TSTP Solution File: SET927+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET927+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n025.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 15:14:01 EDT 2024
% Result : Theorem 0.10s 0.36s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 3
% Syntax : Number of formulae : 43 ( 5 unt; 0 def)
% Number of atoms : 149 ( 83 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 168 ( 62 ~; 76 |; 25 &)
% ( 3 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 30 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f116,plain,
$false,
inference(resolution,[],[f115,f55]) ).
fof(f55,plain,
~ in(sK0,sK2),
inference(trivial_inequality_removal,[],[f54]) ).
fof(f54,plain,
( singleton(sK0) != singleton(sK0)
| ~ in(sK0,sK2) ),
inference(superposition,[],[f26,f51]) ).
fof(f51,plain,
singleton(sK0) = set_difference(unordered_pair(sK0,sK0),sK2),
inference(duplicate_literal_removal,[],[f50]) ).
fof(f50,plain,
( singleton(sK0) = set_difference(unordered_pair(sK0,sK0),sK2)
| singleton(sK0) = set_difference(unordered_pair(sK0,sK0),sK2) ),
inference(resolution,[],[f48,f32]) ).
fof(f32,plain,
! [X2,X1] :
( in(X1,X2)
| set_difference(unordered_pair(X1,X1),X2) = singleton(X1) ),
inference(equality_resolution,[],[f29]) ).
fof(f29,plain,
! [X2,X0,X1] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| X0 != X1
| in(X0,X2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| ( X0 != X1
& ~ in(X1,X2) )
| in(X0,X2) )
& ( ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) )
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ) ),
inference(flattening,[],[f14]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| ( X0 != X1
& ~ in(X1,X2) )
| in(X0,X2) )
& ( ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) )
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<=> ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(f48,plain,
( ~ in(sK0,sK2)
| singleton(sK0) = set_difference(unordered_pair(sK0,sK0),sK2) ),
inference(trivial_inequality_removal,[],[f47]) ).
fof(f47,plain,
( singleton(sK0) != singleton(sK0)
| ~ in(sK0,sK2)
| singleton(sK0) = set_difference(unordered_pair(sK0,sK0),sK2) ),
inference(superposition,[],[f26,f42]) ).
fof(f42,plain,
( set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0)
| singleton(sK0) = set_difference(unordered_pair(sK0,sK0),sK2) ),
inference(resolution,[],[f32,f20]) ).
fof(f20,plain,
( ~ in(sK0,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f13,plain,
( ( ( sK0 != sK1
& ~ in(sK1,sK2) )
| in(sK0,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0) )
& ( ( ( sK0 = sK1
| in(sK1,sK2) )
& ~ in(sK0,sK2) )
| set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f12]) ).
fof(f12,plain,
( ? [X0,X1,X2] :
( ( ( X0 != X1
& ~ in(X1,X2) )
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) )
& ( ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) )
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ) )
=> ( ( ( sK0 != sK1
& ~ in(sK1,sK2) )
| in(sK0,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0) )
& ( ( ( sK0 = sK1
| in(sK1,sK2) )
& ~ in(sK0,sK2) )
| set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f11,plain,
? [X0,X1,X2] :
( ( ( X0 != X1
& ~ in(X1,X2) )
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) )
& ( ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) )
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ) ),
inference(flattening,[],[f10]) ).
fof(f10,plain,
? [X0,X1,X2] :
( ( ( X0 != X1
& ~ in(X1,X2) )
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) )
& ( ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) )
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,plain,
? [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<~> ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,negated_conjecture,
~ ! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<=> ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) ),
inference(negated_conjecture,[],[f5]) ).
fof(f5,conjecture,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<=> ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_zfmisc_1) ).
fof(f26,plain,
! [X2,X0,X1] :
( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f115,plain,
in(sK0,sK2),
inference(trivial_inequality_removal,[],[f114]) ).
fof(f114,plain,
( sK0 != sK0
| in(sK0,sK2) ),
inference(backward_demodulation,[],[f53,f112]) ).
fof(f112,plain,
sK0 = sK1,
inference(duplicate_literal_removal,[],[f109]) ).
fof(f109,plain,
( sK0 = sK1
| sK0 = sK1 ),
inference(resolution,[],[f98,f90]) ).
fof(f90,plain,
( in(sK1,sK2)
| sK0 = sK1 ),
inference(trivial_inequality_removal,[],[f89]) ).
