TSTP Solution File: BOO008-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : BOO008-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 10:42:00 EDT 2024
% Result : Unsatisfiable 57.77s 8.69s
% Output : Refutation 57.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 36
% Syntax : Number of formulae : 173 ( 125 unt; 0 def)
% Number of atoms : 283 ( 19 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 262 ( 152 ~; 98 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 330 ( 330 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f583522,plain,
$false,
inference(subsumption_resolution,[],[f583521,f54011]) ).
fof(f54011,plain,
! [X0,X1] : product(add(X0,X1),X0,X0),
inference(unit_resulting_resolution,[],[f62,f43383,f54]) ).
fof(f54,plain,
! [X3,X0,X1,X6,X4] :
( ~ sum(X1,X0,X3)
| product(X3,X4,X6)
| sP13(X4,X0,X6,X1) ),
inference(cnf_transformation,[],[f54_D]) ).
fof(f54_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(f43383,plain,
! [X0,X1] : ~ sP13(X0,X0,X0,X1),
inference(forward_demodulation,[],[f43362,f153]) ).
fof(f153,plain,
! [X0] : add(X0,additive_identity) = X0,
inference(unit_resulting_resolution,[],[f62,f5,f21]) ).
fof(f21,axiom,
! [X0,X1,X8,X7] :
( ~ sum(X0,X1,X8)
| X7 = X8
| ~ sum(X0,X1,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f5,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
fof(f43362,plain,
! [X0,X1] : ~ sP13(X0,X0,add(X0,additive_identity),X1),
inference(unit_resulting_resolution,[],[f62,f40570,f55]) ).
fof(f55,plain,
! [X0,X1,X6,X4,X5] :
( ~ sP13(X4,X0,X6,X1)
| ~ sP12(X4,X0,X5,X1)
| ~ sum(X5,X0,X6) ),
inference(general_splitting,[],[f53,f54_D]) ).
fof(f53,plain,
! [X3,X0,X1,X6,X4,X5] :
( ~ sum(X5,X0,X6)
| ~ sum(X1,X0,X3)
| product(X3,X4,X6)
| ~ sP12(X4,X0,X5,X1) ),
inference(general_splitting,[],[f15,f52_D]) ).
fof(f52,plain,
! [X2,X0,X1,X4,X5] :
( ~ product(X1,X2,X5)
| ~ sum(X2,X0,X4)
| sP12(X4,X0,X5,X1) ),
inference(cnf_transformation,[],[f52_D]) ).
fof(f52_D,plain,
! [X1,X5,X0,X4] :
( ! [X2] :
( ~ product(X1,X2,X5)
| ~ sum(X2,X0,X4) )
<=> ~ sP12(X4,X0,X5,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP12])]) ).
fof(f15,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X1,X2,X5)
| ~ sum(X5,X0,X6)
| ~ sum(X2,X0,X4)
| ~ sum(X1,X0,X3)
| product(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity7) ).
fof(f40570,plain,
! [X0,X1] : sP12(X1,X1,additive_identity,X0),
inference(superposition,[],[f4401,f40263]) ).
fof(f40263,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(unit_resulting_resolution,[],[f6,f7906,f21]) ).
fof(f7906,plain,
! [X0] : sum(multiply(X0,additive_identity),additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f2,f6828,f30]) ).
fof(f30,plain,
! [X3,X0,X1,X6,X4] :
( ~ product(X0,X1,X3)
| sum(X3,X4,X6)
| sP1(X4,X0,X6,X1) ),
inference(cnf_transformation,[],[f30_D]) ).
fof(f30_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(f6828,plain,
! [X0] : ~ sP1(additive_identity,X0,additive_identity,additive_identity),
inference(forward_demodulation,[],[f6827,f458]) ).
fof(f458,plain,
! [X0] : additive_identity = multiply(X0,inverse(X0)),
inference(unit_resulting_resolution,[],[f19,f92,f22]) ).
fof(f22,axiom,
! [X0,X1,X8,X7] :
( ~ product(X0,X1,X8)
| X7 = X8
| ~ product(X0,X1,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
fof(f92,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(unit_resulting_resolution,[],[f2,f4]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| product(X1,X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_multiplication) ).
