TSTP Solution File: RNG008-6 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : RNG008-6 : TPTP v8.2.0. Released v1.0.0.
% 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 May 21 02:40:28 EDT 2024
% Result : Unsatisfiable 67.51s 10.03s
% Output : Refutation 67.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 34
% Syntax : Number of formulae : 217 ( 165 unt; 0 def)
% Number of atoms : 331 ( 38 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 265 ( 151 ~; 102 |; 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 416 ( 416 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f592690,plain,
$false,
inference(subsumption_resolution,[],[f592649,f171075]) ).
fof(f171075,plain,
sP10(add(a,b),c,b,add(b,c)),
inference(forward_demodulation,[],[f170980,f141273]) ).
fof(f141273,plain,
add(b,c) = multiply(add(a,b),b),
inference(unit_resulting_resolution,[],[f66966,f94]) ).
fof(f94,plain,
! [X2,X0,X1] :
( ~ sum(X2,X1,X0)
| add(X1,X2) = X0 ),
inference(resolution,[],[f16,f51]) ).
fof(f51,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(unit_resulting_resolution,[],[f4,f9]) ).
fof(f9,axiom,
! [X3,X0,X1] :
( ~ sum(X0,X1,X3)
| sum(X1,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
fof(f4,axiom,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f16,axiom,
! [X2,X0,X1,X4] :
( ~ sum(X0,X1,X4)
| X2 = X4
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f66966,plain,
sum(c,b,multiply(add(a,b),b)),
inference(forward_demodulation,[],[f66964,f802]) ).
fof(f802,plain,
! [X0,X1] : multiply(X0,X1) = multiply(multiply(X0,X1),X1),
inference(unit_resulting_resolution,[],[f372,f210]) ).
fof(f210,plain,
! [X2,X0,X1] :
( ~ product(X1,X2,X0)
| multiply(X1,X2) = X0 ),
inference(resolution,[],[f17,f3]) ).
fof(f3,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f17,axiom,
! [X2,X0,X1,X4] :
( ~ product(X0,X1,X4)
| X2 = X4
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
fof(f372,plain,
! [X0,X1] : product(X0,X1,multiply(multiply(X0,X1),X1)),
inference(unit_resulting_resolution,[],[f20,f266,f24]) ).
fof(f24,plain,
! [X3,X0,X1,X4,X5] :
( ~ sP0(X5,X0,X3,X1)
| product(X0,X4,X5)
| ~ product(X1,X3,X4) ),
inference(general_splitting,[],[f10,f23_D]) ).
fof(f23,plain,
! [X2,X3,X0,X1,X5] :
( ~ product(X0,X1,X2)
| ~ product(X2,X3,X5)
| sP0(X5,X0,X3,X1) ),
inference(cnf_transformation,[],[f23_D]) ).
fof(f23_D,plain,
! [X1,X3,X0,X5] :
( ! [X2] :
( ~ product(X0,X1,X2)
| ~ product(X2,X3,X5) )
<=> ~ sP0(X5,X0,X3,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP0])]) ).
fof(f10,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| product(X0,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication1) ).
fof(f266,plain,
! [X2,X0,X1] : sP0(multiply(multiply(X0,X1),X2),X0,X2,X1),
inference(unit_resulting_resolution,[],[f3,f3,f23]) ).
fof(f20,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_squared_is_x) ).
fof(f66964,plain,
sum(c,b,multiply(multiply(add(a,b),b),b)),
inference(unit_resulting_resolution,[],[f372,f40427,f38]) ).
fof(f38,plain,
! [X0,X8,X6,X9,X7] :
( ~ sP7(X0,X8,X6,X7)
| sum(X6,X7,X9)
| ~ product(X8,X0,X9) ),
inference(general_splitting,[],[f36,f37_D]) ).
fof(f37,plain,
! [X0,X1,X8,X6,X7] :
( ~ sP6(X0,X8,X1,X7)
| ~ product(X1,X0,X6)
| sP7(X0,X8,X6,X7) ),
inference(cnf_transformation,[],[f37_D]) ).
fof(f37_D,plain,
! [X7,X6,X8,X0] :
( ! [X1] :
( ~ sP6(X0,X8,X1,X7)
| ~ product(X1,X0,X6) )
<=> ~ sP7(X0,X8,X6,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP7])]) ).
fof(f36,plain,
! [X0,X1,X8,X6,X9,X7] :
( ~ product(X1,X0,X6)
| ~ product(X8,X0,X9)
| sum(X6,X7,X9)
| ~ sP6(X0,X8,X1,X7) ),
inference(general_splitting,[],[f14,f35_D]) ).
fof(f35,plain,
! [X3,X0,X1,X8,X7] :
( ~ product(X3,X0,X7)
| ~ sum(X1,X3,X8)
| sP6(X0,X8,X1,X7) ),
inference(cnf_transformation,[],[f35_D]) ).
fof(f35_D,plain,
! [X7,X1,X8,X0] :
( ! [X3] :
( ~ product(X3,X0,X7)
| ~ sum(X1,X3,X8) )
<=> ~ sP6(X0,X8,X1,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP6])]) ).
