TSTP Solution File: BOO015-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : BOO015-1 : TPTP v8.2.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n018.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 18:58:50 EDT 2024
% Result : Unsatisfiable 85.06s 12.58s
% Output : Refutation 85.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 35
% Syntax : Number of formulae : 180 ( 126 unt; 0 def)
% Number of atoms : 297 ( 22 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 266 ( 149 ~; 105 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 341 ( 341 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f974417,plain,
$false,
inference(subsumption_resolution,[],[f974372,f189703]) ).
fof(f189703,plain,
sum(multiply(x_times_y,inverse(y)),additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f76,f158243,f28]) ).
fof(f28,plain,
! [X3,X0,X1,X6,X4] :
( ~ product(X0,X1,X3)
| sum(X3,X4,X6)
| sP1(X4,X0,X6,X1) ),
inference(cnf_transformation,[],[f28_D]) ).
fof(f28_D,plain,
! [X1,X6,X0,X4] :
( ! [X3] :
( ~ product(X0,X1,X3)
| sum(X3,X4,X6) )
<=> ~ sP1(X4,X0,X6,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP1])]) ).
fof(f158243,plain,
~ sP1(additive_identity,inverse(y),additive_identity,x_times_y),
inference(forward_demodulation,[],[f158242,f327]) ).
fof(f327,plain,
! [X0] : additive_identity = multiply(X0,inverse(X0)),
inference(unit_resulting_resolution,[],[f76,f19,f22]) ).
fof(f22,axiom,
! [X0,X1,X8,X7] :
( ~ product(X0,X1,X8)
| X7 = X8
| ~ product(X0,X1,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
fof(f19,axiom,
! [X0] : product(inverse(X0),X0,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse1) ).
fof(f158242,plain,
~ sP1(additive_identity,inverse(y),multiply(y,inverse(y)),x_times_y),
inference(unit_resulting_resolution,[],[f76,f60652,f29]) ).
fof(f29,plain,
! [X0,X1,X6,X4,X5] :
( ~ sP1(X4,X0,X6,X1)
| ~ sP0(X5,X0,X4,X1)
| ~ product(X0,X5,X6) ),
inference(general_splitting,[],[f27,f28_D]) ).
fof(f27,plain,
! [X3,X0,X1,X6,X4,X5] :
( ~ product(X0,X1,X3)
| ~ product(X0,X5,X6)
| sum(X3,X4,X6)
| ~ sP0(X5,X0,X4,X1) ),
inference(general_splitting,[],[f9,f26_D]) ).
fof(f26,plain,
! [X2,X0,X1,X4,X5] :
( ~ product(X0,X2,X4)
| ~ sum(X1,X2,X5)
| sP0(X5,X0,X4,X1) ),
inference(cnf_transformation,[],[f26_D]) ).
fof(f26_D,plain,
! [X1,X4,X0,X5] :
( ! [X2] :
( ~ product(X0,X2,X4)
| ~ sum(X1,X2,X5) )
<=> ~ sP0(X5,X0,X4,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP0])]) ).
fof(f9,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X0,X1,X3)
| ~ product(X0,X5,X6)
| ~ sum(X1,X2,X5)
| ~ product(X0,X2,X4)
| sum(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f60652,plain,
sP0(y,inverse(y),additive_identity,x_times_y),
inference(unit_resulting_resolution,[],[f60458,f538]) ).
fof(f538,plain,
! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sP0(X2,inverse(X1),additive_identity,X0) ),
inference(resolution,[],[f26,f19]) ).
fof(f60458,plain,
sum(x_times_y,y,y),
inference(unit_resulting_resolution,[],[f59638,f566]) ).
fof(f566,plain,
! [X0,X1] :
( sP1(X0,y,X1,x)
| sum(x_times_y,X0,X1) ),
inference(resolution,[],[f28,f79]) ).
fof(f79,plain,
product(y,x,x_times_y),
inference(unit_resulting_resolution,[],[f23,f4]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| product(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiplication) ).
fof(f23,axiom,
product(x,y,x_times_y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_times_y) ).
fof(f59638,plain,
! [X0] : ~ sP1(X0,X0,X0,x),
inference(forward_demodulation,[],[f59625,f322]) ).
fof(f322,plain,
! [X0] : multiply(multiplicative_identity,X0) = X0,
inference(unit_resulting_resolution,[],[f2,f7,f22]) ).
fof(f7,axiom,
! [X0] : product(multiplicative_identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity1) ).
