TSTP Solution File: SET664+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET664+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:10:06 EDT 2024
% Result : Theorem 0.12s 0.29s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 9 unt; 0 def)
% Number of atoms : 210 ( 44 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 250 ( 94 ~; 81 |; 43 &)
% ( 2 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 78 ( 63 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f533,plain,
$false,
inference(trivial_inequality_removal,[],[f532]) ).
fof(f532,plain,
empty_set != empty_set,
inference(superposition,[],[f132,f519]) ).
fof(f519,plain,
empty_set = sK6,
inference(resolution,[],[f518,f134]) ).
fof(f134,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33) ).
fof(f518,plain,
( ~ ilf_type(sK5,set_type)
| empty_set = sK6 ),
inference(resolution,[],[f517,f134]) ).
fof(f517,plain,
( ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK5,set_type)
| empty_set = sK6 ),
inference(resolution,[],[f515,f134]) ).
fof(f515,plain,
( ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK5,set_type)
| empty_set = sK6 ),
inference(resolution,[],[f514,f130]) ).
fof(f130,plain,
ilf_type(sK6,relation_type(sK5,sK4)),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
( empty_set != sK6
& ilf_type(sK6,relation_type(sK5,empty_set))
& ilf_type(sK6,relation_type(sK5,sK4))
& ilf_type(sK5,set_type)
& ilf_type(sK4,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f40,f88,f87,f86]) ).
fof(f86,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(X1,empty_set))
& ilf_type(X2,relation_type(X1,X0)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(X1,empty_set))
& ilf_type(X2,relation_type(X1,sK4)) )
& ilf_type(X1,set_type) )
& ilf_type(sK4,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
( ? [X1] :
( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(X1,empty_set))
& ilf_type(X2,relation_type(X1,sK4)) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(sK5,empty_set))
& ilf_type(X2,relation_type(sK5,sK4)) )
& ilf_type(sK5,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(sK5,empty_set))
& ilf_type(X2,relation_type(sK5,sK4)) )
=> ( empty_set != sK6
& ilf_type(sK6,relation_type(sK5,empty_set))
& ilf_type(sK6,relation_type(sK5,sK4)) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(X1,empty_set))
& ilf_type(X2,relation_type(X1,X0)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f39]) ).
fof(f39,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(X1,empty_set))
& ilf_type(X2,relation_type(X1,X0)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ( ilf_type(X2,relation_type(X1,empty_set))
=> empty_set = X2 ) ) ) ),
inference(negated_conjecture,[],[f35]) ).
fof(f35,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ( ilf_type(X2,relation_type(X1,empty_set))
=> empty_set = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_27) ).
fof(f514,plain,
! [X0,X1] :
( ~ ilf_type(sK6,relation_type(X1,X0))
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| empty_set = sK6 ),
inference(duplicate_literal_removal,[],[f513]) ).
fof(f513,plain,
! [X0,X1] :
( empty_set = sK6
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK6,relation_type(X1,X0))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) ),
inference(resolution,[],[f472,f173]) ).
fof(f173,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1))) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(X2,subset_type(cross_product(X0,X1))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
=> ilf_type(X3,relation_type(X0,X1)) ) ) ) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
fof(f472,plain,
! [X0,X1] :
( ~ ilf_type(sK6,subset_type(cross_product(X0,X1)))
| empty_set = sK6
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[],[f471,f190]) ).
fof(f190,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> relation_like(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p28) ).
fof(f471,plain,
( ~ relation_like(sK6)
| ~ ilf_type(sK6,set_type)
| empty_set = sK6 ),
inference(resolution,[],[f468,f200]) ).
fof(f200,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) ),
inference(duplicate_literal_removal,[],[f169]) ).
fof(f169,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f108]) ).
fof(f108,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
fof(f468,plain,
( ~ ilf_type(sK6,binary_relation_type)
| empty_set = sK6 ),
inference(trivial_inequality_removal,[],[f467]) ).