fof(f19,axiom,
! [X0] : product(inverse(X0),X0,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse1) ).
fof(f6827,plain,
! [X0] : ~ sP1(multiply(X0,inverse(X0)),X0,additive_identity,additive_identity),
inference(forward_demodulation,[],[f6550,f460]) ).
fof(f460,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(unit_resulting_resolution,[],[f2,f92,f22]) ).
fof(f6550,plain,
! [X0] : ~ sP1(multiply(inverse(X0),X0),X0,additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f20,f535,f31]) ).
fof(f31,plain,
! [X0,X1,X6,X4,X5] :
( ~ sP1(X4,X0,X6,X1)
| ~ sP0(X5,X0,X4,X1)
| ~ product(X0,X5,X6) ),
inference(general_splitting,[],[f29,f30_D]) ).
fof(f29,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,f28_D]) ).
fof(f28,plain,
! [X2,X0,X1,X4,X5] :
( ~ product(X0,X2,X4)
| ~ sum(X1,X2,X5)
| sP0(X5,X0,X4,X1) ),
inference(cnf_transformation,[],[f28_D]) ).
fof(f28_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)
| ~ product(X0,X2,X4)
| ~ sum(X1,X2,X5)
| sum(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
fof(f535,plain,
! [X0,X1] : sP0(X0,X1,multiply(X0,X1),additive_identity),
inference(unit_resulting_resolution,[],[f5,f92,f28]) ).
fof(f20,axiom,
! [X0] : product(X0,inverse(X0),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse2) ).
fof(f2,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
fof(f4401,plain,
! [X0,X1] : sP12(X0,X0,multiply(X1,additive_identity),X1),
inference(unit_resulting_resolution,[],[f5,f2,f52]) ).
fof(f62,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/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
fof(f1,axiom,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f583521,plain,
~ product(add(x_plus_y__plus_z,x),x_plus_y__plus_z,x_plus_y__plus_z),
inference(unit_resulting_resolution,[],[f62,f462281,f50]) ).
fof(f50,plain,
! [X3,X0,X1,X6,X4] :
( ~ product(X3,X4,X6)
| ~ sum(X1,X0,X3)
| sP11(X4,X0,X6,X1) ),
inference(cnf_transformation,[],[f50_D]) ).
fof(f50_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(f462281,plain,
~ sP11(x_plus_y__plus_z,x_plus_y__plus_z,x_plus_y__plus_z,x),
inference(unit_resulting_resolution,[],[f47389,f457905,f51]) ).
fof(f51,plain,
! [X0,X1,X6,X4,X5] :
( ~ sP11(X4,X0,X6,X1)
| ~ sP10(X5,X4,X0,X1)
| sum(X5,X0,X6) ),
inference(general_splitting,[],[f49,f50_D]) ).
fof(f49,plain,
! [X3,X0,X1,X6,X4,X5] :
( ~ product(X3,X4,X6)
| ~ sum(X1,X0,X3)
| sum(X5,X0,X6)
| ~ sP10(X5,X4,X0,X1) ),
inference(general_splitting,[],[f16,f48_D]) ).
fof(f48,plain,
! [X2,X0,X1,X4,X5] :
( ~ product(X1,X2,X5)
| ~ sum(X2,X0,X4)
| sP10(X5,X4,X0,X1) ),
inference(cnf_transformation,[],[f48_D]) ).
fof(f48_D,plain,
! [X1,X0,X4,X5] :
( ! [X2] :
( ~ product(X1,X2,X5)
| ~ sum(X2,X0,X4) )
<=> ~ sP10(X5,X4,X0,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP10])]) ).
fof(f16,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X3,X4,X6)
| ~ product(X1,X2,X5)
| ~ sum(X2,X0,X4)
| ~ sum(X1,X0,X3)
| sum(X5,X0,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity8) ).
fof(f457905,plain,
~ sum(x,x_plus_y__plus_z,x_plus_y__plus_z),
inference(unit_resulting_resolution,[],[f410465,f456067,f58]) ).
