TSTP Solution File: HWV003-2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : HWV003-2 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n006.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 : Tue Apr 30 12:21:40 EDT 2024
% Result : Unsatisfiable 146.10s 21.33s
% Output : Refutation 146.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 36
% Syntax : Number of formulae : 611 ( 609 unt; 0 def)
% Number of atoms : 613 ( 612 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 6 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 16 con; 0-2 aty)
% Number of variables : 275 ( 275 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f519142,plain,
$false,
inference(trivial_inequality_removal,[],[f519141]) ).
fof(f519141,plain,
carry_def != carry_def,
inference(superposition,[],[f115795,f509624]) ).
fof(f509624,plain,
carry_def = carry,
inference(superposition,[],[f509463,f6]) ).
fof(f6,axiom,
! [X0] : and(X0,ll1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_identity) ).
fof(f509463,plain,
carry_def = and(carry,ll1),
inference(forward_demodulation,[],[f509462,f18]) ).
fof(f18,axiom,
! [X0,X1] : or(X0,and(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_absorption) ).
fof(f509462,plain,
and(carry,ll1) = or(carry_def,and(carry_def,not(cin))),
inference(forward_demodulation,[],[f509461,f174693]) ).
fof(f174693,plain,
not(or(cin,t1)) = and(carry_def,not(cin)),
inference(forward_demodulation,[],[f174692,f8465]) ).
fof(f8465,plain,
! [X0,X1] : and(X0,not(X1)) = xor(X0,and(X1,X0)),
inference(forward_demodulation,[],[f8464,f923]) ).
fof(f923,plain,
! [X0,X1] : and(X0,X1) = and(X0,or(X1,not(X0))),
inference(forward_demodulation,[],[f798,f5]) ).
fof(f5,axiom,
! [X0] : or(X0,ll0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_identity) ).
fof(f798,plain,
! [X0,X1] : or(and(X0,X1),ll0) = and(X0,or(X1,not(X0))),
inference(superposition,[],[f7,f10]) ).
fof(f10,axiom,
! [X0] : ll0 = and(X0,not(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_complement) ).
fof(f7,axiom,
! [X2,X0,X1] : and(X0,or(X1,X2)) = or(and(X0,X1),and(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_distributive) ).
fof(f8464,plain,
! [X0,X1] : and(X0,not(X1)) = xor(X0,and(X1,or(X0,not(X1)))),
inference(forward_demodulation,[],[f8463,f367]) ).
fof(f367,plain,
! [X0,X1] : or(X0,not(X1)) = not(and(not(X0),X1)),
inference(superposition,[],[f21,f13]) ).
fof(f13,axiom,
! [X0] : not(not(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_involution) ).
fof(f21,axiom,
! [X0,X1] : not(and(X0,X1)) = or(not(X0),not(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_demorgan) ).
fof(f8463,plain,
! [X0,X1] : and(X0,not(X1)) = xor(X0,and(X1,not(and(not(X0),X1)))),
inference(forward_demodulation,[],[f8462,f4107]) ).
fof(f4107,plain,
! [X2,X0,X1] : and(X0,X2) = and(X0,or(X2,and(not(X0),X1))),
inference(forward_demodulation,[],[f4074,f5]) ).
fof(f4074,plain,
! [X2,X0,X1] : and(X0,or(X2,and(not(X0),X1))) = or(and(X0,X2),ll0),
inference(superposition,[],[f7,f575]) ).
fof(f575,plain,
! [X0,X1] : ll0 = and(X0,and(not(X0),X1)),
inference(forward_demodulation,[],[f508,f97]) ).
fof(f97,plain,
! [X0] : ll0 = and(ll0,X0),
inference(superposition,[],[f2,f17]) ).
fof(f17,axiom,
! [X0] : ll0 = and(X0,ll0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_boundedness) ).
fof(f2,axiom,
! [X0,X1] : and(X0,X1) = and(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_commutative) ).
fof(f508,plain,
! [X0,X1] : and(ll0,X1) = and(X0,and(not(X0),X1)),
inference(superposition,[],[f4,f10]) ).
fof(f4,axiom,
! [X2,X0,X1] : and(and(X0,X1),X2) = and(X0,and(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_associative) ).
fof(f8462,plain,
! [X0,X1] : xor(X0,and(X1,not(and(not(X0),X1)))) = and(X0,or(not(X1),and(not(X0),X1))),
inference(forward_demodulation,[],[f8461,f75]) ).
fof(f75,plain,
! [X0] : or(ll0,X0) = X0,
inference(superposition,[],[f1,f5]) ).
fof(f1,axiom,
! [X0,X1] : or(X0,X1) = or(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_commutative) ).
fof(f8461,plain,
! [X0,X1] : xor(X0,and(X1,not(and(not(X0),X1)))) = or(ll0,and(X0,or(not(X1),and(not(X0),X1)))),
inference(forward_demodulation,[],[f8368,f370]) ).
fof(f370,plain,
! [X0,X1] : not(and(X1,not(X0))) = or(not(X1),X0),
inference(superposition,[],[f21,f13]) ).
fof(f8368,plain,
! [X0,X1] : xor(X0,and(X1,not(and(not(X0),X1)))) = or(ll0,and(X0,not(and(X1,not(and(not(X0),X1)))))),
inference(superposition,[],[f22,f563]) ).
fof(f563,plain,
! [X0,X1] : ll0 = and(X0,and(X1,not(and(X0,X1)))),
inference(superposition,[],[f4,f10]) ).
fof(f22,axiom,
! [X0,X1] : or(and(not(X0),X1),and(X0,not(X1))) = xor(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_definition) ).
fof(f174692,plain,
not(or(cin,t1)) = xor(carry_def,and(cin,carry_def)),
inference(forward_demodulation,[],[f174691,f173482]) ).
fof(f173482,plain,
or(cin,t1) = or(and(cin,carry_def),not(carry_def)),
inference(forward_demodulation,[],[f173428,f3103]) ).
fof(f3103,plain,
! [X2,X0,X1] : or(X0,X2) = or(and(X0,X1),or(X0,X2)),
inference(superposition,[],[f3,f917]) ).
fof(f917,plain,
! [X0,X1] : or(and(X0,X1),X0) = X0,
inference(forward_demodulation,[],[f791,f143]) ).
fof(f143,plain,
! [X0,X1] : and(X0,or(X1,X0)) = X0,
inference(superposition,[],[f19,f1]) ).
fof(f19,axiom,
! [X0,X1] : and(X0,or(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_absorption) ).
fof(f791,plain,
! [X0,X1] : or(and(X0,X1),X0) = and(X0,or(X1,X0)),
inference(superposition,[],[f7,f12]) ).
fof(f12,axiom,
! [X0] : and(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_idempotent) ).
fof(f3,axiom,
! [X2,X0,X1] : or(or(X0,X1),X2) = or(X0,or(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_associative) ).
fof(f173428,plain,
or(and(cin,carry_def),not(carry_def)) = or(and(cin,carry_def),or(cin,t1)),
inference(superposition,[],[f1246,f16585]) ).
fof(f16585,plain,
not(carry_def) = and(or(cin,t1),not(and(cin,carry_def))),
inference(backward_demodulation,[],[f15986,f16556]) ).
fof(f16556,plain,
xor(carry_def,or(cin,t1)) = not(and(cin,carry_def)),
inference(backward_demodulation,[],[f15982,f16517]) ).
fof(f16517,plain,
and(cin,or(a,b)) = and(cin,carry_def),
inference(backward_demodulation,[],[f16221,f16516]) ).
fof(f16516,plain,
and(cin,carry_def) = and(carry_def,or(cin,t1)),
inference(forward_demodulation,[],[f16515,f2]) ).
fof(f16515,plain,
and(carry_def,cin) = and(carry_def,or(cin,t1)),
inference(forward_demodulation,[],[f16480,f427]) ).
fof(f427,plain,
! [X0,X1] : or(X0,X1) = or(X0,or(X0,X1)),
inference(superposition,[],[f3,f11]) ).
fof(f11,axiom,
! [X0] : or(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_idempotent) ).
fof(f16480,plain,
and(carry_def,cin) = and(carry_def,or(cin,or(cin,t1))),
inference(superposition,[],[f16235,f917]) ).
fof(f16235,plain,
! [X0] : and(carry_def,or(and(cin,or(a,b)),X0)) = and(carry_def,or(cin,or(X0,t1))),
inference(backward_demodulation,[],[f1106,f16234]) ).
fof(f16234,plain,
! [X0] : or(and(cin,or(a,b)),and(not(or(cin,t1)),X0)) = and(carry_def,or(cin,or(X0,t1))),
inference(forward_demodulation,[],[f16233,f430]) ).
fof(f430,plain,
! [X2,X0,X1] : or(X0,X2) = or(X0,or(and(X0,X1),X2)),
inference(superposition,[],[f3,f18]) ).
fof(f16233,plain,
! [X0] : or(and(cin,or(a,b)),and(not(or(cin,t1)),X0)) = and(carry_def,or(cin,or(and(cin,or(a,b)),or(X0,t1)))),
inference(forward_demodulation,[],[f16232,f12089]) ).
fof(f12089,plain,
! [X2,X3,X0,X1] : or(X3,or(X0,or(X1,X2))) = or(X1,or(X0,or(X2,X3))),
inference(forward_demodulation,[],[f11490,f3]) ).
fof(f11490,plain,
! [X2,X3,X0,X1] : or(X1,or(X0,or(X2,X3))) = or(X3,or(or(X0,X1),X2)),
inference(superposition,[],[f460,f428]) ).
fof(f428,plain,
! [X2,X0,X1] : or(X0,or(X1,X2)) = or(or(X1,X0),X2),
inference(superposition,[],[f3,f1]) ).
fof(f460,plain,
! [X2,X0,X1] : or(X0,or(X1,X2)) = or(X2,or(X0,X1)),
inference(superposition,[],[f3,f1]) ).
fof(f16232,plain,
! [X0] : or(and(cin,or(a,b)),and(not(or(cin,t1)),X0)) = and(carry_def,or(t1,or(and(cin,or(a,b)),or(cin,X0)))),
inference(forward_demodulation,[],[f16231,f11234]) ).
fof(f11234,plain,
! [X2,X3,X0,X1] : or(X3,or(X1,or(X0,X2))) = or(X2,or(X3,or(X0,X1))),
inference(superposition,[],[f460,f428]) ).
fof(f16231,plain,
! [X0] : or(and(cin,or(a,b)),and(not(or(cin,t1)),X0)) = and(carry_def,or(and(cin,or(a,b)),or(X0,or(cin,t1)))),
inference(forward_demodulation,[],[f16193,f13]) ).
fof(f16193,plain,
! [X0] : or(and(cin,or(a,b)),and(not(or(cin,t1)),X0)) = and(carry_def,or(and(cin,or(a,b)),or(X0,not(not(or(cin,t1)))))),
inference(superposition,[],[f1106,f923]) ).
fof(f1106,plain,
! [X0] : or(and(cin,or(a,b)),and(not(or(cin,t1)),X0)) = and(carry_def,or(and(cin,or(a,b)),X0)),
inference(superposition,[],[f8,f50]) ).
fof(f50,plain,
carry_def = or(and(cin,or(a,b)),not(or(cin,t1))),
inference(forward_demodulation,[],[f48,f20]) ).
