TSTP Solution File: SYN084+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SYN084+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n004.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 : Wed Aug 31 19:36:51 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 5
% Syntax : Number of formulae : 59 ( 5 unt; 0 def)
% Number of atoms : 267 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 362 ( 154 ~; 142 |; 50 &)
% ( 5 <=>; 8 =>; 0 <=; 3 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 2 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 35 ( 29 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f97,plain,
$false,
inference(resolution,[],[f95,f66]) ).
fof(f66,plain,
~ sP1,
inference(duplicate_literal_removal,[],[f65]) ).
fof(f65,plain,
( ~ sP1
| ~ sP1 ),
inference(resolution,[],[f59,f53]) ).
fof(f53,plain,
( ~ big_p(a)
| ~ sP1 ),
inference(duplicate_literal_removal,[],[f52]) ).
fof(f52,plain,
( ~ sP1
| ~ big_p(a)
| ~ sP1
| ~ big_p(a) ),
inference(resolution,[],[f50,f41]) ).
fof(f41,plain,
( ~ big_p(sK3)
| ~ big_p(a)
| ~ sP1 ),
inference(resolution,[],[f39,f27]) ).
fof(f27,plain,
! [X0] :
( sP0(X0)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0] :
( ( sP0(X0)
| ( ~ big_p(X0)
& big_p(a)
& ~ big_p(f(f(X0))) ) )
& ( big_p(X0)
| ~ big_p(a)
| big_p(f(f(X0)))
| ~ sP0(X0) ) ),
inference(flattening,[],[f13]) ).
fof(f13,plain,
! [X0] :
( ( sP0(X0)
| ( ~ big_p(X0)
& big_p(a)
& ~ big_p(f(f(X0))) ) )
& ( big_p(X0)
| ~ big_p(a)
| big_p(f(f(X0)))
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,plain,
! [X0] :
( sP0(X0)
<=> ( big_p(X0)
| ~ big_p(a)
| big_p(f(f(X0))) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f39,plain,
( ~ sP0(sK3)
| ~ big_p(a)
| ~ sP1 ),
inference(duplicate_literal_removal,[],[f38]) ).
fof(f38,plain,
( ~ sP0(sK3)
| ~ sP1
| ~ sP0(sK3)
| ~ sP1
| ~ big_p(a) ),
inference(resolution,[],[f37,f30]) ).
fof(f30,plain,
( big_p(f(sK3))
| ~ sP0(sK3)
| ~ sP1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
( ( ( big_p(a)
& ~ big_p(f(f(sK3)))
& big_p(f(sK3)) )
| ~ sP0(sK3)
| ~ sP1 )
& ( ! [X1] :
( ( ~ big_p(a)
| big_p(f(f(X1)))
| ~ big_p(f(X1)) )
& sP0(X1) )
| sP1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f16,f17]) ).
fof(f17,plain,
( ? [X0] :
( ( big_p(a)
& ~ big_p(f(f(X0)))
& big_p(f(X0)) )
| ~ sP0(X0) )
=> ( ( big_p(a)
& ~ big_p(f(f(sK3)))
& big_p(f(sK3)) )
| ~ sP0(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
( ( ? [X0] :
( ( big_p(a)
& ~ big_p(f(f(X0)))
& big_p(f(X0)) )
| ~ sP0(X0) )
| ~ sP1 )
& ( ! [X1] :
( ( ~ big_p(a)
| big_p(f(f(X1)))
| ~ big_p(f(X1)) )
& sP0(X1) )
| sP1 ) ),
inference(rectify,[],[f15]) ).
fof(f15,plain,
( ( ? [X0] :
( ( big_p(a)
& ~ big_p(f(f(X0)))
& big_p(f(X0)) )
| ~ sP0(X0) )
| ~ sP1 )
& ( ! [X0] :
( ( ~ big_p(a)
| big_p(f(f(X0)))
| ~ big_p(f(X0)) )
& sP0(X0) )
| sP1 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,plain,
( sP1
<~> ! [X0] :
( ( ~ big_p(a)
| big_p(f(f(X0)))
| ~ big_p(f(X0)) )
& sP0(X0) ) ),
inference(definition_folding,[],[f5,f7,f6]) ).
fof(f7,plain,
( sP1
<=> ! [X1] :
( ( ~ big_p(f(X1))
& big_p(X1) )
| ~ big_p(a)
| big_p(f(f(X1))) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f5,plain,
( ! [X1] :
( ( ~ big_p(f(X1))
& big_p(X1) )
| ~ big_p(a)
| big_p(f(f(X1))) )
<~> ! [X0] :
( ( ~ big_p(a)
| big_p(f(f(X0)))
| ~ big_p(f(X0)) )
& ( big_p(X0)
| ~ big_p(a)
| big_p(f(f(X0))) ) ) ),
inference(flattening,[],[f4]) ).
