TSTP Solution File: LCL686+1.001 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL686+1.001 : TPTP v8.1.2. Released v4.0.0.
% 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 : Tue Apr 30 13:48:55 EDT 2024
% Result : Theorem 0.11s 0.37s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 51 ( 10 unt; 0 def)
% Number of atoms : 293 ( 0 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 415 ( 173 ~; 141 |; 95 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 119 ( 78 !; 41 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f165,plain,
$false,
inference(subsumption_resolution,[],[f164,f130]) ).
fof(f130,plain,
p1(sK6(sK8)),
inference(subsumption_resolution,[],[f129,f90]) ).
fof(f90,plain,
( p2(sK6(sK8))
| p1(sK6(sK8)) ),
inference(resolution,[],[f45,f58]) ).
fof(f58,plain,
sP0(sK8),
inference(resolution,[],[f39,f55]) ).
fof(f55,plain,
sP3(sK8),
inference(resolution,[],[f53,f52]) ).
fof(f52,plain,
! [X2] :
( ~ r1(sK8,X2)
| sP3(X2) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
( ! [X2] :
( sP3(X2)
| ~ r1(sK8,X2) )
& r1(sK7,sK8)
& p1(sK10)
& r1(sK9,sK10)
& p3(sK9)
& r1(sK7,sK9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10])],[f30,f34,f33,f32,f31]) ).
fof(f31,plain,
( ? [X0] :
( ? [X1] :
( ! [X2] :
( sP3(X2)
| ~ r1(X1,X2) )
& r1(X0,X1) )
& ? [X3] :
( ? [X4] :
( p1(X4)
& r1(X3,X4) )
& p3(X3)
& r1(X0,X3) ) )
=> ( ? [X1] :
( ! [X2] :
( sP3(X2)
| ~ r1(X1,X2) )
& r1(sK7,X1) )
& ? [X3] :
( ? [X4] :
( p1(X4)
& r1(X3,X4) )
& p3(X3)
& r1(sK7,X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
( ? [X1] :
( ! [X2] :
( sP3(X2)
| ~ r1(X1,X2) )
& r1(sK7,X1) )
=> ( ! [X2] :
( sP3(X2)
| ~ r1(sK8,X2) )
& r1(sK7,sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
( ? [X3] :
( ? [X4] :
( p1(X4)
& r1(X3,X4) )
& p3(X3)
& r1(sK7,X3) )
=> ( ? [X4] :
( p1(X4)
& r1(sK9,X4) )
& p3(sK9)
& r1(sK7,sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
( ? [X4] :
( p1(X4)
& r1(sK9,X4) )
=> ( p1(sK10)
& r1(sK9,sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
? [X0] :
( ? [X1] :
( ! [X2] :
( sP3(X2)
| ~ r1(X1,X2) )
& r1(X0,X1) )
& ? [X3] :
( ? [X4] :
( p1(X4)
& r1(X3,X4) )
& p3(X3)
& r1(X0,X3) ) ),
inference(rectify,[],[f15]) ).
fof(f15,plain,
? [X0] :
( ? [X1] :
( ! [X2] :
( sP3(X2)
| ~ r1(X1,X2) )
& r1(X0,X1) )
& ? [X7] :
( ? [X8] :
( p1(X8)
& r1(X7,X8) )
& p3(X7)
& r1(X0,X7) ) ),
inference(definition_folding,[],[f8,f14,f13,f12,f11]) ).
fof(f11,plain,
! [X2] :
( ? [X3] :
( ( ~ p1(X3)
| ~ p2(X3) )
& ( p2(X3)
| p1(X3) )
& r1(X2,X3) )
| ~ sP0(X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f12,plain,
! [X2] :
( ! [X5] :
( ( ( ~ p1(X5)
| p2(X5) )
& ( p1(X5)
| ~ p2(X5) ) )
| ~ r1(X2,X5) )
| ~ sP1(X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f13,plain,
! [X2] :
( ? [X4] :
( ~ p3(X4)
& r1(X2,X4) )
| ~ sP2(X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f14,plain,
! [X2] :
( ( sP0(X2)
& sP2(X2)
& sP1(X2)
& ? [X6] : r1(X2,X6) )
| ~ sP3(X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f8,plain,
? [X0] :
( ? [X1] :
( ! [X2] :
( ( ? [X3] :
( ( ~ p1(X3)
| ~ p2(X3) )
& ( p2(X3)
| p1(X3) )
& r1(X2,X3) )
& ? [X4] :
( ~ p3(X4)
& r1(X2,X4) )
& ! [X5] :
( ( ( ~ p1(X5)
| p2(X5) )
& ( p1(X5)
| ~ p2(X5) ) )
| ~ r1(X2,X5) )
& ? [X6] : r1(X2,X6) )
| ~ r1(X1,X2) )
& r1(X0,X1) )
& ? [X7] :
( ? [X8] :
( p1(X8)
& r1(X7,X8) )
& p3(X7)
& r1(X0,X7) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,plain,
? [X0] :
~ ( ! [X1] :
( ~ ! [X2] :
( ~ ( ! [X3] :
( ( p1(X3)
& p2(X3) )
| ( ~ p2(X3)
& ~ p1(X3) )
| ~ r1(X2,X3) )
| ! [X4] :
( p3(X4)
| ~ r1(X2,X4) )
| ~ ! [X5] :
( ~ ( ( p1(X5)
& ~ p2(X5) )
| ( ~ p1(X5)
& p2(X5) ) )
| ~ r1(X2,X5) )
| ! [X6] : ~ r1(X2,X6) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) )
| ! [X7] :
( ! [X8] :
( ~ p1(X8)
| ~ r1(X7,X8) )
| ~ p3(X7)
| ~ r1(X0,X7) ) ),
inference(flattening,[],[f6]) ).
