%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET961+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 12:42:25 PM UTC 2026
% Result : Theorem 3.47s 1.44s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 43 ( 8 unt; 0 def)
% Number of atoms : 123 ( 45 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 143 ( 63 ~; 54 |; 19 &)
% ( 3 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 83 ( 75 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f10,conjecture,
! [X0,X1] :
( cartesian_product2(X0,X1) = cartesian_product2(X1,X0)
=> ( X0 = empty_set
| X1 = empty_set
| X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] :
( cartesian_product2(X0,X1) = cartesian_product2(X1,X0)
=> ( X0 = empty_set
| X1 = empty_set
| X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f13,plain,
? [X0,X1] :
( empty_set != X0
& empty_set != X1
& X0 != X1
& cartesian_product2(X0,X1) = cartesian_product2(X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f14,plain,
? [X0,X1] :
( empty_set != X0
& empty_set != X1
& X0 != X1
& cartesian_product2(X0,X1) = cartesian_product2(X1,X0) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f17,plain,
( empty_set != sK0
& empty_set != sK1
& sK0 != sK1
& cartesian_product2(sK0,sK1) = cartesian_product2(sK1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f14]) ).
fof(f18,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f19,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f18]) ).
fof(f20,plain,
! [X0] :
( ( X0 = empty_set
| in(sK2(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f19]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK5(X0,X1),X1)
| ~ in(sK5(X0,X1),X0) )
& ( in(sK5(X0,X1),X1)
| in(sK5(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f25]) ).
fof(f27,plain,
cartesian_product2(sK0,sK1) = cartesian_product2(sK1,sK0),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f17]) ).
fof(f29,plain,
empty_set != sK1,
inference(cnf_transformation,[],[f17]) ).
fof(f30,plain,
empty_set != sK0,
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f20]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
! [X0,X1] :
( in(sK5(X0,X1),X1)
| X0 = X1
| in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f40,plain,
! [X0,X1] :
( ~ in(sK5(X0,X1),X1)
| X0 = X1
| ~ in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f43,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f32]) ).
fof(f47,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(sK0,sK1))
| in(X1,sK0) ),
inference(superposition,[],[f34,f27]) ).
fof(f48,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(sK0,sK1))
| in(X0,sK1) ),
inference(superposition,[],[f35,f27]) ).
fof(f51,plain,
! [X0,X1] :
( in(X1,sK0)
| ~ in(X1,sK1)
| ~ in(X0,sK0) ),
inference(resolution,[],[f36,f47]) ).
fof(f57,plain,
! [X0] :
( in(sK5(X0,empty_set),X0)
| empty_set = X0 ),
inference(resolution,[],[f39,f43]) ).
fof(f62,plain,
! [X0,X1] :
( ~ in(sK5(X0,sK0),sK1)
| ~ in(sK5(X0,sK0),X0)
| sK0 = X0
| ~ in(X1,sK0) ),
inference(resolution,[],[f40,f51]) ).
fof(f65,plain,
! [X0,X1] :
( in(X0,sK1)
| ~ in(X0,sK0)
| ~ in(X1,sK1) ),
inference(resolution,[],[f48,f36]) ).
fof(f92,plain,
! [X0] :
( ~ in(sK5(sK1,sK0),sK1)
| sK0 = sK1
| ~ in(X0,sK0) ),
inference(factoring,[],[f62]) ).
fof(f94,plain,
! [X0] :
( ~ in(sK5(sK1,sK0),sK1)
| ~ in(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f92,f28]) ).
fof(f98,plain,
! [X0,X1] :
( ~ in(sK5(sK1,sK0),sK0)
| ~ in(X0,sK0)
| ~ in(X1,sK1) ),
inference(resolution,[],[f94,f65]) ).
fof(f101,plain,
! [X0,X1] :
( ~ in(X0,sK0)
| ~ in(X1,sK1)
| sK0 = sK1
| in(sK5(sK1,sK0),sK1) ),
inference(resolution,[],[f98,f39]) ).
fof(f104,plain,
! [X0,X1] :
( ~ in(X0,sK0)
| ~ in(X1,sK1)
| sK0 = sK1 ),
inference(forward_subsumption_resolution,[],[f101,f94]) ).
fof(f105,plain,
! [X0,X1] :
( ~ in(X1,sK1)
| ~ in(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f104,f28]) ).
