%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET047-5 : 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 : 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 12:39:48 PM UTC 2026
% Result : Unsatisfiable 3.49s 1.46s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 55 ( 6 unt; 6 def)
% Number of atoms : 138 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 145 ( 62 ~; 77 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( element(X2,X1)
| ~ element(X2,X0)
| ~ set_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_substitution1) ).
fof(f2,axiom,
! [X2,X0,X1] :
( element(X2,X0)
| ~ element(X2,X1)
| ~ set_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_substitution2) ).
fof(f3,axiom,
! [X0,X1] :
( element(f(X0,X1),X1)
| element(f(X0,X1),X0)
| set_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
fof(f4,axiom,
! [X0,X1] :
( set_equal(X0,X1)
| ~ element(f(X0,X1),X0)
| ~ element(f(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
fof(f5,negated_conjecture,
( set_equal(a,b)
| set_equal(b,a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_symmetry1) ).
fof(f6,negated_conjecture,
( ~ set_equal(b,a)
| ~ set_equal(a,b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_symmetry2) ).
fof(f8,definition,
( spl0_1
<=> set_equal(a,b) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f9,plain,
( ~ set_equal(a,b)
| spl0_1 ),
inference(avatar_component_clause,[],[f8]) ).
fof(f11,definition,
( spl0_2
<=> set_equal(b,a) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f12,plain,
( ~ set_equal(b,a)
| spl0_2 ),
inference(avatar_component_clause,[],[f11]) ).
fof(f13,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f6,f11,f8]) ).
fof(f16,plain,
( spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f5,f8,f11]) ).
fof(f19,definition,
( spl0_3
<=> element(f(a,b),b) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f20,plain,
( ~ element(f(a,b),b)
| spl0_3 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f22,definition,
( spl0_4
<=> element(f(a,b),a) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f23,plain,
( ~ element(f(a,b),a)
| spl0_4 ),
inference(avatar_component_clause,[],[f22]) ).
fof(f26,plain,
( ! [X0] :
( ~ element(f(a,b),X0)
| ~ set_equal(b,X0) )
| spl0_3 ),
inference(resolution,[],[f20,f2]) ).
fof(f28,plain,
( element(f(a,b),a)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f22]) ).
fof(f33,plain,
( ~ set_equal(b,a)
| spl0_3
| ~ spl0_4 ),
inference(resolution,[],[f26,f28]) ).
fof(f34,plain,
( ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f33,f22,f19,f11]) ).
fof(f35,plain,
( ~ element(f(b,a),b)
| ~ element(f(b,a),a)
| spl0_2 ),
inference(resolution,[],[f12,f4]) ).
fof(f37,definition,
( spl0_5
<=> element(f(b,a),a) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f38,plain,
( ~ element(f(b,a),a)
| spl0_5 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f40,definition,
( spl0_6
<=> element(f(b,a),b) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f41,plain,
( ~ element(f(b,a),b)
| spl0_6 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f42,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_2 ),
inference(avatar_split_clause,[],[f35,f11,f40,f37]) ).
fof(f46,plain,
( element(f(b,a),b)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f49,plain,
( ! [X0] :
( ~ element(f(b,a),X0)
| ~ set_equal(X0,b) )
| spl0_6 ),
inference(resolution,[],[f41,f1]) ).
fof(f58,plain,
( ~ set_equal(a,b)
| element(f(b,a),b)
| set_equal(b,a)
| spl0_6 ),
inference(resolution,[],[f49,f3]) ).
fof(f61,plain,
( spl0_2
| spl0_6
| ~ spl0_1
| spl0_6 ),
inference(avatar_split_clause,[],[f58,f40,f8,f40,f11]) ).
fof(f63,plain,
( ! [X0] :
( ~ element(f(b,a),X0)
| ~ set_equal(a,X0) )
| spl0_5 ),
inference(resolution,[],[f38,f2]) ).
fof(f69,plain,
( ~ set_equal(a,b)
| spl0_5
| ~ spl0_6 ),
inference(resolution,[],[f63,f46]) ).
fof(f70,plain,
( ~ spl0_1
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f69,f40,f37,f8]) ).
fof(f71,plain,
( ~ element(f(a,b),a)
| ~ element(f(a,b),b)
| spl0_1 ),
inference(resolution,[],[f9,f4]) ).
fof(f72,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_1 ),
inference(avatar_split_clause,[],[f71,f8,f22,f19]) ).
fof(f74,plain,
( ! [X0] :
( ~ element(f(a,b),X0)
| ~ set_equal(X0,a) )
| spl0_4 ),
inference(resolution,[],[f23,f1]) ).