fof(f20,axiom,
! [X0,X1] : not(or(X0,X1)) = and(not(X0),not(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_demorgan) ).
fof(f48,plain,
carry_def = or(and(cin,or(a,b)),and(not(cin),not(t1))),
inference(backward_demodulation,[],[f26,f37]) ).
fof(f37,plain,
and(a,b) = not(t1),
inference(superposition,[],[f13,f27]) ).
fof(f27,axiom,
not(and(a,b)) = t1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
fof(f26,axiom,
or(and(cin,or(a,b)),and(not(cin),and(a,b))) = carry_def,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',carry_def) ).
fof(f8,axiom,
! [X2,X0,X1] : or(X0,and(X1,X2)) = and(or(X0,X1),or(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_distributive) ).
fof(f16221,plain,
and(cin,or(a,b)) = and(carry_def,or(cin,t1)),
inference(forward_demodulation,[],[f16220,f3103]) ).
fof(f16220,plain,
and(cin,or(a,b)) = and(carry_def,or(and(cin,or(a,b)),or(cin,t1))),
inference(forward_demodulation,[],[f16184,f5]) ).
fof(f16184,plain,
and(carry_def,or(and(cin,or(a,b)),or(cin,t1))) = or(and(cin,or(a,b)),ll0),
inference(superposition,[],[f1106,f64]) ).
fof(f64,plain,
! [X0] : ll0 = and(not(X0),X0),
inference(superposition,[],[f10,f13]) ).
fof(f15982,plain,
not(and(cin,or(a,b))) = xor(carry_def,or(cin,t1)),
inference(forward_demodulation,[],[f15981,f2]) ).
fof(f15981,plain,
xor(carry_def,or(cin,t1)) = not(and(or(a,b),cin)),
inference(forward_demodulation,[],[f15980,f12776]) ).
fof(f12776,plain,
! [X2,X0,X1] : and(X0,X1) = and(X1,and(X0,or(X1,X2))),
inference(forward_demodulation,[],[f12686,f3126]) ).
fof(f3126,plain,
! [X2,X0,X1] : and(X0,or(X1,X2)) = and(X0,or(and(X0,X1),X2)),
inference(forward_demodulation,[],[f3104,f7]) ).
fof(f3104,plain,
! [X2,X0,X1] : or(and(X0,X1),and(X0,X2)) = and(X0,or(and(X0,X1),X2)),
inference(superposition,[],[f8,f917]) ).
fof(f12686,plain,
! [X2,X0,X1] : and(X0,X1) = and(X1,and(X0,or(and(X0,X1),X2))),
inference(superposition,[],[f502,f19]) ).
fof(f502,plain,
! [X2,X0,X1] : and(X0,and(X1,X2)) = and(and(X1,X0),X2),
inference(superposition,[],[f4,f2]) ).
fof(f15980,plain,
xor(carry_def,or(cin,t1)) = not(and(cin,and(or(a,b),or(cin,t1)))),
inference(forward_demodulation,[],[f15979,f557]) ).
fof(f557,plain,
! [X2,X0,X1] : and(X0,and(X1,X2)) = and(X2,and(X0,X1)),
inference(superposition,[],[f4,f2]) ).
fof(f15979,plain,
xor(carry_def,or(cin,t1)) = not(and(or(a,b),and(or(cin,t1),cin))),
inference(forward_demodulation,[],[f15978,f557]) ).
fof(f15978,plain,
not(and(or(cin,t1),and(cin,or(a,b)))) = xor(carry_def,or(cin,t1)),
inference(forward_demodulation,[],[f15891,f23]) ).
fof(f23,axiom,
! [X0,X1] : xor(X0,X1) = xor(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_commutative) ).
fof(f15891,plain,
not(and(or(cin,t1),and(cin,or(a,b)))) = xor(or(cin,t1),carry_def),
inference(superposition,[],[f1595,f213]) ).
fof(f213,plain,
carry_def = or(not(or(cin,t1)),and(cin,or(a,b))),
inference(superposition,[],[f50,f1]) ).
fof(f1595,plain,
! [X0,X1] : not(and(X0,X1)) = xor(X0,or(not(X0),X1)),
inference(forward_demodulation,[],[f1594,f21]) ).
fof(f1594,plain,
! [X0,X1] : or(not(X0),not(X1)) = xor(X0,or(not(X0),X1)),
inference(forward_demodulation,[],[f1593,f1209]) ).
fof(f1209,plain,
! [X0,X1] : or(not(X0),X1) = or(not(X0),and(X0,X1)),
inference(forward_demodulation,[],[f1110,f98]) ).
fof(f98,plain,
! [X0] : and(ll1,X0) = X0,
inference(superposition,[],[f2,f6]) ).
fof(f1110,plain,
! [X0,X1] : or(not(X0),and(X0,X1)) = and(ll1,or(not(X0),X1)),
inference(superposition,[],[f8,f61]) ).
fof(f61,plain,
! [X0] : ll1 = or(not(X0),X0),
inference(superposition,[],[f9,f13]) ).
fof(f9,axiom,
! [X0] : ll1 = or(X0,not(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_complement) ).
fof(f1593,plain,
! [X0,X1] : xor(X0,or(not(X0),X1)) = or(not(X0),and(X0,not(X1))),
inference(forward_demodulation,[],[f1592,f501]) ).
fof(f501,plain,
! [X0,X1] : and(X0,X1) = and(X0,and(X0,X1)),
inference(superposition,[],[f4,f12]) ).
fof(f1592,plain,
! [X0,X1] : xor(X0,or(not(X0),X1)) = or(not(X0),and(X0,and(X0,not(X1)))),
inference(forward_demodulation,[],[f1508,f291]) ).
fof(f291,plain,
! [X0,X1] : and(X0,not(X1)) = not(or(not(X0),X1)),
inference(superposition,[],[f20,f13]) ).
fof(f1508,plain,
! [X0,X1] : xor(X0,or(not(X0),X1)) = or(not(X0),and(X0,not(or(not(X0),X1)))),
inference(superposition,[],[f22,f19]) ).
fof(f15986,plain,
not(carry_def) = and(or(cin,t1),xor(carry_def,or(cin,t1))),
inference(backward_demodulation,[],[f5184,f15982]) ).
fof(f5184,plain,
and(or(cin,t1),not(and(cin,or(a,b)))) = not(carry_def),
inference(superposition,[],[f291,f213]) ).
fof(f1246,plain,
! [X0,X1] : or(X0,X1) = or(X0,and(X1,not(X0))),
inference(forward_demodulation,[],[f1146,f6]) ).
fof(f1146,plain,
! [X0,X1] : and(or(X0,X1),ll1) = or(X0,and(X1,not(X0))),
inference(superposition,[],[f8,f9]) ).
fof(f174691,plain,
xor(carry_def,and(cin,carry_def)) = not(or(and(cin,carry_def),not(carry_def))),
inference(forward_demodulation,[],[f174690,f13]) ).
fof(f174690,plain,
not(or(and(cin,carry_def),not(carry_def))) = not(not(xor(carry_def,and(cin,carry_def)))),
inference(forward_demodulation,[],[f174689,f2104]) ).
fof(f2104,plain,
! [X0,X1] : xor(not(X0),X1) = not(xor(X0,X1)),
inference(forward_demodulation,[],[f2100,f1561]) ).
fof(f1561,plain,
! [X0] : not(X0) = xor(ll1,X0),
inference(forward_demodulation,[],[f1560,f75]) ).
fof(f1560,plain,
! [X0] : or(ll0,not(X0)) = xor(ll1,X0),
inference(forward_demodulation,[],[f1559,f97]) ).
fof(f1559,plain,
! [X0] : xor(ll1,X0) = or(and(ll0,X0),not(X0)),
inference(forward_demodulation,[],[f1480,f98]) ).
fof(f1480,plain,
! [X0] : xor(ll1,X0) = or(and(ll0,X0),and(ll1,not(X0))),
inference(superposition,[],[f22,f15]) ).
fof(f15,axiom,
ll0 = not(ll1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ll1_inverse) ).
fof(f2100,plain,
! [X0,X1] : xor(not(X0),X1) = xor(ll1,xor(X0,X1)),
inference(superposition,[],[f24,f1561]) ).
fof(f24,axiom,
! [X2,X0,X1] : xor(X0,xor(X1,X2)) = xor(xor(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_associative) ).
fof(f174689,plain,
not(or(and(cin,carry_def),not(carry_def))) = not(xor(not(carry_def),and(cin,carry_def))),
inference(forward_demodulation,[],[f174688,f23]) ).
fof(f174688,plain,
not(or(and(cin,carry_def),not(carry_def))) = not(xor(and(cin,carry_def),not(carry_def))),
inference(forward_demodulation,[],[f174604,f75]) ).
fof(f174604,plain,
not(xor(and(cin,carry_def),not(carry_def))) = or(ll0,not(or(and(cin,carry_def),not(carry_def)))),
inference(superposition,[],[f2105,f174349]) ).
fof(f174349,plain,
ll0 = and(and(cin,carry_def),not(carry_def)),
inference(superposition,[],[f575,f16586]) ).
fof(f16586,plain,
not(carry_def) = and(not(and(cin,carry_def)),or(cin,t1)),
inference(backward_demodulation,[],[f15985,f16556]) ).
fof(f15985,plain,
not(carry_def) = and(xor(carry_def,or(cin,t1)),or(cin,t1)),
inference(backward_demodulation,[],[f5440,f15982]) ).
fof(f5440,plain,
not(carry_def) = and(not(and(cin,or(a,b))),or(cin,t1)),
inference(superposition,[],[f294,f50]) ).
fof(f294,plain,
! [X0,X1] : not(or(X1,not(X0))) = and(not(X1),X0),
inference(superposition,[],[f20,f13]) ).
fof(f2105,plain,
! [X0,X1] : or(and(X0,X1),not(or(X0,X1))) = not(xor(X0,X1)),
inference(backward_demodulation,[],[f1562,f2104]) ).
fof(f1562,plain,
! [X0,X1] : xor(not(X0),X1) = or(and(X0,X1),not(or(X0,X1))),
inference(forward_demodulation,[],[f1481,f20]) ).
fof(f1481,plain,
! [X0,X1] : xor(not(X0),X1) = or(and(X0,X1),and(not(X0),not(X1))),
inference(superposition,[],[f22,f13]) ).
fof(f509461,plain,
and(carry,ll1) = or(carry_def,not(or(cin,t1))),
inference(forward_demodulation,[],[f509460,f20]) ).
fof(f509460,plain,
and(carry,ll1) = or(carry_def,and(not(cin),not(t1))),
inference(forward_demodulation,[],[f509459,f9]) ).
fof(f509459,plain,
or(carry_def,and(not(cin),not(t1))) = and(carry,or(cin,not(cin))),
inference(forward_demodulation,[],[f509319,f256359]) ).
fof(f256359,plain,
! [X0] : and(carry,or(cin,X0)) = or(and(cin,carry_def),and(X0,carry)),
inference(backward_demodulation,[],[f256356,f256358]) ).
fof(f256358,plain,
! [X0] : and(carry,or(cin,X0)) = and(carry,or(X0,and(cin,carry_def))),
inference(forward_demodulation,[],[f256331,f255420]) ).
fof(f255420,plain,
! [X0] : and(carry,or(cin,X0)) = or(and(cin,carry_def),and(carry,X0)),
inference(superposition,[],[f726,f254339]) ).