fof(f58,plain,
! [X3,X0,X1,X6,X4] :
( ~ sum(X0,X1,X3)
| product(X3,X4,X6)
| sP15(X4,X0,X6,X1) ),
inference(cnf_transformation,[],[f58_D]) ).
fof(f58_D,plain,
! [X1,X6,X0,X4] :
( ! [X3] :
( ~ sum(X0,X1,X3)
| product(X3,X4,X6) )
<=> ~ sP15(X4,X0,X6,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP15])]) ).
fof(f456067,plain,
~ product(x_plus_y__plus_z,x__plus_y_plus_z,x__plus_y_plus_z),
inference(unit_resulting_resolution,[],[f454993,f4]) ).
fof(f454993,plain,
~ product(x__plus_y_plus_z,x_plus_y__plus_z,x__plus_y_plus_z),
inference(unit_resulting_resolution,[],[f411972,f454750,f46]) ).
fof(f46,plain,
! [X3,X0,X1,X6,X4] :
( ~ product(X3,X4,X6)
| ~ sum(X0,X1,X3)
| sP9(X4,X0,X6,X1) ),
inference(cnf_transformation,[],[f46_D]) ).
fof(f46_D,plain,
! [X1,X6,X0,X4] :
( ! [X3] :
( ~ product(X3,X4,X6)
| ~ sum(X0,X1,X3) )
<=> ~ sP9(X4,X0,X6,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP9])]) ).
fof(f454750,plain,
sum(z,x__plus_y_plus_z,x__plus_y_plus_z),
inference(forward_demodulation,[],[f454748,f379643]) ).
fof(f379643,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = X0,
inference(unit_resulting_resolution,[],[f227672,f466]) ).
fof(f466,plain,
! [X2,X0,X1] :
( ~ product(X1,X2,X0)
| multiply(X1,X2) = X0 ),
inference(resolution,[],[f22,f2]) ).
fof(f227672,plain,
! [X0,X1] : product(X0,add(X0,X1),X0),
inference(forward_demodulation,[],[f227671,f153]) ).
fof(f227671,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,additive_identity)),
inference(forward_demodulation,[],[f227587,f40562]) ).
fof(f40562,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(superposition,[],[f40263,f460]) ).
fof(f227587,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,multiply(additive_identity,X1))),
inference(unit_resulting_resolution,[],[f19890,f5962]) ).
fof(f5962,plain,
! [X2,X0,X1] :
( sP15(X1,X0,X2,additive_identity)
| product(X0,X1,X2) ),
inference(resolution,[],[f58,f6]) ).
fof(f19890,plain,
! [X2,X0,X1] : ~ sP15(add(X0,X1),X0,add(X0,multiply(X2,X1)),X2),
inference(unit_resulting_resolution,[],[f1,f5576,f59]) ).
fof(f59,plain,
! [X0,X1,X6,X4,X5] :
( ~ sP15(X4,X0,X6,X1)
| ~ sP14(X4,X0,X5,X1)
| ~ sum(X0,X5,X6) ),
inference(general_splitting,[],[f57,f58_D]) ).
fof(f57,plain,
! [X3,X0,X1,X6,X4,X5] :
( ~ sum(X0,X5,X6)
| ~ sum(X0,X1,X3)
| product(X3,X4,X6)
| ~ sP14(X4,X0,X5,X1) ),
inference(general_splitting,[],[f13,f56_D]) ).
fof(f56,plain,
! [X2,X0,X1,X4,X5] :
( ~ product(X1,X2,X5)
| ~ sum(X0,X2,X4)
| sP14(X4,X0,X5,X1) ),
inference(cnf_transformation,[],[f56_D]) ).
fof(f56_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(f13,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X1,X2,X5)
| ~ sum(X0,X5,X6)
| ~ sum(X0,X2,X4)
| ~ sum(X0,X1,X3)
| product(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity5) ).
fof(f5576,plain,
! [X2,X0,X1] : sP14(add(X0,X1),X0,multiply(X2,X1),X2),
inference(unit_resulting_resolution,[],[f1,f2,f56]) ).