fof(f4,plain,
( ! [X0] :
( ( ~ big_p(a)
| big_p(f(f(X0)))
| ~ big_p(f(X0)) )
& ( big_p(X0)
| ~ big_p(a)
| big_p(f(f(X0))) ) )
<~> ! [X1] :
( big_p(f(f(X1)))
| ~ big_p(a)
| ( ~ big_p(f(X1))
& big_p(X1) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,plain,
~ ( ! [X0] :
( ( ~ big_p(a)
| big_p(f(f(X0)))
| ~ big_p(f(X0)) )
& ( big_p(X0)
| ~ big_p(a)
| big_p(f(f(X0))) ) )
<=> ! [X1] :
( ( big_p(a)
& ( big_p(X1)
=> big_p(f(X1)) ) )
=> big_p(f(f(X1))) ) ),
inference(rectify,[],[f2]) ).
fof(f2,negated_conjecture,
~ ( ! [X1] :
( ( big_p(X1)
| ~ big_p(a)
| big_p(f(f(X1))) )
& ( ~ big_p(a)
| big_p(f(f(X1)))
| ~ big_p(f(X1)) ) )
<=> ! [X0] :
( ( ( big_p(X0)
=> big_p(f(X0)) )
& big_p(a) )
=> big_p(f(f(X0))) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
( ! [X1] :
( ( big_p(X1)
| ~ big_p(a)
| big_p(f(f(X1))) )
& ( ~ big_p(a)
| big_p(f(f(X1)))
| ~ big_p(f(X1)) ) )
<=> ! [X0] :
( ( ( big_p(X0)
=> big_p(f(X0)) )
& big_p(a) )
=> big_p(f(f(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel62) ).
fof(f37,plain,
( ~ big_p(f(sK3))
| ~ sP0(sK3)
| ~ sP1
| ~ big_p(a) ),
inference(duplicate_literal_removal,[],[f36]) ).
fof(f36,plain,
( ~ sP0(sK3)
| ~ big_p(f(sK3))
| ~ big_p(a)
| ~ sP1
| ~ sP1 ),
inference(resolution,[],[f20,f31]) ).
fof(f31,plain,
( ~ big_p(f(f(sK3)))
| ~ sP0(sK3)
| ~ sP1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f20,plain,
! [X1] :
( big_p(f(f(X1)))
| ~ big_p(a)
| ~ sP1
| ~ big_p(f(X1)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
( ( sP1
| ( ( big_p(f(sK2))
| ~ big_p(sK2) )
& big_p(a)
& ~ big_p(f(f(sK2))) ) )
& ( ! [X1] :
( ( ~ big_p(f(X1))
& big_p(X1) )
| ~ big_p(a)
| big_p(f(f(X1))) )
| ~ sP1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f10,f11]) ).
fof(f11,plain,
( ? [X0] :
( ( big_p(f(X0))
| ~ big_p(X0) )
& big_p(a)
& ~ big_p(f(f(X0))) )
=> ( ( big_p(f(sK2))
| ~ big_p(sK2) )
& big_p(a)
& ~ big_p(f(f(sK2))) ) ),
introduced(choice_axiom,[]) ).
fof(f10,plain,
( ( sP1
| ? [X0] :
( ( big_p(f(X0))
| ~ big_p(X0) )
& big_p(a)
& ~ big_p(f(f(X0))) ) )
& ( ! [X1] :
( ( ~ big_p(f(X1))
& big_p(X1) )
| ~ big_p(a)
| big_p(f(f(X1))) )
| ~ sP1 ) ),
inference(rectify,[],[f9]) ).
fof(f9,plain,
( ( sP1
| ? [X1] :
( ( big_p(f(X1))
| ~ big_p(X1) )
& big_p(a)
& ~ big_p(f(f(X1))) ) )
& ( ! [X1] :
( ( ~ big_p(f(X1))
& big_p(X1) )
| ~ big_p(a)
| big_p(f(f(X1))) )
| ~ sP1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f50,plain,
( big_p(sK3)
| ~ big_p(a)
| ~ sP1 ),
inference(duplicate_literal_removal,[],[f47]) ).
fof(f47,plain,
( big_p(sK3)
| ~ big_p(a)
| ~ sP1
| ~ big_p(a)
| ~ sP1 ),
inference(resolution,[],[f40,f19]) ).
fof(f19,plain,
! [X1] :
( big_p(f(f(X1)))
| ~ sP1
| big_p(X1)
| ~ big_p(a) ),
inference(cnf_transformation,[],[f12]) ).
fof(f40,plain,
( ~ big_p(f(f(sK3)))
| ~ sP1
| ~ big_p(a) ),
inference(resolution,[],[f39,f25]) ).
