TSTP Solution File: SET902+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET902+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 : n005.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 : Sun May 5 09:19:38 EDT 2024
% Result : Theorem 0.12s 0.37s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 20 unt; 0 def)
% Number of atoms : 128 ( 116 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 146 ( 67 ~; 49 |; 28 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 30 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f144,plain,
$false,
inference(trivial_inequality_removal,[],[f143]) ).
fof(f143,plain,
empty_set != empty_set,
inference(superposition,[],[f32,f140]) ).
fof(f140,plain,
empty_set = singleton(sK0),
inference(forward_demodulation,[],[f138,f34]) ).
fof(f34,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f138,plain,
singleton(sK0) = set_union2(empty_set,empty_set),
inference(backward_demodulation,[],[f125,f134]) ).
fof(f134,plain,
empty_set = sK2,
inference(trivial_inequality_removal,[],[f133]) ).
fof(f133,plain,
( empty_set != empty_set
| empty_set = sK2 ),
inference(backward_demodulation,[],[f93,f121]) ).
fof(f121,plain,
empty_set = sK1,
inference(trivial_inequality_removal,[],[f120]) ).
fof(f120,plain,
( empty_set != empty_set
| empty_set = sK1 ),
inference(duplicate_literal_removal,[],[f117]) ).
fof(f117,plain,
( empty_set != empty_set
| empty_set = sK1
| empty_set = sK1 ),
inference(superposition,[],[f79,f108]) ).
fof(f108,plain,
( empty_set = sK2
| empty_set = sK1 ),
inference(trivial_inequality_removal,[],[f107]) ).
fof(f107,plain,
( sK1 != sK1
| empty_set = sK1
| empty_set = sK2 ),
inference(duplicate_literal_removal,[],[f99]) ).
fof(f99,plain,
( sK1 != sK1
| empty_set = sK1
| empty_set = sK2
| empty_set = sK1 ),
inference(superposition,[],[f78,f80]) ).
fof(f80,plain,
( sK1 = sK2
| empty_set = sK2
| empty_set = sK1 ),
inference(superposition,[],[f67,f66]) ).
fof(f66,plain,
( sK1 = singleton(sK0)
| empty_set = sK1 ),
inference(resolution,[],[f39,f48]) ).
fof(f48,plain,
subset(sK1,singleton(sK0)),
inference(superposition,[],[f35,f27]) ).
fof(f27,plain,
singleton(sK0) = set_union2(sK1,sK2),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
( ( empty_set != sK2
| sK1 != singleton(sK0) )
& ( sK2 != singleton(sK0)
| empty_set != sK1 )
& ( sK2 != singleton(sK0)
| sK1 != singleton(sK0) )
& singleton(sK0) = set_union2(sK1,sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f19]) ).
fof(f19,plain,
( ? [X0,X1,X2] :
( ( empty_set != X2
| singleton(X0) != X1 )
& ( singleton(X0) != X2
| empty_set != X1 )
& ( singleton(X0) != X2
| singleton(X0) != X1 )
& singleton(X0) = set_union2(X1,X2) )
=> ( ( empty_set != sK2
| sK1 != singleton(sK0) )
& ( sK2 != singleton(sK0)
| empty_set != sK1 )
& ( sK2 != singleton(sK0)
| sK1 != singleton(sK0) )
& singleton(sK0) = set_union2(sK1,sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
? [X0,X1,X2] :
( ( empty_set != X2
| singleton(X0) != X1 )
& ( singleton(X0) != X2
| empty_set != X1 )
& ( singleton(X0) != X2
| singleton(X0) != X1 )
& singleton(X0) = set_union2(X1,X2) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( ~ ( empty_set = X2
& singleton(X0) = X1 )
& ~ ( singleton(X0) = X2
& empty_set = X1 )
& ~ ( singleton(X0) = X2
& singleton(X0) = X1 )
& singleton(X0) = set_union2(X1,X2) ),
inference(negated_conjecture,[],[f11]) ).
