TSTP Solution File: ALG069+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG069+1 : TPTP v8.2.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n028.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 : Mon May 20 18:25:44 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 25
% Syntax : Number of formulae : 192 ( 7 unt; 0 def)
% Number of atoms : 516 ( 78 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 556 ( 232 ~; 234 |; 37 &)
% ( 18 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 22 ( 20 usr; 19 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 106 ( 100 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2045,plain,
$false,
inference(avatar_sat_refutation,[],[f72,f76,f86,f111,f114,f126,f339,f342,f374,f407,f410,f435,f468,f472,f504,f665,f669,f767,f771,f1546,f1562,f1622,f1716,f1719,f1781,f2044]) ).
fof(f2044,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_contradiction_clause,[],[f2043]) ).
fof(f2043,plain,
( $false
| ~ spl2_1
| ~ spl2_2 ),
inference(subsumption_resolution,[],[f2042,f66]) ).
fof(f66,plain,
( sorti2(h(sK1(j(sK0))))
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f65,plain,
( spl2_1
<=> sorti2(h(sK1(j(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
fof(f2042,plain,
( ~ sorti2(h(sK1(j(sK0))))
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f2039]) ).
fof(f2039,plain,
( sK0 != sK0
| ~ sorti2(h(sK1(j(sK0))))
| ~ spl2_2 ),
inference(superposition,[],[f26,f2036]) ).
fof(f2036,plain,
( sK0 = op2(h(sK1(j(sK0))),h(sK1(j(sK0))))
| ~ spl2_2 ),
inference(forward_demodulation,[],[f2035,f31]) ).
fof(f31,plain,
sK0 = h(j(sK0)),
inference(resolution,[],[f23,f25]) ).
fof(f25,plain,
sorti2(sK0),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
( ! [X1] :
( op2(X1,X1) != sK0
| ~ sorti2(X1) )
& sorti2(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f10,f15]) ).
fof(f15,plain,
( ? [X0] :
( ! [X1] :
( op2(X1,X1) != X0
| ~ sorti2(X1) )
& sorti2(X0) )
=> ( ! [X1] :
( op2(X1,X1) != sK0
| ~ sorti2(X1) )
& sorti2(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f10,plain,
? [X0] :
( ! [X1] :
( op2(X1,X1) != X0
| ~ sorti2(X1) )
& sorti2(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
~ ! [X0] :
( sorti2(X0)
=> ? [X1] :
( op2(X1,X1) = X0
& sorti2(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f23,plain,
! [X1] :
( ~ sorti2(X1)
| h(j(X1)) = X1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
( ! [X0] :
( j(h(X0)) = X0
| ~ sorti1(X0) )
& ! [X1] :
( h(j(X1)) = X1
| ~ sorti2(X1) )
& ! [X2] :
( ! [X3] :
( j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X3) )
| ~ sorti2(X2) )
& ! [X4] :
( ! [X5] :
( h(op1(X4,X5)) = op2(h(X4),h(X5))
| ~ sorti1(X5) )
| ~ sorti1(X4) )
& ! [X6] :
( sorti1(j(X6))
| ~ sorti2(X6) )
& ! [X7] :
( sorti2(h(X7))
| ~ sorti1(X7) ) ),
inference(rectify,[],[f9]) ).
fof(f9,plain,
( ! [X2] :
( j(h(X2)) = X2
| ~ sorti1(X2) )
& ! [X3] :
( h(j(X3)) = X3
| ~ sorti2(X3) )
& ! [X4] :
( ! [X5] :
( j(op2(X4,X5)) = op1(j(X4),j(X5))
| ~ sorti2(X5) )
| ~ sorti2(X4) )
& ! [X6] :
( ! [X7] :
( h(op1(X6,X7)) = op2(h(X6),h(X7))
| ~ sorti1(X7) )
| ~ sorti1(X6) )
& ! [X0] :
( sorti1(j(X0))
| ~ sorti2(X0) )
& ! [X1] :
( sorti2(h(X1))
| ~ sorti1(X1) ) ),
inference(flattening,[],[f8]) ).
