%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET012-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 12:39:30 PM UTC 2026
% Result : Unsatisfiable 6.14s 11.84s
% Output : Refutation 6.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 37 ( 11 unt; 2 def)
% Number of atoms : 76 ( 16 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 72 ( 33 ~; 37 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| little_set(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
fof(f2,axiom,
! [X0,X1] :
( little_set(f1(X0,X1))
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality1) ).
fof(f3,axiom,
! [X0,X1] :
( member(f1(X0,X1),X1)
| member(f1(X0,X1),X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality2) ).
fof(f4,axiom,
! [X0,X1] :
( ~ member(f1(X0,X1),X1)
| ~ member(f1(X0,X1),X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality3) ).
fof(f37,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f38,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ little_set(X0)
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
fof(f162,axiom,
complement(as) = bs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_a_is_b) ).
fof(f163,axiom,
complement(bs) = cs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_b_is_c) ).
fof(f164,negated_conjecture,
as != cs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_equals_c) ).
fof(f207,plain,
! [X0] :
( ~ member(X0,bs)
| ~ member(X0,as) ),
inference(superposition,[],[f37,f162]) ).
fof(f208,plain,
! [X0] :
( ~ member(X0,cs)
| ~ member(X0,bs) ),
inference(superposition,[],[f37,f163]) ).
fof(f210,plain,
! [X0] :
( member(X0,bs)
| ~ little_set(X0)
| member(X0,as) ),
inference(superposition,[],[f38,f162]) ).
fof(f211,plain,
! [X0] :
( member(X0,cs)
| ~ little_set(X0)
| member(X0,bs) ),
inference(superposition,[],[f38,f163]) ).
fof(f219,plain,
! [X0] :
( ~ member(f1(X0,cs),X0)
| cs = X0
| ~ little_set(f1(X0,cs))
| member(f1(X0,cs),bs) ),
inference(resolution,[],[f4,f211]) ).
fof(f220,plain,
! [X0] :
( member(f1(X0,cs),bs)
| cs = X0
| ~ member(f1(X0,cs),X0) ),
inference(forward_subsumption_resolution,[],[f219,f1]) ).
fof(f223,plain,
! [X0] :
( ~ member(f1(X0,cs),as)
| ~ member(f1(X0,cs),X0)
| cs = X0 ),
inference(resolution,[],[f220,f207]) ).
fof(f230,plain,
! [X0] :
( member(f1(X0,cs),X0)
| cs = X0
| ~ member(f1(X0,cs),bs) ),
inference(resolution,[],[f3,f208]) ).
fof(f234,plain,
( as = cs
| ~ member(f1(as,cs),bs)
| ~ member(f1(as,cs),as)
| as = cs ),
inference(resolution,[],[f230,f223]) ).
fof(f240,plain,
( as = cs
| ~ member(f1(as,cs),bs)
| ~ member(f1(as,cs),as) ),
inference(duplicate_literal_removal,[],[f234]) ).
fof(f242,plain,
( as = cs
| ~ member(f1(as,cs),bs) ),
inference(forward_subsumption_resolution,[],[f240,f230]) ).
fof(f243,plain,
~ member(f1(as,cs),bs),
inference(forward_subsumption_resolution,[],[f242,f164]) ).
fof(f244,plain,
( as = cs
| ~ member(f1(as,cs),as) ),
inference(resolution,[],[f243,f220]) ).
fof(f245,plain,
( ~ little_set(f1(as,cs))
| member(f1(as,cs),as) ),
inference(resolution,[],[f243,f210]) ).
fof(f247,definition,
( spl0_1
<=> member(f1(as,cs),as) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f251,definition,
( spl0_2
<=> little_set(f1(as,cs)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f253,plain,
( ~ little_set(f1(as,cs))
| spl0_2 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f254,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f245,f251,f247]) ).
fof(f255,plain,
~ member(f1(as,cs),as),
inference(forward_subsumption_resolution,[],[f244,f164]) ).
fof(f256,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f255,f247]) ).
fof(f263,plain,
( as = cs
| spl0_2 ),
inference(resolution,[],[f2,f253]) ).
fof(f264,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f263,f164]) ).
fof(f265,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f264]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f254]) ).
cnf(s2,plain,
~ spl0_1,
inference(sat_conversion,[],[f256]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f265]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f266,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET012-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/10.38 % Computer : n020.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Mon Sep 28 00:04:30 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/10.42 Running first-order theorem proving
% 0.14/10.42 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
% 5.36/11.64 % (3905222)Input is clausal, will run a generic CNF schedule.
