TSTP Solution File: ALG203+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : ALG203+1 : TPTP v8.1.0. Released v2.7.0.
% 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 : n027.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 15:43:36 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 63 ( 11 unt; 0 def)
% Number of atoms : 223 ( 67 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 261 ( 101 ~; 81 |; 43 &)
% ( 5 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 82 ( 74 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f163,plain,
$false,
inference(avatar_sat_refutation,[],[f41,f45,f101,f135,f162]) ).
fof(f162,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[],[f161]) ).
fof(f161,plain,
( $false
| ~ spl3_3 ),
inference(resolution,[],[f160,f20]) ).
fof(f20,plain,
sorti1(sK1),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
( sorti1(sK0)
& sK0 != op1(sK0,sK0)
& op1(sK1,sK1) = sK1
& sorti1(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f15,f14]) ).
fof(f14,plain,
( ? [X0] :
( sorti1(X0)
& op1(X0,X0) != X0 )
=> ( sorti1(sK0)
& sK0 != op1(sK0,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
( ? [X1] :
( op1(X1,X1) = X1
& sorti1(X1) )
=> ( op1(sK1,sK1) = sK1
& sorti1(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f8,plain,
( ? [X0] :
( sorti1(X0)
& op1(X0,X0) != X0 )
& ? [X1] :
( op1(X1,X1) = X1
& sorti1(X1) ) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
( ? [X1] :
( op1(X1,X1) != X1
& sorti1(X1) )
& ? [X0] :
( sorti1(X0)
& op1(X0,X0) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f160,plain,
( ~ sorti1(sK1)
| ~ spl3_3 ),
inference(resolution,[],[f153,f27]) ).
fof(f27,plain,
! [X4] :
( sorti2(h(X4))
| ~ sorti1(X4) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
( ! [X0] :
( ~ sorti2(X0)
| h(j(X0)) = X0 )
& ! [X1] :
( ~ sorti2(X1)
| ! [X2] :
( ~ sorti2(X2)
| op1(j(X1),j(X2)) = j(op2(X1,X2)) ) )
& ! [X3] :
( j(h(X3)) = X3
| ~ sorti1(X3) )
& ! [X4] :
( ~ sorti1(X4)
| sorti2(h(X4)) )
& ! [X5] :
( ~ sorti1(X5)
| ! [X6] :
( ~ sorti1(X6)
| h(op1(X5,X6)) = op2(h(X5),h(X6)) ) )
& ! [X7] :
( sorti1(j(X7))
| ~ sorti2(X7) ) ),
inference(rectify,[],[f11]) ).
fof(f11,plain,
( ! [X5] :
( ~ sorti2(X5)
| h(j(X5)) = X5 )
& ! [X2] :
( ~ sorti2(X2)
| ! [X3] :
( ~ sorti2(X3)
| j(op2(X2,X3)) = op1(j(X2),j(X3)) ) )
& ! [X4] :
( j(h(X4)) = X4
| ~ sorti1(X4) )
& ! [X1] :
( ~ sorti1(X1)
| sorti2(h(X1)) )
& ! [X6] :
( ~ sorti1(X6)
| ! [X7] :
( ~ sorti1(X7)
| op2(h(X6),h(X7)) = h(op1(X6,X7)) ) )
& ! [X0] :
( sorti1(j(X0))
| ~ sorti2(X0) ) ),
inference(flattening,[],[f10]) ).