fof(f8,plain,
( ! [X2] :
( j(h(X2)) = X2
| ~ sorti1(X2) )
& ! [X3] :
( h(j(X3)) = X3
| ~ sorti2(X3) )
& ! [X4] :
( ! [X5] :
( j(op2(X4,X5)) = op1(j(X4),j(X5))
| ~ sorti2(X5) )
| ~ sorti2(X4) )
& ! [X6] :
( ! [X7] :
( h(op1(X6,X7)) = op2(h(X6),h(X7))
| ~ sorti1(X7) )
| ~ sorti1(X6) )
& ! [X0] :
( sorti1(j(X0))
| ~ sorti2(X0) )
& ! [X1] :
( sorti2(h(X1))
| ~ sorti1(X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,plain,
~ ( ( ! [X0] :
( sorti2(X0)
=> sorti1(j(X0)) )
& ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) ) )
=> ~ ( ! [X2] :
( sorti1(X2)
=> j(h(X2)) = X2 )
& ! [X3] :
( sorti2(X3)
=> h(j(X3)) = X3 )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X6] :
( sorti1(X6)
=> ! [X7] :
( sorti1(X7)
=> h(op1(X6,X7)) = op2(h(X6),h(X7)) ) ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,negated_conjecture,
~ ( ( ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) )
& ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) ) )
=> ~ ( ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 )
& ! [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)) ) ) ) ),
inference(negated_conjecture,[],[f5]) ).
fof(f5,conjecture,
( ( ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) )
& ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) ) )
=> ~ ( ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 )
& ! [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)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f2035,plain,
( h(j(sK0)) = op2(h(sK1(j(sK0))),h(sK1(j(sK0))))
| ~ spl2_2 ),
inference(forward_demodulation,[],[f2022,f134]) ).
fof(f134,plain,
j(sK0) = op1(sK1(j(sK0)),sK1(j(sK0))),
inference(resolution,[],[f47,f25]) ).
fof(f47,plain,
! [X0] :
( ~ sorti2(X0)
| j(X0) = op1(sK1(j(X0)),sK1(j(X0))) ),
inference(resolution,[],[f30,f20]) ).
fof(f20,plain,
! [X6] :
( sorti1(j(X6))
| ~ sorti2(X6) ),
inference(cnf_transformation,[],[f14]) ).
fof(f30,plain,
! [X0] :
( ~ sorti1(X0)
| op1(sK1(X0),sK1(X0)) = X0 ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0] :
( ( op1(sK1(X0),sK1(X0)) = X0
& sorti1(sK1(X0)) )
| ~ sorti1(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f13,f17]) ).
fof(f17,plain,
! [X0] :
( ? [X1] :
( op1(X1,X1) = X0
& sorti1(X1) )
=> ( op1(sK1(X0),sK1(X0)) = X0
& sorti1(sK1(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f13,plain,
! [X0] :
( ? [X1] :
( op1(X1,X1) = X0
& sorti1(X1) )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( sorti1(X0)
=> ? [X1] :
( op1(X1,X1) = X0
& sorti1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f2022,plain,
( h(op1(sK1(j(sK0)),sK1(j(sK0)))) = op2(h(sK1(j(sK0))),h(sK1(j(sK0))))
| ~ spl2_2 ),
inference(resolution,[],[f1467,f71]) ).
fof(f71,plain,
( sorti1(sK1(j(sK0)))
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f69,plain,
( spl2_2
<=> sorti1(sK1(j(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
fof(f1467,plain,
! [X0] :
( ~ sorti1(X0)
| h(op1(X0,sK1(j(sK0)))) = op2(h(X0),h(sK1(j(sK0)))) ),
inference(resolution,[],[f343,f25]) ).
fof(f343,plain,
! [X0,X1] :
( ~ sorti2(X1)
| h(op1(X0,sK1(j(X1)))) = op2(h(X0),h(sK1(j(X1))))
| ~ sorti1(X0) ),
inference(resolution,[],[f95,f20]) ).
fof(f95,plain,
! [X0,X1] :
( ~ sorti1(X1)
| ~ sorti1(X0)
| h(op1(X0,sK1(X1))) = op2(h(X0),h(sK1(X1))) ),
inference(resolution,[],[f21,f29]) ).
fof(f29,plain,
! [X0] :
( sorti1(sK1(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f21,plain,
! [X4,X5] :
( ~ sorti1(X5)
| h(op1(X4,X5)) = op2(h(X4),h(X5))
| ~ sorti1(X4) ),
inference(cnf_transformation,[],[f14]) ).