fof(f6,plain,
~ ~ ? [X0] :
~ ( ! [X1] :
( ~ ! [X2] :
( ~ ( ! [X3] :
( ( p1(X3)
& p2(X3) )
| ( ~ p2(X3)
& ~ p1(X3) )
| ~ r1(X2,X3) )
| ! [X4] :
( p3(X4)
| ~ r1(X2,X4) )
| ~ ! [X5] :
( ~ ( ( p1(X5)
& ~ p2(X5) )
| ( ~ p1(X5)
& p2(X5) ) )
| ~ r1(X2,X5) )
| ! [X6] : ~ r1(X2,X6) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) )
| ! [X7] :
( ! [X8] :
( ~ p1(X8)
| ~ r1(X7,X8) )
| ~ p3(X7)
| ~ r1(X0,X7) ) ),
inference(true_and_false_elimination,[],[f5]) ).
fof(f5,plain,
~ ~ ? [X0] :
~ ( ! [X1] :
( ~ ! [X2] :
( ~ ( ! [X3] :
( ( p1(X3)
& p2(X3) )
| ( ~ p2(X3)
& ~ p1(X3) )
| ~ r1(X2,X3) )
| ! [X4] :
( p3(X4)
| ~ r1(X2,X4) )
| ~ ! [X5] :
( ~ ( ( p1(X5)
& ~ p2(X5) )
| ( ~ p1(X5)
& p2(X5) ) )
| ~ r1(X2,X5) )
| ! [X6] :
( $false
| ~ r1(X2,X6) ) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) )
| ! [X7] :
( ! [X8] :
( ~ p1(X8)
| ~ r1(X7,X8) )
| ~ p3(X7)
| ~ r1(X0,X7) ) ),
inference(rectify,[],[f4]) ).
fof(f4,negated_conjecture,
~ ~ ? [X0] :
~ ( ! [X1] :
( ~ ! [X0] :
( ~ ( ! [X1] :
( ( p1(X1)
& p2(X1) )
| ( ~ p2(X1)
& ~ p1(X1) )
| ~ r1(X0,X1) )
| ! [X1] :
( p3(X1)
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( ( p1(X1)
& ~ p2(X1) )
| ( ~ p1(X1)
& p2(X1) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( $false
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( ~ p1(X0)
| ~ r1(X1,X0) )
| ~ p3(X1)
| ~ r1(X0,X1) ) ),
inference(negated_conjecture,[],[f3]) ).
fof(f3,conjecture,
~ ? [X0] :
~ ( ! [X1] :
( ~ ! [X0] :
( ~ ( ! [X1] :
( ( p1(X1)
& p2(X1) )
| ( ~ p2(X1)
& ~ p1(X1) )
| ~ r1(X0,X1) )
| ! [X1] :
( p3(X1)
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( ( p1(X1)
& ~ p2(X1) )
| ( ~ p1(X1)
& p2(X1) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( $false
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( ~ p1(X0)
| ~ r1(X1,X0) )
| ~ p3(X1)
| ~ r1(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
fof(f53,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] : r1(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
fof(f39,plain,
! [X0] :
( ~ sP3(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0] :
( ( sP0(X0)
& sP2(X0)
& sP1(X0)
& r1(X0,sK4(X0)) )
| ~ sP3(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f17,f18]) ).
fof(f18,plain,
! [X0] :
( ? [X1] : r1(X0,X1)
=> r1(X0,sK4(X0)) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X0] :
( ( sP0(X0)
& sP2(X0)
& sP1(X0)
& ? [X1] : r1(X0,X1) )
| ~ sP3(X0) ),
inference(rectify,[],[f16]) ).
fof(f16,plain,
! [X2] :
( ( sP0(X2)
& sP2(X2)
& sP1(X2)
& ? [X6] : r1(X2,X6) )
| ~ sP3(X2) ),
inference(nnf_transformation,[],[f14]) ).