fof(f14,axiom,
! [X3,X0,X1,X8,X6,X9,X7] :
( ~ product(X1,X0,X6)
| ~ product(X8,X0,X9)
| ~ product(X3,X0,X7)
| ~ sum(X1,X3,X8)
| sum(X6,X7,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).
fof(f40427,plain,
sP7(b,add(a,b),c,b),
inference(forward_demodulation,[],[f40426,f87]) ).
fof(f87,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(unit_resulting_resolution,[],[f4,f51,f16]) ).
fof(f40426,plain,
sP7(b,add(b,a),c,b),
inference(forward_demodulation,[],[f39771,f460]) ).
fof(f460,plain,
c = multiply(c,b),
inference(forward_demodulation,[],[f453,f203]) ).
fof(f203,plain,
c = multiply(a,b),
inference(unit_resulting_resolution,[],[f3,f21,f17]) ).
fof(f21,axiom,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f453,plain,
multiply(a,b) = multiply(c,b),
inference(unit_resulting_resolution,[],[f377,f210]) ).
fof(f377,plain,
product(a,b,multiply(c,b)),
inference(unit_resulting_resolution,[],[f20,f269,f24]) ).
fof(f269,plain,
! [X0] : sP0(multiply(c,X0),a,X0,b),
inference(unit_resulting_resolution,[],[f3,f21,f23]) ).
fof(f39771,plain,
sP7(b,add(b,a),multiply(c,b),b),
inference(unit_resulting_resolution,[],[f377,f19261,f37]) ).
fof(f19261,plain,
! [X0,X1] : sP6(X0,add(X0,X1),X1,X0),
inference(unit_resulting_resolution,[],[f51,f20,f35]) ).
fof(f170980,plain,
sP10(add(a,b),c,b,multiply(add(a,b),b)),
inference(unit_resulting_resolution,[],[f367,f141309,f43]) ).
fof(f43,plain,
! [X3,X0,X1,X8,X7] :
( ~ product(X0,X3,X7)
| ~ sum(X1,X3,X8)
| sP10(X0,X8,X1,X7) ),
inference(cnf_transformation,[],[f43_D]) ).
fof(f43_D,plain,
! [X7,X1,X8,X0] :
( ! [X3] :
( ~ product(X0,X3,X7)
| ~ sum(X1,X3,X8) )
<=> ~ sP10(X0,X8,X1,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP10])]) ).
fof(f141309,plain,
sum(b,multiply(add(a,b),b),c),
inference(forward_demodulation,[],[f141276,f43850]) ).
fof(f43850,plain,
! [X0] : additive_inverse(X0) = X0,
inference(forward_demodulation,[],[f43381,f83]) ).
fof(f83,plain,
! [X0] : add(X0,additive_identity) = X0,
inference(unit_resulting_resolution,[],[f1,f51,f16]) ).
fof(f1,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
fof(f43381,plain,
! [X0] : additive_inverse(X0) = add(X0,additive_identity),
inference(unit_resulting_resolution,[],[f5674,f41134,f16]) ).
fof(f41134,plain,
! [X0] : sum(additive_identity,additive_inverse(X0),X0),
inference(unit_resulting_resolution,[],[f4659,f40795,f27]) ).
fof(f27,plain,
! [X2,X3,X0,X1,X5] :
( ~ sum(X0,X1,X2)
| sum(X2,X3,X5)
| sP2(X3,X0,X5,X1) ),
inference(cnf_transformation,[],[f27_D]) ).
fof(f27_D,plain,
! [X1,X5,X0,X3] :
( ! [X2] :
( ~ sum(X0,X1,X2)
| sum(X2,X3,X5) )
<=> ~ sP2(X3,X0,X5,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).
fof(f40795,plain,
! [X0] : sum(X0,X0,additive_identity),
inference(forward_demodulation,[],[f40794,f207]) ).
fof(f207,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(unit_resulting_resolution,[],[f3,f19,f17]) ).
fof(f19,axiom,
! [X0] : product(additive_identity,X0,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_times_x_is_identity) ).
fof(f40794,plain,
! [X0] : sum(X0,X0,multiply(additive_identity,X0)),
inference(forward_demodulation,[],[f40780,f802]) ).
fof(f40780,plain,
! [X0] : sum(X0,X0,multiply(multiply(additive_identity,X0),X0)),
inference(unit_resulting_resolution,[],[f372,f40193,f38]) ).
fof(f40193,plain,
! [X0] : sP7(X0,additive_identity,X0,X0),
inference(forward_demodulation,[],[f40067,f197]) ).
fof(f197,plain,
! [X0] : multiply(X0,X0) = X0,
inference(unit_resulting_resolution,[],[f20,f3,f17]) ).
fof(f40067,plain,
! [X0] : sP7(X0,additive_identity,X0,multiply(X0,X0)),
inference(unit_resulting_resolution,[],[f38389,f20300,f37]) ).
fof(f20300,plain,
! [X2,X0] : sP6(X0,additive_identity,additive_inverse(X2),multiply(X2,X0)),
inference(forward_demodulation,[],[f20299,f6485]) ).
