TSTP Solution File: ALG070+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : ALG070+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_uns --cores 0 -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 : Wed Aug 31 15:39:21 EDT 2022
% Result : Theorem 1.37s 0.56s
% Output : Refutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 12 unt; 0 def)
% Number of atoms : 207 ( 69 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 234 ( 82 ~; 68 |; 46 &)
% ( 1 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 90 ( 82 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f313,plain,
$false,
inference(avatar_sat_refutation,[],[f126,f311]) ).
fof(f311,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f310]) ).
fof(f310,plain,
( $false
| ~ spl2_1 ),
inference(subsumption_resolution,[],[f309,f21]) ).
fof(f21,plain,
op2(sK0,sK1) != sK0,
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
( sorti2(sK0)
& sK1 = op2(sK0,sK0)
& op2(sK0,sK1) != sK0
& sorti2(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f14,f17,f16]) ).
fof(f16,plain,
( ? [X0] :
( sorti2(X0)
& ? [X1] :
( op2(X0,X0) = X1
& op2(X0,X1) != X0
& sorti2(X1) ) )
=> ( sorti2(sK0)
& ? [X1] :
( op2(sK0,sK0) = X1
& sK0 != op2(sK0,X1)
& sorti2(X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
( ? [X1] :
( op2(sK0,sK0) = X1
& sK0 != op2(sK0,X1)
& sorti2(X1) )
=> ( sK1 = op2(sK0,sK0)
& op2(sK0,sK1) != sK0
& sorti2(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
? [X0] :
( sorti2(X0)
& ? [X1] :
( op2(X0,X0) = X1
& op2(X0,X1) != X0
& sorti2(X1) ) ),
inference(flattening,[],[f13]) ).
fof(f13,plain,
? [X0] :
( ? [X1] :
( op2(X0,X1) != X0
& op2(X0,X0) = X1
& sorti2(X1) )
& sorti2(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
~ ! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> ( op2(X0,X1) = X0
| op2(X0,X0) != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f309,plain,
( op2(sK0,sK1) = sK0
| ~ spl2_1 ),
inference(forward_demodulation,[],[f308,f35]) ).
fof(f35,plain,
h(j(sK0)) = sK0,
inference(resolution,[],[f27,f23]) ).
fof(f23,plain,
sorti2(sK0),
inference(cnf_transformation,[],[f18]) ).
fof(f27,plain,
! [X6] :
( ~ sorti2(X6)
| h(j(X6)) = X6 ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
( ! [X0] :
( ~ sorti2(X0)
| ! [X1] :
( ~ sorti2(X1)
| j(op2(X0,X1)) = op1(j(X0),j(X1)) ) )
& ! [X2] :
( ~ sorti1(X2)
| j(h(X2)) = X2 )
& ! [X3] :
( sorti2(h(X3))
| ~ sorti1(X3) )
& ! [X4] :
( ! [X5] :
( ~ sorti1(X5)
| op2(h(X4),h(X5)) = h(op1(X4,X5)) )
| ~ sorti1(X4) )
& ! [X6] :
( h(j(X6)) = X6
| ~ sorti2(X6) )
& ! [X7] :
( sorti1(j(X7))
| ~ sorti2(X7) ) ),
inference(rectify,[],[f9]) ).
fof(f9,plain,
( ! [X3] :
( ~ sorti2(X3)
| ! [X4] :
( ~ sorti2(X4)
| j(op2(X3,X4)) = op1(j(X3),j(X4)) ) )
& ! [X7] :
( ~ sorti1(X7)
| j(h(X7)) = X7 )
& ! [X0] :
( sorti2(h(X0))
| ~ sorti1(X0) )
& ! [X5] :
( ! [X6] :
( ~ sorti1(X6)
| op2(h(X5),h(X6)) = h(op1(X5,X6)) )
| ~ sorti1(X5) )
& ! [X2] :
( h(j(X2)) = X2
| ~ sorti2(X2) )
& ! [X1] :
( sorti1(j(X1))
| ~ sorti2(X1) ) ),
inference(flattening,[],[f8]) ).