fof(f10,plain,
( ! [X2] :
( ~ sorti2(X2)
| ! [X3] :
( ~ sorti2(X3)
| j(op2(X2,X3)) = op1(j(X2),j(X3)) ) )
& ! [X4] :
( j(h(X4)) = X4
| ~ sorti1(X4) )
& ! [X6] :
( ~ sorti1(X6)
| ! [X7] :
( ~ sorti1(X7)
| op2(h(X6),h(X7)) = h(op1(X6,X7)) ) )
& ! [X5] :
( ~ sorti2(X5)
| h(j(X5)) = X5 )
& ! [X1] :
( ~ sorti1(X1)
| sorti2(h(X1)) )
& ! [X0] :
( sorti1(j(X0))
| ~ sorti2(X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,plain,
~ ( ( ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) )
& ! [X0] :
( sorti2(X0)
=> sorti1(j(X0)) ) )
=> ~ ( ! [X2] :
( sorti2(X2)
=> ! [X3] :
( sorti2(X3)
=> j(op2(X2,X3)) = op1(j(X2),j(X3)) ) )
& ! [X4] :
( sorti1(X4)
=> j(h(X4)) = X4 )
& ! [X6] :
( sorti1(X6)
=> ! [X7] :
( sorti1(X7)
=> op2(h(X6),h(X7)) = h(op1(X6,X7)) ) )
& ! [X5] :
( sorti2(X5)
=> h(j(X5)) = X5 ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,negated_conjecture,
~ ( ( ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) )
& ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) ) )
=> ~ ( ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) ) ) ),
inference(negated_conjecture,[],[f5]) ).
fof(f5,conjecture,
( ( ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) )
& ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) ) )
=> ~ ( ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f153,plain,
( ~ sorti2(h(sK1))
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f152]) ).
fof(f152,plain,
( h(sK1) != h(sK1)
| ~ sorti2(h(sK1))
| ~ spl3_3 ),
inference(superposition,[],[f44,f136]) ).
fof(f136,plain,
h(sK1) = op2(h(sK1),h(sK1)),
inference(forward_demodulation,[],[f82,f21]) ).
fof(f21,plain,
op1(sK1,sK1) = sK1,
inference(cnf_transformation,[],[f16]) ).
fof(f82,plain,
h(op1(sK1,sK1)) = op2(h(sK1),h(sK1)),
inference(resolution,[],[f60,f20]) ).
fof(f60,plain,
! [X6] :
( ~ sorti1(X6)
| op2(h(X6),h(sK1)) = h(op1(X6,sK1)) ),
inference(resolution,[],[f26,f20]) ).
fof(f26,plain,
! [X6,X5] :
( ~ sorti1(X6)
| ~ sorti1(X5)
| h(op1(X5,X6)) = op2(h(X5),h(X6)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f44,plain,
( ! [X1] :
( op2(X1,X1) != X1
| ~ sorti2(X1) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f43,plain,
( spl3_3
<=> ! [X1] :
( ~ sorti2(X1)
| op2(X1,X1) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f135,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f134]) ).
fof(f134,plain,
( $false
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f131]) ).
fof(f131,plain,
( sK0 != sK0
| ~ spl3_2
| ~ spl3_4 ),
inference(superposition,[],[f22,f126]) ).
fof(f126,plain,
( sK0 = op1(sK0,sK0)
| ~ spl3_2
| ~ spl3_4 ),
inference(forward_demodulation,[],[f125,f47]) ).
fof(f47,plain,
sK0 = j(h(sK0)),
inference(resolution,[],[f28,f23]) ).
fof(f23,plain,
sorti1(sK0),
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
! [X3] :
( ~ sorti1(X3)
| j(h(X3)) = X3 ),
inference(cnf_transformation,[],[f18]) ).
fof(f125,plain,
( op1(sK0,sK0) = j(h(sK0))
| ~ spl3_2
| ~ spl3_4 ),
inference(forward_demodulation,[],[f112,f78]) ).
fof(f78,plain,
( h(sK0) = h(op1(sK0,sK0))
| ~ spl3_2 ),
inference(forward_demodulation,[],[f76,f72]) ).
fof(f72,plain,
( op2(h(sK0),h(sK0)) = h(sK0)
| ~ spl3_2 ),
inference(resolution,[],[f50,f23]) ).
fof(f50,plain,
( ! [X0] :
( ~ sorti1(X0)
| h(X0) = op2(h(X0),h(X0)) )
| ~ spl3_2 ),
inference(resolution,[],[f40,f27]) ).
fof(f40,plain,
( ! [X0] :
( ~ sorti2(X0)
| op2(X0,X0) = X0 )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f39,plain,
( spl3_2
<=> ! [X0] :
( ~ sorti2(X0)
| op2(X0,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f76,plain,
op2(h(sK0),h(sK0)) = h(op1(sK0,sK0)),
inference(resolution,[],[f59,f23]) ).