fof(f6485,plain,
! [X0,X1] : additive_inverse(X0) = add(X1,additive_inverse(add(X0,X1))),
inference(superposition,[],[f5171,f5171]) ).
fof(f5171,plain,
! [X0,X1] : add(add(X0,X1),additive_inverse(X0)) = X1,
inference(unit_resulting_resolution,[],[f4725,f93]) ).
fof(f93,plain,
! [X2,X0,X1] :
( ~ sum(X1,X2,X0)
| add(X1,X2) = X0 ),
inference(resolution,[],[f16,f4]) ).
fof(f4725,plain,
! [X0,X1] : sum(add(X0,X1),additive_inverse(X0),X1),
inference(unit_resulting_resolution,[],[f51,f4659,f27]) ).
fof(f20299,plain,
! [X2,X0,X1] : sP6(X0,additive_identity,add(X1,additive_inverse(add(X2,X1))),multiply(X2,X0)),
inference(forward_demodulation,[],[f19320,f802]) ).
fof(f19320,plain,
! [X2,X0,X1] : sP6(X0,additive_identity,add(X1,additive_inverse(add(X2,X1))),multiply(multiply(X2,X0),X0)),
inference(unit_resulting_resolution,[],[f5990,f372,f35]) ).
fof(f5990,plain,
! [X0,X1] : sum(add(X0,additive_inverse(add(X1,X0))),X1,additive_identity),
inference(unit_resulting_resolution,[],[f51,f4656,f27]) ).
fof(f4656,plain,
! [X0,X1] : ~ sP2(X0,additive_inverse(add(X0,X1)),additive_identity,X1),
inference(unit_resulting_resolution,[],[f5,f51,f28]) ).
fof(f28,plain,
! [X3,X0,X1,X4,X5] :
( ~ sP2(X3,X0,X5,X1)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X4,X5) ),
inference(general_splitting,[],[f8,f27_D]) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| sum(X2,X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).
fof(f5,axiom,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f38389,plain,
! [X0] : product(additive_inverse(X0),X0,X0),
inference(superposition,[],[f3,f37837]) ).
fof(f37837,plain,
! [X0] : multiply(additive_inverse(X0),X0) = X0,
inference(forward_demodulation,[],[f37755,f83]) ).
fof(f37755,plain,
! [X0] : add(X0,additive_identity) = multiply(additive_inverse(X0),X0),
inference(unit_resulting_resolution,[],[f37010,f94]) ).
fof(f37010,plain,
! [X0] : sum(additive_identity,X0,multiply(additive_inverse(X0),X0)),
inference(forward_demodulation,[],[f36488,f4741]) ).
fof(f4741,plain,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
inference(unit_resulting_resolution,[],[f1,f4723,f16]) ).
fof(f4723,plain,
! [X0] : sum(additive_identity,additive_inverse(additive_inverse(X0)),X0),
inference(unit_resulting_resolution,[],[f6,f4659,f27]) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f36488,plain,
! [X0] : sum(additive_identity,X0,multiply(additive_inverse(X0),additive_inverse(additive_inverse(X0)))),
inference(unit_resulting_resolution,[],[f4662,f36468,f27]) ).
fof(f36468,plain,
! [X0] : sum(multiply(X0,additive_inverse(X0)),X0,additive_identity),
inference(forward_demodulation,[],[f36457,f198]) ).
fof(f198,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(unit_resulting_resolution,[],[f18,f3,f17]) ).
fof(f18,axiom,
! [X0] : product(X0,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_times_identity_x_is_identity) ).
fof(f36457,plain,
! [X0] : sum(multiply(X0,additive_inverse(X0)),X0,multiply(multiply(X0,additive_identity),additive_identity)),
inference(unit_resulting_resolution,[],[f372,f35431,f34]) ).
fof(f34,plain,
! [X0,X8,X6,X9,X7] :
( ~ sP5(X0,X8,X6,X7)
| sum(X6,X7,X9)
| ~ product(X0,X8,X9) ),
inference(general_splitting,[],[f32,f33_D]) ).
fof(f33,plain,
! [X0,X1,X8,X6,X7] :
( ~ sP4(X0,X8,X1,X7)
| ~ product(X0,X1,X6)
| sP5(X0,X8,X6,X7) ),
inference(cnf_transformation,[],[f33_D]) ).
fof(f33_D,plain,
! [X7,X6,X8,X0] :
( ! [X1] :
( ~ sP4(X0,X8,X1,X7)
| ~ product(X0,X1,X6) )
<=> ~ sP5(X0,X8,X6,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP5])]) ).
fof(f32,plain,
! [X0,X1,X8,X6,X9,X7] :
( ~ product(X0,X1,X6)
| ~ product(X0,X8,X9)
| sum(X6,X7,X9)
| ~ sP4(X0,X8,X1,X7) ),
inference(general_splitting,[],[f12,f31_D]) ).
fof(f31,plain,
! [X3,X0,X1,X8,X7] :
( ~ product(X0,X3,X7)
| ~ sum(X1,X3,X8)
| sP4(X0,X8,X1,X7) ),
inference(cnf_transformation,[],[f31_D]) ).