fof(f454748,plain,
sum(z,x__plus_y_plus_z,multiply(x__plus_y_plus_z,add(x__plus_y_plus_z,z))),
inference(unit_resulting_resolution,[],[f3909,f49957,f51]) ).
fof(f49957,plain,
sP10(z,x__plus_y_plus_z,x__plus_y_plus_z,z),
inference(unit_resulting_resolution,[],[f44154,f49406,f48]) ).
fof(f49406,plain,
sum(y_plus_z,x__plus_y_plus_z,x__plus_y_plus_z),
inference(unit_resulting_resolution,[],[f31758,f49358,f34]) ).
fof(f34,plain,
! [X3,X0,X1,X6,X4] :
( ~ product(X1,X0,X3)
| sum(X3,X4,X6)
| sP3(X4,X0,X6,X1) ),
inference(cnf_transformation,[],[f34_D]) ).
fof(f34_D,plain,
! [X1,X6,X0,X4] :
( ! [X3] :
( ~ product(X1,X0,X3)
| sum(X3,X4,X6) )
<=> ~ sP3(X4,X0,X6,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP3])]) ).
fof(f49358,plain,
product(y_plus_z,x__plus_y_plus_z,y_plus_z),
inference(forward_demodulation,[],[f49354,f153]) ).
fof(f49354,plain,
product(add(y_plus_z,additive_identity),x__plus_y_plus_z,y_plus_z),
inference(unit_resulting_resolution,[],[f62,f42521,f54]) ).
fof(f42521,plain,
~ sP13(x__plus_y_plus_z,y_plus_z,y_plus_z,additive_identity),
inference(forward_demodulation,[],[f42520,f153]) ).
fof(f42520,plain,
~ sP13(x__plus_y_plus_z,y_plus_z,add(y_plus_z,additive_identity),additive_identity),
inference(unit_resulting_resolution,[],[f62,f40758,f55]) ).
fof(f40758,plain,
sP12(x__plus_y_plus_z,y_plus_z,additive_identity,additive_identity),
inference(superposition,[],[f4422,f40263]) ).
fof(f4422,plain,
! [X0] : sP12(x__plus_y_plus_z,y_plus_z,multiply(x,X0),X0),
inference(unit_resulting_resolution,[],[f24,f92,f52]) ).
fof(f24,axiom,
sum(x,y_plus_z,x__plus_y_plus_z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_plus__y_plus_z) ).
fof(f31758,plain,
! [X0,X1] : ~ sP3(X0,X0,X0,X1),
inference(forward_demodulation,[],[f31741,f456]) ).
fof(f456,plain,
! [X0] : multiply(X0,multiplicative_identity) = X0,
inference(unit_resulting_resolution,[],[f7,f92,f22]) ).
fof(f7,axiom,
! [X0] : product(multiplicative_identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity1) ).
fof(f31741,plain,
! [X0,X1] : ~ sP3(X0,X0,multiply(X0,multiplicative_identity),X1),
inference(unit_resulting_resolution,[],[f92,f30074,f35]) ).
fof(f35,plain,
! [X0,X1,X6,X4,X5] :
( ~ sP3(X4,X0,X6,X1)
| ~ sP2(X5,X0,X4,X1)
| ~ product(X5,X0,X6) ),
inference(general_splitting,[],[f33,f34_D]) ).
fof(f33,plain,
! [X3,X0,X1,X6,X4,X5] :
( ~ product(X1,X0,X3)
| ~ product(X5,X0,X6)
| sum(X3,X4,X6)
| ~ sP2(X5,X0,X4,X1) ),
inference(general_splitting,[],[f11,f32_D]) ).
fof(f32,plain,
! [X2,X0,X1,X4,X5] :
( ~ product(X2,X0,X4)
| ~ sum(X1,X2,X5)
| sP2(X5,X0,X4,X1) ),
inference(cnf_transformation,[],[f32_D]) ).
fof(f32_D,plain,
! [X1,X4,X0,X5] :
( ! [X2] :
( ~ product(X2,X0,X4)
| ~ sum(X1,X2,X5) )
<=> ~ sP2(X5,X0,X4,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).
