TSTP Solution File: BOO014-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : BOO014-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n009.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 : Sun May 5 04:42:48 EDT 2024
% Result : Unsatisfiable 55.27s 8.29s
% Output : Refutation 55.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 37
% Syntax : Number of formulae : 166 ( 108 unt; 0 def)
% Number of atoms : 297 ( 15 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 298 ( 167 ~; 117 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 375 ( 375 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f622220,plain,
$false,
inference(subsumption_resolution,[],[f621901,f126820]) ).
fof(f126820,plain,
! [X0] : ~ product(multiplicative_identity,add(inverse(x_plus_y),X0),x_inverse_times_y_inverse),
inference(unit_resulting_resolution,[],[f504,f55174,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(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(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(f55174,plain,
! [X0] : sP1(X0,multiplicative_identity,x_inverse_times_y_inverse,inverse(x_plus_y)),
inference(unit_resulting_resolution,[],[f51295,f557]) ).
fof(f557,plain,
! [X2,X0,X1] :
( sP1(X1,multiplicative_identity,X2,X0)
| sum(X0,X1,X2) ),
inference(resolution,[],[f28,f7]) ).
fof(f7,axiom,
! [X0] : product(multiplicative_identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity1) ).
fof(f51295,plain,
! [X0] : ~ sum(inverse(x_plus_y),X0,x_inverse_times_y_inverse),
inference(unit_resulting_resolution,[],[f15799,f50931,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(f50931,plain,
! [X0] : ~ product(x_inverse_times_y_inverse,X0,inverse(x_plus_y)),
inference(unit_resulting_resolution,[],[f41341,f49613,f28]) ).
fof(f49613,plain,
~ sum(inverse(x_plus_y),x_inverse_times_y_inverse,x_inverse_times_y_inverse),
inference(unit_resulting_resolution,[],[f21912,f49252,f54]) ).
fof(f54,plain,
! [X2,X0,X1,X4,X5] :
( ~ product(X1,X2,X5)
| ~ sum(X0,X2,X4)
| sP14(X4,X0,X5,X1) ),
inference(cnf_transformation,[],[f54_D]) ).
fof(f54_D,plain,
! [X1,X5,X0,X4] :
( ! [X2] :
( ~ product(X1,X2,X5)
| ~ sum(X0,X2,X4) )
<=> ~ sP14(X4,X0,X5,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP14])]) ).
fof(f49252,plain,
product(x_plus_y,x_inverse_times_y_inverse,additive_identity),
inference(unit_resulting_resolution,[],[f49246,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(f49246,plain,
product(x_inverse_times_y_inverse,x_plus_y,additive_identity),
inference(unit_resulting_resolution,[],[f47137,f48406,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(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(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(f48406,plain,
sP3(additive_identity,x_inverse_times_y_inverse,additive_identity,y),
inference(unit_resulting_resolution,[],[f76,f44942,f32]) ).
fof(f44942,plain,
sum(multiply(y,x_inverse_times_y_inverse),additive_identity,additive_identity),
inference(forward_demodulation,[],[f44939,f308]) ).
fof(f308,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(unit_resulting_resolution,[],[f2,f76,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(f2,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f44939,plain,
sum(multiply(x_inverse_times_y_inverse,y),additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f76,f44933,f28]) ).
fof(f44933,plain,
~ sP1(additive_identity,y,additive_identity,x_inverse_times_y_inverse),
inference(unit_resulting_resolution,[],[f20,f43593,f29]) ).
fof(f43593,plain,
sP0(inverse(y),y,additive_identity,x_inverse_times_y_inverse),
inference(unit_resulting_resolution,[],[f20,f42461,f26]) ).
fof(f42461,plain,
sum(x_inverse_times_y_inverse,inverse(y),inverse(y)),
inference(unit_resulting_resolution,[],[f41341,f564]) ).
fof(f564,plain,
! [X0,X1] :
( sP1(X0,inverse(y),X1,inverse(x))
| sum(x_inverse_times_y_inverse,X0,X1) ),
inference(resolution,[],[f28,f79]) ).
fof(f79,plain,
product(inverse(y),inverse(x),x_inverse_times_y_inverse),
inference(unit_resulting_resolution,[],[f24,f4]) ).
fof(f24,axiom,
product(inverse(x),inverse(y),x_inverse_times_y_inverse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_inverse_times_y_inverse) ).
fof(f20,axiom,
! [X0] : product(X0,inverse(X0),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse2) ).
fof(f76,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(unit_resulting_resolution,[],[f2,f4]) ).
fof(f47137,plain,
sP2(additive_identity,x_inverse_times_y_inverse,x_plus_y,y),
inference(superposition,[],[f876,f46835]) ).