fof(f2,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f59625,plain,
! [X0] : ~ sP1(X0,X0,multiply(multiplicative_identity,X0),x),
inference(unit_resulting_resolution,[],[f76,f58712,f29]) ).
fof(f58712,plain,
! [X0] : sP0(multiplicative_identity,X0,X0,x),
inference(superposition,[],[f484,f58579]) ).
fof(f58579,plain,
multiplicative_identity = add(multiplicative_identity,x),
inference(forward_demodulation,[],[f58482,f27178]) ).
fof(f27178,plain,
multiplicative_identity = add(x,x_inverse_plus_y_inverse),
inference(unit_resulting_resolution,[],[f8,f18109,f22]) ).
fof(f18109,plain,
product(add(x,x_inverse_plus_y_inverse),multiplicative_identity,multiplicative_identity),
inference(forward_demodulation,[],[f18106,f120]) ).
fof(f120,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(unit_resulting_resolution,[],[f1,f60,f21]) ).
fof(f21,axiom,
! [X0,X1,X8,X7] :
( ~ sum(X0,X1,X8)
| X7 = X8
| ~ sum(X0,X1,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f60,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(unit_resulting_resolution,[],[f1,f3]) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
fof(f1,axiom,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f18106,plain,
product(add(x_inverse_plus_y_inverse,x),multiplicative_identity,multiplicative_identity),
inference(unit_resulting_resolution,[],[f60,f18100,f44]) ).
fof(f44,plain,
! [X3,X0,X1,X6,X4] :
( ~ sum(X0,X1,X3)
| product(X3,X4,X6)
| sP9(X4,X0,X6,X1) ),
inference(cnf_transformation,[],[f44_D]) ).
fof(f44_D,plain,
! [X1,X6,X0,X4] :
( ! [X3] :
( ~ sum(X0,X1,X3)
| product(X3,X4,X6) )
<=> ~ sP9(X4,X0,X6,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP9])]) ).
fof(f18100,plain,
~ sP9(multiplicative_identity,x,multiplicative_identity,x_inverse_plus_y_inverse),
inference(unit_resulting_resolution,[],[f18,f17663,f45]) ).
fof(f45,plain,
! [X0,X1,X6,X4,X5] :
( ~ sP9(X4,X0,X6,X1)
| ~ sP8(X5,X0,X4,X1)
| ~ sum(X0,X5,X6) ),
inference(general_splitting,[],[f43,f44_D]) ).
fof(f43,plain,
! [X3,X0,X1,X6,X4,X5] :
( ~ sum(X0,X1,X3)
| ~ sum(X0,X5,X6)
| product(X3,X4,X6)
| ~ sP8(X5,X0,X4,X1) ),
inference(general_splitting,[],[f13,f42_D]) ).
fof(f42,plain,
! [X2,X0,X1,X4,X5] :
( ~ product(X1,X2,X5)
| ~ sum(X0,X2,X4)
| sP8(X5,X0,X4,X1) ),
inference(cnf_transformation,[],[f42_D]) ).
fof(f42_D,plain,
! [X1,X4,X0,X5] :
( ! [X2] :
( ~ product(X1,X2,X5)
| ~ sum(X0,X2,X4) )
<=> ~ sP8(X5,X0,X4,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP8])]) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sum(X0,X1,X3)
| ~ sum(X0,X5,X6)
| ~ product(X1,X2,X5)
| ~ sum(X0,X2,X4)
| product(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity5) ).
fof(f17663,plain,
sP8(inverse(x),x,multiplicative_identity,x_inverse_plus_y_inverse),
inference(unit_resulting_resolution,[],[f18,f17448,f42]) ).
fof(f17448,plain,
product(x_inverse_plus_y_inverse,inverse(x),inverse(x)),
inference(unit_resulting_resolution,[],[f16997,f2889]) ).
fof(f2889,plain,
! [X0,X1] :
( sP9(X0,inverse(x),X1,inverse(y))
| product(x_inverse_plus_y_inverse,X0,X1) ),
inference(resolution,[],[f44,f24]) ).
fof(f24,axiom,
sum(inverse(x),inverse(y),x_inverse_plus_y_inverse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_inverse_plus_y_inverse) ).
fof(f16997,plain,
! [X0,X1] : ~ sP9(X0,X0,X0,X1),
inference(forward_demodulation,[],[f16514,f119]) ).
fof(f119,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(unit_resulting_resolution,[],[f6,f60,f21]) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
fof(f16514,plain,
! [X0,X1] : ~ sP9(X0,X0,add(additive_identity,X0),X1),
inference(unit_resulting_resolution,[],[f60,f6960,f45]) ).