fof(f11,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X1,X0,X3)
| ~ product(X5,X0,X6)
| ~ product(X2,X0,X4)
| ~ sum(X1,X2,X5)
| sum(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity3) ).
fof(f30074,plain,
! [X0,X1] : sP2(multiplicative_identity,X1,X1,X0),
inference(superposition,[],[f1146,f29853]) ).
fof(f29853,plain,
! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
inference(unit_resulting_resolution,[],[f8,f19197,f22]) ).
fof(f19197,plain,
! [X0] : product(add(multiplicative_identity,X0),multiplicative_identity,multiplicative_identity),
inference(unit_resulting_resolution,[],[f1,f19007,f54]) ).
fof(f19007,plain,
! [X0] : ~ sP13(multiplicative_identity,X0,multiplicative_identity,multiplicative_identity),
inference(forward_demodulation,[],[f18654,f157]) ).
fof(f157,plain,
! [X0] : multiplicative_identity = add(X0,inverse(X0)),
inference(unit_resulting_resolution,[],[f62,f17,f21]) ).
fof(f17,axiom,
! [X0] : sum(inverse(X0),X0,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f18654,plain,
! [X0] : ~ sP13(multiplicative_identity,X0,add(X0,inverse(X0)),multiplicative_identity),
inference(unit_resulting_resolution,[],[f62,f4365,f55]) ).
fof(f4365,plain,
! [X0] : sP12(multiplicative_identity,X0,inverse(X0),multiplicative_identity),
inference(unit_resulting_resolution,[],[f17,f7,f52]) ).
fof(f8,axiom,
! [X0] : product(X0,multiplicative_identity,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity2) ).
fof(f1146,plain,
! [X0,X1] : sP2(add(multiplicative_identity,X0),X1,X1,X0),
inference(unit_resulting_resolution,[],[f62,f7,f32]) ).
fof(f44154,plain,
product(z,y_plus_z,z),
inference(forward_demodulation,[],[f44150,f153]) ).
fof(f44150,plain,
product(add(z,additive_identity),y_plus_z,z),
inference(unit_resulting_resolution,[],[f62,f42010,f54]) ).
fof(f42010,plain,
~ sP13(y_plus_z,z,z,additive_identity),
inference(forward_demodulation,[],[f42009,f153]) ).
fof(f42009,plain,
~ sP13(y_plus_z,z,add(z,additive_identity),additive_identity),
inference(unit_resulting_resolution,[],[f62,f40714,f55]) ).
fof(f40714,plain,
sP12(y_plus_z,z,additive_identity,additive_identity),
inference(superposition,[],[f4417,f40263]) ).
fof(f4417,plain,
! [X0] : sP12(y_plus_z,z,multiply(y,X0),X0),
inference(unit_resulting_resolution,[],[f23,f92,f52]) ).
fof(f23,axiom,
sum(y,z,y_plus_z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',y_plus_z) ).
fof(f3909,plain,
! [X2,X0,X1] : sP11(X0,X1,multiply(X0,add(X1,X2)),X2),
inference(unit_resulting_resolution,[],[f62,f92,f50]) ).
fof(f411972,plain,
~ sP9(x_plus_y__plus_z,z,x__plus_y_plus_z,x__plus_y_plus_z),
inference(unit_resulting_resolution,[],[f167,f140029,f47]) ).
fof(f47,plain,
! [X0,X1,X6,X4,X5] :
( ~ sP9(X4,X0,X6,X1)
| ~ sP8(X5,X4,X0,X1)
| sum(X0,X5,X6) ),
inference(general_splitting,[],[f45,f46_D]) ).
fof(f45,plain,
! [X3,X0,X1,X6,X4,X5] :
( ~ product(X3,X4,X6)
| ~ sum(X0,X1,X3)
| sum(X0,X5,X6)
| ~ sP8(X5,X4,X0,X1) ),
inference(general_splitting,[],[f14,f44_D]) ).
fof(f44,plain,
! [X2,X0,X1,X4,X5] :
( ~ product(X1,X2,X5)
| ~ sum(X0,X2,X4)
| sP8(X5,X4,X0,X1) ),
inference(cnf_transformation,[],[f44_D]) ).