fof(f46835,plain,
additive_identity = multiply(x,x_inverse_times_y_inverse),
inference(unit_resulting_resolution,[],[f6,f44498,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(f44498,plain,
sum(multiply(x,x_inverse_times_y_inverse),additive_identity,additive_identity),
inference(forward_demodulation,[],[f44495,f308]) ).
fof(f44495,plain,
sum(multiply(x_inverse_times_y_inverse,x),additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f76,f44489,f28]) ).
fof(f44489,plain,
~ sP1(additive_identity,x,additive_identity,x_inverse_times_y_inverse),
inference(unit_resulting_resolution,[],[f20,f42950,f29]) ).
fof(f42950,plain,
sP0(inverse(x),x,additive_identity,x_inverse_times_y_inverse),
inference(unit_resulting_resolution,[],[f20,f42460,f26]) ).
fof(f42460,plain,
sum(x_inverse_times_y_inverse,inverse(x),inverse(x)),
inference(unit_resulting_resolution,[],[f41341,f563]) ).
fof(f563,plain,
! [X0,X1] :
( sP1(X0,inverse(x),X1,inverse(y))
| sum(x_inverse_times_y_inverse,X0,X1) ),
inference(resolution,[],[f28,f24]) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
fof(f876,plain,
! [X0] : sP2(multiply(x,X0),X0,x_plus_y,y),
inference(unit_resulting_resolution,[],[f63,f76,f30]) ).
fof(f63,plain,
sum(y,x,x_plus_y),
inference(unit_resulting_resolution,[],[f23,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(f23,axiom,
sum(x,y,x_plus_y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_plus_y) ).
fof(f21912,plain,
~ sP14(x_inverse_times_y_inverse,inverse(x_plus_y),additive_identity,x_plus_y),
inference(unit_resulting_resolution,[],[f94,f4676,f57]) ).
fof(f57,plain,
! [X0,X1,X6,X4,X5] :
( ~ sP15(X4,X0,X6,X1)
| ~ sP14(X4,X0,X5,X1)
| sum(X0,X5,X6) ),
inference(general_splitting,[],[f55,f56_D]) ).
fof(f56,plain,
! [X3,X0,X1,X6,X4] :
( ~ product(X3,X4,X6)
| ~ sum(X0,X1,X3)
| sP15(X4,X0,X6,X1) ),
inference(cnf_transformation,[],[f56_D]) ).
fof(f56_D,plain,
! [X1,X6,X0,X4] :
( ! [X3] :
( ~ product(X3,X4,X6)
| ~ sum(X0,X1,X3) )
<=> ~ sP15(X4,X0,X6,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP15])]) ).
fof(f55,plain,
! [X3,X0,X1,X6,X4,X5] :
( ~ sum(X0,X1,X3)
| ~ product(X3,X4,X6)
| sum(X0,X5,X6)
| ~ sP14(X4,X0,X5,X1) ),
inference(general_splitting,[],[f14,f54_D]) ).
fof(f14,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sum(X0,X1,X3)
| ~ product(X3,X4,X6)
| ~ product(X1,X2,X5)
| ~ sum(X0,X2,X4)
| sum(X0,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity6) ).
fof(f4676,plain,
! [X0,X1] : sP15(X0,inverse(X1),X0,X1),
inference(forward_demodulation,[],[f4649,f306]) ).
fof(f306,plain,
! [X0] : multiply(X0,multiplicative_identity) = X0,
inference(unit_resulting_resolution,[],[f7,f76,f22]) ).
fof(f4649,plain,
! [X0,X1] : sP15(X0,inverse(X1),multiply(X0,multiplicative_identity),X1),
inference(unit_resulting_resolution,[],[f17,f76,f56]) ).
fof(f17,axiom,
! [X0] : sum(inverse(X0),X0,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f94,plain,
~ sum(inverse(x_plus_y),additive_identity,x_inverse_times_y_inverse),
inference(unit_resulting_resolution,[],[f25,f6,f21]) ).
fof(f25,axiom,
x_inverse_times_y_inverse != inverse(x_plus_y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
fof(f41341,plain,
! [X0,X1] : ~ sP1(X0,X0,X0,X1),
inference(forward_demodulation,[],[f41326,f307]) ).
fof(f307,plain,
! [X0] : multiply(multiplicative_identity,X0) = X0,
inference(unit_resulting_resolution,[],[f8,f76,f22]) ).
fof(f8,axiom,
! [X0] : product(X0,multiplicative_identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity2) ).