fof(f8,plain,
( ! [X7] :
( ~ sorti1(X7)
| j(h(X7)) = X7 )
& ! [X2] :
( h(j(X2)) = X2
| ~ sorti2(X2) )
& ! [X3] :
( ~ sorti2(X3)
| ! [X4] :
( ~ sorti2(X4)
| j(op2(X3,X4)) = op1(j(X3),j(X4)) ) )
& ! [X5] :
( ! [X6] :
( ~ sorti1(X6)
| op2(h(X5),h(X6)) = h(op1(X5,X6)) )
| ~ sorti1(X5) )
& ! [X1] :
( sorti1(j(X1))
| ~ sorti2(X1) )
& ! [X0] :
( sorti2(h(X0))
| ~ sorti1(X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,plain,
~ ( ( ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) )
& ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) ) )
=> ~ ( ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 )
& ! [X2] :
( sorti2(X2)
=> h(j(X2)) = X2 )
& ! [X3] :
( sorti2(X3)
=> ! [X4] :
( sorti2(X4)
=> j(op2(X3,X4)) = op1(j(X3),j(X4)) ) )
& ! [X5] :
( sorti1(X5)
=> ! [X6] :
( sorti1(X6)
=> op2(h(X5),h(X6)) = h(op1(X5,X6)) ) ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,negated_conjecture,
~ ( ( ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) )
& ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) ) )
=> ~ ( ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
& ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 ) ) ),
inference(negated_conjecture,[],[f5]) ).
fof(f5,conjecture,
( ( ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) )
& ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) ) )
=> ~ ( ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
& ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f308,plain,
( h(j(sK0)) = op2(sK0,sK1)
| ~ spl2_1 ),
inference(forward_demodulation,[],[f307,f137]) ).
fof(f137,plain,
( j(op2(sK0,sK1)) = j(sK0)
| ~ spl2_1 ),
inference(backward_demodulation,[],[f85,f136]) ).
fof(f136,plain,
( j(sK0) = op1(j(sK0),j(sK1))
| ~ spl2_1 ),
inference(forward_demodulation,[],[f132,f82]) ).
fof(f82,plain,
j(sK1) = op1(j(sK0),j(sK0)),
inference(forward_demodulation,[],[f80,f22]) ).
fof(f22,plain,
sK1 = op2(sK0,sK0),
inference(cnf_transformation,[],[f18]) ).
fof(f80,plain,
j(op2(sK0,sK0)) = op1(j(sK0),j(sK0)),
inference(resolution,[],[f71,f23]) ).
fof(f71,plain,
! [X5] :
( ~ sorti2(X5)
| op1(j(X5),j(sK0)) = j(op2(X5,sK0)) ),
inference(resolution,[],[f31,f23]) ).
fof(f31,plain,
! [X0,X1] :
( ~ sorti2(X1)
| ~ sorti2(X0)
| j(op2(X0,X1)) = op1(j(X0),j(X1)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f132,plain,
( op1(j(sK0),op1(j(sK0),j(sK0))) = j(sK0)
| ~ spl2_1 ),
inference(resolution,[],[f103,f59]) ).
fof(f59,plain,
! [X0] :
( ~ sorti1(X0)
| op1(X0,op1(X0,X0)) = X0 ),
inference(duplicate_literal_removal,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ~ sorti1(X0)
| ~ sorti1(X0)
| ~ sorti1(X0)
| op1(X0,op1(X0,X0)) = X0 ),
inference(resolution,[],[f33,f32]) ).