fof(f31_D,plain,
! [X7,X1,X8,X0] :
( ! [X3] :
( ~ product(X0,X3,X7)
| ~ sum(X1,X3,X8) )
<=> ~ sP4(X0,X8,X1,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP4])]) ).
fof(f12,axiom,
! [X3,X0,X1,X8,X6,X9,X7] :
( ~ product(X0,X1,X6)
| ~ product(X0,X8,X9)
| ~ product(X0,X3,X7)
| ~ sum(X1,X3,X8)
| sum(X6,X7,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f35431,plain,
! [X0] : sP5(X0,additive_identity,multiply(X0,additive_inverse(X0)),X0),
inference(forward_demodulation,[],[f35324,f802]) ).
fof(f35324,plain,
! [X0] : sP5(X0,additive_identity,multiply(multiply(X0,additive_inverse(X0)),additive_inverse(X0)),X0),
inference(unit_resulting_resolution,[],[f372,f13021,f33]) ).
fof(f13021,plain,
! [X0] : sP4(X0,additive_identity,additive_inverse(X0),X0),
inference(unit_resulting_resolution,[],[f5,f20,f31]) ).
fof(f4662,plain,
! [X0,X1] : ~ sP2(X0,X1,X1,additive_inverse(X0)),
inference(forward_demodulation,[],[f4645,f84]) ).
fof(f84,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(unit_resulting_resolution,[],[f2,f51,f16]) ).
fof(f2,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
fof(f4645,plain,
! [X0,X1] : ~ sP2(X0,X1,add(additive_identity,X1),additive_inverse(X0)),
inference(unit_resulting_resolution,[],[f51,f5,f28]) ).
fof(f4659,plain,
! [X0,X1] : ~ sP2(additive_inverse(X0),X1,X1,X0),
inference(forward_demodulation,[],[f4650,f84]) ).
fof(f4650,plain,
! [X0,X1] : ~ sP2(additive_inverse(X0),X1,add(additive_identity,X1),X0),
inference(unit_resulting_resolution,[],[f51,f6,f28]) ).
fof(f5674,plain,
! [X0,X1] : sum(X0,additive_inverse(add(X1,X0)),additive_inverse(X1)),
inference(unit_resulting_resolution,[],[f4725,f5653,f27]) ).
fof(f5653,plain,
! [X0,X1] : ~ sP2(additive_inverse(X0),X0,X1,X1),
inference(superposition,[],[f5601,f4741]) ).
fof(f5601,plain,
! [X0,X1] : ~ sP2(X0,additive_inverse(X0),X1,X1),
inference(unit_resulting_resolution,[],[f4,f5086,f28]) ).
fof(f5086,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1),
inference(unit_resulting_resolution,[],[f4724,f9]) ).
fof(f4724,plain,
! [X0,X1] : sum(add(X0,X1),additive_inverse(X1),X0),
inference(unit_resulting_resolution,[],[f4,f4659,f27]) ).
fof(f141276,plain,
sum(additive_inverse(b),multiply(add(a,b),b),c),
inference(unit_resulting_resolution,[],[f66966,f10213]) ).
fof(f10213,plain,
! [X2,X0,X1] :
( ~ sum(X2,X0,X1)
| sum(additive_inverse(X0),X1,X2) ),
inference(resolution,[],[f30,f7461]) ).
fof(f7461,plain,
! [X0,X1] : sP3(X0,additive_inverse(X1),X1,X0),
inference(unit_resulting_resolution,[],[f4731,f51,f29]) ).
fof(f29,plain,
! [X2,X3,X0,X1,X5] :
( ~ sum(X0,X1,X2)
| ~ sum(X2,X3,X5)
| sP3(X5,X0,X3,X1) ),
inference(cnf_transformation,[],[f29_D]) ).
fof(f29_D,plain,
! [X1,X3,X0,X5] :
( ! [X2] :
( ~ sum(X0,X1,X2)
| ~ sum(X2,X3,X5) )
<=> ~ sP3(X5,X0,X3,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP3])]) ).
fof(f4731,plain,
! [X0,X1] : sum(add(X0,additive_inverse(X1)),X1,X0),
inference(unit_resulting_resolution,[],[f4,f4662,f27]) ).
fof(f30,plain,
! [X3,X0,X1,X4,X5] :
( ~ sP3(X5,X0,X3,X1)
| sum(X0,X4,X5)
| ~ sum(X1,X3,X4) ),
inference(general_splitting,[],[f7,f29_D]) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X0,X1,X2)
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4)
| sum(X0,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition1) ).
fof(f367,plain,
! [X0,X1] : product(X0,multiply(X0,X1),multiply(X0,X1)),
inference(unit_resulting_resolution,[],[f3,f257,f24]) ).
fof(f257,plain,
! [X0,X1] : sP0(multiply(X0,X1),X0,X1,X0),
inference(unit_resulting_resolution,[],[f3,f20,f23]) ).
fof(f592649,plain,
~ sP10(add(a,b),c,b,add(b,c)),
inference(unit_resulting_resolution,[],[f66978,f253661,f45]) ).