fof(f26,plain,
! [X1] :
( op2(X1,X1) != sK0
| ~ sorti2(X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f1781,plain,
( spl2_17
| ~ spl2_18 ),
inference(avatar_contradiction_clause,[],[f1780]) ).
fof(f1780,plain,
( $false
| spl2_17
| ~ spl2_18 ),
inference(subsumption_resolution,[],[f1779,f1715]) ).
fof(f1715,plain,
( sorti1(sK1(sK1(sK1(sK1(j(sK0))))))
| ~ spl2_18 ),
inference(avatar_component_clause,[],[f1713]) ).
fof(f1713,plain,
( spl2_18
<=> sorti1(sK1(sK1(sK1(sK1(j(sK0)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).
fof(f1779,plain,
( ~ sorti1(sK1(sK1(sK1(sK1(j(sK0))))))
| spl2_17 ),
inference(resolution,[],[f1711,f19]) ).
fof(f19,plain,
! [X7] :
( sorti2(h(X7))
| ~ sorti1(X7) ),
inference(cnf_transformation,[],[f14]) ).
fof(f1711,plain,
( ~ sorti2(h(sK1(sK1(sK1(sK1(j(sK0)))))))
| spl2_17 ),
inference(avatar_component_clause,[],[f1709]) ).
fof(f1709,plain,
( spl2_17
<=> sorti2(h(sK1(sK1(sK1(sK1(j(sK0))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).
fof(f1719,plain,
( ~ spl2_8
| spl2_18 ),
inference(avatar_contradiction_clause,[],[f1718]) ).
fof(f1718,plain,
( $false
| ~ spl2_8
| spl2_18 ),
inference(subsumption_resolution,[],[f1717,f406]) ).
fof(f406,plain,
( sorti1(sK1(sK1(sK1(j(sK0)))))
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f404]) ).
fof(f404,plain,
( spl2_8
<=> sorti1(sK1(sK1(sK1(j(sK0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).
fof(f1717,plain,
( ~ sorti1(sK1(sK1(sK1(j(sK0)))))
| spl2_18 ),
inference(resolution,[],[f1714,f29]) ).
fof(f1714,plain,
( ~ sorti1(sK1(sK1(sK1(sK1(j(sK0))))))
| spl2_18 ),
inference(avatar_component_clause,[],[f1713]) ).
fof(f1716,plain,
( ~ spl2_17
| spl2_18
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f1500,f69,f1713,f1709]) ).
fof(f1500,plain,
( sorti1(sK1(sK1(sK1(sK1(j(sK0))))))
| ~ sorti2(h(sK1(sK1(sK1(sK1(j(sK0)))))))
| ~ spl2_2 ),
inference(superposition,[],[f20,f296]) ).
fof(f296,plain,
( sK1(sK1(sK1(sK1(j(sK0))))) = j(h(sK1(sK1(sK1(sK1(j(sK0)))))))
| ~ spl2_2 ),
inference(resolution,[],[f99,f71]) ).
fof(f99,plain,
! [X0] :
( ~ sorti1(X0)
| sK1(sK1(sK1(X0))) = j(h(sK1(sK1(sK1(X0))))) ),
inference(resolution,[],[f41,f29]) ).
fof(f41,plain,
! [X0] :
( ~ sorti1(X0)
| sK1(sK1(X0)) = j(h(sK1(sK1(X0)))) ),
inference(resolution,[],[f35,f29]) ).
fof(f35,plain,
! [X0] :
( ~ sorti1(X0)
| sK1(X0) = j(h(sK1(X0))) ),
inference(resolution,[],[f24,f29]) ).
fof(f24,plain,
! [X0] :
( ~ sorti1(X0)
| j(h(X0)) = X0 ),
inference(cnf_transformation,[],[f14]) ).
fof(f1622,plain,
( spl2_15
| ~ spl2_16 ),
inference(avatar_contradiction_clause,[],[f1621]) ).
fof(f1621,plain,
( $false
| spl2_15
| ~ spl2_16 ),
inference(subsumption_resolution,[],[f1620,f1545]) ).
fof(f1545,plain,
( sorti1(sK1(sK1(j(op2(sK0,sK0)))))
| ~ spl2_16 ),
inference(avatar_component_clause,[],[f1543]) ).
fof(f1543,plain,
( spl2_16
<=> sorti1(sK1(sK1(j(op2(sK0,sK0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).
