TSTP Solution File: ALG203+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---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_uns --cores 0 -t %d %s
% Computer : n011.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 15:40:36 EDT 2022
% Result : Theorem 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 18 unt; 0 def)
% Number of atoms : 201 ( 62 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 224 ( 82 ~; 62 |; 43 &)
% ( 4 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 84 ( 76 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f213,plain,
$false,
inference(avatar_sat_refutation,[],[f53,f70,f141,f160,f209]) ).
fof(f209,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f208]) ).
fof(f208,plain,
( $false
| ~ spl2_1 ),
inference(subsumption_resolution,[],[f207,f20]) ).
fof(f20,plain,
sK1 != op1(sK1,sK1),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
( sorti1(sK0)
& sK0 = op1(sK0,sK0)
& sK1 != op1(sK1,sK1)
& sorti1(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f3,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) )
=> ( sK1 != op1(sK1,sK1)
& sorti1(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f3,axiom,
( ? [X0] :
( sorti1(X0)
& op1(X0,X0) = X0 )
& ? [X1] :
( op1(X1,X1) != X1
& sorti1(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f207,plain,
( sK1 = op1(sK1,sK1)
| ~ spl2_1 ),
inference(forward_demodulation,[],[f206,f100]) ).
fof(f100,plain,
sK1 = j(h(sK1)),
inference(resolution,[],[f29,f19]) ).
fof(f19,plain,
sorti1(sK1),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X0] :
( ~ sorti1(X0)
| j(h(X0)) = X0 ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
( ! [X0] :
( j(h(X0)) = X0
| ~ sorti1(X0) )
& ! [X1] :
( ~ sorti2(X1)
| h(j(X1)) = X1 )
& ! [X2] :
( ~ sorti2(X2)
| sorti1(j(X2)) )
& ! [X3] :
( ! [X4] :
( op1(j(X3),j(X4)) = j(op2(X3,X4))
| ~ sorti2(X4) )
| ~ sorti2(X3) )
& ! [X5] :
( ! [X6] :
( h(op1(X5,X6)) = op2(h(X5),h(X6))
| ~ sorti1(X6) )
| ~ sorti1(X5) )
& ! [X7] :
( sorti2(h(X7))
| ~ sorti1(X7) ) ),
inference(rectify,[],[f11]) ).
fof(f11,plain,
( ! [X5] :
( j(h(X5)) = X5
| ~ sorti1(X5) )
& ! [X4] :
( ~ sorti2(X4)
| h(j(X4)) = X4 )
& ! [X1] :
( ~ sorti2(X1)
| sorti1(j(X1)) )
& ! [X6] :
( ! [X7] :
( j(op2(X6,X7)) = op1(j(X6),j(X7))
| ~ sorti2(X7) )
| ~ sorti2(X6) )
& ! [X2] :
( ! [X3] :
( h(op1(X2,X3)) = op2(h(X2),h(X3))
| ~ sorti1(X3) )
| ~ sorti1(X2) )
& ! [X0] :
( sorti2(h(X0))
| ~ sorti1(X0) ) ),
inference(flattening,[],[f10]) ).
fof(f10,plain,
( ! [X6] :
( ! [X7] :
( j(op2(X6,X7)) = op1(j(X6),j(X7))
| ~ sorti2(X7) )
| ~ sorti2(X6) )
& ! [X4] :
( ~ sorti2(X4)
| h(j(X4)) = X4 )
& ! [X2] :
( ! [X3] :
( h(op1(X2,X3)) = op2(h(X2),h(X3))
| ~ sorti1(X3) )
| ~ sorti1(X2) )
& ! [X5] :
( j(h(X5)) = X5
| ~ sorti1(X5) )
& ! [X1] :
( ~ sorti2(X1)
| sorti1(j(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)) ) )
=> ~ ( ! [X6] :
( sorti2(X6)
=> ! [X7] :
( sorti2(X7)
=> j(op2(X6,X7)) = op1(j(X6),j(X7)) ) )
& ! [X4] :
( sorti2(X4)
=> h(j(X4)) = X4 )
& ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
& ! [X5] :
( sorti1(X5)
=> j(h(X5)) = X5 ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,negated_conjecture,
~ ( ( ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) )
& ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) ) )
=> ~ ( ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) ) ) ),
inference(negated_conjecture,[],[f5]) ).
fof(f5,conjecture,
( ( ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) )
& ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) ) )
=> ~ ( ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f206,plain,
( j(h(sK1)) = op1(sK1,sK1)
| ~ spl2_1 ),
inference(forward_demodulation,[],[f182,f161]) ).
fof(f161,plain,
( h(op1(sK1,sK1)) = h(sK1)
| ~ spl2_1 ),
inference(backward_demodulation,[],[f121,f44]) ).
fof(f44,plain,
( op2(h(sK1),h(sK1)) = h(sK1)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f43,plain,
( spl2_1
<=> op2(h(sK1),h(sK1)) = h(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
fof(f121,plain,
h(op1(sK1,sK1)) = op2(h(sK1),h(sK1)),
inference(unit_resulting_resolution,[],[f19,f19,f25]) ).
fof(f25,plain,
! [X6,X5] :
( ~ sorti1(X6)
| h(op1(X5,X6)) = op2(h(X5),h(X6))
| ~ sorti1(X5) ),
inference(cnf_transformation,[],[f17]) ).
fof(f182,plain,
j(h(op1(sK1,sK1))) = op1(sK1,sK1),
inference(resolution,[],[f105,f29]) ).
fof(f105,plain,
sorti1(op1(sK1,sK1)),
inference(backward_demodulation,[],[f84,f100]) ).
fof(f84,plain,
sorti1(op1(j(h(sK1)),j(h(sK1)))),
inference(unit_resulting_resolution,[],[f71,f71,f30]) ).