fof(f45,plain,
! [X0,X1,X8,X6,X7] :
( ~ sP10(X0,X8,X1,X7)
| ~ product(X0,X1,X6)
| sP11(X0,X8,X6,X7) ),
inference(cnf_transformation,[],[f45_D]) ).
fof(f45_D,plain,
! [X7,X6,X8,X0] :
( ! [X1] :
( ~ sP10(X0,X8,X1,X7)
| ~ product(X0,X1,X6) )
<=> ~ sP11(X0,X8,X6,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP11])]) ).
fof(f253661,plain,
! [X0] : ~ sP11(add(a,b),c,X0,X0),
inference(forward_demodulation,[],[f253660,f83]) ).
fof(f253660,plain,
! [X0] : ~ sP11(add(a,b),c,X0,add(X0,additive_identity)),
inference(forward_demodulation,[],[f253659,f73]) ).
fof(f73,plain,
additive_identity = additive_inverse(additive_identity),
inference(unit_resulting_resolution,[],[f1,f6,f16]) ).
fof(f253659,plain,
! [X0] : ~ sP11(add(a,b),c,X0,add(X0,additive_inverse(additive_identity))),
inference(forward_demodulation,[],[f253465,f43866]) ).
fof(f43866,plain,
! [X0,X1] : add(X1,X0) = additive_inverse(add(X0,X1)),
inference(superposition,[],[f43850,f6021]) ).
fof(f6021,plain,
! [X0,X1] : add(X0,X1) = additive_inverse(additive_inverse(add(X1,X0))),
inference(unit_resulting_resolution,[],[f4744,f4984,f16]) ).
fof(f4984,plain,
! [X0,X1] : sum(add(X0,X1),additive_identity,add(X1,X0)),
inference(unit_resulting_resolution,[],[f51,f4639,f27]) ).
fof(f4639,plain,
! [X0,X1] : ~ sP2(additive_identity,X0,add(X0,X1),X1),
inference(unit_resulting_resolution,[],[f4,f2,f28]) ).
fof(f4744,plain,
! [X0] : sum(X0,additive_identity,additive_inverse(additive_inverse(X0))),
inference(unit_resulting_resolution,[],[f4635,f4723,f27]) ).
fof(f4635,plain,
! [X0] : ~ sP2(additive_identity,additive_identity,X0,X0),
inference(unit_resulting_resolution,[],[f1,f2,f28]) ).
fof(f253465,plain,
! [X0] : ~ sP11(add(a,b),c,X0,additive_inverse(add(additive_inverse(additive_identity),X0))),
inference(unit_resulting_resolution,[],[f5675,f191433,f46]) ).
fof(f46,plain,
! [X0,X8,X6,X9,X7] :
( ~ sP11(X0,X8,X6,X7)
| product(X0,X8,X9)
| ~ sum(X6,X7,X9) ),
inference(general_splitting,[],[f44,f45_D]) ).
fof(f44,plain,
! [X0,X1,X8,X6,X9,X7] :
( ~ product(X0,X1,X6)
| ~ sum(X6,X7,X9)
| product(X0,X8,X9)
| ~ sP10(X0,X8,X1,X7) ),
inference(general_splitting,[],[f13,f43_D]) ).
fof(f13,axiom,
! [X3,X0,X1,X8,X6,X9,X7] :
( ~ product(X0,X1,X6)
| ~ product(X0,X3,X7)
| ~ sum(X6,X7,X9)
| ~ sum(X1,X3,X8)
| product(X0,X8,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
fof(f191433,plain,
~ product(add(a,b),c,additive_identity),
inference(unit_resulting_resolution,[],[f39224,f185618,f41]) ).
fof(f41,plain,
! [X0,X1,X8,X6,X7] :
( ~ sP8(X0,X8,X1,X7)
| ~ product(X1,X0,X6)
| sP9(X0,X8,X6,X7) ),
inference(cnf_transformation,[],[f41_D]) ).
fof(f41_D,plain,
! [X7,X6,X8,X0] :
( ! [X1] :
( ~ sP8(X0,X8,X1,X7)
| ~ product(X1,X0,X6) )
<=> ~ sP9(X0,X8,X6,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP9])]) ).
fof(f185618,plain,
~ sP9(c,b,additive_identity,c),
inference(forward_demodulation,[],[f185459,f37837]) ).
fof(f185459,plain,
~ sP9(c,b,additive_identity,multiply(additive_inverse(c),c)),
inference(unit_resulting_resolution,[],[f37836,f184601,f42]) ).
fof(f42,plain,
! [X0,X8,X6,X9,X7] :
( ~ sP9(X0,X8,X6,X7)
| product(X8,X0,X9)
| ~ sum(X6,X7,X9) ),
inference(general_splitting,[],[f40,f41_D]) ).
fof(f40,plain,
! [X0,X1,X8,X6,X9,X7] :
( ~ product(X1,X0,X6)
| ~ sum(X6,X7,X9)
| product(X8,X0,X9)
| ~ sP8(X0,X8,X1,X7) ),
inference(general_splitting,[],[f15,f39_D]) ).