fof(f44_D,plain,
! [X1,X0,X4,X5] :
( ! [X2] :
( ~ product(X1,X2,X5)
| ~ sum(X0,X2,X4) )
<=> ~ sP8(X5,X4,X0,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP8])]) ).
fof(f14,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X3,X4,X6)
| ~ product(X1,X2,X5)
| ~ sum(X0,X2,X4)
| ~ sum(X0,X1,X3)
| sum(X0,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity6) ).
fof(f140029,plain,
sP8(x_plus_y,x_plus_y__plus_z,z,x__plus_y_plus_z),
inference(unit_resulting_resolution,[],[f68,f139777,f44]) ).
fof(f139777,plain,
product(x__plus_y_plus_z,x_plus_y,x_plus_y),
inference(forward_demodulation,[],[f139776,f180]) ).
fof(f180,plain,
x_plus_y = add(x,y),
inference(unit_resulting_resolution,[],[f1,f25,f21]) ).
fof(f25,axiom,
sum(x,y,x_plus_y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_plus_y) ).
fof(f139776,plain,
product(x__plus_y_plus_z,x_plus_y,add(x,y)),
inference(forward_demodulation,[],[f139775,f46086]) ).
fof(f46086,plain,
y = multiply(y,y_plus_z),
inference(unit_resulting_resolution,[],[f45957,f466]) ).
fof(f45957,plain,
product(y,y_plus_z,y),
inference(forward_demodulation,[],[f45953,f153]) ).
fof(f45953,plain,
product(add(y,additive_identity),y_plus_z,y),
inference(unit_resulting_resolution,[],[f62,f42202,f54]) ).
fof(f42202,plain,
~ sP13(y_plus_z,y,y,additive_identity),
inference(forward_demodulation,[],[f42201,f153]) ).
fof(f42201,plain,
~ sP13(y_plus_z,y,add(y,additive_identity),additive_identity),
inference(unit_resulting_resolution,[],[f62,f40730,f55]) ).
fof(f40730,plain,
sP12(y_plus_z,y,additive_identity,additive_identity),
inference(superposition,[],[f4419,f40263]) ).
fof(f4419,plain,
! [X0] : sP12(y_plus_z,y,multiply(z,X0),X0),
inference(unit_resulting_resolution,[],[f65,f92,f52]) ).
fof(f65,plain,
sum(z,y,y_plus_z),
inference(unit_resulting_resolution,[],[f23,f3]) ).
fof(f139775,plain,
product(x__plus_y_plus_z,x_plus_y,add(x,multiply(y,y_plus_z))),
inference(forward_demodulation,[],[f139729,f460]) ).
fof(f139729,plain,
product(x__plus_y_plus_z,x_plus_y,add(x,multiply(y_plus_z,y))),
inference(unit_resulting_resolution,[],[f24,f20418,f58]) ).
fof(f20418,plain,
! [X0] : ~ sP15(x_plus_y,x,add(x,multiply(X0,y)),X0),
inference(forward_demodulation,[],[f19812,f135]) ).
fof(f135,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(unit_resulting_resolution,[],[f1,f62,f21]) ).
fof(f19812,plain,
! [X0] : ~ sP15(x_plus_y,x,add(multiply(X0,y),x),X0),
inference(unit_resulting_resolution,[],[f62,f5586,f59]) ).
fof(f5586,plain,
! [X0] : sP14(x_plus_y,x,multiply(X0,y),X0),
inference(unit_resulting_resolution,[],[f25,f2,f56]) ).
fof(f68,plain,
sum(z,x_plus_y,x_plus_y__plus_z),
inference(unit_resulting_resolution,[],[f26,f3]) ).
fof(f26,axiom,
sum(x_plus_y,z,x_plus_y__plus_z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_plus_y__plus_z) ).
fof(f167,plain,
~ sum(z,x_plus_y,x__plus_y_plus_z),
inference(unit_resulting_resolution,[],[f27,f68,f21]) ).