fof(f1620,plain,
( ~ sorti1(sK1(sK1(j(op2(sK0,sK0)))))
| spl2_15 ),
inference(resolution,[],[f1541,f19]) ).
fof(f1541,plain,
( ~ sorti2(h(sK1(sK1(j(op2(sK0,sK0))))))
| spl2_15 ),
inference(avatar_component_clause,[],[f1539]) ).
fof(f1539,plain,
( spl2_15
<=> sorti2(h(sK1(sK1(j(op2(sK0,sK0)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).
fof(f1562,plain,
( ~ spl2_6
| spl2_16 ),
inference(avatar_contradiction_clause,[],[f1561]) ).
fof(f1561,plain,
( $false
| ~ spl2_6
| spl2_16 ),
inference(subsumption_resolution,[],[f1560,f338]) ).
fof(f338,plain,
( sorti1(sK1(j(op2(sK0,sK0))))
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f336,plain,
( spl2_6
<=> sorti1(sK1(j(op2(sK0,sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
fof(f1560,plain,
( ~ sorti1(sK1(j(op2(sK0,sK0))))
| spl2_16 ),
inference(resolution,[],[f1544,f29]) ).
fof(f1544,plain,
( ~ sorti1(sK1(sK1(j(op2(sK0,sK0)))))
| spl2_16 ),
inference(avatar_component_clause,[],[f1543]) ).
fof(f1546,plain,
( ~ spl2_15
| spl2_16
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f1009,f69,f1543,f1539]) ).
fof(f1009,plain,
( sorti1(sK1(sK1(j(op2(sK0,sK0)))))
| ~ sorti2(h(sK1(sK1(j(op2(sK0,sK0))))))
| ~ spl2_2 ),
inference(superposition,[],[f20,f179]) ).
fof(f179,plain,
( sK1(sK1(j(op2(sK0,sK0)))) = j(h(sK1(sK1(j(op2(sK0,sK0))))))
| ~ spl2_2 ),
inference(resolution,[],[f171,f41]) ).
fof(f171,plain,
( sorti1(j(op2(sK0,sK0)))
| ~ spl2_2 ),
inference(subsumption_resolution,[],[f170,f143]) ).
fof(f143,plain,
( sorti1(j(sK0))
| ~ spl2_2 ),
inference(subsumption_resolution,[],[f142,f71]) ).
fof(f142,plain,
( sorti1(j(sK0))
| ~ sorti1(sK1(j(sK0))) ),
inference(duplicate_literal_removal,[],[f141]) ).
fof(f141,plain,
( sorti1(j(sK0))
| ~ sorti1(sK1(j(sK0)))
| ~ sorti1(sK1(j(sK0))) ),
inference(superposition,[],[f27,f134]) ).
fof(f27,plain,
! [X0,X1] :
( sorti1(op1(X0,X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f11,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/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f170,plain,
( sorti1(j(op2(sK0,sK0)))
| ~ sorti1(j(sK0)) ),
inference(duplicate_literal_removal,[],[f169]) ).
fof(f169,plain,
( sorti1(j(op2(sK0,sK0)))
| ~ sorti1(j(sK0))
| ~ sorti1(j(sK0)) ),
inference(superposition,[],[f27,f162]) ).
fof(f162,plain,
j(op2(sK0,sK0)) = op1(j(sK0),j(sK0)),
inference(resolution,[],[f155,f25]) ).
fof(f155,plain,
! [X0] :
( ~ sorti2(X0)
| j(op2(X0,sK0)) = op1(j(X0),j(sK0)) ),
inference(resolution,[],[f22,f25]) ).
fof(f22,plain,
! [X2,X3] :
( ~ sorti2(X3)
| j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f771,plain,
( ~ spl2_1
| spl2_13 ),
inference(avatar_contradiction_clause,[],[f770]) ).
fof(f770,plain,
( $false
| ~ spl2_1
| spl2_13 ),
inference(subsumption_resolution,[],[f769,f25]) ).
fof(f769,plain,
( ~ sorti2(sK0)
| ~ spl2_1
| spl2_13 ),
inference(subsumption_resolution,[],[f768,f66]) ).
fof(f768,plain,
( ~ sorti2(h(sK1(j(sK0))))
| ~ sorti2(sK0)
| spl2_13 ),
inference(resolution,[],[f762,f28]) ).