fof(f39,plain,
! [X3,X0,X1,X8,X7] :
( ~ product(X3,X0,X7)
| ~ sum(X1,X3,X8)
| sP8(X0,X8,X1,X7) ),
inference(cnf_transformation,[],[f39_D]) ).
fof(f39_D,plain,
! [X7,X1,X8,X0] :
( ! [X3] :
( ~ product(X3,X0,X7)
| ~ sum(X1,X3,X8) )
<=> ~ sP8(X0,X8,X1,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP8])]) ).
fof(f15,axiom,
! [X3,X0,X1,X8,X6,X9,X7] :
( ~ product(X1,X0,X6)
| ~ product(X3,X0,X7)
| ~ sum(X6,X7,X9)
| ~ sum(X1,X3,X8)
| product(X8,X0,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity4) ).
fof(f184601,plain,
~ product(b,c,c),
inference(unit_resulting_resolution,[],[f2587,f184451,f26]) ).
fof(f26,plain,
! [X3,X0,X1,X4,X5] :
( ~ sP1(X3,X0,X5,X1)
| ~ product(X1,X3,X4)
| ~ product(X0,X4,X5) ),
inference(general_splitting,[],[f11,f25_D]) ).
fof(f25,plain,
! [X2,X3,X0,X1,X5] :
( ~ product(X0,X1,X2)
| product(X2,X3,X5)
| sP1(X3,X0,X5,X1) ),
inference(cnf_transformation,[],[f25_D]) ).
fof(f25_D,plain,
! [X1,X5,X0,X3] :
( ! [X2] :
( ~ product(X0,X1,X2)
| product(X2,X3,X5) )
<=> ~ sP1(X3,X0,X5,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP1])]) ).
fof(f11,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| product(X2,X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication2) ).
fof(f184451,plain,
product(c,a,c),
inference(forward_demodulation,[],[f184449,f42121]) ).
fof(f42121,plain,
c = additive_inverse(c),
inference(forward_demodulation,[],[f41735,f4741]) ).
fof(f41735,plain,
c = additive_inverse(additive_inverse(additive_inverse(c))),
inference(unit_resulting_resolution,[],[f4729,f40809,f16]) ).
fof(f40809,plain,
sum(additive_identity,additive_inverse(c),c),
inference(unit_resulting_resolution,[],[f4659,f40788,f27]) ).
fof(f40788,plain,
sum(c,c,additive_identity),
inference(forward_demodulation,[],[f40787,f207]) ).
fof(f40787,plain,
sum(c,c,multiply(additive_identity,c)),
inference(forward_demodulation,[],[f40785,f1858]) ).
fof(f1858,plain,
! [X0] : multiply(X0,c) = multiply(multiply(X0,c),b),
inference(unit_resulting_resolution,[],[f494,f210]) ).
fof(f494,plain,
! [X0] : product(X0,c,multiply(multiply(X0,c),b)),
inference(unit_resulting_resolution,[],[f266,f478,f24]) ).
fof(f478,plain,
product(c,b,c),
inference(superposition,[],[f3,f460]) ).
fof(f40785,plain,
sum(c,c,multiply(multiply(additive_identity,c),b)),
inference(unit_resulting_resolution,[],[f494,f40193,f38]) ).
fof(f4729,plain,
! [X0] : sum(additive_identity,X0,additive_inverse(additive_inverse(X0))),
inference(unit_resulting_resolution,[],[f5,f4662,f27]) ).
fof(f184449,plain,
product(c,a,additive_inverse(c)),
inference(unit_resulting_resolution,[],[f41138,f184131,f46]) ).
fof(f184131,plain,
sP11(c,a,additive_identity,c),
inference(forward_demodulation,[],[f184106,f43905]) ).
fof(f43905,plain,
! [X0,X1] : add(X0,add(X1,X0)) = X1,
inference(superposition,[],[f5114,f43850]) ).
fof(f5114,plain,
! [X0,X1] : add(additive_inverse(X0),add(X1,X0)) = X1,
inference(unit_resulting_resolution,[],[f4724,f94]) ).
fof(f184106,plain,
sP11(c,add(c,add(a,c)),additive_identity,c),
inference(unit_resulting_resolution,[],[f30139,f183719,f45]) ).
fof(f183719,plain,
product(c,add(a,c),additive_identity),
inference(superposition,[],[f3,f183066]) ).
fof(f183066,plain,
additive_identity = multiply(c,add(a,c)),
inference(forward_demodulation,[],[f183047,f198]) ).
fof(f183047,plain,
multiply(c,additive_identity) = multiply(c,add(a,c)),
inference(unit_resulting_resolution,[],[f166148,f210]) ).
fof(f166148,plain,
product(c,additive_identity,multiply(c,add(a,c))),
inference(unit_resulting_resolution,[],[f264,f68458,f24]) ).
fof(f68458,plain,
! [X0] : product(add(a,c),multiply(c,X0),additive_identity),
inference(unit_resulting_resolution,[],[f367,f67392,f24]) ).
fof(f67392,plain,
! [X0] : sP0(additive_identity,add(a,c),X0,c),
inference(forward_demodulation,[],[f67391,f207]) ).