fof(f467,plain,
( empty_set != empty_set
| empty_set = sK6
| ~ ilf_type(sK6,binary_relation_type) ),
inference(superposition,[],[f139,f461]) ).
fof(f461,plain,
empty_set = range_of(sK6),
inference(resolution,[],[f460,f134]) ).
fof(f460,plain,
( ~ ilf_type(empty_set,set_type)
| empty_set = range_of(sK6) ),
inference(resolution,[],[f451,f134]) ).
fof(f451,plain,
( ~ ilf_type(sK5,set_type)
| empty_set = range_of(sK6)
| ~ ilf_type(empty_set,set_type) ),
inference(resolution,[],[f448,f134]) ).
fof(f448,plain,
( ~ ilf_type(range_of(sK6),set_type)
| ~ ilf_type(sK5,set_type)
| empty_set = range_of(sK6)
| ~ ilf_type(empty_set,set_type) ),
inference(resolution,[],[f226,f131]) ).
fof(f131,plain,
ilf_type(sK6,relation_type(sK5,empty_set)),
inference(cnf_transformation,[],[f89]) ).
fof(f226,plain,
! [X0,X1] :
( ~ ilf_type(X0,relation_type(X1,empty_set))
| ~ ilf_type(empty_set,set_type)
| ~ ilf_type(X1,set_type)
| empty_set = range_of(X0)
| ~ ilf_type(range_of(X0),set_type) ),
inference(resolution,[],[f189,f154]) ).
fof(f154,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f52]) ).
fof(f52,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( subset(X0,empty_set)
=> empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f189,plain,
! [X2,X0,X1] :
( subset(range_of(X2),X1)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( subset(range_of(X2),X1)
& subset(domain_of(X2),X0) )
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(range_of(X2),X1)
& subset(domain_of(X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f139,plain,
! [X0] :
( empty_set != range_of(X0)
| empty_set = X0
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( empty_set = X0
| ( empty_set != range_of(X0)
& empty_set != domain_of(X0) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(flattening,[],[f44]) ).
fof(f44,plain,
! [X0] :
( empty_set = X0
| ( empty_set != range_of(X0)
& empty_set != domain_of(X0) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ( ( empty_set = range_of(X0)
| empty_set = domain_of(X0) )
=> empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f132,plain,
empty_set != sK6,
inference(cnf_transformation,[],[f89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : SET664+3 : TPTP v8.1.2. Released v2.2.0.
% 0.02/0.08 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.08/0.27 % Computer : n021.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Tue Apr 30 01:25:40 EDT 2024
% 0.12/0.27 % CPUTime :
% 0.12/0.27 % (18589)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.28 % (18592)WARNING: value z3 for option sas not known
% 0.12/0.28 % (18591)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.28 % (18593)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.28 % (18594)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.12/0.28 % (18592)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.28 % (18595)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.12/0.28 % (18596)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.12/0.28 TRYING [1]
% 0.12/0.29 TRYING [2]
% 0.12/0.29 TRYING [3]
% 0.12/0.29 % (18590)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.29 TRYING [1]
% 0.12/0.29 TRYING [2]
% 0.12/0.29 % (18595)First to succeed.
% 0.12/0.29 % (18595)Refutation found. Thanks to Tanya!
% 0.12/0.29 % SZS status Theorem for theBenchmark
% 0.12/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.29 % (18595)------------------------------
% 0.12/0.29 % (18595)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.12/0.29 % (18595)Termination reason: Refutation
% 0.12/0.29
% 0.12/0.29 % (18595)Memory used [KB]: 1118
% 0.12/0.29 % (18595)Time elapsed: 0.012 s
% 0.12/0.29 % (18595)Instructions burned: 34 (million)
% 0.12/0.29 % (18595)------------------------------
% 0.12/0.29 % (18595)------------------------------
% 0.12/0.29 % (18589)Success in time 0.016 s
%------------------------------------------------------------------------------