fof(f6960,plain,
! [X0,X1] : sP8(additive_identity,X1,X1,X0),
inference(superposition,[],[f2626,f6776]) ).
fof(f6776,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(unit_resulting_resolution,[],[f6,f5486,f21]) ).
fof(f5486,plain,
! [X0] : sum(multiply(X0,additive_identity),additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f2,f5345,f28]) ).
fof(f5345,plain,
! [X0] : ~ sP1(additive_identity,X0,additive_identity,additive_identity),
inference(forward_demodulation,[],[f5344,f327]) ).
fof(f5344,plain,
! [X0] : ~ sP1(additive_identity,X0,multiply(X0,inverse(X0)),additive_identity),
inference(forward_demodulation,[],[f5133,f311]) ).
fof(f311,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(unit_resulting_resolution,[],[f2,f76,f22]) ).
fof(f5133,plain,
! [X0] : ~ sP1(additive_identity,X0,multiply(inverse(X0),X0),additive_identity),
inference(unit_resulting_resolution,[],[f76,f486,f29]) ).
fof(f486,plain,
! [X0] : sP0(inverse(X0),X0,additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f5,f20,f26]) ).
fof(f20,axiom,
! [X0] : product(X0,inverse(X0),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse2) ).
fof(f5,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
fof(f2626,plain,
! [X0,X1] : sP8(multiply(X0,additive_identity),X1,X1,X0),
inference(unit_resulting_resolution,[],[f6,f2,f42]) ).
fof(f18,axiom,
! [X0] : sum(X0,inverse(X0),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse2) ).
fof(f8,axiom,
! [X0] : product(X0,multiplicative_identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity2) ).
fof(f58482,plain,
add(multiplicative_identity,x) = add(x,x_inverse_plus_y_inverse),
inference(unit_resulting_resolution,[],[f28233,f145]) ).
fof(f145,plain,
! [X2,X0,X1] :
( ~ sum(X2,X1,X0)
| add(X1,X2) = X0 ),
inference(resolution,[],[f21,f60]) ).
fof(f28233,plain,
sum(x_inverse_plus_y_inverse,x,add(multiplicative_identity,x)),
inference(forward_demodulation,[],[f28232,f120]) ).
fof(f28232,plain,
sum(x_inverse_plus_y_inverse,x,add(x,multiplicative_identity)),
inference(forward_demodulation,[],[f28231,f323]) ).
fof(f323,plain,
! [X0] : multiply(X0,multiplicative_identity) = X0,
inference(unit_resulting_resolution,[],[f76,f7,f22]) ).
fof(f28231,plain,
sum(x_inverse_plus_y_inverse,x,multiply(add(x,multiplicative_identity),multiplicative_identity)),
inference(unit_resulting_resolution,[],[f3423,f27422,f49]) ).
fof(f49,plain,
! [X0,X1,X6,X4,X5] :
( ~ sP11(X4,X0,X6,X1)
| ~ sP10(X4,X0,X5,X1)
| sum(X5,X0,X6) ),
inference(general_splitting,[],[f47,f48_D]) ).
fof(f48,plain,
! [X3,X0,X1,X6,X4] :
( ~ product(X3,X4,X6)
| ~ sum(X1,X0,X3)
| sP11(X4,X0,X6,X1) ),
inference(cnf_transformation,[],[f48_D]) ).
fof(f48_D,plain,
! [X1,X6,X0,X4] :
( ! [X3] :
( ~ product(X3,X4,X6)
| ~ sum(X1,X0,X3) )
<=> ~ sP11(X4,X0,X6,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP11])]) ).
fof(f47,plain,
! [X3,X0,X1,X6,X4,X5] :
( ~ sum(X1,X0,X3)
| ~ product(X3,X4,X6)
| sum(X5,X0,X6)
| ~ sP10(X4,X0,X5,X1) ),
inference(general_splitting,[],[f16,f46_D]) ).
fof(f46,plain,
! [X2,X0,X1,X4,X5] :
( ~ product(X1,X2,X5)
| ~ sum(X2,X0,X4)
| sP10(X4,X0,X5,X1) ),
inference(cnf_transformation,[],[f46_D]) ).
fof(f46_D,plain,
! [X1,X5,X0,X4] :
( ! [X2] :
( ~ product(X1,X2,X5)
| ~ sum(X2,X0,X4) )
<=> ~ sP10(X4,X0,X5,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP10])]) ).