fof(f28,plain,
! [X0,X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0] :
( ! [X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1) )
| ~ sorti2(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> sorti2(op2(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f762,plain,
( ~ sorti2(op2(sK0,h(sK1(j(sK0)))))
| spl2_13 ),
inference(avatar_component_clause,[],[f760]) ).
fof(f760,plain,
( spl2_13
<=> sorti2(op2(sK0,h(sK1(j(sK0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).
fof(f767,plain,
( ~ spl2_13
| spl2_14
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f656,f69,f764,f760]) ).
fof(f764,plain,
( spl2_14
<=> sorti1(op1(j(sK0),sK1(j(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).
fof(f656,plain,
( sorti1(op1(j(sK0),sK1(j(sK0))))
| ~ sorti2(op2(sK0,h(sK1(j(sK0)))))
| ~ spl2_2 ),
inference(superposition,[],[f20,f564]) ).
fof(f564,plain,
( j(op2(sK0,h(sK1(j(sK0))))) = op1(j(sK0),sK1(j(sK0)))
| ~ spl2_2 ),
inference(forward_demodulation,[],[f555,f60]) ).
fof(f60,plain,
sK1(j(sK0)) = j(h(sK1(j(sK0)))),
inference(resolution,[],[f40,f25]) ).
fof(f40,plain,
! [X0] :
( ~ sorti2(X0)
| sK1(j(X0)) = j(h(sK1(j(X0)))) ),
inference(resolution,[],[f35,f20]) ).
fof(f555,plain,
( j(op2(sK0,h(sK1(j(sK0))))) = op1(j(sK0),j(h(sK1(j(sK0)))))
| ~ spl2_2 ),
inference(resolution,[],[f489,f71]) ).
fof(f489,plain,
! [X0] :
( ~ sorti1(X0)
| j(op2(sK0,h(X0))) = op1(j(sK0),j(h(X0))) ),
inference(resolution,[],[f156,f25]) ).
fof(f156,plain,
! [X0,X1] :
( ~ sorti2(X0)
| j(op2(X0,h(X1))) = op1(j(X0),j(h(X1)))
| ~ sorti1(X1) ),
inference(resolution,[],[f22,f19]) ).
fof(f669,plain,
( ~ spl2_1
| spl2_11 ),
inference(avatar_contradiction_clause,[],[f668]) ).
fof(f668,plain,
( $false
| ~ spl2_1
| spl2_11 ),
inference(subsumption_resolution,[],[f667,f66]) ).
fof(f667,plain,
( ~ sorti2(h(sK1(j(sK0))))
| spl2_11 ),
inference(subsumption_resolution,[],[f666,f25]) ).
fof(f666,plain,
( ~ sorti2(sK0)
| ~ sorti2(h(sK1(j(sK0))))
| spl2_11 ),
inference(resolution,[],[f660,f28]) ).
fof(f660,plain,
( ~ sorti2(op2(h(sK1(j(sK0))),sK0))
| spl2_11 ),
inference(avatar_component_clause,[],[f658]) ).
fof(f658,plain,
( spl2_11
<=> sorti2(op2(h(sK1(j(sK0))),sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
fof(f665,plain,
( ~ spl2_11
| spl2_12
| ~ spl2_1 ),
inference(avatar_split_clause,[],[f604,f65,f662,f658]) ).
fof(f662,plain,
( spl2_12
<=> sorti1(op1(sK1(j(sK0)),j(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).
fof(f604,plain,
( sorti1(op1(sK1(j(sK0)),j(sK0)))
| ~ sorti2(op2(h(sK1(j(sK0))),sK0))
| ~ spl2_1 ),
inference(superposition,[],[f20,f167]) ).
fof(f167,plain,
( j(op2(h(sK1(j(sK0))),sK0)) = op1(sK1(j(sK0)),j(sK0))
| ~ spl2_1 ),
inference(forward_demodulation,[],[f164,f60]) ).
fof(f164,plain,
( j(op2(h(sK1(j(sK0))),sK0)) = op1(j(h(sK1(j(sK0)))),j(sK0))
| ~ spl2_1 ),
inference(resolution,[],[f155,f66]) ).
fof(f504,plain,
( spl2_9
| ~ spl2_10 ),
inference(avatar_contradiction_clause,[],[f503]) ).