fof(f27,axiom,
x__plus_y_plus_z != x_plus_y__plus_z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equality) ).
fof(f410465,plain,
~ sP15(x__plus_y_plus_z,x,x__plus_y_plus_z,x_plus_y__plus_z),
inference(forward_demodulation,[],[f410463,f178]) ).
fof(f178,plain,
x__plus_y_plus_z = add(y_plus_z,x),
inference(unit_resulting_resolution,[],[f62,f24,f21]) ).
fof(f410463,plain,
~ sP15(x__plus_y_plus_z,x,add(y_plus_z,x),x_plus_y__plus_z),
inference(unit_resulting_resolution,[],[f62,f132336,f59]) ).
fof(f132336,plain,
sP14(x__plus_y_plus_z,x,y_plus_z,x_plus_y__plus_z),
inference(unit_resulting_resolution,[],[f24,f132028,f56]) ).
fof(f132028,plain,
product(x_plus_y__plus_z,y_plus_z,y_plus_z),
inference(forward_demodulation,[],[f132027,f165]) ).
fof(f165,plain,
y_plus_z = add(z,y),
inference(unit_resulting_resolution,[],[f1,f65,f21]) ).
fof(f132027,plain,
product(x_plus_y__plus_z,y_plus_z,add(z,y)),
inference(forward_demodulation,[],[f132026,f50817]) ).
fof(f50817,plain,
y = multiply(y,x_plus_y),
inference(unit_resulting_resolution,[],[f50677,f466]) ).
fof(f50677,plain,
product(y,x_plus_y,y),
inference(forward_demodulation,[],[f50673,f153]) ).
fof(f50673,plain,
product(add(y,additive_identity),x_plus_y,y),
inference(unit_resulting_resolution,[],[f62,f42528,f54]) ).
fof(f42528,plain,
~ sP13(x_plus_y,y,y,additive_identity),
inference(forward_demodulation,[],[f42527,f153]) ).
fof(f42527,plain,
~ sP13(x_plus_y,y,add(y,additive_identity),additive_identity),
inference(unit_resulting_resolution,[],[f62,f40759,f55]) ).
fof(f40759,plain,
sP12(x_plus_y,y,additive_identity,additive_identity),
inference(superposition,[],[f4423,f40263]) ).
fof(f4423,plain,
! [X0] : sP12(x_plus_y,y,multiply(x,X0),X0),
inference(unit_resulting_resolution,[],[f25,f92,f52]) ).
fof(f132026,plain,
product(x_plus_y__plus_z,y_plus_z,add(z,multiply(y,x_plus_y))),
inference(forward_demodulation,[],[f132004,f460]) ).
fof(f132004,plain,
product(x_plus_y__plus_z,y_plus_z,add(z,multiply(x_plus_y,y))),
inference(unit_resulting_resolution,[],[f26,f18472,f54]) ).
fof(f18472,plain,
! [X0] : ~ sP13(y_plus_z,z,add(z,multiply(X0,y)),X0),
inference(unit_resulting_resolution,[],[f62,f4403,f55]) ).
fof(f4403,plain,
! [X0] : sP12(y_plus_z,z,multiply(X0,y),X0),
inference(unit_resulting_resolution,[],[f23,f2,f52]) ).
fof(f47389,plain,
sP10(x,x_plus_y__plus_z,x_plus_y__plus_z,x),
inference(unit_resulting_resolution,[],[f45062,f46875,f48]) ).
fof(f46875,plain,
sum(x_plus_y,x_plus_y__plus_z,x_plus_y__plus_z),
inference(unit_resulting_resolution,[],[f31758,f46830,f34]) ).
fof(f46830,plain,
product(x_plus_y,x_plus_y__plus_z,x_plus_y),
inference(forward_demodulation,[],[f46826,f153]) ).
fof(f46826,plain,
product(add(x_plus_y,additive_identity),x_plus_y__plus_z,x_plus_y),
inference(unit_resulting_resolution,[],[f62,f42209,f54]) ).
fof(f42209,plain,
~ sP13(x_plus_y__plus_z,x_plus_y,x_plus_y,additive_identity),
inference(forward_demodulation,[],[f42208,f153]) ).