fof(f41326,plain,
! [X0,X1] : ~ sP1(X0,X0,multiply(multiplicative_identity,X0),X1),
inference(unit_resulting_resolution,[],[f76,f39272,f29]) ).
fof(f39272,plain,
! [X0,X1] : sP0(multiplicative_identity,X1,X1,X0),
inference(superposition,[],[f490,f39033]) ).
fof(f39033,plain,
! [X0] : multiplicative_identity = add(X0,multiplicative_identity),
inference(unit_resulting_resolution,[],[f8,f20552,f22]) ).
fof(f20552,plain,
! [X0] : product(add(X0,multiplicative_identity),multiplicative_identity,multiplicative_identity),
inference(unit_resulting_resolution,[],[f1,f15717,f44]) ).
fof(f15717,plain,
! [X0] : ~ sP9(multiplicative_identity,X0,multiplicative_identity,multiplicative_identity),
inference(forward_demodulation,[],[f15716,f131]) ).
fof(f131,plain,
! [X0] : multiplicative_identity = add(X0,inverse(X0)),
inference(unit_resulting_resolution,[],[f60,f17,f21]) ).
fof(f60,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(unit_resulting_resolution,[],[f1,f3]) ).
fof(f15716,plain,
! [X0] : ~ sP9(multiplicative_identity,X0,add(X0,inverse(X0)),multiplicative_identity),
inference(forward_demodulation,[],[f15352,f115]) ).
fof(f115,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(unit_resulting_resolution,[],[f1,f60,f21]) ).
fof(f15352,plain,
! [X0] : ~ sP9(multiplicative_identity,X0,add(inverse(X0),X0),multiplicative_identity),
inference(unit_resulting_resolution,[],[f60,f2470,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(f2470,plain,
! [X0] : sP8(inverse(X0),X0,multiplicative_identity,multiplicative_identity),
inference(unit_resulting_resolution,[],[f18,f7,f42]) ).
fof(f18,axiom,
! [X0] : sum(X0,inverse(X0),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse2) ).
fof(f1,axiom,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f490,plain,
! [X0,X1] : sP0(add(X0,multiplicative_identity),X1,X1,X0),
inference(unit_resulting_resolution,[],[f1,f8,f26]) ).
fof(f15799,plain,
! [X0,X1] : ~ sP9(X0,X0,X0,X1),
inference(forward_demodulation,[],[f15265,f6289]) ).
fof(f6289,plain,
! [X0] : multiply(X0,X0) = X0,
inference(unit_resulting_resolution,[],[f6,f5617,f21]) ).
fof(f5617,plain,
! [X0] : sum(multiply(X0,X0),additive_identity,X0),
inference(unit_resulting_resolution,[],[f76,f5504,f28]) ).
fof(f5504,plain,
! [X0] : ~ sP1(additive_identity,X0,X0,X0),
inference(forward_demodulation,[],[f5084,f307]) ).
fof(f5084,plain,
! [X0] : ~ sP1(additive_identity,X0,multiply(multiplicative_identity,X0),X0),
inference(unit_resulting_resolution,[],[f76,f518,f29]) ).
fof(f518,plain,
! [X0] : sP0(multiplicative_identity,X0,additive_identity,X0),
inference(unit_resulting_resolution,[],[f18,f20,f26]) ).
fof(f15265,plain,
! [X0,X1] : ~ sP9(multiply(X0,X0),multiply(X0,X0),X0,X1),
inference(unit_resulting_resolution,[],[f5617,f8740,f45]) ).
fof(f8740,plain,
! [X0,X1] : sP8(additive_identity,X1,X1,X0),
inference(superposition,[],[f2481,f8539]) ).
fof(f8539,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(unit_resulting_resolution,[],[f6,f5638,f21]) ).
fof(f5638,plain,
! [X0] : sum(multiply(X0,additive_identity),additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f2,f5453,f28]) ).
fof(f5453,plain,
! [X0] : ~ sP1(additive_identity,X0,additive_identity,additive_identity),
inference(forward_demodulation,[],[f5176,f320]) ).
fof(f320,plain,
! [X0] : additive_identity = multiply(inverse(X0),X0),
inference(unit_resulting_resolution,[],[f76,f20,f22]) ).
fof(f5176,plain,
! [X0] : ~ sP1(multiply(inverse(X0),X0),X0,additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f20,f506,f29]) ).
fof(f506,plain,
! [X0,X1] : sP0(X0,X1,multiply(X0,X1),additive_identity),
inference(unit_resulting_resolution,[],[f5,f76,f26]) ).
fof(f5,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
fof(f2481,plain,
! [X0,X1] : sP8(multiply(X0,additive_identity),X1,X1,X0),
inference(unit_resulting_resolution,[],[f6,f2,f42]) ).
fof(f504,plain,
! [X2,X0,X1] : sP0(add(X0,X1),X2,multiply(X1,X2),X0),
inference(unit_resulting_resolution,[],[f1,f76,f26]) ).
fof(f621901,plain,
product(multiplicative_identity,add(inverse(x_plus_y),x_inverse_times_y_inverse),x_inverse_times_y_inverse),
inference(unit_resulting_resolution,[],[f20257,f619702,f52]) ).