fof(f16,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sum(X1,X0,X3)
| ~ product(X3,X4,X6)
| ~ product(X1,X2,X5)
| ~ sum(X2,X0,X4)
| sum(X5,X0,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity8) ).
fof(f27422,plain,
sP10(multiplicative_identity,x,x_inverse_plus_y_inverse,multiplicative_identity),
inference(superposition,[],[f3373,f27178]) ).
fof(f3373,plain,
! [X0,X1] : sP10(add(X0,X1),X0,X1,multiplicative_identity),
inference(unit_resulting_resolution,[],[f60,f7,f46]) ).
fof(f3423,plain,
! [X2,X0,X1] : sP11(X0,X1,multiply(add(X1,X2),X0),X2),
inference(unit_resulting_resolution,[],[f60,f2,f48]) ).
fof(f484,plain,
! [X0,X1] : sP0(add(multiplicative_identity,X0),X1,X1,X0),
inference(unit_resulting_resolution,[],[f60,f8,f26]) ).
fof(f76,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(unit_resulting_resolution,[],[f2,f4]) ).
fof(f974372,plain,
~ sum(multiply(x_times_y,inverse(y)),additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f643647,f969557,f32]) ).
fof(f32,plain,
! [X3,X0,X1,X6,X4] :
( ~ product(X0,X1,X3)
| ~ sum(X3,X4,X6)
| sP3(X4,X0,X6,X1) ),
inference(cnf_transformation,[],[f32_D]) ).
fof(f32_D,plain,
! [X1,X6,X0,X4] :
( ! [X3] :
( ~ product(X0,X1,X3)
| ~ sum(X3,X4,X6) )
<=> ~ sP3(X4,X0,X6,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP3])]) ).
fof(f969557,plain,
~ sP3(additive_identity,x_times_y,additive_identity,x_inverse_plus_y_inverse),
inference(unit_resulting_resolution,[],[f6957,f968808,f33]) ).
fof(f33,plain,
! [X0,X1,X6,X4,X5] :
( ~ sP3(X4,X0,X6,X1)
| ~ sP2(X4,X0,X5,X1)
| product(X0,X5,X6) ),
inference(general_splitting,[],[f31,f32_D]) ).
fof(f31,plain,
! [X3,X0,X1,X6,X4,X5] :
( ~ product(X0,X1,X3)
| ~ sum(X3,X4,X6)
| product(X0,X5,X6)
| ~ sP2(X4,X0,X5,X1) ),
inference(general_splitting,[],[f10,f30_D]) ).
fof(f30,plain,
! [X2,X0,X1,X4,X5] :
( ~ product(X0,X2,X4)
| ~ sum(X1,X2,X5)
| sP2(X4,X0,X5,X1) ),
inference(cnf_transformation,[],[f30_D]) ).
fof(f30_D,plain,
! [X1,X5,X0,X4] :
( ! [X2] :
( ~ product(X0,X2,X4)
| ~ sum(X1,X2,X5) )
<=> ~ sP2(X4,X0,X5,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).
fof(f10,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X0,X1,X3)
| ~ sum(X3,X4,X6)
| ~ sum(X1,X2,X5)
| ~ product(X0,X2,X4)
| product(X0,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
fof(f968808,plain,
~ product(x_times_y,x_inverse_plus_y_inverse,additive_identity),
inference(unit_resulting_resolution,[],[f21878,f968096,f50]) ).
fof(f50,plain,
! [X2,X0,X1,X4,X5] :
( ~ product(X1,X2,X5)
| ~ sum(X2,X0,X4)
| sP12(X5,X0,X4,X1) ),
inference(cnf_transformation,[],[f50_D]) ).
fof(f50_D,plain,
! [X1,X4,X0,X5] :
( ! [X2] :
( ~ product(X1,X2,X5)
| ~ sum(X2,X0,X4) )
<=> ~ sP12(X5,X0,X4,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP12])]) ).
fof(f968096,plain,
sum(x_inverse_plus_y_inverse,inverse(x_times_y),x_inverse_plus_y_inverse),
inference(superposition,[],[f1,f967705]) ).
fof(f967705,plain,
x_inverse_plus_y_inverse = add(x_inverse_plus_y_inverse,inverse(x_times_y)),
inference(forward_demodulation,[],[f967704,f119]) ).
fof(f967704,plain,
add(additive_identity,x_inverse_plus_y_inverse) = add(x_inverse_plus_y_inverse,inverse(x_times_y)),
inference(forward_demodulation,[],[f967505,f120]) ).
