TSTP Solution File: SEU165+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU165+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n029.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 09:27:32 EDT 2024
% Result : Theorem 0.22s 0.37s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 87 ( 45 unt; 0 def)
% Number of atoms : 170 ( 32 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 152 ( 69 ~; 55 |; 18 &)
% ( 5 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 130 ( 110 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f100,plain,
$false,
inference(avatar_sat_refutation,[],[f46,f88,f93,f97,f99]) ).
fof(f99,plain,
spl6_2,
inference(avatar_contradiction_clause,[],[f98]) ).
fof(f98,plain,
( $false
| spl6_2 ),
inference(global_subsumption,[],[f28,f27,f36,f37,f29,f32,f30,f26,f31,f51,f52,f54,f55,f56,f33,f34,f50,f59,f60,f62,f63,f64,f65,f53,f66,f67,f68,f69,f70,f71,f72,f61,f75,f76,f77,f78,f79,f80,f81,f35,f85,f91,f95,f44]) ).
fof(f44,plain,
( ~ in(sK0,sK2)
| spl6_2 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f43,plain,
( spl6_2
<=> in(sK0,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
fof(f95,plain,
~ in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)),
inference(subsumption_resolution,[],[f94,f34]) ).
fof(f94,plain,
( ~ in(sK1,sK3)
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) ),
inference(subsumption_resolution,[],[f28,f33]) ).
fof(f91,plain,
in(sK1,sK3),
inference(subsumption_resolution,[],[f27,f34]) ).
fof(f85,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X3)
| ~ in(cartesian_product2(X3,X1),ordered_pair(X2,X0)) ),
inference(resolution,[],[f35,f32]) ).
fof(f35,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,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,[],[f20]) ).
fof(f20,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,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f81,plain,
! [X0,X1] : unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = ordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f31,f61]) ).
fof(f80,plain,
! [X0,X1] : ordered_pair(unordered_pair(X1,X0),singleton(X0)) = unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X1,X0))),
inference(superposition,[],[f50,f61]) ).
fof(f79,plain,
! [X0,X1] : unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = ordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f53,f61]) ).
fof(f78,plain,
! [X0,X1] : ordered_pair(unordered_pair(X1,X0),singleton(X0)) = unordered_pair(singleton(unordered_pair(X1,X0)),ordered_pair(X0,X1)),
inference(superposition,[],[f61,f61]) ).
fof(f77,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X0,X1)),
inference(superposition,[],[f61,f53]) ).
fof(f76,plain,
! [X0,X1] : ordered_pair(singleton(X1),unordered_pair(X0,X1)) = unordered_pair(singleton(singleton(X1)),ordered_pair(X1,X0)),
inference(superposition,[],[f61,f50]) ).
fof(f75,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)),
inference(superposition,[],[f61,f31]) ).
fof(f61,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
inference(superposition,[],[f50,f30]) ).
fof(f72,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))),
inference(superposition,[],[f31,f53]) ).
fof(f71,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))),
inference(superposition,[],[f50,f53]) ).
fof(f70,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)),
inference(superposition,[],[f53,f53]) ).
fof(f69,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X1)) = unordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X1,X0)),
inference(superposition,[],[f53,f50]) ).
fof(f68,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X0,X1)),
inference(superposition,[],[f53,f31]) ).
fof(f67,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f53,f30]) ).
fof(f66,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f53,f30]) ).
fof(f53,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f31,f30]) ).
fof(f65,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
inference(superposition,[],[f30,f50]) ).
fof(f64,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
inference(superposition,[],[f30,f50]) ).
fof(f63,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X1)) = unordered_pair(ordered_pair(X1,X0),singleton(unordered_pair(X0,X1))),
inference(superposition,[],[f31,f50]) ).
fof(f62,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
inference(superposition,[],[f50,f30]) ).
fof(f60,plain,
! [X0,X1] : ordered_pair(singleton(X1),unordered_pair(X0,X1)) = unordered_pair(ordered_pair(X1,X0),singleton(singleton(X1))),
inference(superposition,[],[f50,f50]) ).
fof(f59,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))),
inference(superposition,[],[f50,f31]) ).
fof(f50,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X1,X0),singleton(X0)),
inference(superposition,[],[f31,f30]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f21]) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f56,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f30,f31]) ).
fof(f55,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f30,f31]) ).
fof(f54,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f31,f30]) ).
fof(f52,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))),
inference(superposition,[],[f31,f31]) ).
fof(f51,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X1,X0),singleton(X0)),
inference(superposition,[],[f31,f30]) ).
fof(f31,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f26,plain,
( in(sK0,sK2)
| in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
( ( ~ in(sK1,sK3)
| ~ in(sK0,sK2)
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) )
& ( ( in(sK1,sK3)
& in(sK0,sK2) )
| in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f17,f18]) ).
