%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC175-1 : 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 : n026.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 01:02:47 PM UTC 2026
% Result : Unsatisfiable 3.69s 1.41s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 21
% Syntax : Number of formulae : 68 ( 22 unt; 4 def)
% Number of atoms : 180 ( 23 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 223 ( 111 ~; 108 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f63,axiom,
! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause63) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause85) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
fof(f104,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| neq(X1,X0)
| X1 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause102) ).
fof(f105,plain,
! [X0,X1] :
( neq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0)
| X0 = X1 ),
inference(reorient_equations,[],[f104]) ).
fof(f125,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = cons(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).
fof(f126,plain,
! [X0,X1] :
( cons(X0,X1) = app(cons(X0,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f125]) ).
fof(f161,axiom,
! [X2,X0,X1] :
( app(app(X2,X1),X0) = app(X2,app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause149) ).
fof(f195,axiom,
! [X2,X3,X0,X1,X4,X5] :
( app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ strictorderedP(X5)
| ~ ssList(X5)
| lt(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause181) ).
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(f209,negated_conjecture,
strictorderedP(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f212,negated_conjecture,
ssItem(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f213,negated_conjecture,
ssItem(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f214,negated_conjecture,
ssList(sk8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f215,negated_conjecture,
ssList(sk9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
fof(f216,negated_conjecture,
app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
fof(f217,plain,
sk1 = app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9),
inference(reorient_equations,[],[f216]) ).
fof(f218,negated_conjecture,
~ neq(sk6,sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
fof(f222,plain,
! [X2,X3,X0,X1,X4] :
( ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X4)
| lt(X1,X3) ),
inference(equality_resolution,[],[f195]) ).
fof(f241,plain,
( ~ ssItem(sk6)
| ~ ssItem(sk7)
| sk6 = sk7 ),
inference(resolution,[],[f218,f105]) ).
fof(f242,plain,
( ~ ssItem(sk7)
| sk6 = sk7 ),
inference(forward_subsumption_resolution,[],[f241,f212]) ).
fof(f244,definition,
( spl0_3
<=> sk6 = sk7 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f245,plain,
( sk6 = sk7
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f253,plain,
sk6 = sk7,
inference(forward_subsumption_resolution,[],[f242,f213]) ).
fof(f254,plain,
spl0_3,
inference(avatar_split_clause,[],[f253,f244]) ).
fof(f294,plain,
( sk1 = app(app(app(sk8,cons(sk6,nil)),cons(sk6,nil)),sk9)
| ~ spl0_3 ),
inference(forward_demodulation,[],[f217,f245]) ).
fof(f295,plain,
( sk3 = app(app(app(sk8,cons(sk6,nil)),cons(sk6,nil)),sk9)
| ~ spl0_3 ),
inference(forward_demodulation,[],[f294,f205]) ).
fof(f332,plain,
( sk3 = app(app(sk8,cons(sk6,nil)),app(cons(sk6,nil),sk9))
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk8,cons(sk6,nil)))
| ~ ssList(sk9)
| ~ spl0_3 ),
inference(superposition,[],[f295,f161]) ).
fof(f351,plain,
( sk3 = app(app(sk8,cons(sk6,nil)),app(cons(sk6,nil),sk9))
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk8,cons(sk6,nil)))
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f332,f215]) ).
fof(f378,definition,
( spl0_17
<=> ssList(app(sk8,cons(sk6,nil))) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f379,plain,
( ~ ssList(app(sk8,cons(sk6,nil)))
| spl0_17 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f381,definition,
( spl0_18
<=> ssList(cons(sk6,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f382,plain,
( ~ ssList(cons(sk6,nil))
| spl0_18 ),
inference(avatar_component_clause,[],[f381]) ).
fof(f384,definition,
( spl0_19
<=> sk3 = app(app(sk8,cons(sk6,nil)),app(cons(sk6,nil),sk9)) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f385,plain,
( sk3 = app(app(sk8,cons(sk6,nil)),app(cons(sk6,nil),sk9))
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f387,plain,
( ~ spl0_17
| ~ spl0_18
| spl0_19
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f351,f244,f384,f381,f378]) ).