fof(f59,plain,
! [X5] :
( ~ sorti1(X5)
| op2(h(X5),h(sK0)) = h(op1(X5,sK0)) ),
inference(resolution,[],[f26,f23]) ).
fof(f112,plain,
( op1(sK0,sK0) = j(h(op1(sK0,sK0)))
| ~ spl3_4 ),
inference(resolution,[],[f87,f28]) ).
fof(f87,plain,
( sorti1(op1(sK0,sK0))
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f86,plain,
( spl3_4
<=> sorti1(op1(sK0,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f22,plain,
sK0 != op1(sK0,sK0),
inference(cnf_transformation,[],[f16]) ).
fof(f101,plain,
spl3_4,
inference(avatar_contradiction_clause,[],[f100]) ).
fof(f100,plain,
( $false
| spl3_4 ),
inference(resolution,[],[f99,f23]) ).
fof(f99,plain,
( ~ sorti1(sK0)
| spl3_4 ),
inference(duplicate_literal_removal,[],[f98]) ).
fof(f98,plain,
( ~ sorti1(sK0)
| ~ sorti1(sK0)
| spl3_4 ),
inference(resolution,[],[f88,f19]) ).
fof(f19,plain,
! [X0,X1] :
( sorti1(op1(X0,X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0] :
( ! [X1] :
( ~ sorti1(X1)
| sorti1(op1(X0,X1)) )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> sorti1(op1(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(f88,plain,
( ~ sorti1(op1(sK0,sK0))
| spl3_4 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f45,plain,
( ~ spl3_1
| spl3_3 ),
inference(avatar_split_clause,[],[f33,f43,f35]) ).
fof(f35,plain,
( spl3_1
<=> sP2 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f33,plain,
! [X1] :
( ~ sorti2(X1)
| op2(X1,X1) != X1
| ~ sP2 ),
inference(general_splitting,[],[f24,f32_D]) ).
fof(f32,plain,
! [X0] :
( ~ sorti2(X0)
| op2(X0,X0) = X0
| sP2 ),
inference(cnf_transformation,[],[f32_D]) ).
fof(f32_D,plain,
( ! [X0] :
( ~ sorti2(X0)
| op2(X0,X0) = X0 )
<=> ~ sP2 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).
fof(f24,plain,
! [X0,X1] :
( ~ sorti2(X0)
| op2(X0,X0) = X0
| op2(X1,X1) != X1
| ~ sorti2(X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
( ! [X0] :
( ~ sorti2(X0)
| op2(X0,X0) = X0 )
| ! [X1] :
( op2(X1,X1) != X1
| ~ sorti2(X1) ) ),
inference(rectify,[],[f9]) ).
fof(f9,plain,
( ! [X1] :
( ~ sorti2(X1)
| op2(X1,X1) = X1 )
| ! [X0] :
( op2(X0,X0) != X0
| ~ sorti2(X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
~ ( ? [X0] :
( op2(X0,X0) = X0
& sorti2(X0) )
& ? [X1] :
( op2(X1,X1) != X1
& sorti2(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f41,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f32,f39,f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : ALG203+1 : TPTP v8.1.0. Released v2.7.0.
% 0.11/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 29 15:14:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.49 % (5406)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.49 % (5414)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.50 % (5424)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 (2999ds/100Mi)
% 0.19/0.50 % (5411)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.50 % (5414)First to succeed.
% 0.19/0.50 % (5419)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.51 % (5414)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 % (5414)------------------------------
% 0.19/0.51 % (5414)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (5414)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (5414)Termination reason: Refutation
% 0.19/0.51
% 0.19/0.51 % (5414)Memory used [KB]: 5500
% 0.19/0.51 % (5414)Time elapsed: 0.103 s
% 0.19/0.51 % (5414)Instructions burned: 6 (million)
% 0.19/0.51 % (5414)------------------------------
% 0.19/0.51 % (5414)------------------------------
% 0.19/0.51 % (5403)Success in time 0.169 s
%------------------------------------------------------------------------------