fof(f967505,plain,
add(x_inverse_plus_y_inverse,additive_identity) = add(x_inverse_plus_y_inverse,inverse(x_times_y)),
inference(unit_resulting_resolution,[],[f31374,f145]) ).
fof(f31374,plain,
sum(additive_identity,x_inverse_plus_y_inverse,add(x_inverse_plus_y_inverse,inverse(x_times_y))),
inference(forward_demodulation,[],[f31370,f120]) ).
fof(f31370,plain,
sum(additive_identity,x_inverse_plus_y_inverse,add(inverse(x_times_y),x_inverse_plus_y_inverse)),
inference(unit_resulting_resolution,[],[f3348,f29787,f49]) ).
fof(f29787,plain,
! [X0] : sP11(X0,x_inverse_plus_y_inverse,X0,x_times_y),
inference(forward_demodulation,[],[f29728,f323]) ).
fof(f29728,plain,
! [X0] : sP11(X0,x_inverse_plus_y_inverse,multiply(X0,multiplicative_identity),x_times_y),
inference(unit_resulting_resolution,[],[f29558,f3449]) ).
fof(f3449,plain,
! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| sP11(X3,X1,multiply(X3,X2),X0) ),
inference(resolution,[],[f48,f76]) ).
fof(f29558,plain,
sum(x_times_y,x_inverse_plus_y_inverse,multiplicative_identity),
inference(unit_resulting_resolution,[],[f27364,f28893,f49]) ).
fof(f28893,plain,
sP11(multiplicative_identity,x_inverse_plus_y_inverse,multiplicative_identity,y),
inference(unit_resulting_resolution,[],[f1,f18295,f48]) ).
fof(f18295,plain,
product(add(y,x_inverse_plus_y_inverse),multiplicative_identity,multiplicative_identity),
inference(forward_demodulation,[],[f18292,f120]) ).
fof(f18292,plain,
product(add(x_inverse_plus_y_inverse,y),multiplicative_identity,multiplicative_identity),
inference(unit_resulting_resolution,[],[f60,f18286,f44]) ).
fof(f18286,plain,
~ sP9(multiplicative_identity,y,multiplicative_identity,x_inverse_plus_y_inverse),
inference(unit_resulting_resolution,[],[f18,f17829,f45]) ).
fof(f17829,plain,
sP8(inverse(y),y,multiplicative_identity,x_inverse_plus_y_inverse),
inference(unit_resulting_resolution,[],[f18,f17449,f42]) ).
fof(f17449,plain,
product(x_inverse_plus_y_inverse,inverse(y),inverse(y)),
inference(unit_resulting_resolution,[],[f16997,f2890]) ).
fof(f2890,plain,
! [X0,X1] :
( sP9(X0,inverse(y),X1,inverse(x))
| product(x_inverse_plus_y_inverse,X0,X1) ),
inference(resolution,[],[f44,f63]) ).
fof(f63,plain,
sum(inverse(y),inverse(x),x_inverse_plus_y_inverse),
inference(unit_resulting_resolution,[],[f24,f3]) ).
fof(f27364,plain,
sP10(multiplicative_identity,x_inverse_plus_y_inverse,x_times_y,y),
inference(superposition,[],[f3391,f27178]) ).
fof(f3391,plain,
! [X0] : sP10(add(x,X0),X0,x_times_y,y),
inference(unit_resulting_resolution,[],[f1,f79,f46]) ).
fof(f3348,plain,
! [X0,X1] : sP10(add(inverse(X0),X1),X1,additive_identity,X0),
inference(unit_resulting_resolution,[],[f1,f20,f46]) ).
fof(f21878,plain,
~ sP12(additive_identity,inverse(x_times_y),x_inverse_plus_y_inverse,x_times_y),
inference(forward_demodulation,[],[f21703,f6954]) ).
fof(f6954,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(superposition,[],[f6776,f311]) ).
fof(f21703,plain,
~ sP12(multiply(additive_identity,inverse(x_times_y)),inverse(x_times_y),x_inverse_plus_y_inverse,x_times_y),
inference(unit_resulting_resolution,[],[f5574,f4134,f53]) ).
fof(f53,plain,
! [X0,X1,X6,X4,X5] :
( ~ sP13(X4,X0,X6,X1)
| ~ sP12(X5,X0,X4,X1)
| ~ sum(X5,X0,X6) ),
inference(general_splitting,[],[f51,f52_D]) ).
fof(f52,plain,
! [X3,X0,X1,X6,X4] :
( ~ sum(X1,X0,X3)
| product(X3,X4,X6)
| sP13(X4,X0,X6,X1) ),
inference(cnf_transformation,[],[f52_D]) ).