fof(f11,conjecture,
! [X0,X1,X2] :
~ ( ~ ( empty_set = X2
& singleton(X0) = X1 )
& ~ ( singleton(X0) = X2
& empty_set = X1 )
& ~ ( singleton(X0) = X2
& singleton(X0) = X1 )
& singleton(X0) = set_union2(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_zfmisc_1) ).
fof(f35,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f39,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| empty_set = X0
| singleton(X1) = X0 ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) )
& ( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) )
& ( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( singleton(X1) = X0
| empty_set = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f67,plain,
( sK2 = singleton(sK0)
| empty_set = sK2 ),
inference(resolution,[],[f60,f39]) ).
fof(f60,plain,
subset(sK2,singleton(sK0)),
inference(superposition,[],[f56,f27]) ).
fof(f56,plain,
! [X0,X1] : subset(X0,set_union2(X1,X0)),
inference(superposition,[],[f35,f36]) ).
fof(f36,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f78,plain,
( sK1 != sK2
| empty_set = sK1 ),
inference(trivial_inequality_removal,[],[f70]) ).
fof(f70,plain,
( sK1 != sK1
| sK1 != sK2
| empty_set = sK1 ),
inference(superposition,[],[f47,f66]) ).
fof(f47,plain,
( sK1 != singleton(sK0)
| sK1 != sK2 ),
inference(inner_rewriting,[],[f46]) ).
fof(f46,plain,
( sK2 != singleton(sK0)
| sK1 != sK2 ),
inference(inner_rewriting,[],[f28]) ).
fof(f28,plain,
( sK2 != singleton(sK0)
| sK1 != singleton(sK0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f79,plain,
( empty_set != sK2
| empty_set = sK1 ),
inference(trivial_inequality_removal,[],[f69]) ).
fof(f69,plain,
( sK1 != sK1
| empty_set != sK2
| empty_set = sK1 ),
inference(superposition,[],[f30,f66]) ).
fof(f30,plain,
( sK1 != singleton(sK0)
| empty_set != sK2 ),
inference(cnf_transformation,[],[f20]) ).
fof(f93,plain,
( empty_set != sK1
| empty_set = sK2 ),
inference(trivial_inequality_removal,[],[f81]) ).
fof(f81,plain,
( sK2 != sK2
| empty_set != sK1
| empty_set = sK2 ),
inference(superposition,[],[f29,f67]) ).
fof(f29,plain,
( sK2 != singleton(sK0)
| empty_set != sK1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f125,plain,
singleton(sK0) = set_union2(empty_set,sK2),
inference(backward_demodulation,[],[f27,f121]) ).
fof(f32,plain,
! [X0] : empty_set != singleton(X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : empty_set != singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SET902+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.35 % Computer : n005.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri May 3 16:28:52 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.12/0.35 % (20961)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.36 % (20964)WARNING: value z3 for option sas not known
% 0.12/0.37 % (20967)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)
% 0.12/0.37 % (20965)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.37 % (20964)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)
% 0.12/0.37 % (20963)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.37 % (20966)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)
% 0.12/0.37 % (20968)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)
% 0.12/0.37 TRYING [1]
% 0.12/0.37 TRYING [2]
% 0.12/0.37 TRYING [3]
% 0.12/0.37 TRYING [4]
% 0.12/0.37 % (20962)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.37 % (20967)First to succeed.
% 0.12/0.37 % (20964)Also succeeded, but the first one will report.
% 0.12/0.37 % (20967)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-20961"
% 0.12/0.37 TRYING [1]
% 0.12/0.37 TRYING [2]
% 0.12/0.37 % (20967)Refutation found. Thanks to Tanya!
% 0.12/0.37 % SZS status Theorem for theBenchmark
% 0.12/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.37 % (20967)------------------------------
% 0.12/0.37 % (20967)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.37 % (20967)Termination reason: Refutation
% 0.12/0.37
% 0.12/0.37 % (20967)Memory used [KB]: 776
% 0.12/0.37 % (20967)Time elapsed: 0.005 s
% 0.12/0.37 % (20967)Instructions burned: 7 (million)
% 0.12/0.37 % (20961)Success in time 0.019 s
%------------------------------------------------------------------------------