fof(f415,plain,
( ~ ssList(nil)
| ~ ssItem(sk6)
| spl0_18 ),
inference(resolution,[],[f382,f86]) ).
fof(f416,plain,
( ~ ssItem(sk6)
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f415,f8]) ).
fof(f417,plain,
( $false
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f416,f212]) ).
fof(f418,plain,
spl0_18,
inference(avatar_contradiction_clause,[],[f417]) ).
fof(f419,plain,
( ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| spl0_17 ),
inference(resolution,[],[f379,f85]) ).
fof(f420,plain,
( ~ ssList(cons(sk6,nil))
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f419,f214]) ).
fof(f421,plain,
( ~ spl0_18
| spl0_17 ),
inference(avatar_split_clause,[],[f420,f378,f381]) ).
fof(f2637,plain,
( sk3 = app(app(sk8,cons(sk6,nil)),cons(sk6,sk9))
| ~ ssList(sk9)
| ~ ssItem(sk6)
| ~ spl0_19 ),
inference(superposition,[],[f385,f126]) ).
fof(f2668,plain,
( sk3 = app(app(sk8,cons(sk6,nil)),cons(sk6,sk9))
| ~ ssItem(sk6)
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f2637,f215]) ).
fof(f2675,plain,
( sk3 = app(app(sk8,cons(sk6,nil)),cons(sk6,sk9))
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f2668,f212]) ).
fof(f3306,plain,
( ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssItem(sk6)
| ~ strictorderedP(sk3)
| ~ ssList(sk9)
| lt(sk6,sk6)
| ~ spl0_19 ),
inference(superposition,[],[f222,f2675]) ).
fof(f3320,plain,
( ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ strictorderedP(sk3)
| ~ ssList(sk9)
| lt(sk6,sk6)
| ~ spl0_19 ),
inference(duplicate_literal_removal,[],[f3306]) ).
fof(f3337,plain,
( ~ ssList(nil)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ strictorderedP(sk3)
| ~ ssList(sk9)
| lt(sk6,sk6)
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f3320,f202]) ).
fof(f3344,plain,
( ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ strictorderedP(sk3)
| ~ ssList(sk9)
| lt(sk6,sk6)
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f3337,f8]) ).
fof(f3347,plain,
( ~ ssItem(sk6)
| ~ strictorderedP(sk3)
| ~ ssList(sk9)
| lt(sk6,sk6)
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f3344,f214]) ).
fof(f3348,plain,
( ~ strictorderedP(sk3)
| ~ ssList(sk9)
| lt(sk6,sk6)
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f3347,f212]) ).
fof(f3349,plain,
( ~ ssList(sk9)
| lt(sk6,sk6)
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f3348,f209]) ).
fof(f3350,plain,
( lt(sk6,sk6)
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f3349,f215]) ).
fof(f3358,plain,
( ~ ssItem(sk6)
| ~ spl0_19 ),
inference(resolution,[],[f3350,f63]) ).
fof(f3366,plain,
( $false
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f3358,f212]) ).
fof(f3367,plain,
~ spl0_19,
inference(avatar_contradiction_clause,[],[f3366]) ).
cnf(s3,plain,
spl0_3,
inference(sat_conversion,[],[f254]) ).
cnf(s15,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| spl0_19 ),
inference(sat_conversion,[],[f387]) ).
cnf(s18,plain,
spl0_18,
inference(sat_conversion,[],[f418]) ).
cnf(s19,plain,
( spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f421]) ).
cnf(s417,plain,
~ spl0_19,
inference(sat_conversion,[],[f3367]) ).
cnf(s434,plain,
spl0_17,
inference(rat,[],[s19,s18]) ).
cnf(s440,plain,
~ spl0_3,
inference(rat,[],[s15,s417,s18,s434]) ).
cnf(s441,plain,
$false,
inference(rat,[],[s3,s440]) ).
fof(f3369,plain,
$false,
inference(avatar_sat_refutation,[],[s441]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC175-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n026.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Mon Sep 28 08:20:12 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 2.62/1.32 % (3692563)Input is clausal, will run a generic CNF schedule.
