%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET974+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 : n016.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 4.30s 1.68s
% Output : Refutation 4.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 7 unt; 2 def)
% Number of atoms : 85 ( 3 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 90 ( 42 ~; 27 |; 17 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-5 aty)
% Number of variables : 81 ( 0 sgn 72 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0,X1,X2,X3,X4] :
~ ( in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
& ! [X5,X6] :
~ ( X0 = ordered_pair(X5,X6)
& in(X5,set_intersection2(X1,X3))
& in(X6,set_intersection2(X2,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_zfmisc_1) ).
fof(f11,conjecture,
! [X0,X1,X2,X3] :
( ( disjoint(X0,X1)
| disjoint(X2,X3) )
=> disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( disjoint(X0,X1)
| disjoint(X2,X3) )
=> disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,axiom,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ~ ( ? [X2] : in(X2,set_intersection2(X0,X1))
& disjoint(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f15,plain,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X0,X1))
& disjoint(X0,X1) ) ),
inference(rectify,[],[f13]) ).
fof(f18,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
| ? [X5,X6] :
( X0 = ordered_pair(X5,X6)
& in(X5,set_intersection2(X1,X3))
& in(X6,set_intersection2(X2,X4)) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f19,plain,
? [X0,X1,X2,X3] :
( ~ disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
& ( disjoint(X0,X1)
| disjoint(X2,X3) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f20,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f23,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
| ( ordered_pair(sK2(X0,X1,X2,X3,X4),sK3(X0,X1,X2,X3,X4)) = X0
& in(sK2(X0,X1,X2,X3,X4),set_intersection2(X1,X3))
& in(sK3(X0,X1,X2,X3,X4),set_intersection2(X2,X4)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X5,sK2(X0,X1,X2,X3,X4)),skolemize(X6,sK3(X0,X1,X2,X3,X4))],[f18]) ).
fof(f24,plain,
( ~ disjoint(cartesian_product2(sK4,sK6),cartesian_product2(sK5,sK7))
& ( disjoint(sK4,sK5)
| disjoint(sK6,sK7) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f19]) ).
fof(f25,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| in(sK8(X0,X1),set_intersection2(X0,X1)) )
& ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X2,sK8(X0,X1))],[f20]) ).
fof(f35,plain,
! [X2,X3,X0,X1,X4] :
( in(sK3(X0,X1,X2,X3,X4),set_intersection2(X2,X4))
| ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
inference(cnf_transformation,[],[f23]) ).
fof(f36,plain,
! [X2,X3,X0,X1,X4] :
( in(sK2(X0,X1,X2,X3,X4),set_intersection2(X1,X3))
| ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
inference(cnf_transformation,[],[f23]) ).
fof(f38,plain,
( disjoint(sK4,sK5)
| disjoint(sK6,sK7) ),
inference(cnf_transformation,[],[f24]) ).
fof(f39,plain,
~ disjoint(cartesian_product2(sK4,sK6),cartesian_product2(sK5,sK7)),
inference(cnf_transformation,[],[f24]) ).
fof(f40,plain,
! [X3,X0,X1] :
( ~ in(X3,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f41,plain,
! [X0,X1] :
( in(sK8(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f43,definition,
( spl9_1
<=> disjoint(sK6,sK7) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f45,plain,
( disjoint(sK6,sK7)
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f47,definition,
( spl9_2
<=> disjoint(sK4,sK5) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f49,plain,
( disjoint(sK4,sK5)
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,plain,
( spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f38,f47,f43]) ).
fof(f54,plain,
! [X2,X3,X0,X1,X4] :
( ~ disjoint(X2,X4)
| ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
inference(resolution,[],[f35,f40]) ).
fof(f58,plain,
! [X2,X3,X0,X1,X4] :
( ~ disjoint(X1,X3)
| ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
inference(resolution,[],[f36,f40]) ).
fof(f95,plain,
( ! [X2,X0,X1] : ~ in(X0,set_intersection2(cartesian_product2(sK4,X1),cartesian_product2(sK5,X2)))
| ~ spl9_2 ),
inference(resolution,[],[f58,f49]) ).