fof(f254339,plain,
and(cin,carry_def) = and(cin,carry),
inference(backward_demodulation,[],[f253815,f254306]) ).
fof(f254306,plain,
carry_def = and(carry_def,carry),
inference(superposition,[],[f19,f254224]) ).
fof(f254224,plain,
carry = or(carry_def,carry),
inference(forward_demodulation,[],[f254223,f5]) ).
fof(f254223,plain,
or(carry,ll0) = or(carry_def,carry),
inference(forward_demodulation,[],[f254167,f1]) ).
fof(f254167,plain,
or(carry,ll0) = or(carry,carry_def),
inference(superposition,[],[f1202,f254074]) ).
fof(f254074,plain,
ll0 = and(not(carry),carry_def),
inference(forward_demodulation,[],[f254022,f10]) ).
fof(f254022,plain,
and(t5,not(t5)) = and(not(carry),carry_def),
inference(superposition,[],[f12633,f253902]) ).
fof(f253902,plain,
not(t5) = and(t1,carry_def),
inference(backward_demodulation,[],[f231626,f253901]) ).
fof(f253901,plain,
not(t5) = and(cin,and(t1,carry_def)),
inference(forward_demodulation,[],[f253900,f100]) ).
fof(f100,plain,
not(t5) = and(cin,t4),
inference(superposition,[],[f2,f42]) ).
fof(f42,plain,
and(t4,cin) = not(t5),
inference(superposition,[],[f13,f31]) ).
fof(f31,axiom,
not(and(t4,cin)) = t5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5) ).
fof(f253900,plain,
and(cin,t4) = and(cin,and(t1,carry_def)),
inference(forward_demodulation,[],[f253813,f2]) ).
fof(f253813,plain,
and(cin,t4) = and(cin,and(carry_def,t1)),
inference(superposition,[],[f16578,f154465]) ).
fof(f154465,plain,
t4 = and(or(a,b),t1),
inference(forward_demodulation,[],[f154464,f13]) ).
fof(f154464,plain,
not(not(t4)) = and(or(a,b),t1),
inference(forward_demodulation,[],[f154417,f13]) ).
fof(f154417,plain,
not(not(t4)) = and(or(a,b),not(not(t1))),
inference(superposition,[],[f291,f102903]) ).
fof(f102903,plain,
not(t4) = or(not(or(a,b)),not(t1)),
inference(backward_demodulation,[],[f43692,f102873]) ).
fof(f102873,plain,
xor(a,b) = t4,
inference(forward_demodulation,[],[f102872,f31824]) ).
fof(f31824,plain,
t4 = or(not(t3),not(t2)),
inference(backward_demodulation,[],[f27028,f31822]) ).
fof(f31822,plain,
t4 = xor(t2,t3),
inference(forward_demodulation,[],[f31821,f13]) ).
fof(f31821,plain,
not(not(t4)) = xor(t2,t3),
inference(forward_demodulation,[],[f31820,f41]) ).
fof(f41,plain,
and(t2,t3) = not(t4),
inference(superposition,[],[f13,f30]) ).
fof(f30,axiom,
not(and(t2,t3)) = t4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4) ).
fof(f31820,plain,
not(and(t2,t3)) = xor(t2,t3),
inference(forward_demodulation,[],[f31819,f23]) ).
fof(f31819,plain,
not(and(t2,t3)) = xor(t3,t2),
inference(forward_demodulation,[],[f31788,f2]) ).
fof(f31788,plain,
xor(t3,t2) = not(and(t3,t2)),
inference(superposition,[],[f1595,f30025]) ).
fof(f30025,plain,
t2 = or(not(t3),t2),
inference(superposition,[],[f917,f26927]) ).
fof(f26927,plain,
not(t3) = and(t2,not(t3)),
inference(superposition,[],[f15758,f2]) ).
fof(f15758,plain,
not(t3) = and(not(t3),t2),
inference(superposition,[],[f294,f15707]) ).
fof(f15707,plain,
t3 = or(t3,not(t2)),
inference(superposition,[],[f8819,f259]) ).
fof(f259,plain,
not(t2) = and(a,not(t2)),
inference(superposition,[],[f232,f2]) ).
fof(f232,plain,
not(t2) = and(not(t2),a),
inference(superposition,[],[f143,f129]) ).
fof(f129,plain,
a = or(a,not(t2)),
inference(superposition,[],[f18,f38]) ).
fof(f38,plain,
and(a,t1) = not(t2),
inference(superposition,[],[f13,f28]) ).
fof(f28,axiom,
not(and(a,t1)) = t2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2) ).
fof(f8819,plain,
! [X0] : t3 = or(t3,and(a,X0)),
inference(forward_demodulation,[],[f8811,f19]) ).
fof(f8811,plain,
! [X0] : and(t3,or(t3,X0)) = or(t3,and(a,X0)),
inference(superposition,[],[f8,f8766]) ).
fof(f8766,plain,
t3 = or(t3,a),
inference(superposition,[],[f122,f8718]) ).
fof(f8718,plain,
a = and(a,t3),
inference(forward_demodulation,[],[f8653,f6]) ).
fof(f8653,plain,
and(a,ll1) = and(a,t3),
inference(superposition,[],[f876,f6709]) ).
fof(f6709,plain,
ll1 = or(not(a),t3),
inference(forward_demodulation,[],[f6636,f14]) ).
fof(f14,axiom,
ll1 = not(ll0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ll0_inverse) ).
fof(f6636,plain,
not(ll0) = or(not(a),t3),
inference(superposition,[],[f370,f614]) ).
fof(f614,plain,
ll0 = and(a,not(t3)),
inference(forward_demodulation,[],[f600,f64]) ).
fof(f600,plain,
and(not(t1),t1) = and(a,not(t3)),
inference(superposition,[],[f532,f39]) ).
fof(f39,plain,
and(b,t1) = not(t3),
inference(superposition,[],[f13,f29]) ).
fof(f29,axiom,
not(and(b,t1)) = t3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3) ).
fof(f532,plain,
! [X0] : and(not(t1),X0) = and(a,and(b,X0)),
inference(superposition,[],[f4,f37]) ).
fof(f876,plain,
! [X0,X1] : and(X0,X1) = and(X0,or(not(X0),X1)),
inference(forward_demodulation,[],[f732,f75]) ).
fof(f732,plain,
! [X0,X1] : or(ll0,and(X0,X1)) = and(X0,or(not(X0),X1)),
inference(superposition,[],[f7,f10]) ).
fof(f122,plain,
! [X0,X1] : or(X0,and(X1,X0)) = X0,
inference(superposition,[],[f18,f2]) ).
fof(f27028,plain,
or(not(t3),not(t2)) = xor(t2,t3),
inference(backward_demodulation,[],[f26962,f26996]) ).
fof(f26996,plain,
not(t2) = and(t3,not(t2)),
inference(superposition,[],[f15763,f2]) ).
fof(f15763,plain,
not(t2) = and(not(t2),t3),
inference(superposition,[],[f143,f15707]) ).
fof(f26962,plain,
or(not(t3),and(t3,not(t2))) = xor(t2,t3),
inference(forward_demodulation,[],[f26935,f23]) ).
fof(f26935,plain,
xor(t3,t2) = or(not(t3),and(t3,not(t2))),
inference(superposition,[],[f22,f15758]) ).
fof(f102872,plain,
xor(a,b) = or(not(t3),not(t2)),
inference(forward_demodulation,[],[f102871,f102482]) ).
fof(f102482,plain,
not(t3) = and(b,not(a)),
inference(forward_demodulation,[],[f102412,f9025]) ).
fof(f9025,plain,
not(t3) = and(not(t3),not(a)),
inference(superposition,[],[f380,f8870]) ).
fof(f8870,plain,
a = and(t3,a),
inference(superposition,[],[f1239,f8802]) ).
fof(f8802,plain,
t3 = or(a,t3),
inference(superposition,[],[f8766,f1]) ).
fof(f1239,plain,
! [X0,X1] : and(or(X0,X1),X0) = X0,
inference(forward_demodulation,[],[f1139,f122]) ).
fof(f1139,plain,
! [X0,X1] : and(or(X0,X1),X0) = or(X0,and(X1,X0)),
inference(superposition,[],[f8,f11]) ).
fof(f380,plain,
! [X0,X1] : not(X0) = and(not(X0),not(and(X0,X1))),
inference(superposition,[],[f19,f21]) ).
fof(f102412,plain,
and(not(t3),not(a)) = and(b,not(a)),
inference(superposition,[],[f536,f5187]) ).
fof(f5187,plain,
not(a) = and(t1,not(a)),
inference(superposition,[],[f291,f3067]) ).
fof(f3067,plain,
a = or(not(t1),a),
inference(superposition,[],[f917,f253]) ).
fof(f253,plain,
not(t1) = and(a,not(t1)),
inference(superposition,[],[f231,f2]) ).
fof(f231,plain,
not(t1) = and(not(t1),a),
inference(superposition,[],[f143,f128]) ).
fof(f128,plain,
a = or(a,not(t1)),
inference(superposition,[],[f18,f37]) ).
fof(f536,plain,
! [X0] : and(not(t3),X0) = and(b,and(t1,X0)),
inference(superposition,[],[f4,f39]) ).
fof(f102871,plain,
xor(a,b) = or(and(b,not(a)),not(t2)),
inference(forward_demodulation,[],[f102825,f2]) ).
fof(f102825,plain,
xor(a,b) = or(and(not(a),b),not(t2)),
inference(superposition,[],[f22,f101638]) ).
fof(f101638,plain,
not(t2) = and(a,not(b)),
inference(forward_demodulation,[],[f101565,f15763]) ).
fof(f101565,plain,
and(not(t2),t3) = and(a,not(b)),
inference(superposition,[],[f533,f16377]) ).
fof(f16377,plain,
not(b) = and(t1,t3),
inference(forward_demodulation,[],[f16347,f5188]) ).
fof(f5188,plain,
not(b) = and(t1,not(b)),
inference(superposition,[],[f291,f3074]) ).
fof(f3074,plain,
b = or(not(t1),b),
inference(superposition,[],[f917,f271]) ).
fof(f271,plain,
not(t1) = and(b,not(t1)),
inference(superposition,[],[f234,f2]) ).
fof(f234,plain,
not(t1) = and(not(t1),b),
inference(superposition,[],[f143,f193]) ).
fof(f193,plain,
b = or(b,not(t1)),
inference(superposition,[],[f122,f37]) ).
fof(f16347,plain,
and(t1,not(b)) = and(t1,t3),
inference(superposition,[],[f876,f15998]) ).
fof(f15998,plain,
t3 = or(not(t1),not(b)),
inference(backward_demodulation,[],[f5258,f15997]) ).
fof(f15997,plain,
t3 = xor(b,t1),
inference(forward_demodulation,[],[f15996,f13]) ).
fof(f15996,plain,
not(not(t3)) = xor(b,t1),
inference(forward_demodulation,[],[f15898,f39]) ).
fof(f15898,plain,
not(and(b,t1)) = xor(b,t1),
inference(superposition,[],[f1595,f6711]) ).
fof(f6711,plain,
t1 = or(not(b),t1),
inference(forward_demodulation,[],[f6638,f13]) ).
fof(f6638,plain,
not(not(t1)) = or(not(b),t1),
inference(superposition,[],[f370,f271]) ).