% 2.62/1.32 % (3692574)dis-21_1_sil=8000:lcm=predicate:random_seed=3437265086: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)
% 2.62/1.32 % (3692571)lrs+10_1_sil=8000:sp=occurrence:random_seed=3959381831:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.62/1.32 % (3692570)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3364183563:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.62/1.32 % (3692569)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=474678937:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.62/1.32 % (3692572)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1875414792:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.62/1.32 % (3692568)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=4202379778:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.62/1.32 % (3692573)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2395434832:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.62/1.32 % (3692574)Instruction limit reached!
% 2.62/1.32 % (3692574)------------------------------
% 2.62/1.32 % (3692574)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.32 % (3692574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.32 % (3692574)CaDiCaL version: 2.1.3
% 2.62/1.32 % (3692574)Termination reason: Instruction limit
% 2.62/1.32 % (3692574)Termination phase: Saturation
% 2.62/1.32 % (3692574)Time elapsed: 0.036 s
% 2.62/1.32 % (3692574)Peak memory usage: 90 MB
% 2.62/1.32 % (3692574)Instructions burned: 120 (million)
% 2.62/1.32 % (3692572)Instruction limit reached!
% 2.62/1.32 % (3692572)------------------------------
% 2.62/1.32 % (3692572)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.32 % (3692572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.32 % (3692572)CaDiCaL version: 2.1.3
% 2.62/1.32 % (3692572)Termination reason: Instruction limit
% 2.62/1.32 % (3692572)Termination phase: Saturation
% 2.62/1.32 % (3692572)Time elapsed: 0.067 s
% 2.62/1.32 % (3692572)Peak memory usage: 89 MB
% 2.62/1.32 % (3692572)Instructions burned: 115 (million)
% 2.62/1.32 % (3692571)Instruction limit reached!
% 2.62/1.32 % (3692571)------------------------------
% 2.62/1.32 % (3692571)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.32 % (3692571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.32 % (3692571)CaDiCaL version: 2.1.3
% 2.62/1.32 % (3692571)Termination reason: Instruction limit
% 2.62/1.32 % (3692571)Termination phase: Saturation
% 2.62/1.32 % (3692571)Time elapsed: 0.068 s
% 2.62/1.32 % (3692571)Peak memory usage: 90 MB
% 2.62/1.32 % (3692571)Instructions burned: 108 (million)
% 2.62/1.32 % (3692582)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=3657776584:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.62/1.32 % (3692573)Instruction limit reached!
% 2.62/1.32 % (3692573)------------------------------
% 2.62/1.32 % (3692573)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.32 % (3692573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.32 % (3692573)CaDiCaL version: 2.1.3
% 2.62/1.32 % (3692573)Termination reason: Instruction limit
% 2.62/1.32 % (3692573)Termination phase: Saturation
% 2.62/1.32 % (3692573)Time elapsed: 0.120 s
% 2.62/1.32 % (3692573)Peak memory usage: 90 MB
% 2.62/1.32 % (3692573)Instructions burned: 182 (million)
% 2.62/1.32 % (3692582)First to succeed.
% 2.62/1.32 % (3692582)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3692563"
% 2.62/1.32 % (3692584)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=4153670072:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 2.62/1.32 % (3692583)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=365413165:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 2.62/1.32 % (3692586)lrs+10_64_to=lpo:sil=8000:random_seed=1013699086:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 3.69/1.41 % (3692584)Also succeeded, but the first one will report.
% 3.69/1.41 % (3692582)Refutation found. Thanks to Tanya!
% 3.69/1.41 % SZS status Unsatisfiable for theBenchmark
% 3.69/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.41 % (3692582)------------------------------
% 3.69/1.41 % (3692582)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.41 % (3692582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.41 % (3692582)CaDiCaL version: 2.1.3
% 3.69/1.41 % (3692582)Termination reason: Refutation
% 3.69/1.41 % (3692582)Time elapsed: 0.040 s
% 3.69/1.41 % (3692582)Peak memory usage: 91 MB
% 3.69/1.41 % (3692582)Instructions burned: 115 (million)
% 3.69/1.41 % (3692582)------------------------------
% 3.69/1.41 % (3692582)------------------------------
% 3.69/1.41 % (3692563)Success in time 0.444 s
% 3.69/1.41 % Vampire exiting
%------------------------------------------------------------------------------