% 5.36/11.64 % (3905229)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2450385486:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.36/11.64 % (3905232)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4194938673:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.36/11.64 % (3905230)lrs+10_1_sil=8000:sp=occurrence:random_seed=1195325535:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.36/11.64 % (3905233)dis-21_1_sil=8000:lcm=predicate:random_seed=2249000894: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)
% 5.36/11.64 % (3905227)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=1360720058:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.36/11.64 % (3905230)Refutation not found, incomplete strategy
% 5.36/11.64 % (3905230)------------------------------
% 5.36/11.64 % (3905230)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/11.64 % (3905230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/11.64 % (3905230)CaDiCaL version: 2.1.3
% 5.36/11.64 % (3905230)Termination reason: Refutation not found, incomplete strategy
% 5.36/11.64 % (3905230)Time elapsed: 0.002 s
% 5.36/11.64 % (3905230)Peak memory usage: 88 MB
% 5.36/11.64 % (3905230)Instructions burned: 2 (million)
% 5.36/11.64 % (3905228)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1139456802:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.36/11.64 % (3905231)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3941923173:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.36/11.64 % (3905231)Refutation not found, incomplete strategy
% 5.36/11.64 % (3905231)------------------------------
% 5.36/11.64 % (3905231)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/11.64 % (3905231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/11.64 % (3905231)CaDiCaL version: 2.1.3
% 5.36/11.64 % (3905231)Termination reason: Refutation not found, incomplete strategy
% 5.36/11.64 % (3905231)Time elapsed: 0.001 s
% 5.36/11.64 % (3905231)Peak memory usage: 88 MB
% 5.36/11.64 % (3905231)Instructions burned: 1 (million)
% 5.36/11.64 % (3905233)Instruction limit reached!
% 5.36/11.64 % (3905233)------------------------------
% 5.36/11.64 % (3905233)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/11.64 % (3905233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/11.64 % (3905233)CaDiCaL version: 2.1.3
% 5.36/11.64 % (3905233)Termination reason: Instruction limit
% 5.36/11.64 % (3905233)Termination phase: Saturation
% 5.36/11.64 % (3905233)Time elapsed: 0.067 s
% 5.36/11.64 % (3905233)Peak memory usage: 90 MB
% 5.36/11.64 % (3905233)Instructions burned: 117 (million)
% 5.36/11.64 % (3905232)Instruction limit reached!
% 5.36/11.64 % (3905232)------------------------------
% 5.36/11.64 % (3905232)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/11.64 % (3905232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/11.64 % (3905232)CaDiCaL version: 2.1.3
% 5.36/11.64 % (3905232)Termination reason: Instruction limit
% 5.36/11.64 % (3905232)Termination phase: Saturation
% 5.36/11.64 % (3905232)Time elapsed: 0.122 s
% 5.36/11.64 % (3905232)Peak memory usage: 90 MB
% 5.36/11.64 % (3905232)Instructions burned: 180 (million)
% 5.36/11.64 % (3905241)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=3381153979:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.36/11.64 % (3905230)------------------------------
% 5.36/11.64 % (3905230)------------------------------
% 5.36/11.64 % (3905242)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1028618399: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)
% 5.36/11.64 % (3905242)Refutation not found, incomplete strategy
% 5.36/11.64 % (3905242)------------------------------
% 5.36/11.64 % (3905242)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/11.64 % (3905242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.14/11.84 % (3905242)CaDiCaL version: 2.1.3
% 6.14/11.84 % (3905242)Termination reason: Refutation not found, incomplete strategy
% 6.14/11.84 % (3905242)Time elapsed: 0.005 s
% 6.14/11.84 % (3905242)Peak memory usage: 88 MB
% 6.14/11.84 % (3905242)Instructions burned: 7 (million)
% 6.14/11.84 % (3905231)------------------------------
% 6.14/11.84 % (3905231)------------------------------
% 6.14/11.84 % (3905241)Instruction limit reached!