fof(f52_D,plain,
! [X1,X6,X0,X4] :
( ! [X3] :
( ~ sum(X1,X0,X3)
| product(X3,X4,X6) )
<=> ~ sP13(X4,X0,X6,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP13])]) ).
fof(f51,plain,
! [X3,X0,X1,X6,X4,X5] :
( ~ sum(X1,X0,X3)
| ~ sum(X5,X0,X6)
| product(X3,X4,X6)
| ~ sP12(X5,X0,X4,X1) ),
inference(general_splitting,[],[f15,f50_D]) ).
fof(f15,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sum(X1,X0,X3)
| ~ sum(X5,X0,X6)
| ~ product(X1,X2,X5)
| ~ sum(X2,X0,X4)
| product(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity7) ).
fof(f4134,plain,
! [X0] : sP13(x_inverse_plus_y_inverse,inverse(X0),inverse(x_times_y),X0),
inference(unit_resulting_resolution,[],[f318,f18,f52]) ).
fof(f318,plain,
~ product(multiplicative_identity,x_inverse_plus_y_inverse,inverse(x_times_y)),
inference(unit_resulting_resolution,[],[f25,f7,f22]) ).
fof(f25,axiom,
x_inverse_plus_y_inverse != inverse(x_times_y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
fof(f5574,plain,
! [X0] : sum(multiply(additive_identity,X0),X0,X0),
inference(unit_resulting_resolution,[],[f76,f5399,f28]) ).
fof(f5399,plain,
! [X0] : ~ sP1(X0,X0,X0,additive_identity),
inference(forward_demodulation,[],[f5040,f322]) ).
fof(f5040,plain,
! [X0] : ~ sP1(multiply(multiplicative_identity,X0),X0,X0,additive_identity),
inference(unit_resulting_resolution,[],[f8,f501,f29]) ).
fof(f501,plain,
! [X0,X1] : sP0(X0,X1,multiply(X0,X1),additive_identity),
inference(unit_resulting_resolution,[],[f5,f76,f26]) ).
fof(f6957,plain,
! [X0,X1] : sP2(additive_identity,X0,X1,X1),
inference(superposition,[],[f799,f6776]) ).
fof(f799,plain,
! [X0,X1] : sP2(multiply(X0,additive_identity),X0,X1,X1),
inference(unit_resulting_resolution,[],[f6,f2,f30]) ).
fof(f643647,plain,
product(x_times_y,x_inverse_plus_y_inverse,multiply(x_times_y,inverse(y))),
inference(forward_demodulation,[],[f643646,f311]) ).
fof(f643646,plain,
product(x_times_y,x_inverse_plus_y_inverse,multiply(inverse(y),x_times_y)),
inference(forward_demodulation,[],[f643643,f119]) ).
fof(f643643,plain,
product(x_times_y,x_inverse_plus_y_inverse,add(additive_identity,multiply(inverse(y),x_times_y))),
inference(unit_resulting_resolution,[],[f1281,f632690,f33]) ).
fof(f632690,plain,
sP2(additive_identity,x_times_y,x_inverse_plus_y_inverse,inverse(y)),
inference(unit_resulting_resolution,[],[f63,f630897,f30]) ).
fof(f630897,plain,
product(x_times_y,inverse(x),additive_identity),
inference(forward_demodulation,[],[f629883,f119]) ).
fof(f629883,plain,
product(x_times_y,add(additive_identity,inverse(x)),additive_identity),
inference(unit_resulting_resolution,[],[f3731,f27146,f21787]) ).
fof(f21787,plain,
! [X2,X3,X0,X1] :
( ~ sP12(X0,additive_identity,X1,X2)
| ~ sum(X0,additive_identity,X3)
| product(X2,X1,X3) ),
inference(resolution,[],[f53,f4138]) ).
fof(f4138,plain,
! [X2,X0,X1] :
( sP13(X1,additive_identity,X2,X0)
| product(X0,X1,X2) ),
inference(resolution,[],[f52,f6]) ).
fof(f27146,plain,
sum(multiply(x_times_y,inverse(x)),additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f76,f26636,f28]) ).
fof(f26636,plain,
~ sP1(additive_identity,inverse(x),additive_identity,x_times_y),
inference(forward_demodulation,[],[f26635,f327]) ).
fof(f26635,plain,
~ sP1(additive_identity,inverse(x),multiply(x,inverse(x)),x_times_y),
inference(unit_resulting_resolution,[],[f76,f22955,f29]) ).