fof(f5258,plain,
xor(b,t1) = or(not(t1),not(b)),
inference(backward_demodulation,[],[f1578,f5188]) ).
fof(f1578,plain,
or(not(t1),and(t1,not(b))) = xor(b,t1),
inference(forward_demodulation,[],[f1490,f23]) ).
fof(f1490,plain,
xor(t1,b) = or(not(t1),and(t1,not(b))),
inference(superposition,[],[f22,f234]) ).
fof(f533,plain,
! [X0] : and(not(t2),X0) = and(a,and(t1,X0)),
inference(superposition,[],[f4,f38]) ).
fof(f43692,plain,
not(xor(a,b)) = or(not(or(a,b)),not(t1)),
inference(superposition,[],[f2503,f37]) ).
fof(f2503,plain,
! [X0,X1] : or(not(or(X0,X1)),and(X0,X1)) = not(xor(X0,X1)),
inference(backward_demodulation,[],[f1565,f2502]) ).
fof(f2502,plain,
! [X0,X1] : xor(X0,not(X1)) = not(xor(X0,X1)),
inference(forward_demodulation,[],[f2496,f1601]) ).
fof(f1601,plain,
! [X0] : not(X0) = xor(X0,ll1),
inference(forward_demodulation,[],[f1600,f5]) ).
fof(f1600,plain,
! [X0] : or(not(X0),ll0) = xor(X0,ll1),
inference(forward_demodulation,[],[f1599,f17]) ).
fof(f1599,plain,
! [X0] : xor(X0,ll1) = or(not(X0),and(X0,ll0)),
inference(forward_demodulation,[],[f1511,f15]) ).
fof(f1511,plain,
! [X0] : xor(X0,ll1) = or(not(X0),and(X0,not(ll1))),
inference(superposition,[],[f22,f6]) ).
fof(f2496,plain,
! [X0,X1] : not(xor(X0,X1)) = xor(X0,xor(X1,ll1)),
inference(superposition,[],[f1601,f24]) ).
fof(f1565,plain,
! [X0,X1] : xor(X0,not(X1)) = or(not(or(X0,X1)),and(X0,X1)),
inference(forward_demodulation,[],[f1483,f13]) ).
fof(f1483,plain,
! [X0,X1] : xor(X0,not(X1)) = or(not(or(X0,X1)),and(X0,not(not(X1)))),
inference(superposition,[],[f22,f20]) ).
fof(f16578,plain,
! [X0] : and(cin,and(or(a,b),X0)) = and(cin,and(carry_def,X0)),
inference(forward_demodulation,[],[f16577,f501]) ).
fof(f16577,plain,
! [X0] : and(cin,and(or(a,b),X0)) = and(cin,and(carry_def,and(carry_def,X0))),
inference(forward_demodulation,[],[f16527,f4]) ).
fof(f16527,plain,
! [X0] : and(cin,and(or(a,b),X0)) = and(and(cin,carry_def),and(carry_def,X0)),
inference(backward_demodulation,[],[f3701,f16517]) ).
fof(f3701,plain,
! [X0] : and(cin,and(or(a,b),X0)) = and(and(cin,or(a,b)),and(carry_def,X0)),
inference(forward_demodulation,[],[f3693,f4]) ).
fof(f3693,plain,
! [X0] : and(and(cin,or(a,b)),X0) = and(and(cin,or(a,b)),and(carry_def,X0)),
inference(superposition,[],[f4,f215]) ).
fof(f215,plain,
and(cin,or(a,b)) = and(and(cin,or(a,b)),carry_def),
inference(superposition,[],[f19,f50]) ).
fof(f231626,plain,
and(t1,carry_def) = and(cin,and(t1,carry_def)),
inference(superposition,[],[f3236,f231493]) ).
fof(f231493,plain,
cin = or(cin,and(t1,carry_def)),
inference(forward_demodulation,[],[f231446,f2]) ).
fof(f231446,plain,
cin = or(cin,and(carry_def,t1)),
inference(superposition,[],[f118545,f1183]) ).
fof(f1183,plain,
! [X2,X0,X1] : or(X0,and(X1,X2)) = and(or(X0,X2),or(X0,X1)),
inference(superposition,[],[f8,f2]) ).
fof(f118545,plain,
cin = and(or(cin,t1),or(cin,carry_def)),
inference(forward_demodulation,[],[f118544,f19]) ).
fof(f118544,plain,
and(cin,or(cin,t1)) = and(or(cin,t1),or(cin,carry_def)),
inference(forward_demodulation,[],[f118508,f2]) ).
fof(f118508,plain,
and(or(cin,t1),cin) = and(or(cin,t1),or(cin,carry_def)),
inference(superposition,[],[f923,f10767]) ).
fof(f10767,plain,
or(cin,carry_def) = or(cin,not(or(cin,t1))),
inference(superposition,[],[f430,f50]) ).
fof(f3236,plain,
! [X0,X1] : and(or(X1,X0),X0) = X0,
inference(superposition,[],[f1239,f1]) ).
fof(f12633,plain,
! [X0] : and(not(carry),X0) = and(t5,and(t1,X0)),
inference(superposition,[],[f502,f40]) ).
fof(f40,plain,
and(t1,t5) = not(carry),
inference(superposition,[],[f13,f35]) ).
fof(f35,axiom,
not(and(t1,t5)) = carry,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',carry) ).
fof(f1202,plain,
! [X0,X1] : or(X0,X1) = or(X0,and(not(X0),X1)),
inference(forward_demodulation,[],[f1104,f98]) ).
fof(f1104,plain,
! [X0,X1] : and(ll1,or(X0,X1)) = or(X0,and(not(X0),X1)),
inference(superposition,[],[f8,f9]) ).
fof(f253815,plain,
and(cin,carry) = and(cin,and(carry_def,carry)),
inference(superposition,[],[f16578,f171784]) ).
fof(f171784,plain,
carry = and(or(a,b),carry),
inference(superposition,[],[f1239,f134123]) ).
fof(f134123,plain,
or(a,b) = or(carry,not(t6)),
inference(backward_demodulation,[],[f118290,f134119]) ).
fof(f134119,plain,
or(a,b) = or(t4,carry),
inference(forward_demodulation,[],[f134117,f103606]) ).
fof(f103606,plain,
or(a,b) = not(xor(a,t3)),
inference(backward_demodulation,[],[f40749,f103559]) ).
fof(f103559,plain,
or(a,b) = or(a,not(t3)),
inference(superposition,[],[f1246,f102482]) ).
fof(f40749,plain,
or(a,not(t3)) = not(xor(a,t3)),
inference(forward_demodulation,[],[f39764,f8802]) ).
fof(f39764,plain,
not(xor(a,t3)) = or(a,not(or(a,t3))),
inference(superposition,[],[f2105,f8718]) ).
fof(f134117,plain,
or(t4,carry) = not(xor(a,t3)),
inference(backward_demodulation,[],[f118291,f134115]) ).
fof(f134115,plain,
xor(a,t3) = xor(t6,carry),
inference(forward_demodulation,[],[f134112,f123129]) ).
fof(f123129,plain,
xor(a,t3) = or(ll0,and(t1,not(t4))),
inference(backward_demodulation,[],[f7112,f123125]) ).
fof(f123125,plain,
and(t3,not(a)) = and(t1,not(t4)),
inference(forward_demodulation,[],[f123055,f2]) ).
fof(f123055,plain,
and(t3,not(a)) = and(not(t4),t1),
inference(superposition,[],[f12640,f16792]) ).
fof(f16792,plain,
not(a) = and(t2,t1),
inference(forward_demodulation,[],[f16764,f13]) ).
fof(f16764,plain,
not(a) = and(t2,not(not(t1))),
inference(superposition,[],[f291,f16141]) ).
fof(f16141,plain,
a = or(not(t2),not(t1)),
inference(backward_demodulation,[],[f5262,f16139]) ).
fof(f16139,plain,
a = xor(t1,t2),
inference(forward_demodulation,[],[f16138,f13]) ).
fof(f16138,plain,
xor(t1,t2) = not(not(a)),
inference(forward_demodulation,[],[f16112,f5187]) ).
fof(f16112,plain,
xor(t1,t2) = not(and(t1,not(a))),
inference(superposition,[],[f1595,f15994]) ).
fof(f15994,plain,
t2 = or(not(t1),not(a)),
inference(backward_demodulation,[],[f5256,f15993]) ).
fof(f15993,plain,
t2 = xor(a,t1),
inference(forward_demodulation,[],[f15992,f13]) ).
fof(f15992,plain,
not(not(t2)) = xor(a,t1),
inference(forward_demodulation,[],[f15895,f38]) ).
fof(f15895,plain,
not(and(a,t1)) = xor(a,t1),
inference(superposition,[],[f1595,f6707]) ).
fof(f6707,plain,
t1 = or(not(a),t1),
inference(forward_demodulation,[],[f6634,f13]) ).
fof(f6634,plain,
not(not(t1)) = or(not(a),t1),
inference(superposition,[],[f370,f253]) ).
fof(f5256,plain,
xor(a,t1) = or(not(t1),not(a)),
inference(backward_demodulation,[],[f1575,f5187]) ).
fof(f1575,plain,
or(not(t1),and(t1,not(a))) = xor(a,t1),
inference(forward_demodulation,[],[f1487,f23]) ).
fof(f1487,plain,
xor(t1,a) = or(not(t1),and(t1,not(a))),
inference(superposition,[],[f22,f231]) ).
fof(f5262,plain,
xor(t1,t2) = or(not(t2),not(t1)),
inference(backward_demodulation,[],[f1582,f5190]) ).
fof(f5190,plain,
not(t1) = and(t2,not(t1)),
inference(superposition,[],[f291,f3081]) ).
fof(f3081,plain,
t1 = or(not(t2),t1),
inference(superposition,[],[f917,f283]) ).
fof(f283,plain,
not(t2) = and(t1,not(t2)),
inference(superposition,[],[f238,f2]) ).
fof(f238,plain,
not(t2) = and(not(t2),t1),
inference(superposition,[],[f143,f194]) ).
fof(f194,plain,
t1 = or(t1,not(t2)),
inference(superposition,[],[f122,f38]) ).
fof(f1582,plain,
or(not(t2),and(t2,not(t1))) = xor(t1,t2),
inference(forward_demodulation,[],[f1494,f23]) ).
fof(f1494,plain,
xor(t2,t1) = or(not(t2),and(t2,not(t1))),
inference(superposition,[],[f22,f238]) ).
fof(f12640,plain,
! [X0] : and(not(t4),X0) = and(t3,and(t2,X0)),
inference(superposition,[],[f502,f41]) ).
fof(f7112,plain,
xor(a,t3) = or(ll0,and(t3,not(a))),
inference(forward_demodulation,[],[f7101,f23]) ).
fof(f7101,plain,
or(ll0,and(t3,not(a))) = xor(t3,a),
inference(superposition,[],[f22,f7035]) ).
fof(f7035,plain,
ll0 = and(not(t3),a),
inference(forward_demodulation,[],[f7023,f15]) ).
fof(f7023,plain,
not(ll1) = and(not(t3),a),
inference(superposition,[],[f294,f6746]) ).
fof(f6746,plain,
ll1 = or(t3,not(a)),
inference(superposition,[],[f6709,f1]) ).