fof(f503,plain,
( $false
| spl2_9
| ~ spl2_10 ),
inference(subsumption_resolution,[],[f502,f467]) ).
fof(f467,plain,
( sorti2(op2(sK0,op2(sK0,sK0)))
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f465,plain,
( spl2_10
<=> sorti2(op2(sK0,op2(sK0,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
fof(f502,plain,
( ~ sorti2(op2(sK0,op2(sK0,sK0)))
| spl2_9 ),
inference(resolution,[],[f463,f20]) ).
fof(f463,plain,
( ~ sorti1(j(op2(sK0,op2(sK0,sK0))))
| spl2_9 ),
inference(avatar_component_clause,[],[f461]) ).
fof(f461,plain,
( spl2_9
<=> sorti1(j(op2(sK0,op2(sK0,sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
fof(f472,plain,
( ~ spl2_2
| spl2_10 ),
inference(avatar_contradiction_clause,[],[f471]) ).
fof(f471,plain,
( $false
| ~ spl2_2
| spl2_10 ),
inference(subsumption_resolution,[],[f470,f25]) ).
fof(f470,plain,
( ~ sorti2(sK0)
| ~ spl2_2
| spl2_10 ),
inference(subsumption_resolution,[],[f469,f191]) ).
fof(f191,plain,
( sorti2(op2(sK0,sK0))
| ~ spl2_2 ),
inference(subsumption_resolution,[],[f190,f171]) ).
fof(f190,plain,
( sorti2(op2(sK0,sK0))
| ~ sorti1(j(op2(sK0,sK0)))
| ~ spl2_2 ),
inference(superposition,[],[f19,f189]) ).
fof(f189,plain,
( op2(sK0,sK0) = h(j(op2(sK0,sK0)))
| ~ spl2_2 ),
inference(forward_demodulation,[],[f188,f162]) ).
fof(f188,plain,
( op2(sK0,sK0) = h(op1(j(sK0),j(sK0)))
| ~ spl2_2 ),
inference(forward_demodulation,[],[f182,f31]) ).
fof(f182,plain,
( h(op1(j(sK0),j(sK0))) = op2(h(j(sK0)),sK0)
| ~ spl2_2 ),
inference(resolution,[],[f152,f143]) ).
fof(f152,plain,
( ! [X0] :
( ~ sorti1(X0)
| h(op1(X0,j(sK0))) = op2(h(X0),sK0) )
| ~ spl2_2 ),
inference(forward_demodulation,[],[f144,f31]) ).
fof(f144,plain,
( ! [X0] :
( h(op1(X0,j(sK0))) = op2(h(X0),h(j(sK0)))
| ~ sorti1(X0) )
| ~ spl2_2 ),
inference(resolution,[],[f143,f21]) ).
fof(f469,plain,
( ~ sorti2(op2(sK0,sK0))
| ~ sorti2(sK0)
| spl2_10 ),
inference(resolution,[],[f466,f28]) ).
fof(f466,plain,
( ~ sorti2(op2(sK0,op2(sK0,sK0)))
| spl2_10 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f468,plain,
( ~ spl2_9
| spl2_10
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f330,f69,f465,f461]) ).
fof(f330,plain,
( sorti2(op2(sK0,op2(sK0,sK0)))
| ~ sorti1(j(op2(sK0,op2(sK0,sK0))))
| ~ spl2_2 ),
inference(superposition,[],[f19,f307]) ).
fof(f307,plain,
( op2(sK0,op2(sK0,sK0)) = h(j(op2(sK0,op2(sK0,sK0))))
| ~ spl2_2 ),
inference(forward_demodulation,[],[f301,f189]) ).
fof(f301,plain,
( op2(sK0,h(j(op2(sK0,sK0)))) = h(j(op2(sK0,h(j(op2(sK0,sK0))))))
| ~ spl2_2 ),
inference(resolution,[],[f213,f171]) ).
fof(f213,plain,
! [X0] :
( ~ sorti1(X0)
| op2(sK0,h(X0)) = h(j(op2(sK0,h(X0)))) ),
inference(resolution,[],[f206,f19]) ).
fof(f206,plain,
! [X0] :
( ~ sorti2(X0)
| op2(sK0,X0) = h(j(op2(sK0,X0))) ),
inference(resolution,[],[f46,f25]) ).