fof(f67391,plain,
! [X0] : sP0(multiply(additive_identity,X0),add(a,c),X0,c),
inference(forward_demodulation,[],[f67003,f802]) ).
fof(f67003,plain,
! [X0] : sP0(multiply(multiply(additive_identity,X0),X0),add(a,c),X0,c),
inference(unit_resulting_resolution,[],[f372,f66986,f23]) ).
fof(f66986,plain,
product(add(a,c),c,additive_identity),
inference(forward_demodulation,[],[f66984,f41470]) ).
fof(f41470,plain,
! [X0] : additive_identity = add(X0,X0),
inference(unit_resulting_resolution,[],[f40795,f94]) ).
fof(f66984,plain,
product(add(a,c),c,add(c,c)),
inference(unit_resulting_resolution,[],[f51,f49234,f42]) ).
fof(f49234,plain,
sP9(c,add(a,c),c,c),
inference(forward_demodulation,[],[f48336,f87]) ).
fof(f48336,plain,
sP9(c,add(c,a),c,c),
inference(unit_resulting_resolution,[],[f394,f22567,f41]) ).
fof(f22567,plain,
! [X0,X1] : sP8(X0,add(X0,X1),X1,X0),
inference(unit_resulting_resolution,[],[f51,f20,f39]) ).
fof(f394,plain,
product(a,c,c),
inference(forward_demodulation,[],[f381,f203]) ).
fof(f381,plain,
product(a,multiply(a,b),c),
inference(unit_resulting_resolution,[],[f3,f258,f24]) ).
fof(f258,plain,
sP0(c,a,b,a),
inference(unit_resulting_resolution,[],[f21,f20,f23]) ).
fof(f264,plain,
! [X0,X1] : sP0(multiply(X0,X1),X0,multiply(X0,X1),X1),
inference(unit_resulting_resolution,[],[f20,f3,f23]) ).
fof(f30139,plain,
! [X0,X1] : sP10(X0,add(X0,X1),X1,X0),
inference(unit_resulting_resolution,[],[f51,f20,f43]) ).
fof(f41138,plain,
! [X0] : sum(additive_identity,X0,additive_inverse(X0)),
inference(unit_resulting_resolution,[],[f5601,f40795,f27]) ).
fof(f2587,plain,
sP1(a,b,c,c),
inference(unit_resulting_resolution,[],[f3,f2582,f25]) ).
fof(f2582,plain,
~ product(multiply(b,c),a,c),
inference(forward_demodulation,[],[f2581,f802]) ).
fof(f2581,plain,
~ product(multiply(multiply(b,c),c),a,c),
inference(unit_resulting_resolution,[],[f372,f2572,f23]) ).
fof(f2572,plain,
~ sP0(c,b,a,c),
inference(unit_resulting_resolution,[],[f3,f2248,f24]) ).
fof(f2248,plain,
~ product(b,multiply(c,a),c),
inference(forward_demodulation,[],[f2247,f802]) ).
fof(f2247,plain,
~ product(b,multiply(multiply(c,a),a),c),
inference(forward_demodulation,[],[f2235,f802]) ).
fof(f2235,plain,
~ product(b,multiply(multiply(multiply(c,a),a),a),c),
inference(unit_resulting_resolution,[],[f372,f1608,f26]) ).
fof(f1608,plain,
sP1(a,b,c,multiply(c,a)),
inference(unit_resulting_resolution,[],[f423,f1254,f25]) ).
fof(f1254,plain,
product(b,multiply(c,a),multiply(b,a)),
inference(unit_resulting_resolution,[],[f264,f379,f24]) ).
fof(f379,plain,
! [X0] : product(a,multiply(b,X0),multiply(c,X0)),
inference(unit_resulting_resolution,[],[f3,f269,f24]) ).
fof(f423,plain,
~ product(multiply(b,a),a,c),
inference(unit_resulting_resolution,[],[f3,f345,f23]) ).
fof(f345,plain,
~ sP0(c,b,a,a),
inference(unit_resulting_resolution,[],[f20,f22,f24]) ).
fof(f22,axiom,
~ product(b,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
fof(f37836,plain,
! [X0] : sum(additive_identity,multiply(additive_inverse(X0),X0),X0),
inference(forward_demodulation,[],[f37759,f73]) ).
fof(f37759,plain,
! [X0] : sum(additive_inverse(additive_identity),multiply(additive_inverse(X0),X0),X0),
inference(unit_resulting_resolution,[],[f37010,f10219]) ).
fof(f10219,plain,
! [X2,X0,X1] :
( ~ sum(X0,X2,X1)
| sum(additive_inverse(X0),X1,X2) ),
inference(resolution,[],[f30,f7636]) ).
fof(f7636,plain,
! [X0,X1] : sP3(X0,additive_inverse(X1),X0,X1),
inference(forward_demodulation,[],[f7417,f4741]) ).
fof(f7417,plain,
! [X0,X1] : sP3(additive_inverse(additive_inverse(X0)),additive_inverse(X1),X0,X1),
inference(unit_resulting_resolution,[],[f4729,f5,f29]) ).