fof(f134112,plain,
or(ll0,and(t1,not(t4))) = xor(t6,carry),
inference(backward_demodulation,[],[f108621,f134032]) ).
fof(f134032,plain,
and(t1,not(t4)) = and(t6,not(carry)),
inference(superposition,[],[f14075,f16693]) ).
fof(f16693,plain,
not(t4) = and(t5,t6),
inference(forward_demodulation,[],[f16665,f5195]) ).
fof(f5195,plain,
not(t4) = and(t5,not(t4)),
inference(superposition,[],[f291,f3086]) ).
fof(f3086,plain,
t4 = or(not(t5),t4),
inference(superposition,[],[f917,f42]) ).
fof(f16665,plain,
and(t5,not(t4)) = and(t5,t6),
inference(superposition,[],[f876,f16029]) ).
fof(f16029,plain,
t6 = or(not(t5),not(t4)),
inference(backward_demodulation,[],[f5272,f16028]) ).
fof(f16028,plain,
t6 = xor(t5,t4),
inference(forward_demodulation,[],[f16027,f13]) ).
fof(f16027,plain,
not(not(t6)) = xor(t5,t4),
inference(forward_demodulation,[],[f16026,f101]) ).
fof(f101,plain,
not(t6) = and(t5,t4),
inference(superposition,[],[f2,f43]) ).
fof(f43,plain,
and(t4,t5) = not(t6),
inference(superposition,[],[f13,f32]) ).
fof(f32,axiom,
not(and(t4,t5)) = t6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6) ).
fof(f16026,plain,
xor(t5,t4) = not(and(t5,t4)),
inference(forward_demodulation,[],[f16025,f2]) ).
fof(f16025,plain,
not(and(t4,t5)) = xor(t5,t4),
inference(forward_demodulation,[],[f15915,f23]) ).
fof(f15915,plain,
not(and(t4,t5)) = xor(t4,t5),
inference(superposition,[],[f1595,f5427]) ).
fof(f5427,plain,
t5 = or(not(t4),t5),
inference(superposition,[],[f917,f5195]) ).
fof(f5272,plain,
xor(t5,t4) = or(not(t5),not(t4)),
inference(backward_demodulation,[],[f1498,f5195]) ).
fof(f1498,plain,
xor(t5,t4) = or(not(t5),and(t5,not(t4))),
inference(superposition,[],[f22,f242]) ).
fof(f242,plain,
not(t5) = and(not(t5),t4),
inference(superposition,[],[f143,f133]) ).
fof(f133,plain,
t4 = or(t4,not(t5)),
inference(superposition,[],[f18,f42]) ).
fof(f14075,plain,
! [X0] : and(t1,and(t5,X0)) = and(X0,not(carry)),
inference(superposition,[],[f557,f40]) ).
fof(f108621,plain,
xor(t6,carry) = or(ll0,and(t6,not(carry))),
inference(superposition,[],[f1506,f108520]) ).
fof(f108520,plain,
ll0 = and(carry,not(t6)),
inference(forward_demodulation,[],[f108472,f101]) ).
fof(f108472,plain,
ll0 = and(carry,and(t5,t4)),
inference(superposition,[],[f105194,f502]) ).
fof(f105194,plain,
ll0 = and(and(t5,carry),t4),
inference(superposition,[],[f12768,f103709]) ).
fof(f103709,plain,
t4 = and(t1,or(a,b)),
inference(forward_demodulation,[],[f103708,f102948]) ).
fof(f102948,plain,
t4 = xor(b,a),
inference(forward_demodulation,[],[f102947,f31823]) ).
fof(f31823,plain,
t4 = or(not(t2),not(t3)),
inference(backward_demodulation,[],[f27031,f31822]) ).
fof(f27031,plain,
xor(t2,t3) = or(not(t2),not(t3)),
inference(forward_demodulation,[],[f27003,f26927]) ).
fof(f27003,plain,
xor(t2,t3) = or(not(t2),and(t2,not(t3))),
inference(superposition,[],[f22,f15763]) ).
fof(f102947,plain,
xor(b,a) = or(not(t2),not(t3)),
inference(forward_demodulation,[],[f102829,f102482]) ).
fof(f102829,plain,
xor(b,a) = or(not(t2),and(b,not(a))),
inference(superposition,[],[f1506,f101638]) ).
fof(f103708,plain,
xor(b,a) = and(t1,or(a,b)),
inference(forward_demodulation,[],[f103707,f1]) ).
fof(f103707,plain,
xor(b,a) = and(t1,or(b,a)),
inference(forward_demodulation,[],[f103706,f13]) ).
fof(f103706,plain,
and(t1,or(b,a)) = not(not(xor(b,a))),
inference(forward_demodulation,[],[f103705,f2502]) ).
fof(f103705,plain,
and(t1,or(b,a)) = not(xor(b,not(a))),
inference(forward_demodulation,[],[f103704,f17031]) ).
fof(f17031,plain,
! [X0] : and(t1,or(b,X0)) = or(not(t3),and(not(b),X0)),
inference(forward_demodulation,[],[f17007,f16457]) ).
fof(f16457,plain,
! [X0] : and(t1,or(not(t3),X0)) = and(t1,or(b,X0)),
inference(backward_demodulation,[],[f775,f16446]) ).
fof(f16446,plain,
! [X0] : or(not(t3),and(t1,X0)) = and(t1,or(b,X0)),
inference(superposition,[],[f7,f16407]) ).
fof(f16407,plain,
not(t3) = and(t1,b),
inference(forward_demodulation,[],[f16348,f13]) ).
fof(f16348,plain,
not(t3) = and(t1,not(not(b))),
inference(superposition,[],[f291,f15998]) ).
fof(f775,plain,
! [X0] : and(t1,or(not(t3),X0)) = or(not(t3),and(t1,X0)),
inference(superposition,[],[f7,f317]) ).
fof(f317,plain,
not(t3) = and(t1,not(t3)),
inference(superposition,[],[f239,f2]) ).
fof(f239,plain,
not(t3) = and(not(t3),t1),
inference(superposition,[],[f143,f195]) ).
fof(f195,plain,
t1 = or(t1,not(t3)),
inference(superposition,[],[f122,f39]) ).
fof(f17007,plain,
! [X0] : and(t1,or(not(t3),X0)) = or(not(t3),and(not(b),X0)),
inference(superposition,[],[f8,f16411]) ).
fof(f16411,plain,
t1 = or(not(t3),not(b)),
inference(backward_demodulation,[],[f5264,f16410]) ).
fof(f16410,plain,
t1 = xor(b,t3),
inference(forward_demodulation,[],[f16409,f13]) ).
fof(f16409,plain,
not(not(t1)) = xor(b,t3),
inference(backward_demodulation,[],[f15897,f16408]) ).
fof(f16408,plain,
not(t1) = and(b,t3),
inference(forward_demodulation,[],[f16350,f271]) ).
fof(f16350,plain,
and(b,not(t1)) = and(b,t3),
inference(superposition,[],[f923,f15998]) ).
fof(f15897,plain,
xor(b,t3) = not(and(b,t3)),
inference(superposition,[],[f1595,f5317]) ).
fof(f5317,plain,
t3 = or(not(b),t3),
inference(superposition,[],[f917,f5191]) ).
fof(f5191,plain,
not(b) = and(t3,not(b)),
inference(superposition,[],[f291,f3072]) ).
fof(f3072,plain,
b = or(not(t3),b),
inference(superposition,[],[f917,f39]) ).
fof(f5264,plain,
xor(b,t3) = or(not(t3),not(b)),
inference(backward_demodulation,[],[f1577,f5191]) ).
fof(f1577,plain,
or(not(t3),and(t3,not(b))) = xor(b,t3),
inference(forward_demodulation,[],[f1489,f23]) ).
fof(f1489,plain,
xor(t3,b) = or(not(t3),and(t3,not(b))),
inference(superposition,[],[f22,f233]) ).
fof(f233,plain,
not(t3) = and(not(t3),b),
inference(superposition,[],[f143,f130]) ).
fof(f130,plain,
b = or(b,not(t3)),
inference(superposition,[],[f18,f39]) ).
fof(f103704,plain,
not(xor(b,not(a))) = or(not(t3),and(not(b),a)),
inference(forward_demodulation,[],[f103595,f294]) ).
fof(f103595,plain,
not(xor(b,not(a))) = or(not(t3),not(or(b,not(a)))),
inference(superposition,[],[f2105,f102482]) ).
fof(f12768,plain,
! [X0] : ll0 = and(and(t5,carry),and(t1,X0)),
inference(forward_demodulation,[],[f12639,f97]) ).
fof(f12639,plain,
! [X0] : and(ll0,X0) = and(and(t5,carry),and(t1,X0)),
inference(superposition,[],[f502,f8407]) ).
fof(f8407,plain,
ll0 = and(t1,and(t5,carry)),
inference(forward_demodulation,[],[f8294,f13]) ).
fof(f8294,plain,
ll0 = and(t1,and(t5,not(not(carry)))),
inference(superposition,[],[f563,f40]) ).
fof(f1506,plain,
! [X0,X1] : xor(X0,X1) = or(and(X1,not(X0)),and(X0,not(X1))),
inference(superposition,[],[f22,f2]) ).
fof(f118291,plain,
or(t4,carry) = not(xor(t6,carry)),
inference(backward_demodulation,[],[f108846,f118290]) ).
fof(f108846,plain,
or(carry,not(t6)) = not(xor(t6,carry)),
inference(backward_demodulation,[],[f108780,f108805]) ).
fof(f108805,plain,
carry = and(t6,carry),
inference(superposition,[],[f108754,f2]) ).
fof(f108754,plain,
carry = and(carry,t6),
inference(superposition,[],[f143,f108665]) ).
fof(f108665,plain,
t6 = or(t6,carry),
inference(forward_demodulation,[],[f108619,f5]) ).
fof(f108619,plain,
or(t6,ll0) = or(t6,carry),
inference(superposition,[],[f1246,f108520]) ).
fof(f108780,plain,
not(xor(t6,carry)) = or(and(t6,carry),not(t6)),
inference(superposition,[],[f2105,f108665]) ).
fof(f118290,plain,
or(t4,carry) = or(carry,not(t6)),
inference(forward_demodulation,[],[f118244,f1]) ).
fof(f118244,plain,
or(carry,t4) = or(carry,not(t6)),
inference(superposition,[],[f1246,f112019]) ).
fof(f112019,plain,
not(t6) = and(t4,not(carry)),
inference(forward_demodulation,[],[f111940,f108882]) ).
fof(f108882,plain,
not(t6) = and(not(t6),not(carry)),
inference(superposition,[],[f380,f108805]) ).
fof(f111940,plain,
and(not(t6),not(carry)) = and(t4,not(carry)),
inference(superposition,[],[f549,f353]) ).
fof(f353,plain,
not(carry) = and(t5,not(carry)),
inference(superposition,[],[f246,f2]) ).
fof(f246,plain,
not(carry) = and(not(carry),t5),
inference(superposition,[],[f143,f198]) ).
fof(f198,plain,
t5 = or(t5,not(carry)),
inference(superposition,[],[f122,f40]) ).
fof(f549,plain,
! [X0] : and(not(t6),X0) = and(t4,and(t5,X0)),
inference(superposition,[],[f4,f43]) ).