fof(f46,plain,
! [X0,X1] :
( ~ sorti2(X1)
| ~ sorti2(X0)
| op2(X1,X0) = h(j(op2(X1,X0))) ),
inference(resolution,[],[f28,f23]) ).
fof(f435,plain,
( spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f434]) ).
fof(f434,plain,
( $false
| spl2_7
| ~ spl2_8 ),
inference(subsumption_resolution,[],[f433,f406]) ).
fof(f433,plain,
( ~ sorti1(sK1(sK1(sK1(j(sK0)))))
| spl2_7 ),
inference(resolution,[],[f402,f19]) ).
fof(f402,plain,
( ~ sorti2(h(sK1(sK1(sK1(j(sK0))))))
| spl2_7 ),
inference(avatar_component_clause,[],[f400]) ).
fof(f400,plain,
( spl2_7
<=> sorti2(h(sK1(sK1(sK1(j(sK0)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).
fof(f410,plain,
( ~ spl2_4
| spl2_8 ),
inference(avatar_contradiction_clause,[],[f409]) ).
fof(f409,plain,
( $false
| ~ spl2_4
| spl2_8 ),
inference(subsumption_resolution,[],[f408,f110]) ).
fof(f110,plain,
( sorti1(sK1(sK1(j(sK0))))
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f108,plain,
( spl2_4
<=> sorti1(sK1(sK1(j(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
fof(f408,plain,
( ~ sorti1(sK1(sK1(j(sK0))))
| spl2_8 ),
inference(resolution,[],[f405,f29]) ).
fof(f405,plain,
( ~ sorti1(sK1(sK1(sK1(j(sK0)))))
| spl2_8 ),
inference(avatar_component_clause,[],[f404]) ).
fof(f407,plain,
( ~ spl2_7
| spl2_8
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f329,f69,f404,f400]) ).
fof(f329,plain,
( sorti1(sK1(sK1(sK1(j(sK0)))))
| ~ sorti2(h(sK1(sK1(sK1(j(sK0))))))
| ~ spl2_2 ),
inference(superposition,[],[f20,f293]) ).
fof(f293,plain,
( sK1(sK1(sK1(j(sK0)))) = j(h(sK1(sK1(sK1(j(sK0))))))
| ~ spl2_2 ),
inference(resolution,[],[f99,f143]) ).
fof(f374,plain,
( spl2_5
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[],[f373]) ).
fof(f373,plain,
( $false
| spl2_5
| ~ spl2_6 ),
inference(subsumption_resolution,[],[f372,f338]) ).
fof(f372,plain,
( ~ sorti1(sK1(j(op2(sK0,sK0))))
| spl2_5 ),
inference(resolution,[],[f334,f19]) ).
fof(f334,plain,
( ~ sorti2(h(sK1(j(op2(sK0,sK0)))))
| spl2_5 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f332,plain,
( spl2_5
<=> sorti2(h(sK1(j(op2(sK0,sK0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
fof(f342,plain,
( ~ spl2_2
| spl2_6 ),
inference(avatar_contradiction_clause,[],[f341]) ).
fof(f341,plain,
( $false
| ~ spl2_2
| spl2_6 ),
inference(subsumption_resolution,[],[f340,f171]) ).
fof(f340,plain,
( ~ sorti1(j(op2(sK0,sK0)))
| spl2_6 ),
inference(resolution,[],[f337,f29]) ).
fof(f337,plain,
( ~ sorti1(sK1(j(op2(sK0,sK0))))
| spl2_6 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f339,plain,
( ~ spl2_5
| spl2_6
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f308,f69,f336,f332]) ).
fof(f308,plain,
( sorti1(sK1(j(op2(sK0,sK0))))
| ~ sorti2(h(sK1(j(op2(sK0,sK0)))))
| ~ spl2_2 ),
inference(superposition,[],[f20,f176]) ).
fof(f176,plain,
( sK1(j(op2(sK0,sK0))) = j(h(sK1(j(op2(sK0,sK0)))))
| ~ spl2_2 ),
inference(resolution,[],[f171,f35]) ).
fof(f126,plain,
( spl2_3
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f125]) ).
fof(f125,plain,
( $false
| spl2_3
| ~ spl2_4 ),
inference(subsumption_resolution,[],[f124,f110]) ).
fof(f124,plain,
( ~ sorti1(sK1(sK1(j(sK0))))
| spl2_3 ),
inference(resolution,[],[f106,f19]) ).
