%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET960+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 3.63s 1.46s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 45 ( 8 unt; 0 def)
% Number of atoms : 173 ( 96 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 209 ( 81 ~; 90 |; 32 &)
% ( 5 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 108 ( 88 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = cartesian_product2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f10,conjecture,
! [X0,X1] :
( cartesian_product2(X0,X1) = empty_set
<=> ( X0 = empty_set
| X1 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] :
( cartesian_product2(X0,X1) = empty_set
<=> ( X0 = empty_set
| X1 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,plain,
? [X0,X1] :
( cartesian_product2(X0,X1) = empty_set
<~> ( X0 = empty_set
| X1 = empty_set ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f14,plain,
? [X0,X1] :
( ( ( empty_set != X0
& empty_set != X1 )
| empty_set != cartesian_product2(X0,X1) )
& ( X0 = empty_set
| X1 = empty_set
| cartesian_product2(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f15,plain,
? [X0,X1] :
( ( ( empty_set != X0
& empty_set != X1 )
| empty_set != cartesian_product2(X0,X1) )
& ( X0 = empty_set
| X1 = empty_set
| cartesian_product2(X0,X1) = empty_set ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
( ( ( empty_set != sK0
& empty_set != sK1 )
| empty_set != cartesian_product2(sK0,sK1) )
& ( empty_set = sK0
| empty_set = sK1
| empty_set = cartesian_product2(sK0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15]) ).
fof(f17,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f18,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f17]) ).
fof(f19,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))],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ? [X3] :
( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,X2) )
& ( ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != X3 ) )
& ( ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) )
| ~ in(X3,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ? [X3] :
( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( in(X6,X0)
& in(X7,X1)
& ordered_pair(X6,X7) = X3 )
| in(X3,X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ~ in(X9,X0)
| ~ in(X10,X1)
| ordered_pair(X9,X10) != X8 ) )
& ( ? [X11,X12] :
( in(X11,X0)
& in(X12,X1)
& ordered_pair(X11,X12) = X8 )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != sK3(X0,X1,X2) )
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( in(sK4(X0,X1,X2),X0)
& in(sK5(X0,X1,X2),X1)
& sK3(X0,X1,X2) = ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2)) )
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ~ in(X9,X0)
| ~ in(X10,X1)
| ordered_pair(X9,X10) != X8 ) )
& ( ( in(sK6(X0,X1,X8),X0)
& in(sK7(X0,X1,X8),X1)
& ordered_pair(sK6(X0,X1,X8),sK7(X0,X1,X8)) = X8 )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7]),skolemize(X3,sK3(X0,X1,X2)),skolemize(X6,sK4(X0,X1,X2)),skolemize(X7,sK5(X0,X1,X2)),skolemize(X11,sK6(X0,X1,X8)),skolemize(X12,sK7(X0,X1,X8))],[f21]) ).
fof(f25,plain,
( empty_set = cartesian_product2(sK0,sK1)
| empty_set = sK1
| empty_set = sK0 ),
inference(cnf_transformation,[],[f16]) ).
fof(f26,plain,
( empty_set != cartesian_product2(sK0,sK1)
| empty_set != sK1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
( empty_set != cartesian_product2(sK0,sK1)
| empty_set != sK0 ),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f19]) ).
fof(f30,plain,
! [X0] :
( in(sK2(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f19]) ).
fof(f32,plain,
! [X2,X0,X1,X8] :
( in(sK7(X0,X1,X8),X1)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f33,plain,
! [X2,X0,X1,X8] :
( in(sK6(X0,X1,X8),X0)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f34,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| ~ in(X9,X0)
| ~ in(X10,X1)
| ordered_pair(X9,X10) != X8
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f43,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f29]) ).
fof(f44,plain,
! [X2,X10,X0,X1,X9] :
( in(ordered_pair(X9,X10),X2)
| ~ in(X9,X0)
| ~ in(X10,X1)
| cartesian_product2(X0,X1) != X2 ),
inference(equality_resolution,[],[f34]) ).
fof(f45,plain,
! [X10,X0,X1,X9] :
( in(ordered_pair(X9,X10),cartesian_product2(X0,X1))
| ~ in(X9,X0)
| ~ in(X10,X1) ),
inference(equality_resolution,[],[f44]) ).
fof(f46,plain,
! [X0,X1,X8] :
( in(sK6(X0,X1,X8),X0)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f33]) ).
fof(f47,plain,
! [X0,X1,X8] :
( in(sK7(X0,X1,X8),X1)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f32]) ).
fof(f54,plain,
! [X0,X1] : ~ in(X0,cartesian_product2(empty_set,X1)),
inference(resolution,[],[f46,f43]) ).
fof(f56,plain,
! [X0] : empty_set = cartesian_product2(empty_set,X0),
inference(resolution,[],[f54,f30]) ).
fof(f59,plain,
! [X0,X1] : ~ in(X0,cartesian_product2(X1,empty_set)),
inference(resolution,[],[f47,f43]) ).
fof(f69,plain,
! [X0,X1] :
( in(ordered_pair(X0,X1),empty_set)
| ~ in(X0,sK0)
| ~ in(X1,sK1)
| empty_set = sK1
| empty_set = sK0 ),
inference(superposition,[],[f45,f25]) ).
fof(f71,plain,
! [X0,X1] :
( ~ in(X1,sK1)
| ~ in(X0,sK0)
| empty_set = sK1
| empty_set = sK0 ),
inference(forward_subsumption_resolution,[],[f69,f43]) ).
