%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET679+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:41:37 PM UTC 2026
% Result : Theorem 2.65s 1.37s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 9 unt; 0 def)
% Number of atoms : 112 ( 8 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 134 ( 59 ~; 44 |; 16 &)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 46 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X1,X0)
<=> member(ordered_pair(X1,X1),identity_relation_of(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ~ member(X0,empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f8,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( not_equal(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
fof(f9,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8) ).
fof(f23,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
fof(f24,conjecture,
! [X0] :
( ( ~ empty(X0)
& ilf_type(X0,set_type) )
=> not_equal(identity_relation_of(X0),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_46) ).
fof(f25,negated_conjecture,
~ ! [X0] :
( ( ~ empty(X0)
& ilf_type(X0,set_type) )
=> not_equal(identity_relation_of(X0),empty_set) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f26,plain,
? [X0] :
( ~ not_equal(identity_relation_of(X0),empty_set)
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f25]) ).
fof(f27,plain,
? [X0] :
( ~ not_equal(identity_relation_of(X0),empty_set)
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(flattening,[],[f26]) ).
fof(f29,plain,
! [X0] :
( ! [X1] :
( ( member(X1,X0)
<=> member(ordered_pair(X1,X1),identity_relation_of(X0)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f30,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f9]) ).
fof(f31,plain,
! [X0] :
( ~ member(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( ( not_equal(X0,X1)
<=> X0 != X1 )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f8]) ).
fof(f39,plain,
( ~ not_equal(identity_relation_of(sK0),empty_set)
& ~ empty(sK0)
& ilf_type(sK0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f27]) ).
fof(f42,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,X0)
| ~ member(ordered_pair(X1,X1),identity_relation_of(X0)) )
& ( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f29]) ).
fof(f43,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f30]) ).
fof(f44,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f43]) ).
fof(f45,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK1(X0),X0)
& ilf_type(sK1(X0),set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f44]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( ( ( not_equal(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ not_equal(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f32]) ).
fof(f55,plain,
~ empty(sK0),
inference(cnf_transformation,[],[f39]) ).
fof(f56,plain,
~ not_equal(identity_relation_of(sK0),empty_set),
inference(cnf_transformation,[],[f39]) ).
fof(f57,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f23]) ).
fof(f61,plain,
! [X0,X1] :
( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f42]) ).
fof(f65,plain,
! [X0] :
( empty(X0)
| member(sK1(X0),X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f45]) ).
fof(f67,plain,
! [X0] :
( ~ member(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f31]) ).
fof(f69,plain,
! [X0,X1] :
( not_equal(X0,X1)
| X0 = X1
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f46]) ).
fof(f91,plain,
! [X0] : ~ member(X0,empty_set),
inference(forward_subsumption_resolution,[],[f67,f57]) ).
fof(f94,plain,
! [X0] :
( member(sK1(X0),X0)
| empty(X0) ),
inference(forward_subsumption_resolution,[],[f65,f57]) ).
fof(f102,plain,
! [X0,X1] :
( not_equal(X0,X1)
| X0 = X1
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f69,f57]) ).
fof(f103,plain,
! [X0,X1] :
( not_equal(X0,X1)
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f102,f57]) ).
fof(f104,plain,
empty_set = identity_relation_of(sK0),
inference(resolution,[],[f103,f56]) ).
fof(f107,plain,
! [X0,X1] :
( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f61,f57]) ).
fof(f108,plain,
! [X0,X1] :
( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0) ),
inference(forward_subsumption_resolution,[],[f107,f57]) ).
fof(f110,plain,
! [X0] :
( member(ordered_pair(X0,X0),empty_set)
| ~ member(X0,sK0) ),
inference(superposition,[],[f108,f104]) ).
fof(f111,plain,
! [X0] : ~ member(X0,sK0),
inference(forward_subsumption_resolution,[],[f110,f91]) ).
fof(f112,plain,
empty(sK0),
inference(resolution,[],[f111,f94]) ).
fof(f114,plain,
$false,
inference(forward_subsumption_resolution,[],[f112,f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET679+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n008.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Mon Sep 28 02:30:54 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 2.65/1.37 % (1813336)Detected formulas, will run a generic FOF schedule.
% 2.65/1.37 % (1813345)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=664310637:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.65/1.37 % (1813345)First to succeed.
% 2.65/1.37 % (1813345)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1813336"
% 2.65/1.37 % (1813344)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2241631717:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.65/1.37 % (1813343)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=585775370:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.65/1.37 % (1813341)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=2760539946:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.65/1.37 % (1813342)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=89232657:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.65/1.37 % (1813344)Refutation not found, incomplete strategy
% 2.65/1.37 % (1813344)------------------------------
% 2.65/1.37 % (1813344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.37 % (1813344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.37 % (1813344)CaDiCaL version: 2.1.3
% 2.65/1.37 % (1813344)Termination reason: Refutation not found, incomplete strategy
% 2.65/1.37 % (1813344)Time elapsed: 0.002 s
% 2.65/1.37 % (1813344)Peak memory usage: 88 MB
% 2.65/1.37 % (1813344)Instructions burned: 1 (million)
% 2.65/1.37 % (1813346)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1981740515:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.65/1.37 % (1813347)dis-21_1_sil=8000:lcm=predicate:random_seed=4228280452: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)
% 2.65/1.37 % (1813346)Also succeeded, but the first one will report.
% 2.65/1.37 % (1813347)Instruction limit reached!
% 2.65/1.37 % (1813347)------------------------------
% 2.65/1.37 % (1813347)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.37 % (1813347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.37 % (1813347)CaDiCaL version: 2.1.3
% 2.65/1.37 % (1813347)Termination reason: Instruction limit
% 2.65/1.37 % (1813347)Termination phase: Saturation
% 2.65/1.37 % (1813347)Time elapsed: 0.079 s
% 2.65/1.37 % (1813347)Peak memory usage: 90 MB
% 2.65/1.37 % (1813347)Instructions burned: 130 (million)
% 2.65/1.37 % (1813345)Refutation found. Thanks to Tanya!
% 2.65/1.37 % SZS status Theorem for theBenchmark
% 2.65/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.37 % (1813345)------------------------------
% 2.65/1.37 % (1813345)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.37 % (1813345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.37 % (1813345)CaDiCaL version: 2.1.3
% 2.65/1.37 % (1813345)Termination reason: Refutation
% 2.65/1.37 % (1813345)Time elapsed: 0.002 s
% 2.65/1.37 % (1813345)Peak memory usage: 88 MB
% 2.65/1.37 % (1813345)Instructions burned: 2 (million)
% 2.65/1.37 % (1813345)------------------------------
% 2.65/1.37 % (1813345)------------------------------
% 2.65/1.37 % (1813336)Success in time 0.286 s
% 2.65/1.37 % Vampire exiting
%------------------------------------------------------------------------------