fof(f89,plain,
( singleton(sK0) != singleton(sK0)
| in(sK1,sK2)
| sK0 = sK1 ),
inference(duplicate_literal_removal,[],[f85]) ).
fof(f85,plain,
( singleton(sK0) != singleton(sK0)
| in(sK1,sK2)
| sK0 = sK1
| sK0 = sK1 ),
inference(superposition,[],[f27,f83]) ).
fof(f83,plain,
( set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0)
| sK0 = sK1 ),
inference(duplicate_literal_removal,[],[f80]) ).
fof(f80,plain,
( set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0)
| sK0 = sK1
| set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0) ),
inference(resolution,[],[f79,f21]) ).
fof(f21,plain,
( in(sK1,sK2)
| sK0 = sK1
| set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f79,plain,
! [X0] :
( ~ in(X0,sK2)
| singleton(sK0) = set_difference(unordered_pair(sK0,X0),sK2) ),
inference(resolution,[],[f28,f55]) ).
fof(f28,plain,
! [X2,X0,X1] :
( in(X0,X2)
| ~ in(X1,X2)
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
! [X2,X0,X1] :
( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
| in(X1,X2)
| X0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f98,plain,
( ~ in(sK1,sK2)
| sK0 = sK1 ),
inference(resolution,[],[f91,f55]) ).
fof(f91,plain,
( in(sK0,sK2)
| ~ in(sK1,sK2)
| sK0 = sK1 ),
inference(trivial_inequality_removal,[],[f84]) ).
fof(f84,plain,
( singleton(sK0) != singleton(sK0)
| in(sK0,sK2)
| ~ in(sK1,sK2)
| sK0 = sK1 ),
inference(superposition,[],[f22,f83]) ).
fof(f22,plain,
( set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0)
| in(sK0,sK2)
| ~ in(sK1,sK2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f53,plain,
( sK0 != sK1
| in(sK0,sK2) ),
inference(trivial_inequality_removal,[],[f52]) ).
fof(f52,plain,
( singleton(sK0) != singleton(sK0)
| in(sK0,sK2)
| sK0 != sK1 ),
inference(backward_demodulation,[],[f33,f51]) ).
fof(f33,plain,
( singleton(sK0) != set_difference(unordered_pair(sK0,sK0),sK2)
| in(sK0,sK2)
| sK0 != sK1 ),
inference(inner_rewriting,[],[f23]) ).
fof(f23,plain,
( sK0 != sK1
| in(sK0,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0) ),
inference(cnf_transformation,[],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET927+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.33 % Computer : n025.cluster.edu
% 0.10/0.33 % Model : x86_64 x86_64
% 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33 % Memory : 8042.1875MB
% 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33 % CPULimit : 300
% 0.10/0.33 % WCLimit : 300
% 0.10/0.33 % DateTime : Tue Apr 30 01:54:26 EDT 2024
% 0.10/0.34 % CPUTime :
% 0.10/0.34 % (8297)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.35 % (8300)WARNING: value z3 for option sas not known
% 0.10/0.35 % (8300)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)
% 0.10/0.35 % (8299)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.35 % (8305)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)
% 0.10/0.35 % (8302)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)
% 0.10/0.35 % (8298)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.35 % (8304)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)
% 0.10/0.35 % (8301)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.35 TRYING [1]
% 0.10/0.35 TRYING [2]
% 0.10/0.36 TRYING [3]
% 0.10/0.36 TRYING [1]
% 0.10/0.36 TRYING [1]
% 0.10/0.36 TRYING [2]
% 0.10/0.36 % (8304)First to succeed.
% 0.10/0.36 TRYING [2]
% 0.10/0.36 TRYING [3]
% 0.10/0.36 % (8300)Also succeeded, but the first one will report.
% 0.10/0.36 TRYING [4]
% 0.10/0.36 % (8304)Refutation found. Thanks to Tanya!
% 0.10/0.36 % SZS status Theorem for theBenchmark
% 0.10/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.36 % (8304)------------------------------
% 0.10/0.36 % (8304)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.10/0.36 % (8304)Termination reason: Refutation
% 0.10/0.36
% 0.10/0.36 % (8304)Memory used [KB]: 776
% 0.10/0.36 % (8304)Time elapsed: 0.006 s
% 0.10/0.36 % (8304)Instructions burned: 9 (million)
% 0.10/0.36 % (8304)------------------------------
% 0.10/0.36 % (8304)------------------------------
% 0.10/0.36 % (8297)Success in time 0.019 s
%------------------------------------------------------------------------------