fof(f25,plain,
! [X0] :
( sP0(X0)
| ~ big_p(f(f(X0))) ),
inference(cnf_transformation,[],[f14]) ).
fof(f59,plain,
( big_p(a)
| ~ sP1 ),
inference(resolution,[],[f56,f26]) ).
fof(f26,plain,
! [X0] :
( sP0(X0)
| big_p(a) ),
inference(cnf_transformation,[],[f14]) ).
fof(f56,plain,
( ~ sP0(sK3)
| ~ sP1 ),
inference(duplicate_literal_removal,[],[f55]) ).
fof(f55,plain,
( ~ sP0(sK3)
| ~ sP1
| ~ sP1 ),
inference(resolution,[],[f53,f32]) ).
fof(f32,plain,
( big_p(a)
| ~ sP1
| ~ sP0(sK3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f95,plain,
sP1,
inference(resolution,[],[f93,f22]) ).
fof(f22,plain,
( big_p(a)
| sP1 ),
inference(cnf_transformation,[],[f12]) ).
fof(f93,plain,
~ big_p(a),
inference(resolution,[],[f92,f66]) ).
fof(f92,plain,
( sP1
| ~ big_p(a) ),
inference(resolution,[],[f88,f28]) ).
fof(f28,plain,
! [X1] :
( sP0(X1)
| sP1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f88,plain,
( ~ sP0(sK2)
| ~ big_p(a) ),
inference(duplicate_literal_removal,[],[f87]) ).
fof(f87,plain,
( ~ big_p(a)
| ~ big_p(a)
| ~ sP0(sK2) ),
inference(resolution,[],[f86,f73]) ).
fof(f73,plain,
( big_p(sK2)
| ~ big_p(a)
| ~ sP0(sK2) ),
inference(resolution,[],[f24,f67]) ).
fof(f67,plain,
~ big_p(f(f(sK2))),
inference(resolution,[],[f66,f21]) ).
fof(f21,plain,
( sP1
| ~ big_p(f(f(sK2))) ),
inference(cnf_transformation,[],[f12]) ).
fof(f24,plain,
! [X0] :
( big_p(f(f(X0)))
| ~ big_p(a)
| big_p(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f86,plain,
( ~ big_p(sK2)
| ~ big_p(a) ),
inference(resolution,[],[f85,f66]) ).
fof(f85,plain,
( sP1
| ~ big_p(sK2)
| ~ big_p(a) ),
inference(resolution,[],[f84,f23]) ).
fof(f23,plain,
( big_p(f(sK2))
| ~ big_p(sK2)
| sP1 ),
inference(cnf_transformation,[],[f12]) ).
fof(f84,plain,
( ~ big_p(f(sK2))
| ~ big_p(a) ),
inference(resolution,[],[f70,f66]) ).
fof(f70,plain,
( sP1
| ~ big_p(f(sK2))
| ~ big_p(a) ),
inference(resolution,[],[f67,f29]) ).
fof(f29,plain,
! [X1] :
( big_p(f(f(X1)))
| sP1
| ~ big_p(f(X1))
| ~ big_p(a) ),
inference(cnf_transformation,[],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN084+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 30 21:26:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.49 % (12772)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/50Mi)
% 0.19/0.50 % (12780)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.19/0.50 % (12775)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.19/0.50 % (12772)Refutation not found, incomplete strategy% (12772)------------------------------
% 0.19/0.50 % (12772)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50 % (12793)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/498Mi)
% 0.19/0.50 % (12772)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50 % (12772)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.50
% 0.19/0.50 % (12772)Memory used [KB]: 5373
% 0.19/0.50 % (12772)Time elapsed: 0.101 s
% 0.19/0.50 % (12772)Instructions burned: 2 (million)
% 0.19/0.50 % (12772)------------------------------
% 0.19/0.50 % (12772)------------------------------
% 0.19/0.51 % (12780)First to succeed.
% 0.19/0.51 % (12790)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/100Mi)
% 0.19/0.51 % (12771)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/191324Mi)
% 0.19/0.51 % (12780)Refutation found. Thanks to Tanya!
% 0.19/0.51 % SZS status Theorem for theBenchmark
% 0.19/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51 % (12780)------------------------------
% 0.19/0.51 % (12780)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (12780)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (12780)Termination reason: Refutation
% 0.19/0.51
% 0.19/0.51 % (12780)Memory used [KB]: 895
% 0.19/0.51 % (12780)Time elapsed: 0.115 s
% 0.19/0.51 % (12780)Instructions burned: 2 (million)
% 0.19/0.51 % (12780)------------------------------
% 0.19/0.51 % (12780)------------------------------
% 0.19/0.51 % (12770)Success in time 0.166 s
%------------------------------------------------------------------------------