%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET075-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:39:58 PM UTC 2026
% Result : Unsatisfiable 3.50s 1.38s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 35 ( 11 unt; 2 def)
% Number of atoms : 65 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 28 ~; 28 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product1) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f69,axiom,
! [X0] :
( X0 = null_class
| intersection(X0,regular(X0)) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f101,negated_conjecture,
member(ordered_pair(x,y),cross_product(u,v)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_1) ).
fof(f102,negated_conjecture,
unordered_pair(x,y) = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_2) ).
fof(f103,plain,
null_class = unordered_pair(x,y),
inference(reorient_equations,[],[f102]) ).
fof(f112,plain,
( member(x,null_class)
| ~ member(x,universal_class) ),
inference(superposition,[],[f9,f103]) ).
fof(f115,definition,
( spl0_1
<=> member(x,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f117,plain,
( ~ member(x,universal_class)
| spl0_1 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f119,definition,
( spl0_2
<=> member(x,null_class) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f121,plain,
( member(x,null_class)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f112,f119,f115]) ).
fof(f161,plain,
( ! [X0] :
( ~ member(x,X0)
| ~ subclass(X0,universal_class) )
| spl0_1 ),
inference(resolution,[],[f1,f117]) ).
fof(f164,plain,
( ! [X0] : ~ member(x,X0)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f161,f4]) ).
fof(f213,plain,
! [X0,X1] :
( ~ member(X0,null_class)
| member(X0,X1)
| null_class = X1 ),
inference(superposition,[],[f21,f70]) ).
fof(f240,plain,
member(x,u),
inference(resolution,[],[f14,f101]) ).
fof(f242,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f240,f164]) ).
fof(f243,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f242]) ).
fof(f693,plain,
( ! [X0] :
( member(x,X0)
| null_class = X0 )
| ~ spl0_2 ),
inference(resolution,[],[f213,f121]) ).
fof(f699,plain,
( ! [X0] :
( ~ member(x,X0)
| complement(X0) = null_class )
| ~ spl0_2 ),
inference(resolution,[],[f693,f24]) ).
fof(f768,plain,
( null_class = complement(null_class)
| ~ spl0_2 ),
inference(resolution,[],[f699,f121]) ).
fof(f842,plain,
( ! [X0] :
( ~ member(X0,null_class)
| ~ member(X0,null_class) )
| ~ spl0_2 ),
inference(superposition,[],[f24,f768]) ).
fof(f852,plain,
( ! [X0] : ~ member(X0,null_class)
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f842]) ).
fof(f914,plain,
( $false
| ~ spl0_2 ),
inference(resolution,[],[f852,f121]) ).
fof(f919,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f914]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f122]) ).
cnf(s9,plain,
spl0_1,
inference(sat_conversion,[],[f243]) ).
cnf(s42,plain,
~ spl0_2,
inference(sat_conversion,[],[f919]) ).
cnf(s44,plain,
$false,
inference(rat,[],[s1,s42,s9]) ).
fof(f920,plain,
$false,
inference(avatar_sat_refutation,[],[s44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET075-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.38 % Computer : n006.cluster.edu
% 0.08/0.38 % Model : x86_64 x86_64
% 0.08/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.38 % Memory : 8046.5625MB
% 0.08/0.38 % OS : Linux 6.8.0-71-generic
% 0.08/0.38 % CPULimit : 300
% 0.08/0.38 % WCLimit : 300
% 0.08/0.38 % DateTime : Mon Sep 28 00:30:56 UTC 2026
% 0.08/0.39 % CPUTime :
% 0.08/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 3.50/1.38 % (3482503)Input is clausal, will run a generic CNF schedule.
% 3.50/1.38 % (3482508)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=2203209508:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.50/1.38 % (3482513)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4186471669:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.50/1.38 % (3482511)lrs+10_1_sil=8000:sp=occurrence:random_seed=3576788125:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.50/1.38 % (3482509)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2200578050:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.50/1.38 % (3482512)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=897741791:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.50/1.38 % (3482510)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1029894885:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.50/1.38 % (3482511)Refutation not found, incomplete strategy
% 3.50/1.38 % (3482511)------------------------------
% 3.50/1.38 % (3482511)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.38 % (3482511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.38 % (3482511)CaDiCaL version: 2.1.3
% 3.50/1.38 % (3482511)Termination reason: Refutation not found, incomplete strategy
% 3.50/1.38 % (3482511)Time elapsed: 0.002 s
% 3.50/1.38 % (3482511)Peak memory usage: 88 MB
% 3.50/1.38 % (3482511)Instructions burned: 1 (million)
% 3.50/1.38 % (3482514)dis-21_1_sil=8000:lcm=predicate:random_seed=3573972177: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)
% 3.50/1.38 % (3482513)First to succeed.
% 3.50/1.38 % (3482513)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3482503"
% 3.50/1.38 % (3482512)Instruction limit reached!
% 3.50/1.38 % (3482512)------------------------------
% 3.50/1.38 % (3482512)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.38 % (3482512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.38 % (3482512)CaDiCaL version: 2.1.3
% 3.50/1.38 % (3482512)Termination reason: Instruction limit
% 3.50/1.38 % (3482512)Termination phase: Saturation
% 3.50/1.38 % (3482512)Time elapsed: 0.070 s
% 3.50/1.38 % (3482512)Peak memory usage: 89 MB
% 3.50/1.38 % (3482512)Instructions burned: 115 (million)
% 3.50/1.38 % (3482514)Instruction limit reached!
% 3.50/1.38 % (3482514)------------------------------
% 3.50/1.38 % (3482514)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.38 % (3482514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.38 % (3482514)CaDiCaL version: 2.1.3
% 3.50/1.38 % (3482514)Termination reason: Instruction limit
% 3.50/1.38 % (3482514)Termination phase: Saturation
% 3.50/1.38 % (3482514)Time elapsed: 0.064 s
% 3.50/1.38 % (3482514)Peak memory usage: 88 MB
% 3.50/1.38 % (3482514)Instructions burned: 117 (million)
% 3.50/1.38 % (3482522)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=1822199065:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.50/1.38 % (3482523)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1711260085: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)
% 3.50/1.38 % (3482511)------------------------------
% 3.50/1.38 % (3482511)------------------------------
% 3.50/1.38 % (3482513)Refutation found. Thanks to Tanya!
% 3.50/1.38 % SZS status Unsatisfiable for theBenchmark
% 3.50/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.50/1.38 % (3482513)------------------------------
% 3.50/1.38 % (3482513)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.38 % (3482513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.38 % (3482513)CaDiCaL version: 2.1.3
% 3.50/1.38 % (3482513)Termination reason: Refutation
% 3.50/1.38 % (3482513)Time elapsed: 0.030 s
% 3.50/1.38 % (3482513)Peak memory usage: 90 MB
% 3.50/1.38 % (3482513)Instructions burned: 33 (million)
% 3.50/1.38 % (3482513)------------------------------
% 3.50/1.38 % (3482513)------------------------------
% 3.50/1.38 % (3482503)Success in time 0.434 s
% 3.50/1.38 % Vampire exiting
%------------------------------------------------------------------------------