fof(f32,plain,
! [X0,X1] :
( sorti1(op1(X0,X1))
| ~ sorti1(X0)
| ~ sorti1(X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0] :
( ~ sorti1(X0)
| ! [X1] :
( ~ sorti1(X1)
| sorti1(op1(X0,X1)) ) ),
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(f33,plain,
! [X0] :
( ~ sorti1(op1(X0,X0))
| ~ sorti1(X0)
| op1(X0,op1(X0,X0)) = X0 ),
inference(equality_resolution,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ~ sorti1(X0)
| ~ sorti1(X1)
| op1(X0,X0) != X1
| op1(X0,X1) = X0 ),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0] :
( ~ sorti1(X0)
| ! [X1] :
( ~ sorti1(X1)
| op1(X0,X0) != X1
| op1(X0,X1) = X0 ) ),
inference(flattening,[],[f11]) ).
fof(f11,plain,
! [X0] :
( ! [X1] :
( op1(X0,X1) = X0
| op1(X0,X0) != X1
| ~ sorti1(X1) )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> ( op1(X0,X1) = X0
| op1(X0,X0) != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f103,plain,
( sorti1(j(sK0))
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f102,plain,
( spl2_1
<=> sorti1(j(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
fof(f85,plain,
j(op2(sK0,sK1)) = op1(j(sK0),j(sK1)),
inference(resolution,[],[f72,f23]) ).
fof(f72,plain,
! [X6] :
( ~ sorti2(X6)
| j(op2(X6,sK1)) = op1(j(X6),j(sK1)) ),
inference(resolution,[],[f31,f20]) ).
fof(f20,plain,
sorti2(sK1),
inference(cnf_transformation,[],[f18]) ).
fof(f307,plain,
op2(sK0,sK1) = h(j(op2(sK0,sK1))),
inference(resolution,[],[f117,f20]) ).
fof(f117,plain,
! [X5] :
( ~ sorti2(X5)
| h(j(op2(sK0,X5))) = op2(sK0,X5) ),
inference(resolution,[],[f40,f23]) ).
fof(f40,plain,
! [X0,X1] :
( ~ sorti2(X1)
| ~ sorti2(X0)
| op2(X1,X0) = h(j(op2(X1,X0))) ),
inference(resolution,[],[f25,f27]) ).
fof(f25,plain,
! [X0,X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f10]) ).
fof(f10,plain,
! [X0] :
( ~ sorti2(X0)
| ! [X1] :
( ~ sorti2(X1)
| sorti2(op2(X0,X1)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> sorti2(op2(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f126,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f125]) ).
fof(f125,plain,
( $false
| spl2_1 ),
inference(subsumption_resolution,[],[f124,f23]) ).
fof(f124,plain,
( ~ sorti2(sK0)
| spl2_1 ),
inference(resolution,[],[f104,f26]) ).
fof(f26,plain,
! [X7] :
( sorti1(j(X7))
| ~ sorti2(X7) ),
inference(cnf_transformation,[],[f19]) ).
fof(f104,plain,
( ~ sorti1(j(sK0))
| spl2_1 ),
inference(avatar_component_clause,[],[f102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG070+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 29 14:53:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.52 % (11444)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.20/0.52 % (11428)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54 % (11421)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.55 % (11444)First to succeed.
% 0.20/0.56 % (11423)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 1.37/0.56 % (11444)Refutation found. Thanks to Tanya!
% 1.37/0.56 % SZS status Theorem for theBenchmark
% 1.37/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 1.37/0.56 % (11444)------------------------------
% 1.37/0.56 % (11444)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.37/0.56 % (11444)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.37/0.56 % (11444)Termination reason: Refutation
% 1.37/0.56
% 1.37/0.56 % (11444)Memory used [KB]: 6268
% 1.37/0.56 % (11444)Time elapsed: 0.135 s
% 1.37/0.56 % (11444)Instructions burned: 19 (million)
% 1.37/0.56 % (11444)------------------------------
% 1.37/0.56 % (11444)------------------------------
% 1.37/0.56 % (11414)Success in time 0.209 s
%------------------------------------------------------------------------------