fof(f116,plain,
! [X0] :
( ~ in(X0,sK0)
| empty_set = sK1 ),
inference(resolution,[],[f105,f57]) ).
fof(f118,plain,
! [X0] : ~ in(X0,sK0),
inference(forward_subsumption_resolution,[],[f116,f29]) ).
fof(f123,plain,
empty_set = sK0,
inference(resolution,[],[f118,f57]) ).
fof(f125,plain,
$false,
inference(forward_subsumption_resolution,[],[f123,f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET961+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 03:16:16 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.47/1.44 % (1404246)Detected formulas, will run a generic FOF schedule.
% 3.47/1.44 % (1404251)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=2568182910:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.47/1.44 % (1404252)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=910412960:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.47/1.44 % (1404253)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3507140881:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.47/1.44 % (1404256)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=972369929:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.47/1.44 % (1404254)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3843840577:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.47/1.44 % (1404255)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1092056934:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.47/1.44 % (1404254)Refutation not found, incomplete strategy
% 3.47/1.44 % (1404254)------------------------------
% 3.47/1.44 % (1404254)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.44 % (1404254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.44 % (1404254)CaDiCaL version: 2.1.3
% 3.47/1.44 % (1404254)Termination reason: Refutation not found, incomplete strategy
% 3.47/1.44 % (1404254)Time elapsed: 0.003 s
% 3.47/1.44 % (1404254)Peak memory usage: 88 MB
% 3.47/1.44 % (1404254)Instructions burned: 2 (million)
% 3.47/1.44 % (1404255)First to succeed.
% 3.47/1.44 % (1404255)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1404246"
% 3.47/1.44 % (1404257)dis-21_1_sil=8000:lcm=predicate:random_seed=3497756557:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.47/1.44 % (1404257)Refutation not found, incomplete strategy
% 3.47/1.44 % (1404257)------------------------------
% 3.47/1.44 % (1404257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.44 % (1404257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.44 % (1404257)CaDiCaL version: 2.1.3
% 3.47/1.44 % (1404257)Termination reason: Refutation not found, incomplete strategy
% 3.47/1.44 % (1404257)Time elapsed: 0.002 s
% 3.47/1.44 % (1404257)Peak memory usage: 88 MB
% 3.47/1.44 % (1404257)Instructions burned: 2 (million)
% 3.47/1.44 % (1404256)Instruction limit reached!
% 3.47/1.44 % (1404256)------------------------------
% 3.47/1.44 % (1404256)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.44 % (1404256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.44 % (1404256)CaDiCaL version: 2.1.3
% 3.47/1.44 % (1404256)Termination reason: Instruction limit
% 3.47/1.44 % (1404256)Termination phase: Saturation
% 3.47/1.44 % (1404256)Time elapsed: 0.090 s
% 3.47/1.44 % (1404256)Peak memory usage: 89 MB
% 3.47/1.44 % (1404256)Instructions burned: 139 (million)
% 3.47/1.44 % (1404265)lrs+10_1_sil=8000:sp=occurrence:random_seed=596864538:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.47/1.44 % (1404265)Also succeeded, but the first one will report.
% 3.47/1.44 % (1404254)------------------------------
% 3.47/1.44 % (1404254)------------------------------
% 3.47/1.44 % (1404257)------------------------------
% 3.47/1.44 % (1404257)------------------------------
% 3.47/1.44 % (1404255)Refutation found. Thanks to Tanya!
% 3.47/1.44 % SZS status Theorem for theBenchmark
% 3.47/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.44 % (1404255)------------------------------
% 3.47/1.44 % (1404255)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.44 % (1404255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.44 % (1404255)CaDiCaL version: 2.1.3
% 3.47/1.44 % (1404255)Termination reason: Refutation
% 3.47/1.44 % (1404255)Time elapsed: 0.005 s
% 3.47/1.44 % (1404255)Peak memory usage: 88 MB
% 3.47/1.44 % (1404255)Instructions burned: 5 (million)
% 3.47/1.44 % (1404255)------------------------------
% 3.47/1.44 % (1404255)------------------------------
% 3.47/1.44 % (1404246)Success in time 0.407 s
% 3.47/1.44 % Vampire exiting
%------------------------------------------------------------------------------