fof(f30,plain,
! [X0,X1] :
( ~ sorti1(X0)
| ~ sorti1(X1)
| sorti1(op1(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0] :
( ! [X1] :
( sorti1(op1(X0,X1))
| ~ sorti1(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(f71,plain,
sorti1(j(h(sK1))),
inference(unit_resulting_resolution,[],[f34,f27]) ).
fof(f27,plain,
! [X2] :
( sorti1(j(X2))
| ~ sorti2(X2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f34,plain,
sorti2(h(sK1)),
inference(resolution,[],[f24,f19]) ).
fof(f24,plain,
! [X7] :
( ~ sorti1(X7)
| sorti2(h(X7)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f160,plain,
~ spl2_5,
inference(avatar_contradiction_clause,[],[f149]) ).
fof(f149,plain,
( $false
| ~ spl2_5 ),
inference(unit_resulting_resolution,[],[f34,f35,f69,f23]) ).
fof(f23,plain,
! [X0,X1] :
( ~ sorti2(X1)
| ~ sorti2(X0)
| sorti2(op2(X0,X1)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f9,plain,
! [X0] :
( ~ sorti2(X0)
| ! [X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(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(f69,plain,
( ! [X1] : ~ sorti2(X1)
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f68,plain,
( spl2_5
<=> ! [X1] : ~ sorti2(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
fof(f35,plain,
sorti2(h(sK0)),
inference(resolution,[],[f24,f22]) ).
fof(f22,plain,
sorti1(sK0),
inference(cnf_transformation,[],[f16]) ).
fof(f141,plain,
spl2_4,
inference(avatar_split_clause,[],[f135,f64]) ).
fof(f64,plain,
( spl2_4
<=> h(sK0) = op2(h(sK0),h(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
fof(f135,plain,
h(sK0) = op2(h(sK0),h(sK0)),
inference(forward_demodulation,[],[f125,f21]) ).
fof(f21,plain,
sK0 = op1(sK0,sK0),
inference(cnf_transformation,[],[f16]) ).
fof(f125,plain,
op2(h(sK0),h(sK0)) = h(op1(sK0,sK0)),
inference(unit_resulting_resolution,[],[f22,f22,f25]) ).
fof(f70,plain,
( ~ spl2_4
| spl2_5
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f62,f51,f68,f64]) ).
fof(f51,plain,
( spl2_3
<=> ! [X0] :
( ~ sorti2(X0)
| op2(X0,X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
fof(f62,plain,
( ! [X1] :
( ~ sorti2(X1)
| h(sK0) != op2(h(sK0),h(sK0)) )
| ~ spl2_3 ),
inference(subsumption_resolution,[],[f59,f52]) ).
fof(f52,plain,
( ! [X0] :
( op2(X0,X0) != X0
| ~ sorti2(X0) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f59,plain,
! [X1] :
( op2(X1,X1) = X1
| ~ sorti2(X1)
| h(sK0) != op2(h(sK0),h(sK0)) ),
inference(resolution,[],[f35,f18]) ).
fof(f18,plain,
! [X0,X1] :
( op2(X0,X0) = X0
| ~ sorti2(X1)
| ~ sorti2(X0)
| op2(X1,X1) != X1 ),
inference(cnf_transformation,[],[f13]) ).
fof(f13,plain,
( ! [X0] :
( op2(X0,X0) = X0
| ~ sorti2(X0) )
| ! [X1] :
( op2(X1,X1) != X1
| ~ sorti2(X1) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,plain,
~ ( ? [X0] :
( sorti2(X0)
& op2(X0,X0) != X0 )
& ? [X1] :
( sorti2(X1)
& op2(X1,X1) = X1 ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
~ ( ? [X1] :
( op2(X1,X1) != X1
& sorti2(X1) )
& ? [X0] :
( op2(X0,X0) = X0
& sorti2(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f53,plain,
( spl2_1
| spl2_3 ),
inference(avatar_split_clause,[],[f38,f51,f43]) ).
fof(f38,plain,
! [X0] :
( ~ sorti2(X0)
| op2(h(sK1),h(sK1)) = h(sK1)
| op2(X0,X0) != X0 ),
inference(resolution,[],[f34,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG203+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
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 29 14:56:09 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.48 % (27229)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.48 % (27221)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.49 % (27221)First to succeed.
% 0.20/0.49 % (27229)Instruction limit reached!
% 0.20/0.49 % (27229)------------------------------
% 0.20/0.49 % (27229)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49 % (27229)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49 % (27229)Termination reason: Unknown
% 0.20/0.49 % (27229)Termination phase: Saturation
% 0.20/0.49
% 0.20/0.49 % (27229)Memory used [KB]: 6012
% 0.20/0.49 % (27229)Time elapsed: 0.013 s
% 0.20/0.49 % (27229)Instructions burned: 7 (million)
% 0.20/0.49 % (27229)------------------------------
% 0.20/0.49 % (27229)------------------------------
% 0.20/0.50 % (27221)Refutation found. Thanks to Tanya!
% 0.20/0.50 % SZS status Theorem for theBenchmark
% 0.20/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50 % (27221)------------------------------
% 0.20/0.50 % (27221)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50 % (27221)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50 % (27221)Termination reason: Refutation
% 0.20/0.50
% 0.20/0.50 % (27221)Memory used [KB]: 6012
% 0.20/0.50 % (27221)Time elapsed: 0.012 s
% 0.20/0.50 % (27221)Instructions burned: 6 (million)
% 0.20/0.50 % (27221)------------------------------
% 0.20/0.50 % (27221)------------------------------
% 0.20/0.50 % (27211)Success in time 0.137 s
%------------------------------------------------------------------------------