fof(f78,plain,
( ~ set_equal(b,a)
| element(f(a,b),a)
| set_equal(a,b)
| spl0_4 ),
inference(resolution,[],[f74,f3]) ).
fof(f81,plain,
( spl0_1
| spl0_4
| ~ spl0_2
| spl0_4 ),
inference(avatar_split_clause,[],[f78,f22,f11,f22,f8]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f13]) ).
cnf(s2,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f16]) ).
cnf(s5,plain,
( ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f34]) ).
cnf(s6,plain,
( spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f42]) ).
cnf(s9,plain,
( spl0_6
| spl0_2
| ~ spl0_1
| spl0_6 ),
inference(sat_conversion,[],[f61]) ).
cnf(s10,plain,
( ~ spl0_1
| spl0_2
| spl0_6 ),
inference(rat,[],[s9]) ).
cnf(s12,plain,
( ~ spl0_1
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f70]) ).
cnf(s13,plain,
( spl0_1
| ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f72]) ).
cnf(s14,plain,
( spl0_4
| ~ spl0_2
| spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f81]) ).
cnf(s15,plain,
( spl0_1
| ~ spl0_2
| spl0_4 ),
inference(rat,[],[s14]) ).
cnf(s16,plain,
( spl0_1
| ~ spl0_2 ),
inference(rat,[],[s5,s13,s15]) ).
cnf(s17,plain,
spl0_1,
inference(rat,[],[s16,s2]) ).
cnf(s18,plain,
~ spl0_2,
inference(rat,[],[s1,s17]) ).
cnf(s19,plain,
spl0_6,
inference(rat,[],[s10,s18,s17]) ).
cnf(s20,plain,
spl0_5,
inference(rat,[],[s12,s17,s19]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s6,s18,s19,s20]) ).
fof(f82,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET047-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 00:25:27 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.49/1.46 % (3362826)Input is clausal, will run a generic CNF schedule.
% 3.49/1.46 % (3362835)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1331353138:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.49/1.46 % (3362835)Refutation not found, incomplete strategy
% 3.49/1.46 % (3362835)------------------------------
% 3.49/1.46 % (3362835)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.46 % (3362835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.46 % (3362835)CaDiCaL version: 2.1.3
% 3.49/1.46 % (3362835)Termination reason: Refutation not found, incomplete strategy
% 3.49/1.46 % (3362835)Time elapsed: 0.001 s
% 3.49/1.46 % (3362835)Peak memory usage: 87 MB
% 3.49/1.46 % (3362831)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=2421381939:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.49/1.46 % (3362833)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=653761035:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.49/1.46 % (3362832)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2696956579:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.49/1.46 % (3362837)dis-21_1_sil=8000:lcm=predicate:random_seed=3370731552: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)
% 3.49/1.46 % (3362834)lrs+10_1_sil=8000:sp=occurrence:random_seed=4164904040:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.49/1.46 % (3362836)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4036344424:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.49/1.46 % (3362837)First to succeed.
% 3.49/1.46 % (3362834)Also succeeded, but the first one will report.
% 3.49/1.46 % (3362837)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3362826"
% 3.49/1.46 % (3362836)Also succeeded, but the first one will report.
% 3.49/1.46 % (3362835)------------------------------
% 3.49/1.46 % (3362835)------------------------------
% 3.49/1.46 % (3362845)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=3078427609:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.49/1.46 % (3362845)Refutation not found, incomplete strategy
% 3.49/1.46 % (3362845)------------------------------
% 3.49/1.46 % (3362845)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.46 % (3362845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.46 % (3362845)CaDiCaL version: 2.1.3
% 3.49/1.46 % (3362845)Termination reason: Refutation not found, incomplete strategy
% 3.49/1.46 % (3362845)Time elapsed: 0.001 s
% 3.49/1.46 % (3362845)Peak memory usage: 87 MB
% 3.49/1.46 % (3362837)Refutation found. Thanks to Tanya!
% 3.49/1.46 % SZS status Unsatisfiable for theBenchmark
% 3.49/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.46 % (3362837)------------------------------
% 3.49/1.46 % (3362837)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.46 % (3362837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.46 % (3362837)CaDiCaL version: 2.1.3
% 3.49/1.46 % (3362837)Termination reason: Refutation
% 3.49/1.46 % (3362837)Time elapsed: 0.003 s
% 3.49/1.46 % (3362837)Peak memory usage: 89 MB
% 3.49/1.46 % (3362837)Instructions burned: 2 (million)
% 3.49/1.46 % (3362837)------------------------------
% 3.49/1.46 % (3362837)------------------------------
% 3.49/1.46 % (3362826)Success in time 0.409 s
% 3.49/1.46 % Vampire exiting
%------------------------------------------------------------------------------