%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET696+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 12:44:27 PM UTC 2026
% Result : Theorem 1.86s 0.76s
% Output : Refutation 1.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 13 unt; 2 def)
% Number of atoms : 112 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 115 ( 46 ~; 40 |; 20 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 71 ( 67 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',intersection) ).
fof(f6,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(f7,axiom,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( member(X0,X2)
& ~ member(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',difference) ).
fof(f12,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> equal_set(intersection(difference(X1,X0),X0),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI28) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> equal_set(intersection(difference(X1,X0),X0),empty_set) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f16,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f17,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(flattening,[],[f16]) ).
fof(f19,plain,
? [X0,X1] :
( ~ equal_set(intersection(difference(X1,X0),X0),empty_set)
& subset(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f20,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f21,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f21]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f24]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) )
& ( ( member(X0,X2)
& ~ member(X0,X1) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) )
& ( ( member(X0,X2)
& ~ member(X0,X1) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f28]) ).
fof(f39,plain,
( ~ equal_set(intersection(difference(sK4,sK3),sK3),empty_set)
& subset(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f19]) ).
fof(f41,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f43,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f52,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f53,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f68,plain,
~ equal_set(intersection(difference(sK4,sK3),sK3),empty_set),
inference(cnf_transformation,[],[f39]) ).
fof(f72,definition,
sF5 = difference(sK4,sK3),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f73,plain,
difference(sK4,sK3) = sF5,
inference(reorient_equations,[],[f72]) ).
fof(f74,definition,
sF6 = intersection(sF5,sK3),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f75,plain,
intersection(sF5,sK3) = sF6,
inference(reorient_equations,[],[f74]) ).
fof(f76,plain,
~ equal_set(sF6,empty_set),
inference(definition_folding,[],[f68,f75,f73]) ).
fof(f81,plain,
! [X0] :
( ~ member(X0,sF6)
| member(X0,sK3) ),
inference(superposition,[],[f46,f75]) ).
fof(f82,plain,
! [X0] :
( ~ member(X0,sF6)
| member(X0,sF5) ),
inference(superposition,[],[f47,f75]) ).
fof(f85,plain,
! [X0] :
( ~ member(X0,sF5)
| ~ member(X0,sK3) ),
inference(superposition,[],[f53,f73]) ).
fof(f95,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| equal_set(X0,X1)
| member(sK0(X1,X0),X1) ),
inference(resolution,[],[f43,f41]) ).
fof(f317,plain,
! [X0,X1] :
( equal_set(X0,X1)
| member(sK0(X1,X0),X1)
| member(sK0(X0,X1),X0) ),
inference(resolution,[],[f95,f41]) ).
fof(f3638,plain,
( member(sK0(empty_set,sF6),empty_set)
| member(sK0(sF6,empty_set),sF6) ),
inference(resolution,[],[f317,f76]) ).
fof(f3639,plain,
member(sK0(sF6,empty_set),sF6),
inference(forward_subsumption_resolution,[],[f3638,f52]) ).
fof(f3640,plain,
member(sK0(sF6,empty_set),sF5),
inference(resolution,[],[f3639,f82]) ).
fof(f3641,plain,
member(sK0(sF6,empty_set),sK3),
inference(resolution,[],[f3639,f81]) ).
fof(f3676,plain,
~ member(sK0(sF6,empty_set),sK3),
inference(resolution,[],[f3640,f85]) ).
fof(f3692,plain,
$false,
inference(forward_subsumption_resolution,[],[f3676,f3641]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET696+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n016.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 02:38:18 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.86/0.76 % (3201497)Will run a generic schedule for satisfiability detection.
% 1.86/0.76 % (3201507)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=602937860:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.86/0.76 % (3201505)dis+10_1_sil=32000:sp=arity:random_seed=1099848857:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.86/0.76 % (3201504)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=369147152:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.86/0.76 % (3201506)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=303478211:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.86/0.76 % (3201508)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=857641550:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.86/0.76 % (3201502)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=484270704_2999 on theBenchmark for (2999ds/0Mi)
% 1.86/0.76 % (3201503)% WARNING: option uhcvi not known.
% 1.86/0.76 % TRYING [1]
% 1.86/0.76 % TRYING [2]
% 1.86/0.76 % TRYING [3]
% 1.86/0.76 % (3201503)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2322031257:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.86/0.76 % TRYING [4]
% 1.86/0.76 % TRYING [5]
% 1.86/0.76 % TRYING [6]
% 1.86/0.76 % (3201507)Instruction limit reached!
% 1.86/0.76 % (3201507)------------------------------
% 1.86/0.76 % (3201507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.86/0.76 % (3201507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.86/0.76 % (3201507)CaDiCaL version: 2.1.3
% 1.86/0.76 % (3201507)Termination reason: Instruction limit
% 1.86/0.76 % (3201507)Termination phase: Saturation
% 1.86/0.76 % (3201507)Time elapsed: 0.045 s
% 1.86/0.76 % (3201507)Peak memory usage: 14 MB
% 1.86/0.76 % (3201507)Instructions burned: 131 (million)
% 1.86/0.76 % (3201516)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=13778794:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.86/0.76 % TRYING [1]
% 1.86/0.76 % TRYING [2]
% 1.86/0.76 % TRYING [3]
% 1.86/0.76 % TRYING [4]
% 1.86/0.76 % TRYING [7]
% 1.86/0.76 % TRYING [5]
% 1.86/0.76 % (3201505)Instruction limit reached!