fof(f726,plain,
! [X2,X0,X1] : and(X0,or(X1,X2)) = or(and(X1,X0),and(X0,X2)),
inference(superposition,[],[f7,f2]) ).
fof(f256331,plain,
! [X0] : or(and(cin,carry_def),and(carry,X0)) = and(carry,or(X0,and(cin,carry_def))),
inference(superposition,[],[f1140,f255438]) ).
fof(f255438,plain,
carry = or(and(cin,carry_def),carry),
inference(superposition,[],[f3029,f254339]) ).
fof(f3029,plain,
! [X0,X1] : or(and(X1,X0),X0) = X0,
inference(superposition,[],[f917,f2]) ).
fof(f1140,plain,
! [X2,X0,X1] : or(X0,and(X2,X1)) = and(or(X0,X2),or(X1,X0)),
inference(superposition,[],[f8,f1]) ).
fof(f256356,plain,
! [X0] : or(and(cin,carry_def),and(X0,carry)) = and(carry,or(X0,and(cin,carry_def))),
inference(forward_demodulation,[],[f256329,f2]) ).
fof(f256329,plain,
! [X0] : or(and(cin,carry_def),and(X0,carry)) = and(or(X0,and(cin,carry_def)),carry),
inference(superposition,[],[f1098,f255438]) ).
fof(f1098,plain,
! [X2,X0,X1] : or(X0,and(X1,X2)) = and(or(X1,X0),or(X0,X2)),
inference(superposition,[],[f8,f1]) ).
fof(f509319,plain,
or(carry_def,and(not(cin),not(t1))) = or(and(cin,carry_def),and(not(cin),carry)),
inference(superposition,[],[f178053,f255218]) ).
fof(f255218,plain,
carry = or(carry_def,not(t1)),
inference(superposition,[],[f255164,f1]) ).
fof(f255164,plain,
carry = or(not(t1),carry_def),
inference(forward_demodulation,[],[f255108,f13]) ).
fof(f255108,plain,
not(not(carry)) = or(not(t1),carry_def),
inference(superposition,[],[f370,f254486]) ).
fof(f254486,plain,
not(carry) = and(t1,not(carry_def)),
inference(backward_demodulation,[],[f144061,f254455]) ).
fof(f254455,plain,
not(carry) = and(not(carry),not(carry_def)),
inference(superposition,[],[f380,f254331]) ).
fof(f254331,plain,
carry_def = and(carry,carry_def),
inference(superposition,[],[f1239,f254224]) ).
fof(f144061,plain,
and(t1,not(carry_def)) = and(not(carry),not(carry_def)),
inference(superposition,[],[f541,f142839]) ).
fof(f142839,plain,
not(carry_def) = and(t5,not(carry_def)),
inference(superposition,[],[f291,f142431]) ).
fof(f142431,plain,
carry_def = or(not(t5),carry_def),
inference(superposition,[],[f917,f142275]) ).
fof(f142275,plain,
not(t5) = and(carry_def,not(t5)),
inference(superposition,[],[f135899,f14099]) ).
fof(f14099,plain,
! [X0] : and(t4,and(cin,X0)) = and(X0,not(t5)),
inference(superposition,[],[f557,f42]) ).
fof(f135899,plain,
not(t5) = and(t4,and(cin,carry_def)),
inference(forward_demodulation,[],[f135810,f129210]) ).
fof(f129210,plain,
not(t5) = and(or(a,b),not(t5)),
inference(forward_demodulation,[],[f129125,f100]) ).
fof(f129125,plain,
and(cin,t4) = and(or(a,b),not(t5)),
inference(superposition,[],[f13939,f111090]) ).
fof(f111090,plain,
t4 = and(or(a,b),t4),
inference(superposition,[],[f1239,f110834]) ).
fof(f110834,plain,
or(a,b) = or(t4,b),
inference(forward_demodulation,[],[f110789,f110472]) ).
fof(f110472,plain,
or(a,b) = or(t4,not(t1)),
inference(forward_demodulation,[],[f110467,f102943]) ).
fof(f102943,plain,
or(a,b) = not(xor(b,t2)),
inference(backward_demodulation,[],[f101880,f102942]) ).
fof(f102942,plain,
or(a,b) = or(b,not(t2)),
inference(forward_demodulation,[],[f102827,f1]) ).
fof(f102827,plain,
or(b,a) = or(b,not(t2)),
inference(superposition,[],[f1246,f101638]) ).
fof(f101880,plain,
or(b,not(t2)) = not(xor(b,t2)),
inference(forward_demodulation,[],[f101859,f101832]) ).
fof(f101832,plain,
b = and(b,t2),
inference(superposition,[],[f19,f101749]) ).
fof(f101749,plain,
t2 = or(b,t2),
inference(forward_demodulation,[],[f101748,f5]) ).
fof(f101748,plain,
or(t2,ll0) = or(b,t2),
inference(forward_demodulation,[],[f101698,f1]) ).
fof(f101698,plain,
or(t2,ll0) = or(t2,b),
inference(superposition,[],[f1202,f101636]) ).
fof(f101636,plain,
ll0 = and(not(t2),b),
inference(forward_demodulation,[],[f101563,f614]) ).
fof(f101563,plain,
and(a,not(t3)) = and(not(t2),b),
inference(superposition,[],[f533,f16407]) ).
fof(f101859,plain,
not(xor(b,t2)) = or(and(b,t2),not(t2)),
inference(superposition,[],[f2105,f101749]) ).
fof(f110467,plain,
not(xor(b,t2)) = or(t4,not(t1)),
inference(backward_demodulation,[],[f105417,f110466]) ).
fof(f110466,plain,
xor(b,t2) = xor(t1,t4),
inference(backward_demodulation,[],[f106914,f110463]) ).
fof(f110463,plain,
xor(b,t2) = or(and(t1,not(t4)),ll0),
inference(backward_demodulation,[],[f101752,f110459]) ).
fof(f110459,plain,
and(t2,not(b)) = and(t1,not(t4)),
inference(forward_demodulation,[],[f110391,f2]) ).
fof(f110391,plain,
and(t2,not(b)) = and(not(t4),t1),
inference(superposition,[],[f545,f16957]) ).
fof(f16957,plain,
not(b) = and(t3,t1),
inference(forward_demodulation,[],[f16929,f13]) ).
fof(f16929,plain,
not(b) = and(t3,not(not(t1))),
inference(superposition,[],[f291,f16375]) ).
fof(f16375,plain,
b = or(not(t3),not(t1)),
inference(backward_demodulation,[],[f5266,f16373]) ).
fof(f16373,plain,
b = xor(t1,t3),
inference(forward_demodulation,[],[f16372,f13]) ).
fof(f16372,plain,
not(not(b)) = xor(t1,t3),
inference(forward_demodulation,[],[f16346,f5188]) ).
fof(f16346,plain,
xor(t1,t3) = not(and(t1,not(b))),
inference(superposition,[],[f1595,f15998]) ).
fof(f5266,plain,
xor(t1,t3) = or(not(t3),not(t1)),
inference(backward_demodulation,[],[f1583,f5192]) ).
fof(f5192,plain,
not(t1) = and(t3,not(t1)),
inference(superposition,[],[f291,f3082]) ).
fof(f3082,plain,
t1 = or(not(t3),t1),
inference(superposition,[],[f917,f317]) ).
fof(f1583,plain,
or(not(t3),and(t3,not(t1))) = xor(t1,t3),
inference(forward_demodulation,[],[f1495,f23]) ).
fof(f1495,plain,
xor(t3,t1) = or(not(t3),and(t3,not(t1))),
inference(superposition,[],[f22,f239]) ).
fof(f545,plain,
! [X0] : and(not(t4),X0) = and(t2,and(t3,X0)),
inference(superposition,[],[f4,f41]) ).
fof(f101752,plain,
xor(b,t2) = or(and(t2,not(b)),ll0),
inference(forward_demodulation,[],[f101700,f2]) ).
fof(f101700,plain,
xor(b,t2) = or(and(not(b),t2),ll0),
inference(superposition,[],[f1518,f101636]) ).
fof(f1518,plain,
! [X0,X1] : xor(X0,X1) = or(and(not(X0),X1),and(not(X1),X0)),
inference(superposition,[],[f22,f2]) ).
fof(f106914,plain,
xor(t1,t4) = or(and(t1,not(t4)),ll0),
inference(forward_demodulation,[],[f106913,f23]) ).
fof(f106913,plain,
xor(t4,t1) = or(and(t1,not(t4)),ll0),
inference(forward_demodulation,[],[f106859,f2]) ).
fof(f106859,plain,
xor(t4,t1) = or(and(not(t4),t1),ll0),
inference(superposition,[],[f1518,f106518]) ).
fof(f106518,plain,
ll0 = and(not(t1),t4),
inference(forward_demodulation,[],[f106477,f614]) ).
fof(f106477,plain,
and(a,not(t3)) = and(not(t1),t4),
inference(superposition,[],[f532,f105233]) ).
fof(f105233,plain,
not(t3) = and(b,t4),
inference(forward_demodulation,[],[f105192,f934]) ).
fof(f934,plain,
! [X0] : not(t3) = and(not(t3),or(X0,b)),
inference(forward_demodulation,[],[f809,f917]) ).
fof(f809,plain,
! [X0] : and(not(t3),or(X0,b)) = or(and(not(t3),X0),not(t3)),
inference(superposition,[],[f7,f233]) ).
fof(f105192,plain,
and(b,t4) = and(not(t3),or(a,b)),
inference(superposition,[],[f536,f103709]) ).
fof(f105417,plain,
not(xor(t1,t4)) = or(t4,not(t1)),
inference(forward_demodulation,[],[f105388,f105205]) ).
fof(f105205,plain,
t4 = and(t1,t4),
inference(superposition,[],[f501,f103709]) ).
fof(f105388,plain,
not(xor(t1,t4)) = or(and(t1,t4),not(t1)),
inference(superposition,[],[f2105,f105201]) ).
fof(f105201,plain,
t1 = or(t1,t4),
inference(superposition,[],[f18,f103709]) ).
fof(f110789,plain,
or(t4,b) = or(t4,not(t1)),
inference(superposition,[],[f1246,f110458]) ).
fof(f110458,plain,
not(t1) = and(b,not(t4)),
inference(forward_demodulation,[],[f110457,f5190]) ).
fof(f110457,plain,
and(t2,not(t1)) = and(b,not(t4)),
inference(forward_demodulation,[],[f110390,f2]) ).
fof(f110390,plain,
and(t2,not(t1)) = and(not(t4),b),
inference(superposition,[],[f545,f17028]) ).
fof(f17028,plain,
not(t1) = and(t3,b),
inference(forward_demodulation,[],[f17000,f13]) ).
fof(f17000,plain,
not(t1) = and(t3,not(not(b))),
inference(superposition,[],[f291,f16411]) ).
fof(f13939,plain,
! [X0] : and(X0,not(t5)) = and(cin,and(X0,t4)),
inference(superposition,[],[f557,f42]) ).
fof(f135810,plain,
and(t4,and(cin,carry_def)) = and(or(a,b),not(t5)),
inference(superposition,[],[f14099,f16517]) ).
fof(f541,plain,
! [X0] : and(not(carry),X0) = and(t1,and(t5,X0)),
inference(superposition,[],[f4,f40]) ).