fof(f72,plain,
! [X0] :
( ~ in(X0,sK0)
| empty_set = sK1
| empty_set = sK0
| empty_set = sK1 ),
inference(resolution,[],[f71,f30]) ).
fof(f75,plain,
! [X0] :
( ~ in(X0,sK0)
| empty_set = sK1
| empty_set = sK0 ),
inference(duplicate_literal_removal,[],[f72]) ).
fof(f78,plain,
( empty_set = sK1
| empty_set = sK0
| empty_set = sK0 ),
inference(resolution,[],[f75,f30]) ).
fof(f81,plain,
( empty_set = sK1
| empty_set = sK0 ),
inference(duplicate_literal_removal,[],[f78]) ).
fof(f83,plain,
! [X0,X1] :
( ~ in(X0,cartesian_product2(X1,sK1))
| empty_set = sK0 ),
inference(superposition,[],[f59,f81]) ).
fof(f186,plain,
! [X0] :
( empty_set = cartesian_product2(X0,sK1)
| empty_set = sK0 ),
inference(resolution,[],[f83,f30]) ).
fof(f281,plain,
( empty_set != empty_set
| empty_set != sK1
| empty_set = sK0 ),
inference(superposition,[],[f26,f186]) ).
fof(f289,plain,
( empty_set != sK1
| empty_set = sK0 ),
inference(trivial_inequality_removal,[],[f281]) ).
fof(f293,plain,
empty_set = sK0,
inference(forward_subsumption_resolution,[],[f289,f81]) ).
fof(f298,plain,
! [X0] : sK0 = cartesian_product2(sK0,X0),
inference(superposition,[],[f56,f293]) ).
fof(f352,plain,
( empty_set != sK0
| empty_set != sK0 ),
inference(superposition,[],[f27,f298]) ).
fof(f365,plain,
empty_set != sK0,
inference(duplicate_literal_removal,[],[f352]) ).
fof(f370,plain,
$false,
inference(forward_subsumption_resolution,[],[f365,f293]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET960+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 03:16:07 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.41 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
% 3.63/1.46 % (4115912)Detected formulas, will run a generic FOF schedule.
% 3.63/1.46 % (4115920)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4087828959:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.63/1.46 % (4115920)Refutation not found, incomplete strategy
% 3.63/1.46 % (4115920)------------------------------
% 3.63/1.46 % (4115920)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.46 % (4115920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.46 % (4115920)CaDiCaL version: 2.1.3
% 3.63/1.46 % (4115920)Termination reason: Refutation not found, incomplete strategy
% 3.63/1.46 % (4115920)Time elapsed: 0.001 s
% 3.63/1.46 % (4115920)Peak memory usage: 88 MB
% 3.63/1.46 % (4115920)Instructions burned: 1 (million)
% 3.63/1.46 % (4115918)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=804634635:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.63/1.46 % (4115919)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=2863437115:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.63/1.46 % (4115917)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=1827531588:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.63/1.46 % (4115922)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=310813143:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.63/1.46 % (4115921)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3933482007:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.63/1.46 % (4115923)dis-21_1_sil=8000:lcm=predicate:random_seed=753146881: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)
% 3.63/1.46 % (4115921)First to succeed.
% 3.63/1.46 % (4115921)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4115912"
% 3.63/1.46 % (4115922)Also succeeded, but the first one will report.
% 3.63/1.46 % (4115923)Instruction limit reached!
% 3.63/1.46 % (4115923)------------------------------
% 3.63/1.46 % (4115923)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.46 % (4115923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.46 % (4115923)CaDiCaL version: 2.1.3
% 3.63/1.46 % (4115923)Termination reason: Instruction limit
% 3.63/1.46 % (4115923)Termination phase: Saturation
% 3.63/1.46 % (4115923)Time elapsed: 0.075 s
% 3.63/1.46 % (4115923)Peak memory usage: 89 MB
% 3.63/1.46 % (4115923)Instructions burned: 130 (million)
% 3.63/1.46 % (4115920)------------------------------
% 3.63/1.46 % (4115920)------------------------------
% 3.63/1.46 % (4115932)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1511219758:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.63/1.46 % (4115932)Also succeeded, but the first one will report.
% 3.63/1.46 % (4115931)lrs+10_1_sil=8000:sp=occurrence:random_seed=2951863863:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.63/1.46 % (4115931)Also succeeded, but the first one will report.
% 3.63/1.46 % (4115921)Refutation found. Thanks to Tanya!
% 3.63/1.46 % SZS status Theorem for theBenchmark
% 3.63/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.46 % (4115921)------------------------------
% 3.63/1.46 % (4115921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.46 % (4115921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.46 % (4115921)CaDiCaL version: 2.1.3
% 3.63/1.46 % (4115921)Termination reason: Refutation
% 3.63/1.46 % (4115921)Time elapsed: 0.009 s
% 3.63/1.46 % (4115921)Peak memory usage: 88 MB
% 3.63/1.46 % (4115921)Instructions burned: 12 (million)
% 3.63/1.46 % (4115921)------------------------------
% 3.63/1.46 % (4115921)------------------------------
% 3.63/1.46 % (4115912)Success in time 0.427 s
% 3.63/1.46 % Vampire exiting
%------------------------------------------------------------------------------