fof(f18,plain,
( ? [X0,X1,X2,X3] :
( ( ~ in(X1,X3)
| ~ in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) )
& ( ( in(X1,X3)
& in(X0,X2) )
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) )
=> ( ( ~ in(sK1,sK3)
| ~ in(sK0,sK2)
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) )
& ( ( in(sK1,sK3)
& in(sK0,sK2) )
| in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X1,X3)
| ~ in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) )
& ( ( in(X1,X3)
& in(X0,X2) )
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f16]) ).
fof(f16,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X1,X3)
| ~ in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) )
& ( ( in(X1,X3)
& in(X0,X2) )
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
? [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<~> ( in(X1,X3)
& in(X0,X2) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
inference(negated_conjecture,[],[f11]) ).
fof(f11,conjecture,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f30,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f32,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f29,plain,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(f37,plain,
empty(sK5),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
empty(sK5),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f4,f24]) ).
fof(f24,plain,
( ? [X0] : empty(X0)
=> empty(sK5) ),
introduced(choice_axiom,[]) ).
fof(f4,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f36,plain,
~ empty(sK4),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
~ empty(sK4),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f5,f22]) ).
fof(f22,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK4) ),
introduced(choice_axiom,[]) ).
fof(f5,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f27,plain,
( in(sK1,sK3)
| in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f28,plain,
( ~ in(sK1,sK3)
| ~ in(sK0,sK2)
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f97,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[],[f96]) ).
fof(f96,plain,
( $false
| ~ spl6_1 ),
inference(global_subsumption,[],[f28,f27,f36,f37,f29,f32,f30,f26,f31,f51,f52,f54,f55,f56,f33,f34,f50,f59,f60,f62,f63,f64,f65,f53,f66,f67,f68,f69,f70,f71,f72,f61,f75,f76,f77,f78,f79,f80,f81,f35,f85,f91,f41,f95]) ).
fof(f41,plain,
( in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3))
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f39,plain,
( spl6_1
<=> in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
fof(f93,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_contradiction_clause,[],[f92]) ).
fof(f92,plain,
( $false
| ~ spl6_1
| ~ spl6_2 ),
inference(global_subsumption,[],[f28,f27,f36,f37,f29,f32,f30,f26,f45,f47,f31,f51,f52,f54,f55,f56,f33,f34,f50,f59,f60,f62,f63,f64,f65,f53,f66,f67,f68,f69,f70,f71,f72,f61,f75,f76,f77,f78,f79,f80,f81,f35,f85,f90,f91,f41]) ).
fof(f90,plain,
( ~ in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3))
| ~ spl6_2 ),
inference(subsumption_resolution,[],[f89,f34]) ).
fof(f89,plain,
( ~ in(sK1,sK3)
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3))
| ~ spl6_2 ),
inference(subsumption_resolution,[],[f28,f45]) ).
fof(f47,plain,
( ~ in(sK2,sK0)
| ~ spl6_2 ),
inference(resolution,[],[f45,f32]) ).
fof(f45,plain,
( in(sK0,sK2)
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f88,plain,
( spl6_1
| ~ spl6_2 ),
inference(avatar_contradiction_clause,[],[f87]) ).
fof(f87,plain,
( $false
| spl6_1
| ~ spl6_2 ),
inference(subsumption_resolution,[],[f86,f45]) ).
fof(f86,plain,
( ~ in(sK0,sK2)
| spl6_1 ),
inference(subsumption_resolution,[],[f82,f48]) ).
fof(f48,plain,
( in(sK1,sK3)
| spl6_1 ),
inference(subsumption_resolution,[],[f27,f40]) ).
fof(f40,plain,
( ~ in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3))
| spl6_1 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f82,plain,
( ~ in(sK1,sK3)
| ~ in(sK0,sK2)
| spl6_1 ),
inference(resolution,[],[f35,f40]) ).
fof(f46,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f26,f43,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU165+1 : TPTP v8.1.2. Released v3.3.0.
% 0.14/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.35 % Computer : n029.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Fri May 3 12:00:52 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.36 % (17804)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.37 % (17807)WARNING: value z3 for option sas not known
% 0.22/0.37 % (17807)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)
% 0.22/0.37 % (17807)First to succeed.
% 0.22/0.37 % (17807)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-17804"
% 0.22/0.37 % (17807)Refutation found. Thanks to Tanya!
% 0.22/0.37 % SZS status Theorem for theBenchmark
% 0.22/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.37 % (17807)------------------------------
% 0.22/0.37 % (17807)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.37 % (17807)Termination reason: Refutation
% 0.22/0.37
% 0.22/0.37 % (17807)Memory used [KB]: 787
% 0.22/0.37 % (17807)Time elapsed: 0.005 s
% 0.22/0.37 % (17807)Instructions burned: 8 (million)
% 0.22/0.37 % (17804)Success in time 0.015 s
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