%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET977+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 12:42:27 PM UTC 2026
% Result : Theorem 2.21s 0.90s
% Output : Refutation 2.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 5 unt; 0 def)
% Number of atoms : 87 ( 39 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 102 ( 45 ~; 35 |; 17 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 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 : 65 ( 61 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
<=> ( X0 = X2
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_zfmisc_1) ).
fof(f10,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
<=> ( in(X0,X2)
& X1 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t129_zfmisc_1) ).
fof(f11,conjecture,
! [X0,X1] :
( X0 != empty_set
=> ( cartesian_product2(singleton(X1),X0) != empty_set
& cartesian_product2(X0,singleton(X1)) != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] :
( X0 != empty_set
=> ( cartesian_product2(singleton(X1),X0) != empty_set
& cartesian_product2(X0,singleton(X1)) != empty_set ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
? [X0,X1] :
( ( empty_set = cartesian_product2(singleton(X1),X0)
| empty_set = cartesian_product2(X0,singleton(X1)) )
& X0 != empty_set ),
inference(ennf_transformation,[],[f12]) ).
fof(f15,plain,
( ( empty_set = cartesian_product2(singleton(sK1),sK0)
| empty_set = cartesian_product2(sK0,singleton(sK1)) )
& empty_set != sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f13]) ).
fof(f16,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f17,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f16]) ).
fof(f18,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))],[f17]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
| ~ in(X0,X2)
| X1 != X3 )
& ( ( in(X0,X2)
& X1 = X3 )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
| ~ in(X0,X2)
| X1 != X3 )
& ( ( in(X0,X2)
& X1 = X3 )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
| X0 != X2
| ~ in(X1,X3) )
& ( ( X0 = X2
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
| X0 != X2
| ~ in(X1,X3) )
& ( ( X0 = X2
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ) ),
inference(flattening,[],[f21]) ).
fof(f25,plain,
empty_set != sK0,
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
( empty_set = cartesian_product2(sK0,singleton(sK1))
| empty_set = cartesian_product2(singleton(sK1),sK0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X0] :
( in(sK2(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
| ~ in(X0,X2)
| X1 != X3 ),
inference(cnf_transformation,[],[f20]) ).
fof(f35,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
| X0 != X2
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f28]) ).
fof(f41,plain,
! [X2,X3,X0] :
( in(ordered_pair(X0,X3),cartesian_product2(X2,singleton(X3)))
| ~ in(X0,X2) ),
inference(equality_resolution,[],[f32]) ).
fof(f42,plain,
! [X2,X3,X1] :
( in(ordered_pair(X2,X1),cartesian_product2(singleton(X2),X3))
| ~ in(X1,X3) ),
inference(equality_resolution,[],[f35]) ).
fof(f53,plain,
! [X0] :
( in(ordered_pair(X0,sK1),empty_set)
| ~ in(X0,sK0)
| empty_set = cartesian_product2(singleton(sK1),sK0) ),
inference(superposition,[],[f41,f26]) ).
fof(f54,plain,
! [X0] :
( empty_set = cartesian_product2(singleton(sK1),sK0)
| ~ in(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f53,f40]) ).
fof(f60,plain,
! [X0,X1] :
( in(ordered_pair(sK1,X0),empty_set)
| ~ in(X0,sK0)
| ~ in(X1,sK0) ),
inference(superposition,[],[f42,f54]) ).
fof(f63,plain,
! [X0,X1] :
( ~ in(X1,sK0)
| ~ in(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f60,f40]) ).
fof(f66,plain,
! [X0] : ~ in(X0,sK0),
inference(factoring,[],[f63]) ).
fof(f68,plain,
empty_set = sK0,
inference(resolution,[],[f66,f29]) ).
fof(f69,plain,
$false,
inference(forward_subsumption_resolution,[],[f68,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET977+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Mon Sep 28 03:17:34 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 2.21/0.90 % (2984129)Detected formulas, will run a generic FOF schedule.
% 2.21/0.90 % (2984134)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=3053748314:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.21/0.90 % (2984136)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=3480172050:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.21/0.90 % (2984140)dis-21_1_sil=8000:lcm=predicate:random_seed=425464781: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)
% 2.21/0.90 % (2984135)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=4265015320:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.21/0.90 % (2984138)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2383845045:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.21/0.90 % (2984137)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=309248561:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.21/0.90 % (2984139)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=636406697:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.21/0.90 % (2984140)Refutation not found, incomplete strategy
% 2.21/0.90 % (2984140)------------------------------
% 2.21/0.90 % (2984140)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.21/0.90 % (2984140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/0.90 % (2984140)CaDiCaL version: 2.1.3
% 2.21/0.90 % (2984140)Termination reason: Refutation not found, incomplete strategy
% 2.21/0.90 % (2984140)Time elapsed: 0.001 s
% 2.21/0.90 % (2984140)Peak memory usage: 88 MB
% 2.21/0.90 % (2984138)First to succeed.
% 2.21/0.90 % (2984140)Instructions burned: 1 (million)
% 2.21/0.90 % (2984137)Also succeeded, but the first one will report.
% 2.21/0.90 % (2984138)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2984129"
% 2.21/0.90 % (2984139)Also succeeded, but the first one will report.
% 2.21/0.90 % (2984140)------------------------------
% 2.21/0.90 % (2984140)------------------------------
% 2.21/0.90 % (2984138)Refutation found. Thanks to Tanya!
% 2.21/0.90 % SZS status Theorem for theBenchmark
% 2.21/0.90 % SZS output start Proof for theBenchmark
% See solution above
% 2.21/0.90 % (2984138)------------------------------
% 2.21/0.90 % (2984138)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.21/0.90 % (2984138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/0.90 % (2984138)CaDiCaL version: 2.1.3
% 2.21/0.90 % (2984138)Termination reason: Refutation
% 2.21/0.90 % (2984138)Time elapsed: 0.001 s
% 2.21/0.90 % (2984138)Peak memory usage: 88 MB
% 2.21/0.90 % (2984138)Instructions burned: 2 (million)
% 2.21/0.90 % (2984138)------------------------------
% 2.21/0.90 % (2984138)------------------------------
% 2.21/0.90 % (2984129)Success in time 0.278 s
% 2.21/0.90 % Vampire exiting
%------------------------------------------------------------------------------