fof(f106,plain,
( ~ sorti2(h(sK1(sK1(j(sK0)))))
| spl2_3 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f104,plain,
( spl2_3
<=> sorti2(h(sK1(sK1(j(sK0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
fof(f114,plain,
( ~ spl2_2
| spl2_4 ),
inference(avatar_contradiction_clause,[],[f113]) ).
fof(f113,plain,
( $false
| ~ spl2_2
| spl2_4 ),
inference(subsumption_resolution,[],[f112,f71]) ).
fof(f112,plain,
( ~ sorti1(sK1(j(sK0)))
| spl2_4 ),
inference(resolution,[],[f109,f29]) ).
fof(f109,plain,
( ~ sorti1(sK1(sK1(j(sK0))))
| spl2_4 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,plain,
( ~ spl2_3
| spl2_4
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f102,f69,f108,f104]) ).
fof(f102,plain,
( sorti1(sK1(sK1(j(sK0))))
| ~ sorti2(h(sK1(sK1(j(sK0)))))
| ~ spl2_2 ),
inference(superposition,[],[f20,f80]) ).
fof(f80,plain,
( sK1(sK1(j(sK0))) = j(h(sK1(sK1(j(sK0)))))
| ~ spl2_2 ),
inference(resolution,[],[f71,f35]) ).
fof(f86,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_contradiction_clause,[],[f85]) ).
fof(f85,plain,
( $false
| spl2_1
| ~ spl2_2 ),
inference(subsumption_resolution,[],[f84,f71]) ).
fof(f84,plain,
( ~ sorti1(sK1(j(sK0)))
| spl2_1 ),
inference(resolution,[],[f67,f19]) ).
fof(f67,plain,
( ~ sorti2(h(sK1(j(sK0))))
| spl2_1 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f76,plain,
spl2_2,
inference(avatar_contradiction_clause,[],[f75]) ).
fof(f75,plain,
( $false
| spl2_2 ),
inference(subsumption_resolution,[],[f74,f25]) ).
fof(f74,plain,
( ~ sorti2(sK0)
| spl2_2 ),
inference(resolution,[],[f73,f20]) ).
fof(f73,plain,
( ~ sorti1(j(sK0))
| spl2_2 ),
inference(resolution,[],[f70,f29]) ).
fof(f70,plain,
( ~ sorti1(sK1(j(sK0)))
| spl2_2 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f63,f69,f65]) ).
fof(f63,plain,
( sorti1(sK1(j(sK0)))
| ~ sorti2(h(sK1(j(sK0)))) ),
inference(superposition,[],[f20,f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ALG069+1 : TPTP v8.2.0. Released v2.7.0.
% 0.09/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n028.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat May 18 23:18:23 EDT 2024
% 0.15/0.31 % CPUTime :
% 0.15/0.31 % (28237)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.33 % (28239)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.33 % (28241)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.33 % (28242)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.33 % (28238)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.33 % (28243)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.33 % (28240)WARNING: value z3 for option sas not known
% 0.15/0.33 % (28244)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.33 TRYING [1]
% 0.15/0.33 TRYING [1]
% 0.15/0.33 TRYING [2]
% 0.15/0.33 TRYING [2]
% 0.15/0.33 % (28240)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.33 TRYING [3]
% 0.15/0.33 TRYING [3]
% 0.15/0.33 TRYING [4]
% 0.15/0.33 TRYING [4]
% 0.15/0.34 TRYING [5]
% 0.15/0.34 TRYING [5]
% 0.15/0.35 TRYING [6]
% 0.15/0.36 TRYING [6]
% 0.15/0.38 TRYING [7]
% 0.15/0.39 TRYING [7]
% 0.15/0.39 % (28240)First to succeed.
% 0.15/0.39 % (28240)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-28237"
% 0.15/0.39 % (28240)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40 % (28240)------------------------------
% 0.15/0.40 % (28240)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.40 % (28240)Termination reason: Refutation
% 0.15/0.40
% 0.15/0.40 % (28240)Memory used [KB]: 1479
% 0.15/0.40 % (28240)Time elapsed: 0.063 s
% 0.15/0.40 % (28240)Instructions burned: 155 (million)
% 0.15/0.40 % (28237)Success in time 0.068 s
%------------------------------------------------------------------------------