% 1.86/0.76 % (3201505)------------------------------
% 1.86/0.76 % (3201505)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.86/0.76 % (3201505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.86/0.76 % (3201505)CaDiCaL version: 2.1.3
% 1.86/0.76 % (3201505)Termination reason: Instruction limit
% 1.86/0.76 % (3201505)Termination phase: Saturation
% 1.86/0.76 % (3201505)Time elapsed: 0.064 s
% 1.86/0.76 % (3201505)Peak memory usage: 12 MB
% 1.86/0.76 % (3201505)Instructions burned: 104 (million)
% 1.86/0.76 % TRYING [6]
% 1.86/0.76 % (3201506)Instruction limit reached!
% 1.86/0.76 % (3201506)------------------------------
% 1.86/0.76 % (3201506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.86/0.76 % (3201506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.86/0.76 % (3201506)CaDiCaL version: 2.1.3
% 1.86/0.76 % (3201506)Termination reason: Instruction limit
% 1.86/0.76 % (3201506)Termination phase: Saturation
% 1.86/0.76 % (3201506)Time elapsed: 0.068 s
% 1.86/0.76 % (3201506)Peak memory usage: 12 MB
% 1.86/0.76 % (3201506)Instructions burned: 116 (million)
% 1.86/0.76 % (3201518)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=210913901:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.86/0.76 % (3201519)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3971337568:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.86/0.76 % TRYING [7]
% 1.86/0.76 % (3201508)Instruction limit reached!
% 1.86/0.76 % (3201508)------------------------------
% 1.86/0.76 % (3201508)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.86/0.76 % (3201508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.86/0.76 % (3201508)CaDiCaL version: 2.1.3
% 1.86/0.76 % (3201508)Termination reason: Instruction limit
% 1.86/0.76 % (3201508)Termination phase: Saturation
% 1.86/0.76 % (3201508)Time elapsed: 0.096 s
% 1.86/0.76 % (3201508)Peak memory usage: 13 MB
% 1.86/0.76 % (3201508)Instructions burned: 159 (million)
% 1.86/0.76 % (3201522)ott-21_1_sil=16000:fs=off:random_seed=2515402482:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.86/0.76 % TRYING [8]
% 1.86/0.76 % (3201518)Instruction limit reached!
% 1.86/0.76 % (3201518)------------------------------
% 1.86/0.76 % (3201518)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.86/0.76 % (3201518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.86/0.76 % (3201518)CaDiCaL version: 2.1.3
% 1.86/0.76 % (3201518)Termination reason: Instruction limit
% 1.86/0.76 % (3201518)Termination phase: Saturation
% 1.86/0.76 % (3201518)Time elapsed: 0.085 s
% 1.86/0.76 % (3201518)Peak memory usage: 14 MB
% 1.86/0.76 % (3201518)Instructions burned: 132 (million)
% 1.86/0.76 % (3201524)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=496294459:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 1.86/0.76 % TRYING [8]
% 1.86/0.76 % (3201522)Instruction limit reached!
% 1.86/0.76 % (3201522)------------------------------
% 1.86/0.76 % (3201522)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.86/0.76 % (3201522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.86/0.76 % (3201522)CaDiCaL version: 2.1.3
% 1.86/0.76 % (3201522)Termination reason: Instruction limit
% 1.86/0.76 % (3201522)Termination phase: Saturation
% 1.86/0.76 % (3201522)Time elapsed: 0.097 s
% 1.86/0.76 % (3201522)Peak memory usage: 13 MB
% 1.86/0.76 % (3201522)Instructions burned: 180 (million)
% 1.86/0.76 % (3201526)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=767189213:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.86/0.76 % (3201516)Instruction limit reached!
% 1.86/0.76 % (3201516)------------------------------
% 1.86/0.76 % (3201516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.86/0.76 % (3201516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.86/0.76 % (3201516)CaDiCaL version: 2.1.3
% 1.86/0.76 % (3201516)Termination reason: Instruction limit
% 1.86/0.76 % (3201516)Termination phase: Finite model building SAT solving
% 1.86/0.76 % (3201516)Time elapsed: 0.186 s
% 1.86/0.76 % (3201516)Peak memory usage: 20 MB
% 1.86/0.76 % (3201516)Instructions burned: 717 (million)
% 1.86/0.76 % TRYING [1]
% 1.86/0.76 % TRYING [2]
% 1.86/0.76 % TRYING [3]
% 1.86/0.76 % TRYING [4]
% 1.86/0.76 % (3201528)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=454004898:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 1.86/0.76 % TRYING [5]
% 1.86/0.76 % TRYING [6]
% 1.86/0.76 % (3201528) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3201497-3201528"...
% 1.86/0.76 % (3201528)...printing done.
% 1.86/0.76 % (3201528)Refutation found. Thanks to Tanya!
% 1.86/0.76 % SZS status Theorem for theBenchmark
% 1.86/0.76 % SZS output start Proof for theBenchmark
% See solution above
% 1.86/0.77 % (3201528)------------------------------
% 1.86/0.77 % (3201528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.86/0.77 % (3201528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.86/0.77 % (3201528)CaDiCaL version: 2.1.3
% 1.86/0.77 % (3201528)Termination reason: Refutation
% 1.86/0.77 % (3201528)Time elapsed: 0.067 s
% 1.86/0.77 % (3201528)Peak memory usage: 14 MB
% 1.86/0.77 % (3201528)Instructions burned: 200 (million)
% 1.86/0.77 % (3201497)Success in time 0.354 s
% 1.86/0.77 % Vampire exiting
%------------------------------------------------------------------------------