(f967,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk5) ),
inference(superposition,[],[f601,f209]) ).
fof(f970,plain,
( ~ ssList(sk5)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f967,f233]) ).
fof(f973,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f970,f207]) ).
fof(f974,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f973]) ).
fof(f985,plain,
( ~ ssList(sk3)
| ~ ssList(nil)
| nil = sk3
| spl0_2 ),
inference(resolution,[],[f237,f102]) ).
fof(f986,plain,
( ~ ssList(nil)
| nil = sk3
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f985,f202]) ).
fof(f988,plain,
( nil = sk3
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f986,f8]) ).
fof(f998,plain,
( $false
| spl0_2
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f988,f242]) ).
fof(f999,plain,
( spl0_2
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f998]) ).
fof(f1000,plain,
( ~ ssList(sk5)
| ~ ssList(sk3)
| nil = sk5
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f293,f246]) ).
fof(f1002,plain,
( ~ ssList(sk3)
| nil = sk5
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f1000,f207]) ).
fof(f1004,plain,
( nil = sk5
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f1002,f202]) ).
fof(f1006,plain,
( $false
| ~ spl0_4
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f1004,f317]) ).
fof(f1007,plain,
( ~ spl0_4
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f1006]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f238]) ).
cnf(s2,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f247]) ).
cnf(s5,plain,
( spl0_2
| ~ spl0_5 ),
inference(sat_conversion,[],[f339]) ).
cnf(s26,plain,
spl0_1,
inference(sat_conversion,[],[f974]) ).
cnf(s28,plain,
( spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f999]) ).
cnf(s29,plain,
( ~ spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f1007]) ).
cnf(s34,plain,
~ spl0_2,
inference(rat,[],[s1,s26]) ).
cnf(s35,plain,
spl0_3,
inference(rat,[],[s28,s34]) ).
cnf(s36,plain,
~ spl0_5,
inference(rat,[],[s5,s34]) ).
cnf(s37,plain,
spl0_4,
inference(rat,[],[s2,s35]) ).
cnf(s42,plain,
$false,
inference(rat,[],[s29,s36,s37]) ).
fof(f1008,plain,
$false,
inference(avatar_sat_refutation,[],[s42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC124-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n017.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 07:57:11 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 3.92/1.53 % (3385692)Input is clausal, will run a generic CNF schedule.
% 3.92/1.53 % (3385703)dis-21_1_sil=8000:lcm=predicate:random_seed=2627989654: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)
% 3.92/1.53 % (3385703)Instruction limit reached!
% 3.92/1.53 % (3385703)------------------------------
% 3.92/1.53 % (3385703)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.53 % (3385703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.53 % (3385703)CaDiCaL version: 2.1.3
% 3.92/1.53 % (3385703)Termination reason: Instruction limit
% 3.92/1.53 % (3385703)Termination phase: Saturation
% 3.92/1.53 % (3385703)Time elapsed: 0.033 s
% 3.92/1.53 % (3385703)Peak memory usage: 90 MB
% 3.92/1.53 % (3385703)Instructions burned: 119 (million)
% 3.92/1.53 % (3385697)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=724852952:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.92/1.53 % (3385702)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3495009139:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.92/1.53 % (3385701)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3023561693:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.92/1.53 % (3385698)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1911702540:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.92/1.53 % (3385699)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=818016817:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.92/1.53 % (3385700)lrs+10_1_sil=8000:sp=occurrence:random_seed=2094682854:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.92/1.53 % (3385700)First to succeed.
% 3.92/1.53 % (3385700)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3385692"
% 3.92/1.53 % (3385701)Also succeeded, but the first one will report.
% 3.92/1.53 % (3385702)Also succeeded, but the first one will report.
% 3.92/1.53 % (3385711)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=1498754812:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.92/1.53 % (3385711)Also succeeded, but the first one will report.
% 3.92/1.53 % (3385700)Refutation found. Thanks to Tanya!
% 3.92/1.53 % SZS status Unsatisfiable for theBenchmark
% 3.92/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 3.92/1.53 % (3385700)------------------------------
% 3.92/1.53 % (3385700)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.53 % (3385700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.53 % (3385700)CaDiCaL version: 2.1.3
% 3.92/1.53 % (3385700)Termination reason: Refutation
% 3.92/1.53 % (3385700)Time elapsed: 0.022 s
% 3.92/1.53 % (3385700)Peak memory usage: 90 MB
% 3.92/1.53 % (3385700)Instructions burned: 31 (million)
% 3.92/1.53 % (3385700)------------------------------
% 3.92/1.53 % (3385700)------------------------------
% 3.92/1.53 % (3385692)Success in time 0.469 s
% 3.92/1.53 % Vampire exiting
%------------------------------------------------------------------------------