fof(f45,plain,
! [X0] :
( ~ sP0(X0)
| p1(sK6(X0))
| p2(sK6(X0)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0] :
( ( ( ~ p1(sK6(X0))
| ~ p2(sK6(X0)) )
& ( p2(sK6(X0))
| p1(sK6(X0)) )
& r1(X0,sK6(X0)) )
| ~ sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f27,f28]) ).
fof(f28,plain,
! [X0] :
( ? [X1] :
( ( ~ p1(X1)
| ~ p2(X1) )
& ( p2(X1)
| p1(X1) )
& r1(X0,X1) )
=> ( ( ~ p1(sK6(X0))
| ~ p2(sK6(X0)) )
& ( p2(sK6(X0))
| p1(sK6(X0)) )
& r1(X0,sK6(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0] :
( ? [X1] :
( ( ~ p1(X1)
| ~ p2(X1) )
& ( p2(X1)
| p1(X1) )
& r1(X0,X1) )
| ~ sP0(X0) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
! [X2] :
( ? [X3] :
( ( ~ p1(X3)
| ~ p2(X3) )
& ( p2(X3)
| p1(X3) )
& r1(X2,X3) )
| ~ sP0(X2) ),
inference(nnf_transformation,[],[f11]) ).
fof(f129,plain,
( ~ p2(sK6(sK8))
| p1(sK6(sK8)) ),
inference(subsumption_resolution,[],[f113,f56]) ).
fof(f56,plain,
sP1(sK8),
inference(resolution,[],[f37,f55]) ).
fof(f37,plain,
! [X0] :
( ~ sP3(X0)
| sP1(X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f113,plain,
( ~ p2(sK6(sK8))
| p1(sK6(sK8))
| ~ sP1(sK8) ),
inference(resolution,[],[f42,f76]) ).
fof(f76,plain,
r1(sK8,sK6(sK8)),
inference(resolution,[],[f44,f58]) ).
fof(f44,plain,
! [X0] :
( ~ sP0(X0)
| r1(X0,sK6(X0)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f42,plain,
! [X0,X1] :
( ~ r1(X0,X1)
| ~ p2(X1)
| p1(X1)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0] :
( ! [X1] :
( ( ( ~ p1(X1)
| p2(X1) )
& ( p1(X1)
| ~ p2(X1) ) )
| ~ r1(X0,X1) )
| ~ sP1(X0) ),
inference(rectify,[],[f24]) ).
fof(f24,plain,
! [X2] :
( ! [X5] :
( ( ( ~ p1(X5)
| p2(X5) )
& ( p1(X5)
| ~ p2(X5) ) )
| ~ r1(X2,X5) )
| ~ sP1(X2) ),
inference(nnf_transformation,[],[f12]) ).
fof(f164,plain,
~ p1(sK6(sK8)),
inference(resolution,[],[f162,f94]) ).
fof(f94,plain,
( ~ p2(sK6(sK8))
| ~ p1(sK6(sK8)) ),
inference(resolution,[],[f46,f58]) ).
fof(f46,plain,
! [X0] :
( ~ sP0(X0)
| ~ p2(sK6(X0))
| ~ p1(sK6(X0)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f162,plain,
p2(sK6(sK8)),
inference(subsumption_resolution,[],[f161,f56]) ).
fof(f161,plain,
( p2(sK6(sK8))
| ~ sP1(sK8) ),
inference(subsumption_resolution,[],[f145,f130]) ).
fof(f145,plain,
( p2(sK6(sK8))
| ~ p1(sK6(sK8))
| ~ sP1(sK8) ),
inference(resolution,[],[f43,f76]) ).
fof(f43,plain,
! [X0,X1] :
( ~ r1(X0,X1)
| p2(X1)
| ~ p1(X1)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LCL686+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue Apr 30 01:39:26 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (7180)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.36 % (7183)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.11/0.36 % (7186)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.11/0.36 % (7185)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.11/0.36 % (7185)First to succeed.
% 0.11/0.36 % (7187)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.11/0.36 % (7182)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.36 TRYING [1,1]
% 0.11/0.36 % (7186)Also succeeded, but the first one will report.
% 0.11/0.37 % (7185)Refutation found. Thanks to Tanya!
% 0.11/0.37 % SZS status Theorem for theBenchmark
% 0.11/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.37 % (7185)------------------------------
% 0.11/0.37 % (7185)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.11/0.37 % (7185)Termination reason: Refutation
% 0.11/0.37
% 0.11/0.37 % (7185)Memory used [KB]: 765
% 0.11/0.37 % (7185)Time elapsed: 0.005 s
% 0.11/0.37 % (7185)Instructions burned: 6 (million)
% 0.11/0.37 % (7185)------------------------------
% 0.11/0.37 % (7185)------------------------------
% 0.11/0.37 % (7180)Success in time 0.035 s
%------------------------------------------------------------------------------