fof(f22955,plain,
sP0(x,inverse(x),additive_identity,x_times_y),
inference(unit_resulting_resolution,[],[f22811,f538]) ).
fof(f22811,plain,
sum(x_times_y,x,x),
inference(forward_demodulation,[],[f22808,f20324]) ).
fof(f20324,plain,
x_times_y = multiply(x,x_times_y),
inference(forward_demodulation,[],[f20323,f119]) ).
fof(f20323,plain,
add(additive_identity,x_times_y) = multiply(x,x_times_y),
inference(forward_demodulation,[],[f20231,f120]) ).
fof(f20231,plain,
add(x_times_y,additive_identity) = multiply(x,x_times_y),
inference(unit_resulting_resolution,[],[f19345,f145]) ).
fof(f19345,plain,
sum(additive_identity,x_times_y,multiply(x,x_times_y)),
inference(forward_demodulation,[],[f19344,f119]) ).
fof(f19344,plain,
sum(additive_identity,x_times_y,multiply(x,add(additive_identity,x_times_y))),
inference(forward_demodulation,[],[f19343,f120]) ).
fof(f19343,plain,
sum(additive_identity,x_times_y,multiply(x,add(x_times_y,additive_identity))),
inference(forward_demodulation,[],[f19058,f311]) ).
fof(f19058,plain,
sum(additive_identity,x_times_y,multiply(add(x_times_y,additive_identity),x)),
inference(unit_resulting_resolution,[],[f16154,f3423,f49]) ).
fof(f16154,plain,
sP10(x,x_times_y,additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f6966,f5589,f46]) ).
fof(f5589,plain,
sum(multiply(x,inverse(y)),x_times_y,x),
inference(forward_demodulation,[],[f5586,f311]) ).
fof(f5586,plain,
sum(multiply(inverse(y),x),x_times_y,x),
inference(unit_resulting_resolution,[],[f76,f5313,f28]) ).
fof(f5313,plain,
~ sP1(x_times_y,x,x,inverse(y)),
inference(forward_demodulation,[],[f5174,f322]) ).
fof(f5174,plain,
~ sP1(x_times_y,x,multiply(multiplicative_identity,x),inverse(y)),
inference(unit_resulting_resolution,[],[f76,f528,f29]) ).
fof(f528,plain,
sP0(multiplicative_identity,x,x_times_y,inverse(y)),
inference(unit_resulting_resolution,[],[f17,f23,f26]) ).
fof(f17,axiom,
! [X0] : sum(inverse(X0),X0,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f6966,plain,
! [X0] : product(additive_identity,X0,additive_identity),
inference(superposition,[],[f76,f6776]) ).
fof(f22808,plain,
sum(multiply(x,x_times_y),x,x),
inference(unit_resulting_resolution,[],[f76,f22781,f36]) ).
fof(f36,plain,
! [X3,X0,X1,X6,X4] :
( ~ product(X1,X0,X3)
| sum(X3,X4,X6)
| sP5(X4,X0,X6,X1) ),
inference(cnf_transformation,[],[f36_D]) ).
fof(f36_D,plain,
! [X1,X6,X0,X4] :
( ! [X3] :
( ~ product(X1,X0,X3)
| sum(X3,X4,X6) )
<=> ~ sP5(X4,X0,X6,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP5])]) ).
fof(f22781,plain,
~ sP5(x,x,x,x_times_y),
inference(forward_demodulation,[],[f22695,f323]) ).
fof(f22695,plain,
~ sP5(multiply(x,multiplicative_identity),x,x,x_times_y),
inference(unit_resulting_resolution,[],[f1711,f22221,f37]) ).
fof(f37,plain,
! [X0,X1,X6,X4,X5] :
( ~ sP5(X4,X0,X6,X1)
| ~ sP4(X5,X0,X4,X1)
| ~ product(X5,X0,X6) ),
inference(general_splitting,[],[f35,f36_D]) ).
fof(f35,plain,
! [X3,X0,X1,X6,X4,X5] :
( ~ product(X1,X0,X3)
| ~ product(X5,X0,X6)
| sum(X3,X4,X6)
| ~ sP4(X5,X0,X4,X1) ),
inference(general_splitting,[],[f11,f34_D]) ).
fof(f34,plain,
! [X2,X0,X1,X4,X5] :
( ~ product(X2,X0,X4)
| ~ sum(X1,X2,X5)
| sP4(X5,X0,X4,X1) ),
inference(cnf_transformation,[],[f34_D]) ).