fof(f101,plain,
( ! [X0,X1] : disjoint(cartesian_product2(sK4,X0),cartesian_product2(sK5,X1))
| ~ spl9_2 ),
inference(resolution,[],[f95,f41]) ).
fof(f106,plain,
( $false
| ~ spl9_2 ),
inference(resolution,[],[f101,f39]) ).
fof(f110,plain,
~ spl9_2,
inference(avatar_contradiction_clause,[],[f106]) ).
fof(f112,plain,
( ! [X2,X0,X1] : ~ in(X0,set_intersection2(cartesian_product2(X1,sK6),cartesian_product2(X2,sK7)))
| ~ spl9_1 ),
inference(resolution,[],[f45,f54]) ).
fof(f128,plain,
( ! [X0,X1] : disjoint(cartesian_product2(X0,sK6),cartesian_product2(X1,sK7))
| ~ spl9_1 ),
inference(resolution,[],[f112,f41]) ).
fof(f133,plain,
( $false
| ~ spl9_1 ),
inference(resolution,[],[f128,f39]) ).
fof(f137,plain,
~ spl9_1,
inference(avatar_contradiction_clause,[],[f133]) ).
cnf(s1,plain,
( spl9_1
| spl9_2 ),
inference(sat_conversion,[],[f50]) ).
cnf(s2,plain,
~ spl9_2,
inference(sat_conversion,[],[f110]) ).
cnf(s3,plain,
~ spl9_1,
inference(sat_conversion,[],[f137]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f138,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET974+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 % Computer : n016.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Mon Sep 28 03:22:17 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 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
% 4.30/1.68 % (3226474)Detected formulas, will run a generic FOF schedule.
% 4.30/1.68 % (3226484)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1812918438:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.30/1.68 % (3226484)First to succeed.
% 4.30/1.68 % (3226484)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3226474"
% 4.30/1.68 % (3226482)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2697421973:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.30/1.68 % (3226479)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=1011937628:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.30/1.68 % (3226483)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=759248154:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.30/1.68 % (3226480)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=1805659222:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.30/1.68 % (3226481)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=1014586931:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.30/1.68 % (3226482)Refutation not found, incomplete strategy
% 4.30/1.68 % (3226482)------------------------------
% 4.30/1.68 % (3226482)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.30/1.68 % (3226482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/1.68 % (3226482)CaDiCaL version: 2.1.3
% 4.30/1.68 % (3226482)Termination reason: Refutation not found, incomplete strategy
% 4.30/1.68 % (3226482)Time elapsed: 0.002 s
% 4.30/1.68 % (3226482)Peak memory usage: 88 MB
% 4.30/1.68 % (3226483)Also succeeded, but the first one will report.
% 4.30/1.68 % (3226485)dis-21_1_sil=8000:lcm=predicate:random_seed=640056445: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)
% 4.30/1.68 % (3226485)Also succeeded, but the first one will report.
% 4.30/1.68 % (3226484)Refutation found. Thanks to Tanya!
% 4.30/1.68 % SZS status Theorem for theBenchmark
% 4.30/1.68 % SZS output start Proof for theBenchmark
% See solution above
% 4.30/1.68 % (3226484)------------------------------
% 4.30/1.68 % (3226484)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.30/1.68 % (3226484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/1.68 % (3226484)CaDiCaL version: 2.1.3
% 4.30/1.68 % (3226484)Termination reason: Refutation
% 4.30/1.68 % (3226484)Time elapsed: 0.006 s
% 4.30/1.68 % (3226484)Peak memory usage: 90 MB
% 4.30/1.68 % (3226484)Instructions burned: 6 (million)
% 4.30/1.68 % (3226484)------------------------------
% 4.30/1.68 % (3226484)------------------------------
% 4.30/1.68 % (3226474)Success in time 0.515 s
% 4.30/1.68 % Vampire exiting
%------------------------------------------------------------------------------