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(f619702,plain,
sum(x_plus_y,x_inverse_times_y_inverse,multiplicative_identity),
inference(unit_resulting_resolution,[],[f619690,f3]) ).
fof(f619690,plain,
sum(x_inverse_times_y_inverse,x_plus_y,multiplicative_identity),
inference(unit_resulting_resolution,[],[f585619,f616196,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(f616196,plain,
sP11(multiplicative_identity,x_plus_y,multiplicative_identity,inverse(x)),
inference(unit_resulting_resolution,[],[f60,f30559,f48]) ).
fof(f30559,plain,
product(add(x_plus_y,inverse(x)),multiplicative_identity,multiplicative_identity),
inference(unit_resulting_resolution,[],[f60,f28475,f44]) ).
fof(f28475,plain,
~ sP9(multiplicative_identity,inverse(x),multiplicative_identity,x_plus_y),
inference(forward_demodulation,[],[f28474,f131]) ).
fof(f28474,plain,
~ sP9(multiplicative_identity,inverse(x),add(x,inverse(x)),x_plus_y),
inference(unit_resulting_resolution,[],[f60,f16530,f45]) ).
fof(f16530,plain,
sP8(x,inverse(x),multiplicative_identity,x_plus_y),
inference(unit_resulting_resolution,[],[f17,f16318,f42]) ).
fof(f16318,plain,
product(x_plus_y,x,x),
inference(unit_resulting_resolution,[],[f16312,f4]) ).
fof(f16312,plain,
product(x,x_plus_y,x),
inference(forward_demodulation,[],[f16308,f126]) ).
fof(f126,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(unit_resulting_resolution,[],[f1,f5,f21]) ).
fof(f16308,plain,
product(add(additive_identity,x),x_plus_y,x),
inference(unit_resulting_resolution,[],[f60,f15771,f44]) ).
fof(f15771,plain,
~ sP9(x_plus_y,x,x,additive_identity),
inference(forward_demodulation,[],[f15302,f126]) ).
fof(f15302,plain,
~ sP9(x_plus_y,x,add(additive_identity,x),additive_identity),
inference(unit_resulting_resolution,[],[f60,f8875,f45]) ).
fof(f8875,plain,
sP8(additive_identity,x,x_plus_y,additive_identity),
inference(superposition,[],[f2495,f8539]) ).
fof(f2495,plain,
! [X0] : sP8(multiply(y,X0),x,x_plus_y,X0),
inference(unit_resulting_resolution,[],[f23,f76,f42]) ).
fof(f585619,plain,
sP10(multiplicative_identity,x_plus_y,x_inverse_times_y_inverse,inverse(x)),
inference(unit_resulting_resolution,[],[f24,f584986,f46]) ).
fof(f584986,plain,
sum(inverse(y),x_plus_y,multiplicative_identity),
inference(forward_demodulation,[],[f583751,f307]) ).
fof(f583751,plain,
sum(inverse(y),multiply(multiplicative_identity,x_plus_y),multiplicative_identity),
inference(unit_resulting_resolution,[],[f1695,f30523,f9783]) ).
fof(f9783,plain,
! [X2,X3,X0,X1] :
( ~ sP4(X0,multiplicative_identity,X1,X2)
| ~ product(X0,multiplicative_identity,X3)
| sum(X2,X1,X3) ),
inference(resolution,[],[f37,f1764]) ).
fof(f1764,plain,
! [X2,X0,X1] :
( sP5(X1,multiplicative_identity,X2,X0)
| sum(X0,X1,X2) ),
inference(resolution,[],[f36,f8]) ).