% 6.14/11.84 % (3905241)------------------------------
% 6.14/11.84 % (3905241)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.14/11.84 % (3905241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.14/11.84 % (3905241)CaDiCaL version: 2.1.3
% 6.14/11.84 % (3905241)Termination reason: Instruction limit
% 6.14/11.84 % (3905241)Termination phase: Saturation
% 6.14/11.84 % (3905241)Time elapsed: 0.075 s
% 6.14/11.84 % (3905241)Peak memory usage: 89 MB
% 6.14/11.84 % (3905241)Instructions burned: 145 (million)
% 6.14/11.84 % (3905244)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=924108358:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 6.14/11.84 % (3905244)Refutation not found, incomplete strategy
% 6.14/11.84 % (3905244)------------------------------
% 6.14/11.84 % (3905244)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.14/11.84 % (3905244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.14/11.84 % (3905244)CaDiCaL version: 2.1.3
% 6.14/11.84 % (3905244)Termination reason: Refutation not found, incomplete strategy
% 6.14/11.84 % (3905244)Time elapsed: 0.002 s
% 6.14/11.84 % (3905244)Peak memory usage: 88 MB
% 6.14/11.84 % (3905244)Instructions burned: 3 (million)
% 6.14/11.84 % (3905229)First to succeed.
% 6.14/11.84 % (3905229)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3905222"
% 6.14/11.84 % (3905246)lrs+10_64_to=lpo:sil=8000:random_seed=4000936564:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 6.14/11.84 % (3905247)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=4282244695:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 6.14/11.84 % (3905246)Instruction limit reached!
% 6.14/11.84 % (3905246)------------------------------
% 6.14/11.84 % (3905246)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.14/11.84 % (3905246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.14/11.84 % (3905246)CaDiCaL version: 2.1.3
% 6.14/11.84 % (3905246)Termination reason: Instruction limit
% 6.14/11.84 % (3905246)Termination phase: Saturation
% 6.14/11.84 % (3905246)Time elapsed: 0.072 s
% 6.14/11.84 % (3905246)Peak memory usage: 90 MB
% 6.14/11.84 % (3905246)Instructions burned: 127 (million)
% 6.14/11.84 % (3905244)------------------------------
% 6.14/11.84 % (3905244)------------------------------
% 6.14/11.84 % (3905242)------------------------------
% 6.14/11.84 % (3905242)------------------------------
% 6.14/11.84 % (3905247)Instruction limit reached!
% 6.14/11.84 % (3905247)------------------------------
% 6.14/11.84 % (3905247)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.14/11.84 % (3905247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.14/11.84 % (3905247)CaDiCaL version: 2.1.3
% 6.14/11.84 % (3905247)Termination reason: Instruction limit
% 6.14/11.84 % (3905247)Termination phase: Saturation
% 6.14/11.84 % (3905247)Time elapsed: 0.131 s
% 6.14/11.84 % (3905247)Peak memory usage: 90 MB
% 6.14/11.84 % (3905247)Instructions burned: 195 (million)
% 6.14/11.84 % (3905252)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=1213032652:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 6.14/11.84 % (3905251)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3460295085:i=157:gtg=all_2993 on theBenchmark for (2993ds/157Mi)
% 6.14/11.84 % (3905229)Refutation found. Thanks to Tanya!
% 6.14/11.84 % SZS status Unsatisfiable for theBenchmark
% 6.14/11.84 % SZS output start Proof for theBenchmark
% See solution above
% 6.14/11.84 % (3905229)------------------------------
% 6.14/11.84 % (3905229)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.14/11.84 % (3905229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.14/11.84 % (3905229)CaDiCaL version: 2.1.3
% 6.14/11.84 % (3905229)Termination reason: Refutation
% 6.14/11.84 % (3905229)Time elapsed: 0.412 s
% 6.14/11.84 % (3905229)Peak memory usage: 131 MB
% 6.14/11.84 % (3905229)Instructions burned: 970 (million)
% 6.14/11.84 % (3905229)------------------------------
% 6.14/11.84 % (3905229)------------------------------
% 6.14/11.84 % (3905222)Success in time 0.787 s
% 6.14/11.84 % Vampire exiting
%------------------------------------------------------------------------------