fof(f34_D,plain,
! [X1,X4,X0,X5] :
( ! [X2] :
( ~ product(X2,X0,X4)
| ~ sum(X1,X2,X5) )
<=> ~ sP4(X5,X0,X4,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP4])]) ).
fof(f11,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X1,X0,X3)
| ~ product(X5,X0,X6)
| ~ sum(X1,X2,X5)
| ~ product(X2,X0,X4)
| sum(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).
fof(f22221,plain,
product(add(multiplicative_identity,x_times_y),x,x),
inference(forward_demodulation,[],[f22218,f120]) ).
fof(f22218,plain,
product(add(x_times_y,multiplicative_identity),x,x),
inference(unit_resulting_resolution,[],[f60,f22084,f52]) ).
fof(f22084,plain,
~ sP13(x,x_times_y,x,multiplicative_identity),
inference(forward_demodulation,[],[f21412,f16186]) ).
fof(f16186,plain,
x = add(x_times_y,multiply(x,inverse(y))),
inference(unit_resulting_resolution,[],[f5589,f145]) ).
fof(f21412,plain,
~ sP13(add(x_times_y,multiply(x,inverse(y))),x_times_y,x,multiplicative_identity),
inference(unit_resulting_resolution,[],[f5589,f3747,f53]) ).
fof(f3747,plain,
! [X0,X1] : sP12(X0,X1,add(X1,X0),multiplicative_identity),
inference(unit_resulting_resolution,[],[f60,f7,f50]) ).
fof(f1711,plain,
! [X2,X0,X1] : sP4(add(X0,X1),X2,multiply(X2,X0),X1),
inference(unit_resulting_resolution,[],[f60,f76,f34]) ).
fof(f3731,plain,
! [X2,X0,X1] : sP12(multiply(X0,X1),X2,add(X2,X1),X0),
inference(unit_resulting_resolution,[],[f60,f2,f50]) ).
fof(f1281,plain,
! [X2,X0,X1] : sP3(X0,X1,add(X0,multiply(X2,X1)),X2),
inference(unit_resulting_resolution,[],[f60,f76,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO015-1 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat May 18 14:26:38 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % (9547)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.38 % (9554)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)
% 0.13/0.38 % (9550)WARNING: value z3 for option sas not known
% 0.13/0.39 % (9550)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)
% 0.13/0.39 % (9553)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)
% 0.13/0.39 % (9551)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.39 % (9552)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)
% 0.13/0.39 % (9548)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.39 % (9549)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.39 TRYING [1]
% 0.13/0.39 TRYING [2]
% 0.13/0.40 TRYING [3]
% 0.13/0.40 TRYING [1]
% 0.13/0.40 TRYING [2]
% 0.13/0.42 TRYING [4]
% 0.13/0.42 TRYING [3]
% 0.22/0.48 TRYING [4]
% 0.22/0.49 TRYING [5]
% 2.18/0.68 TRYING [6]
% 2.61/0.74 TRYING [5]
% 5.72/1.18 TRYING [7]
% 7.78/1.49 TRYING [1]
% 7.78/1.49 TRYING [2]
% 7.78/1.49 TRYING [3]
% 8.06/1.52 TRYING [4]
% 8.30/1.59 TRYING [5]
% 9.02/1.68 TRYING [6]
% 10.01/1.80 TRYING [6]
% 13.73/2.37 TRYING [8]
% 13.73/2.38 TRYING [7]
% 23.73/3.75 TRYING [8]
% 26.55/4.21 TRYING [7]
% 34.68/5.38 TRYING [9]
% 43.31/6.56 TRYING [9]
% 65.13/9.73 TRYING [8]
% 78.73/11.69 TRYING [10]
% 85.06/12.56 % (9554)First to succeed.
% 85.06/12.57 % (9554)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-9547"
% 85.06/12.58 % (9554)Refutation found. Thanks to Tanya!
% 85.06/12.58 % SZS status Unsatisfiable for theBenchmark
% 85.06/12.58 % SZS output start Proof for theBenchmark
% See solution above
% 85.06/12.58 % (9554)------------------------------
% 85.06/12.58 % (9554)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 85.06/12.58 % (9554)Termination reason: Refutation
% 85.06/12.58
% 85.06/12.58 % (9554)Memory used [KB]: 73373
% 85.06/12.58 % (9554)Time elapsed: 12.195 s
% 85.06/12.58 % (9554)Instructions burned: 24768 (million)
% 85.06/12.58 % (9547)Success in time 12.196 s
%------------------------------------------------------------------------------