fof(f39224,plain,
! [X0] : sP8(c,X0,add(a,X0),c),
inference(forward_demodulation,[],[f39223,f4741]) ).
fof(f39223,plain,
! [X0] : sP8(c,X0,add(additive_inverse(additive_inverse(a)),X0),c),
inference(forward_demodulation,[],[f39164,f25870]) ).
fof(f25870,plain,
! [X0,X1] : add(additive_inverse(X1),X0) = additive_inverse(add(X1,additive_inverse(X0))),
inference(superposition,[],[f6335,f5244]) ).
fof(f5244,plain,
! [X0,X1] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(unit_resulting_resolution,[],[f4731,f94]) ).
fof(f6335,plain,
! [X0,X1] : additive_inverse(X0) = add(additive_inverse(add(X1,X0)),X1),
inference(superposition,[],[f5114,f5114]) ).
fof(f39164,plain,
! [X0] : sP8(c,X0,additive_inverse(add(additive_inverse(a),additive_inverse(X0))),c),
inference(unit_resulting_resolution,[],[f6693,f38526,f39]) ).
fof(f38526,plain,
product(additive_inverse(a),c,c),
inference(forward_demodulation,[],[f38441,f203]) ).
fof(f38441,plain,
product(additive_inverse(a),c,multiply(a,b)),
inference(superposition,[],[f375,f37837]) ).
fof(f375,plain,
! [X0] : product(X0,c,multiply(multiply(X0,a),b)),
inference(unit_resulting_resolution,[],[f21,f266,f24]) ).
fof(f6693,plain,
! [X0,X1] : sum(additive_inverse(add(X0,additive_inverse(X1))),X0,X1),
inference(superposition,[],[f5140,f5243]) ).
fof(f5243,plain,
! [X0,X1] : add(add(X0,additive_inverse(X1)),X1) = X0,
inference(unit_resulting_resolution,[],[f4731,f93]) ).
fof(f5140,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X0,X1),X1),
inference(unit_resulting_resolution,[],[f4725,f9]) ).
fof(f5675,plain,
! [X0,X1] : sum(X0,additive_inverse(add(additive_inverse(X1),X0)),X1),
inference(unit_resulting_resolution,[],[f4732,f5653,f27]) ).
fof(f4732,plain,
! [X0,X1] : sum(add(additive_inverse(X0),X1),X0,X1),
inference(unit_resulting_resolution,[],[f51,f4662,f27]) ).
fof(f66978,plain,
product(add(a,b),b,add(b,c)),
inference(unit_resulting_resolution,[],[f51,f49224,f42]) ).
fof(f49224,plain,
sP9(b,add(a,b),c,b),
inference(forward_demodulation,[],[f49223,f87]) ).
fof(f49223,plain,
sP9(b,add(b,a),c,b),
inference(forward_demodulation,[],[f48342,f460]) ).
fof(f48342,plain,
sP9(b,add(b,a),multiply(c,b),b),
inference(unit_resulting_resolution,[],[f377,f22567,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG008-6 : TPTP v8.2.0. Released v1.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n006.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat May 18 12:17:23 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (7010)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (7013)WARNING: value z3 for option sas not known
% 0.14/0.38 % (7011)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (7014)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (7013)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)
% 0.14/0.38 % (7012)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (7015)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)
% 0.14/0.38 % (7016)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)
% 0.14/0.38 % (7017)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)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.40 TRYING [4]
% 0.21/0.40 TRYING [3]
% 0.21/0.44 TRYING [5]
% 0.21/0.45 TRYING [4]
% 0.21/0.56 TRYING [6]
% 0.21/0.56 TRYING [5]
% 3.07/0.81 TRYING [7]
% 4.11/0.98 TRYING [6]
% 7.84/1.48 TRYING [1]
% 7.84/1.48 TRYING [2]
% 7.84/1.48 TRYING [3]
% 8.05/1.49 TRYING [4]
% 8.31/1.55 TRYING [5]
% 8.81/1.66 TRYING [8]
% 9.36/1.73 TRYING [6]
% 12.49/2.19 TRYING [7]
% 13.69/2.30 TRYING [7]
% 19.94/3.29 TRYING [8]
% 29.99/4.70 TRYING [9]
% 47.34/7.14 TRYING [9]
% 52.66/7.94 TRYING [8]
% 64.80/9.66 TRYING [10]
% 67.51/10.01 % (7017)First to succeed.
% 67.51/10.02 % (7017)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-7010"
% 67.51/10.03 % (7017)Refutation found. Thanks to Tanya!
% 67.51/10.03 % SZS status Unsatisfiable for theBenchmark
% 67.51/10.03 % SZS output start Proof for theBenchmark
% See solution above
% 67.51/10.03 % (7017)------------------------------
% 67.51/10.03 % (7017)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 67.51/10.03 % (7017)Termination reason: Refutation
% 67.51/10.03
% 67.51/10.03 % (7017)Memory used [KB]: 33309
% 67.51/10.03 % (7017)Time elapsed: 9.635 s
% 67.51/10.03 % (7017)Instructions burned: 20884 (million)
% 67.51/10.03 % (7010)Success in time 9.633 s
%------------------------------------------------------------------------------