%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET949+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 : n020.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 12:42:24 PM UTC 2026
% Result : Theorem 2.76s 1.33s
% Output : Refutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 4 unt; 0 def)
% Number of atoms : 78 ( 29 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 104 ( 41 ~; 34 |; 27 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 71 ( 56 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,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(f8,conjecture,
! [X0,X1,X2] :
~ ( in(X0,cartesian_product2(X1,X2))
& ! [X3,X4] : ordered_pair(X3,X4) != X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( in(X0,cartesian_product2(X1,X2))
& ! [X3,X4] : ordered_pair(X3,X4) != X0 ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
? [X0,X1,X2] :
( in(X0,cartesian_product2(X1,X2))
& ! [X3,X4] : ordered_pair(X3,X4) != X0 ),
inference(ennf_transformation,[],[f9]) ).
fof(f12,plain,
( in(sK0,cartesian_product2(sK1,sK2))
& ! [X3,X4] : ordered_pair(X3,X4) != sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f10]) ).
fof(f13,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,[],[f3]) ).
fof(f14,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,[],[f13]) ).
fof(f15,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))],[f14]) ).
fof(f16,plain,
! [X3,X4] : ordered_pair(X3,X4) != sK0,
inference(cnf_transformation,[],[f12]) ).
fof(f17,plain,
in(sK0,cartesian_product2(sK1,sK2)),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK6(X0,X1,X8),sK7(X0,X1,X8)) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
! [X0,X1,X8] :
( ordered_pair(sK6(X0,X1,X8),sK7(X0,X1,X8)) = X8
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f19]) ).
fof(f39,plain,
! [X2,X0,X1] :
( sK0 != X0
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[],[f16,f31]) ).
fof(f40,plain,
! [X0,X1] : ~ in(sK0,cartesian_product2(X0,X1)),
inference(equality_resolution,[],[f39]) ).
fof(f42,plain,
$false,
inference(resolution,[],[f40,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET949+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n020.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 28 03:16:49 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 2.76/1.33 % (3992609)Detected formulas, will run a generic FOF schedule.
% 2.76/1.33 % (3992618)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3819741721:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.76/1.33 % (3992618)First to succeed.
% 2.76/1.33 % (3992618)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3992609"
% 2.76/1.33 % (3992617)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1340091273:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.76/1.33 % (3992620)dis-21_1_sil=8000:lcm=predicate:random_seed=2141747999: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)
% 2.76/1.33 % (3992616)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=168053072:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.76/1.33 % (3992615)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=2572047408:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.76/1.33 % (3992614)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=1884823572:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.76/1.33 % (3992619)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2869050104:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.76/1.33 % (3992617)Also succeeded, but the first one will report.
% 2.76/1.33 % (3992620)Also succeeded, but the first one will report.
% 2.76/1.33 % (3992619)Also succeeded, but the first one will report.
% 2.76/1.33 % (3992618)Refutation found. Thanks to Tanya!
% 2.76/1.33 % SZS status Theorem for theBenchmark
% 2.76/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.76/1.34 % (3992618)------------------------------
% 2.76/1.34 % (3992618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.34 % (3992618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.34 % (3992618)CaDiCaL version: 2.1.3
% 2.76/1.34 % (3992618)Termination reason: Refutation
% 2.76/1.34 % (3992618)Time elapsed: 0.002 s
% 2.76/1.34 % (3992618)Peak memory usage: 88 MB
% 2.76/1.34 % (3992618)Instructions burned: 2 (million)
% 2.76/1.34 % (3992618)------------------------------
% 2.76/1.34 % (3992618)------------------------------
% 2.76/1.34 % (3992609)Success in time 0.305 s
% 2.76/1.34 % Vampire exiting
%------------------------------------------------------------------------------