fof(f178053,plain,
! [X0] : or(carry_def,and(not(cin),X0)) = or(and(cin,carry_def),and(not(cin),or(carry_def,X0))),
inference(superposition,[],[f174709,f726]) ).
fof(f174709,plain,
! [X0] : or(carry_def,X0) = or(and(cin,carry_def),or(and(carry_def,not(cin)),X0)),
inference(backward_demodulation,[],[f16521,f174693]) ).
fof(f16521,plain,
! [X0] : or(carry_def,X0) = or(and(cin,carry_def),or(not(or(cin,t1)),X0)),
inference(backward_demodulation,[],[f436,f16517]) ).
fof(f436,plain,
! [X0] : or(and(cin,or(a,b)),or(not(or(cin,t1)),X0)) = or(carry_def,X0),
inference(superposition,[],[f3,f50]) ).
fof(f115795,plain,
carry_def != carry,
inference(trivial_inequality_removal,[],[f115268]) ).
fof(f115268,plain,
( sum_def != sum_def
| carry_def != carry ),
inference(backward_demodulation,[],[f36,f115267]) ).
fof(f115267,plain,
sum_def = sum,
inference(backward_demodulation,[],[f27107,f115266]) ).
fof(f115266,plain,
sum_def = xor(t6,t7),
inference(forward_demodulation,[],[f115265,f13]) ).
fof(f115265,plain,
xor(t6,t7) = not(not(sum_def)),
inference(forward_demodulation,[],[f114883,f113286]) ).
fof(f113286,plain,
not(sum_def) = and(t6,not(sum_def)),
inference(superposition,[],[f291,f113260]) ).
fof(f113260,plain,
sum_def = or(not(t6),sum_def),
inference(superposition,[],[f917,f112790]) ).
fof(f112790,plain,
not(t6) = and(sum_def,t7),
inference(forward_demodulation,[],[f112789,f105322]) ).
fof(f105322,plain,
t6 = xor(t7,sum_def),
inference(forward_demodulation,[],[f105298,f17959]) ).
fof(f17959,plain,
t6 = xor(t4,t5),
inference(forward_demodulation,[],[f17958,f13]) ).
fof(f17958,plain,
not(not(t6)) = xor(t4,t5),
inference(forward_demodulation,[],[f17934,f341]) ).
fof(f341,plain,
not(t6) = and(t4,not(t6)),
inference(superposition,[],[f243,f2]) ).
fof(f243,plain,
not(t6) = and(not(t6),t4),
inference(superposition,[],[f143,f134]) ).
fof(f134,plain,
t4 = or(t4,not(t6)),
inference(superposition,[],[f18,f43]) ).
fof(f17934,plain,
xor(t4,t5) = not(and(t4,not(t6))),
inference(superposition,[],[f1595,f16710]) ).
fof(f16710,plain,
t5 = or(not(t4),not(t6)),
inference(backward_demodulation,[],[f5275,f16708]) ).
fof(f16708,plain,
t5 = xor(t4,t6),
inference(forward_demodulation,[],[f16702,f13]) ).
fof(f16702,plain,
not(not(t5)) = xor(t4,t6),
inference(backward_demodulation,[],[f15916,f16701]) ).
fof(f16701,plain,
not(t5) = and(t4,t6),
inference(forward_demodulation,[],[f16668,f335]) ).
fof(f335,plain,
not(t5) = and(t4,not(t5)),
inference(superposition,[],[f242,f2]) ).
fof(f16668,plain,
and(t4,not(t5)) = and(t4,t6),
inference(superposition,[],[f923,f16029]) ).
fof(f15916,plain,
xor(t4,t6) = not(and(t4,t6)),
inference(superposition,[],[f1595,f5624]) ).
fof(f5624,plain,
t6 = or(not(t4),t6),
inference(superposition,[],[f917,f5197]) ).
fof(f5197,plain,
not(t4) = and(t6,not(t4)),
inference(superposition,[],[f291,f3087]) ).
fof(f3087,plain,
t4 = or(not(t6),t4),
inference(superposition,[],[f917,f43]) ).
fof(f5275,plain,
xor(t4,t6) = or(not(t4),not(t6)),
inference(backward_demodulation,[],[f1661,f5197]) ).
fof(f1661,plain,
xor(t4,t6) = or(and(t6,not(t4)),not(t6)),
inference(forward_demodulation,[],[f1541,f2]) ).
fof(f1541,plain,
xor(t4,t6) = or(and(not(t4),t6),not(t6)),
inference(superposition,[],[f22,f341]) ).
fof(f105298,plain,
xor(t4,t5) = xor(t7,sum_def),
inference(superposition,[],[f102884,f17440]) ).
fof(f17440,plain,
t5 = xor(t7,cin),
inference(forward_demodulation,[],[f17439,f13]) ).
fof(f17439,plain,
not(not(t5)) = xor(t7,cin),
inference(forward_demodulation,[],[f17413,f5199]) ).
fof(f5199,plain,
not(t5) = and(t7,not(t5)),
inference(superposition,[],[f291,f3090]) ).
fof(f3090,plain,
t5 = or(not(t7),t5),
inference(superposition,[],[f917,f44]) ).
fof(f44,plain,
and(t5,cin) = not(t7),
inference(superposition,[],[f13,f33]) ).
fof(f33,axiom,
not(and(t5,cin)) = t7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7) ).
fof(f17413,plain,
xor(t7,cin) = not(and(t7,not(t5))),
inference(superposition,[],[f1595,f17278]) ).
fof(f17278,plain,
cin = or(not(t7),not(t5)),
inference(backward_demodulation,[],[f5280,f17276]) ).
fof(f17276,plain,
cin = xor(t5,t7),
inference(forward_demodulation,[],[f17275,f13]) ).
fof(f17275,plain,
xor(t5,t7) = not(not(cin)),
inference(forward_demodulation,[],[f17249,f5196]) ).
fof(f5196,plain,
not(cin) = and(t5,not(cin)),
inference(superposition,[],[f291,f3075]) ).
fof(f3075,plain,
cin = or(not(t5),cin),
inference(superposition,[],[f917,f100]) ).
fof(f17249,plain,
xor(t5,t7) = not(and(t5,not(cin))),
inference(superposition,[],[f1595,f16002]) ).
fof(f16002,plain,
t7 = or(not(t5),not(cin)),
inference(backward_demodulation,[],[f5274,f16001]) ).
fof(f16001,plain,
t7 = xor(cin,t5),
inference(forward_demodulation,[],[f16000,f13]) ).
fof(f16000,plain,
not(not(t7)) = xor(cin,t5),
inference(forward_demodulation,[],[f15899,f102]) ).
fof(f102,plain,
not(t7) = and(cin,t5),
inference(superposition,[],[f2,f44]) ).
fof(f15899,plain,
xor(cin,t5) = not(and(cin,t5)),
inference(superposition,[],[f1595,f6712]) ).
fof(f6712,plain,
t5 = or(not(cin),t5),
inference(forward_demodulation,[],[f6639,f13]) ).
fof(f6639,plain,
not(not(t5)) = or(not(cin),t5),
inference(superposition,[],[f370,f401]) ).
fof(f401,plain,
not(t5) = and(cin,not(t5)),
inference(superposition,[],[f235,f2]) ).
fof(f235,plain,
not(t5) = and(not(t5),cin),
inference(superposition,[],[f143,f139]) ).
fof(f139,plain,
cin = or(cin,not(t5)),
inference(superposition,[],[f18,f100]) ).
fof(f5274,plain,
xor(cin,t5) = or(not(t5),not(cin)),
inference(backward_demodulation,[],[f1579,f5196]) ).
fof(f1579,plain,
or(not(t5),and(t5,not(cin))) = xor(cin,t5),
inference(forward_demodulation,[],[f1491,f23]) ).
fof(f1491,plain,
xor(t5,cin) = or(not(t5),and(t5,not(cin))),
inference(superposition,[],[f22,f235]) ).
fof(f5280,plain,
xor(t5,t7) = or(not(t7),not(t5)),
inference(backward_demodulation,[],[f1585,f5199]) ).
fof(f1585,plain,
or(not(t7),and(t7,not(t5))) = xor(t5,t7),
inference(forward_demodulation,[],[f1500,f23]) ).
fof(f1500,plain,
xor(t7,t5) = or(not(t7),and(t7,not(t5))),
inference(superposition,[],[f22,f244]) ).
fof(f244,plain,
not(t7) = and(not(t7),t5),
inference(superposition,[],[f143,f135]) ).
fof(f135,plain,
t5 = or(t5,not(t7)),
inference(superposition,[],[f18,f44]) ).
fof(f102884,plain,
! [X0] : xor(X0,sum_def) = xor(t4,xor(X0,cin)),
inference(backward_demodulation,[],[f15351,f102873]) ).
fof(f15351,plain,
! [X0] : xor(X0,sum_def) = xor(xor(a,b),xor(X0,cin)),
inference(superposition,[],[f635,f170]) ).
fof(f170,plain,
sum_def = xor(cin,xor(a,b)),
inference(superposition,[],[f23,f25]) ).
fof(f25,axiom,
xor(xor(a,b),cin) = sum_def,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_def) ).
fof(f635,plain,
! [X2,X0,X1] : xor(X0,xor(X1,X2)) = xor(X2,xor(X0,X1)),
inference(superposition,[],[f24,f23]) ).
fof(f112789,plain,
and(sum_def,t7) = not(xor(t7,sum_def)),
inference(forward_demodulation,[],[f112788,f75]) ).
fof(f112788,plain,
not(xor(t7,sum_def)) = or(ll0,and(sum_def,t7)),
inference(forward_demodulation,[],[f112787,f15]) ).
fof(f112787,plain,
not(xor(t7,sum_def)) = or(not(ll1),and(sum_def,t7)),
inference(forward_demodulation,[],[f112742,f2]) ).
fof(f112742,plain,
not(xor(t7,sum_def)) = or(not(ll1),and(t7,sum_def)),
inference(superposition,[],[f2503,f112603]) ).
fof(f112603,plain,
ll1 = or(t7,sum_def),
inference(superposition,[],[f478,f112465]) ).
fof(f112465,plain,
sum_def = or(not(t7),sum_def),
inference(superposition,[],[f917,f112281]) ).
fof(f112281,plain,
not(t7) = and(sum_def,t6),
inference(forward_demodulation,[],[f112280,f105122]) ).
fof(f105122,plain,
t7 = xor(sum_def,t6),
inference(superposition,[],[f105111,f23]) ).
fof(f105111,plain,
t7 = xor(t6,sum_def),
inference(forward_demodulation,[],[f105074,f16001]) ).
fof(f105074,plain,
xor(cin,t5) = xor(t6,sum_def),
inference(superposition,[],[f102882,f17812]) ).
fof(f17812,plain,
t5 = xor(t6,t4),
inference(forward_demodulation,[],[f17811,f13]) ).
fof(f17811,plain,
not(not(t5)) = xor(t6,t4),
inference(forward_demodulation,[],[f17785,f5198]) ).
fof(f5198,plain,
not(t5) = and(t6,not(t5)),
inference(superposition,[],[f291,f3091]) ).
fof(f3091,plain,
t5 = or(not(t6),t5),
inference(superposition,[],[f917,f101]) ).
fof(f17785,plain,
xor(t6,t4) = not(and(t6,not(t5))),
inference(superposition,[],[f1595,f16691]) ).