fof(f42208,plain,
~ sP13(x_plus_y__plus_z,x_plus_y,add(x_plus_y,additive_identity),additive_identity),
inference(unit_resulting_resolution,[],[f62,f40731,f55]) ).
fof(f40731,plain,
sP12(x_plus_y__plus_z,x_plus_y,additive_identity,additive_identity),
inference(superposition,[],[f4420,f40263]) ).
fof(f4420,plain,
! [X0] : sP12(x_plus_y__plus_z,x_plus_y,multiply(z,X0),X0),
inference(unit_resulting_resolution,[],[f68,f92,f52]) ).
fof(f45062,plain,
product(x,x_plus_y,x),
inference(forward_demodulation,[],[f45058,f153]) ).
fof(f45058,plain,
product(add(x,additive_identity),x_plus_y,x),
inference(unit_resulting_resolution,[],[f62,f42017,f54]) ).
fof(f42017,plain,
~ sP13(x_plus_y,x,x,additive_identity),
inference(forward_demodulation,[],[f42016,f153]) ).
fof(f42016,plain,
~ sP13(x_plus_y,x,add(x,additive_identity),additive_identity),
inference(unit_resulting_resolution,[],[f62,f40715,f55]) ).
fof(f40715,plain,
sP12(x_plus_y,x,additive_identity,additive_identity),
inference(superposition,[],[f4418,f40263]) ).
fof(f4418,plain,
! [X0] : sP12(x_plus_y,x,multiply(y,X0),X0),
inference(unit_resulting_resolution,[],[f67,f92,f52]) ).
fof(f67,plain,
sum(y,x,x_plus_y),
inference(unit_resulting_resolution,[],[f25,f3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO008-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n005.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 : Tue Apr 30 02:22:26 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (21256)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (21259)WARNING: value z3 for option sas not known
% 0.13/0.36 % (21263)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)
% 0.13/0.36 % (21258)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 % (21260)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36 % (21261)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 % (21262)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 % (21259)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)
% 0.13/0.37 TRYING [1]
% 0.13/0.37 TRYING [2]
% 0.13/0.37 % (21257)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37 TRYING [3]
% 0.13/0.38 TRYING [1]
% 0.13/0.38 TRYING [2]
% 0.13/0.39 TRYING [4]
% 0.13/0.40 TRYING [3]
% 0.18/0.44 TRYING [4]
% 0.18/0.44 TRYING [5]
% 1.84/0.61 TRYING [6]
% 2.06/0.68 TRYING [5]
% 4.82/1.05 TRYING [7]
% 7.93/1.48 TRYING [1]
% 7.93/1.48 TRYING [2]
% 7.93/1.48 TRYING [3]
% 7.93/1.50 TRYING [4]
% 8.33/1.55 TRYING [5]
% 9.47/1.76 TRYING [6]
% 12.15/2.08 TRYING [6]
% 12.36/2.20 TRYING [7]
% 14.45/2.44 TRYING [8]
% 22.86/3.69 TRYING [8]
% 36.76/5.60 TRYING [9]
% 43.81/6.63 TRYING [9]
% 51.29/7.69 TRYING [7]
% 57.77/8.66 % (21263)First to succeed.
% 57.77/8.69 % (21263)Refutation found. Thanks to Tanya!
% 57.77/8.69 % SZS status Unsatisfiable for theBenchmark
% 57.77/8.69 % SZS output start Proof for theBenchmark
% See solution above
% 57.77/8.69 % (21263)------------------------------
% 57.77/8.69 % (21263)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 57.77/8.69 % (21263)Termination reason: Refutation
% 57.77/8.69
% 57.77/8.69 % (21263)Memory used [KB]: 69853
% 57.77/8.69 % (21263)Time elapsed: 8.310 s
% 57.77/8.69 % (21263)Instructions burned: 16699 (million)
% 57.77/8.69 % (21263)------------------------------
% 57.77/8.69 % (21263)------------------------------
% 57.77/8.69 % (21256)Success in time 8.316 s
%------------------------------------------------------------------------------