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(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(f30523,plain,
product(add(x_plus_y,inverse(y)),multiplicative_identity,multiplicative_identity),
inference(unit_resulting_resolution,[],[f60,f28403,f44]) ).
fof(f28403,plain,
~ sP9(multiplicative_identity,inverse(y),multiplicative_identity,x_plus_y),
inference(forward_demodulation,[],[f28402,f131]) ).
fof(f28402,plain,
~ sP9(multiplicative_identity,inverse(y),add(y,inverse(y)),x_plus_y),
inference(unit_resulting_resolution,[],[f60,f16209,f45]) ).
fof(f16209,plain,
sP8(y,inverse(y),multiplicative_identity,x_plus_y),
inference(unit_resulting_resolution,[],[f17,f15997,f42]) ).
fof(f15997,plain,
product(x_plus_y,y,y),
inference(unit_resulting_resolution,[],[f15991,f4]) ).
fof(f15991,plain,
product(y,x_plus_y,y),
inference(forward_demodulation,[],[f15987,f126]) ).
fof(f15987,plain,
product(add(additive_identity,y),x_plus_y,y),
inference(unit_resulting_resolution,[],[f60,f15769,f44]) ).
fof(f15769,plain,
~ sP9(x_plus_y,y,y,additive_identity),
inference(forward_demodulation,[],[f15305,f126]) ).
fof(f15305,plain,
~ sP9(x_plus_y,y,add(additive_identity,y),additive_identity),
inference(unit_resulting_resolution,[],[f60,f8867,f45]) ).
fof(f8867,plain,
sP8(additive_identity,y,x_plus_y,additive_identity),
inference(superposition,[],[f2496,f8539]) ).
fof(f2496,plain,
! [X0] : sP8(multiply(x,X0),y,x_plus_y,X0),
inference(unit_resulting_resolution,[],[f63,f76,f42]) ).
fof(f1695,plain,
! [X2,X0,X1] : sP4(add(X0,X1),X2,multiply(X2,X0),X1),
inference(unit_resulting_resolution,[],[f60,f76,f34]) ).
fof(f20257,plain,
! [X0,X1] : ~ sP13(add(inverse(X0),X1),X1,X1,X0),
inference(forward_demodulation,[],[f19767,f127]) ).
fof(f127,plain,
! [X0] : add(X0,additive_identity) = X0,
inference(unit_resulting_resolution,[],[f60,f5,f21]) ).
fof(f19767,plain,
! [X0,X1] : ~ sP13(add(inverse(X0),X1),X1,add(X1,additive_identity),X0),
inference(unit_resulting_resolution,[],[f60,f3779,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(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(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(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(f3779,plain,
! [X0,X1] : sP12(additive_identity,X0,add(inverse(X1),X0),X1),
inference(unit_resulting_resolution,[],[f1,f20,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : BOO014-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.09/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri May 3 18:53:23 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % (7628)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.35 % (7632)WARNING: value z3 for option sas not known
% 0.13/0.35 % (7636)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)
% 0.13/0.35 % (7632)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)
% 0.13/0.35 % (7635)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)
% 0.13/0.36 % (7630)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.36 % (7633)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36 % (7634)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)
% 0.13/0.36 % (7631)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36 TRYING [1]
% 0.13/0.36 TRYING [2]
% 0.13/0.36 TRYING [3]
% 0.13/0.36 TRYING [1]
% 0.13/0.36 TRYING [2]
% 0.13/0.38 TRYING [3]
% 0.13/0.38 TRYING [4]
% 0.19/0.44 TRYING [4]
% 0.19/0.44 TRYING [5]
% 1.94/0.62 TRYING [6]
% 2.19/0.68 TRYING [5]
% 5.18/1.11 TRYING [7]
% 7.91/1.46 TRYING [1]
% 7.91/1.46 TRYING [2]
% 7.91/1.46 TRYING [3]
% 7.91/1.48 TRYING [4]
% 8.55/1.56 TRYING [5]
% 8.55/1.60 TRYING [6]
% 10.15/1.79 TRYING [6]
% 13.63/2.33 TRYING [7]
% 13.63/2.36 TRYING [8]
% 23.50/3.75 TRYING [8]
% 26.23/4.10 TRYING [7]
% 35.06/5.37 TRYING [9]
% 43.11/6.59 TRYING [9]
% 55.27/8.27 % (7636)First to succeed.
% 55.27/8.28 % (7636)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-7628"
% 55.27/8.29 % (7636)Refutation found. Thanks to Tanya!
% 55.27/8.29 % SZS status Unsatisfiable for theBenchmark
% 55.27/8.29 % SZS output start Proof for theBenchmark
% See solution above
% 55.27/8.29 % (7636)------------------------------
% 55.27/8.29 % (7636)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 55.27/8.29 % (7636)Termination reason: Refutation
% 55.27/8.29
% 55.27/8.29 % (7636)Memory used [KB]: 56882
% 55.27/8.29 % (7636)Time elapsed: 7.931 s
% 55.27/8.29 % (7636)Instructions burned: 16180 (million)
% 55.27/8.29 % (7628)Success in time 7.935 s
%------------------------------------------------------------------------------