fof(f16691,plain,
t4 = or(not(t6),not(t5)),
inference(backward_demodulation,[],[f5278,f16689]) ).
fof(f16689,plain,
t4 = xor(t5,t6),
inference(forward_demodulation,[],[f16688,f13]) ).
fof(f16688,plain,
not(not(t4)) = xor(t5,t6),
inference(forward_demodulation,[],[f16664,f5195]) ).
fof(f16664,plain,
xor(t5,t6) = not(and(t5,not(t4))),
inference(superposition,[],[f1595,f16029]) ).
fof(f5278,plain,
xor(t5,t6) = or(not(t6),not(t5)),
inference(backward_demodulation,[],[f1587,f5198]) ).
fof(f1587,plain,
or(not(t6),and(t6,not(t5))) = xor(t5,t6),
inference(forward_demodulation,[],[f1502,f23]) ).
fof(f1502,plain,
xor(t6,t5) = or(not(t6),and(t6,not(t5))),
inference(superposition,[],[f22,f245]) ).
fof(f245,plain,
not(t6) = and(not(t6),t5),
inference(superposition,[],[f143,f140]) ).
fof(f140,plain,
t5 = or(t5,not(t6)),
inference(superposition,[],[f18,f101]) ).
fof(f102882,plain,
! [X0] : xor(X0,sum_def) = xor(cin,xor(X0,t4)),
inference(backward_demodulation,[],[f15344,f102873]) ).
fof(f15344,plain,
! [X0] : xor(X0,sum_def) = xor(cin,xor(X0,xor(a,b))),
inference(superposition,[],[f635,f25]) ).
fof(f112280,plain,
and(sum_def,t6) = not(xor(sum_def,t6)),
inference(forward_demodulation,[],[f112279,f5]) ).
fof(f112279,plain,
not(xor(sum_def,t6)) = or(and(sum_def,t6),ll0),
inference(forward_demodulation,[],[f112235,f15]) ).
fof(f112235,plain,
not(xor(sum_def,t6)) = or(and(sum_def,t6),not(ll1)),
inference(superposition,[],[f2105,f112148]) ).
fof(f112148,plain,
ll1 = or(sum_def,t6),
inference(forward_demodulation,[],[f112147,f9]) ).
fof(f112147,plain,
or(t6,not(t6)) = or(sum_def,t6),
inference(forward_demodulation,[],[f112095,f1]) ).
fof(f112095,plain,
or(t6,not(t6)) = or(t6,sum_def),
inference(superposition,[],[f1202,f112015]) ).
fof(f112015,plain,
not(t6) = and(not(t6),sum_def),
inference(backward_demodulation,[],[f102938,f112014]) ).
fof(f112014,plain,
not(t6) = and(t4,not(cin)),
inference(forward_demodulation,[],[f111936,f9037]) ).
fof(f9037,plain,
not(t6) = and(not(t6),not(cin)),
inference(superposition,[],[f380,f8979]) ).
fof(f8979,plain,
cin = and(t6,cin),
inference(superposition,[],[f1239,f8822]) ).
fof(f8822,plain,
t6 = or(cin,t6),
inference(superposition,[],[f8776,f1]) ).
fof(f8776,plain,
t6 = or(t6,cin),
inference(superposition,[],[f122,f8719]) ).
fof(f8719,plain,
cin = and(cin,t6),
inference(forward_demodulation,[],[f8654,f6]) ).
fof(f8654,plain,
and(cin,ll1) = and(cin,t6),
inference(superposition,[],[f876,f8500]) ).
fof(f8500,plain,
ll1 = or(not(cin),t6),
inference(forward_demodulation,[],[f8489,f14]) ).
fof(f8489,plain,
not(ll0) = or(not(cin),t6),
inference(superposition,[],[f370,f8403]) ).
fof(f8403,plain,
ll0 = and(cin,not(t6)),
inference(forward_demodulation,[],[f8402,f101]) ).
fof(f8402,plain,
ll0 = and(cin,and(t5,t4)),
inference(forward_demodulation,[],[f8401,f2]) ).
fof(f8401,plain,
ll0 = and(cin,and(t4,t5)),
inference(forward_demodulation,[],[f8290,f13]) ).
fof(f8290,plain,
ll0 = and(cin,and(t4,not(not(t5)))),
inference(superposition,[],[f563,f100]) ).
fof(f111936,plain,
and(not(t6),not(cin)) = and(t4,not(cin)),
inference(superposition,[],[f549,f5196]) ).
fof(f102938,plain,
and(t4,not(cin)) = and(and(t4,not(cin)),sum_def),
inference(forward_demodulation,[],[f102898,f2]) ).
fof(f102898,plain,
and(not(cin),t4) = and(and(not(cin),t4),sum_def),
inference(backward_demodulation,[],[f39037,f102873]) ).
fof(f39037,plain,
and(not(cin),xor(a,b)) = and(and(not(cin),xor(a,b)),sum_def),
inference(superposition,[],[f1554,f170]) ).
fof(f1554,plain,
! [X0,X1] : and(not(X0),X1) = and(and(not(X0),X1),xor(X0,X1)),
inference(superposition,[],[f19,f22]) ).
fof(f478,plain,
! [X0,X1] : ll1 = or(X0,or(not(X0),X1)),
inference(forward_demodulation,[],[f434,f76]) ).
fof(f76,plain,
! [X0] : ll1 = or(ll1,X0),
inference(superposition,[],[f1,f16]) ).
fof(f16,axiom,
! [X0] : ll1 = or(X0,ll1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_boundedness) ).
fof(f434,plain,
! [X0,X1] : or(ll1,X1) = or(X0,or(not(X0),X1)),
inference(superposition,[],[f3,f9]) ).
fof(f114883,plain,
xor(t6,t7) = not(and(t6,not(sum_def))),
inference(superposition,[],[f1595,f113331]) ).
fof(f113331,plain,
t7 = or(not(t6),not(sum_def)),
inference(backward_demodulation,[],[f112139,f113286]) ).
fof(f112139,plain,
t7 = or(not(t6),and(t6,not(sum_def))),
inference(forward_demodulation,[],[f112089,f105111]) ).
fof(f112089,plain,
xor(t6,sum_def) = or(not(t6),and(t6,not(sum_def))),
inference(superposition,[],[f22,f112015]) ).
fof(f27107,plain,
sum = xor(t6,t7),
inference(forward_demodulation,[],[f27106,f13]) ).
fof(f27106,plain,
not(not(sum)) = xor(t6,t7),
inference(forward_demodulation,[],[f27105,f45]) ).
fof(f45,plain,
and(t6,t7) = not(sum),
inference(superposition,[],[f13,f34]) ).
fof(f34,axiom,
not(and(t6,t7)) = sum,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum) ).
fof(f27105,plain,
not(and(t6,t7)) = xor(t6,t7),
inference(forward_demodulation,[],[f27104,f23]) ).
fof(f27104,plain,
not(and(t6,t7)) = xor(t7,t6),
inference(forward_demodulation,[],[f27077,f2]) ).
fof(f27077,plain,
xor(t7,t6) = not(and(t7,t6)),
inference(superposition,[],[f1595,f27066]) ).
fof(f27066,plain,
t6 = or(not(t7),t6),
inference(superposition,[],[f917,f23600]) ).
fof(f23600,plain,
not(t7) = and(t6,not(t7)),
inference(superposition,[],[f13765,f2]) ).
fof(f13765,plain,
not(t7) = and(not(t7),t6),
inference(superposition,[],[f294,f13677]) ).
fof(f13677,plain,
t7 = or(t7,not(t6)),
inference(superposition,[],[f8799,f341]) ).
fof(f8799,plain,
! [X0] : t7 = or(t7,and(t4,X0)),
inference(forward_demodulation,[],[f8791,f19]) ).
fof(f8791,plain,
! [X0] : and(t7,or(t7,X0)) = or(t7,and(t4,X0)),
inference(superposition,[],[f8,f8756]) ).
fof(f8756,plain,
t7 = or(t7,t4),
inference(superposition,[],[f122,f8720]) ).
fof(f8720,plain,
t4 = and(t4,t7),
inference(forward_demodulation,[],[f8655,f6]) ).
fof(f8655,plain,
and(t4,ll1) = and(t4,t7),
inference(superposition,[],[f876,f8481]) ).
fof(f8481,plain,
ll1 = or(not(t4),t7),
inference(forward_demodulation,[],[f8470,f14]) ).
fof(f8470,plain,
not(ll0) = or(not(t4),t7),
inference(superposition,[],[f370,f8417]) ).
fof(f8417,plain,
ll0 = and(t4,not(t7)),
inference(forward_demodulation,[],[f8416,f102]) ).
fof(f8416,plain,
ll0 = and(t4,and(cin,t5)),
inference(forward_demodulation,[],[f8302,f13]) ).
fof(f8302,plain,
ll0 = and(t4,and(cin,not(not(t5)))),
inference(superposition,[],[f563,f42]) ).
fof(f36,axiom,
( carry_def != carry
| sum_def != sum ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_circuit) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HWV003-2 : TPTP v8.1.2. Released v2.7.0.
% 0.14/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 05:14:50 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.36 % (22876)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37 % (22879)WARNING: value z3 for option sas not known
% 0.20/0.37 % (22878)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.37 % (22880)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37 % (22877)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.37 % (22879)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)
% 0.20/0.37 % (22881)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)
% 0.20/0.37 % (22882)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)
% 0.20/0.37 % (22883)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)
% 0.20/0.38 TRYING [1]
% 0.20/0.38 TRYING [2]
% 0.20/0.38 TRYING [1]
% 0.20/0.38 TRYING [2]
% 0.20/0.39 TRYING [3]
% 0.20/0.41 TRYING [3]
% 0.20/0.42 TRYING [4]
% 0.20/0.48 TRYING [4]
% 0.20/0.52 TRYING [5]
% 2.20/0.69 TRYING [5]
% 5.66/1.16 TRYING [6]
% 7.75/1.48 TRYING [1]
% 7.75/1.48 TRYING [2]
% 7.93/1.48 TRYING [3]
% 7.93/1.50 TRYING [4]
% 8.36/1.57 TRYING [5]
% 10.04/1.80 TRYING [6]
% 14.12/2.42 TRYING [7]
% 20.32/3.28 TRYING [6]
% 22.65/3.61 TRYING [7]
% 23.93/3.82 TRYING [8]
% 58.89/8.78 TRYING [9]
% 119.18/17.45 TRYING [10]
% 123.18/18.02 TRYING [8]
% 145.66/21.29 % (22882)First to succeed.
% 146.10/21.33 % (22882)Refutation found. Thanks to Tanya!
% 146.10/21.33 % SZS status Unsatisfiable for theBenchmark
% 146.10/21.33 % SZS output start Proof for theBenchmark
% See solution above
% 146.10/21.33 % (22882)------------------------------
% 146.10/21.33 % (22882)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 146.10/21.33 % (22882)Termination reason: Refutation
% 146.10/21.33
% 146.10/21.33 % (22882)Memory used [KB]: 202621
% 146.10/21.33 % (22882)Time elapsed: 20.924 s
% 146.10/21.33 % (22882)Instructions burned: 35681 (million)
% 146.10/21.33 % (22882)------------------------------
% 146.10/21.33 % (22882)------------------------------
% 146.10/21.33 % (22876)Success in time 20.957 s
%------------------------------------------------------------------------------