TSTP Solution File: SET954+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET954+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 : n031.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 15:14:06 EDT 2024
% Result : Theorem 0.12s 0.37s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 44 ( 27 unt; 0 def)
% Number of atoms : 73 ( 11 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 62 ( 33 ~; 13 |; 9 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 76 ( 64 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f47,plain,
$false,
inference(global_subsumption,[],[f29,f30,f22,f20,f21,f25,f31,f23,f24,f32,f33,f34,f35,f36,f37,f38,f26,f39,f40,f27,f41,f28,f46]) ).
fof(f46,plain,
~ in(sK1,sK3),
inference(subsumption_resolution,[],[f42,f39]) ).
fof(f42,plain,
( ~ in(sK0,sK2)
| ~ in(sK1,sK3) ),
inference(resolution,[],[f28,f21]) ).
fof(f28,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f14]) ).
fof(f14,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f41,plain,
in(sK1,sK3),
inference(resolution,[],[f27,f20]) ).
fof(f27,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f15]) ).
fof(f40,plain,
~ in(sK2,sK0),
inference(resolution,[],[f39,f25]) ).
fof(f39,plain,
in(sK0,sK2),
inference(resolution,[],[f26,f20]) ).
fof(f26,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f38,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f23,f24]) ).
fof(f37,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f23,f24]) ).
fof(f36,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f24,f23]) ).
fof(f35,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f24,f23]) ).
fof(f34,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))),
inference(superposition,[],[f24,f24]) ).
fof(f33,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X1,X0),singleton(X0)),
inference(superposition,[],[f24,f23]) ).
fof(f32,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X1,X0),singleton(X0)),
inference(superposition,[],[f24,f23]) ).
fof(f24,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f23,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f31,plain,
~ in(cartesian_product2(sK2,sK3),ordered_pair(sK0,sK1)),
inference(resolution,[],[f25,f20]) ).
fof(f25,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f21,plain,
~ in(ordered_pair(sK1,sK0),cartesian_product2(sK3,sK2)),
inference(cnf_transformation,[],[f13]) ).
fof(f13,plain,
( ~ in(ordered_pair(sK1,sK0),cartesian_product2(sK3,sK2))
& in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f10,f12]) ).
fof(f12,plain,
( ? [X0,X1,X2,X3] :
( ~ in(ordered_pair(X1,X0),cartesian_product2(X3,X2))
& in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) )
=> ( ~ in(ordered_pair(sK1,sK0),cartesian_product2(sK3,sK2))
& in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) ) ),
introduced(choice_axiom,[]) ).
fof(f10,plain,
? [X0,X1,X2,X3] :
( ~ in(ordered_pair(X1,X0),cartesian_product2(X3,X2))
& in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
=> in(ordered_pair(X1,X0),cartesian_product2(X3,X2)) ),
inference(negated_conjecture,[],[f8]) ).
fof(f8,conjecture,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
=> in(ordered_pair(X1,X0),cartesian_product2(X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_zfmisc_1) ).
fof(f20,plain,
in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(f30,plain,
empty(sK5),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
empty(sK5),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f6,f18]) ).
fof(f18,plain,
( ? [X0] : empty(X0)
=> empty(sK5) ),
introduced(choice_axiom,[]) ).
fof(f6,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f29,plain,
~ empty(sK4),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
~ empty(sK4),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f7,f16]) ).
fof(f16,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK4) ),
introduced(choice_axiom,[]) ).
fof(f7,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : SET954+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.35 % Computer : n031.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 : Tue Apr 30 01:38:13 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.12/0.36 % (25686)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.37 % (25689)WARNING: value z3 for option sas not known
% 0.12/0.37 % (25689)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 % (25688)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 % (25691)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 % (25690)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.37 % (25692)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 % (25693)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 % (25689)First to succeed.
% 0.12/0.37 TRYING [1]
% 0.12/0.37 TRYING [1]
% 0.12/0.37 TRYING [2]
% 0.12/0.37 % (25687)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.37 TRYING [2]
% 0.12/0.37 % (25689)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 % (25689)------------------------------
% 0.12/0.37 % (25689)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.12/0.37 % (25689)Termination reason: Refutation
% 0.12/0.37
% 0.12/0.37 % (25689)Memory used [KB]: 764
% 0.12/0.37 % (25689)Time elapsed: 0.005 s
% 0.12/0.37 % (25689)Instructions burned: 4 (million)
% 0.12/0.37 % (25689)------------------------------
% 0.12/0.37 % (25689)------------------------------
% 0.12/0.37 % (25686)Success in time 0.017 s
%------------------------------------------------------------------------------