TSTP Solution File: RNG004-2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : RNG004-2 : 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 : n025.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 08:54:50 EDT 2024
% Result : Unsatisfiable 6.07s 1.16s
% Output : Refutation 6.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 30
% Syntax : Number of formulae : 125 ( 84 unt; 0 def)
% Number of atoms : 220 ( 20 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 222 ( 127 ~; 85 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 281 ( 281 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f64313,plain,
$false,
inference(subsumption_resolution,[],[f64306,f41640]) ).
fof(f41640,plain,
sP7(b,additive_identity,multiply(additive_inverse(a),b),c),
inference(unit_resulting_resolution,[],[f3,f13107,f37]) ).
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(f13107,plain,
sP6(b,additive_identity,additive_inverse(a),c),
inference(unit_resulting_resolution,[],[f5,f20,f35]) ).
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(f20,axiom,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
fof(f5,axiom,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f64306,plain,
~ sP7(b,additive_identity,multiply(additive_inverse(a),b),c),
inference(unit_resulting_resolution,[],[f42197,f64201,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(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(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/sandbox2/benchmark/theBenchmark.p',distributivity3) ).
fof(f64201,plain,
~ sum(multiply(additive_inverse(a),b),c,additive_identity),
inference(forward_demodulation,[],[f64194,f259]) ).
fof(f259,plain,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
inference(unit_resulting_resolution,[],[f5,f6,f18]) ).
fof(f18,axiom,
! [X3,X0,X1,X5] :
( ~ sum(X0,X5,X3)
| X1 = X5
| ~ sum(X0,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation1) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f64194,plain,
~ sum(multiply(additive_inverse(a),b),additive_inverse(additive_inverse(c)),additive_identity),
inference(unit_resulting_resolution,[],[f6342,f63748,f30]) ).
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(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(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/sandbox2/benchmark/theBenchmark.p',associativity_of_addition1) ).
fof(f63748,plain,
~ sum(additive_inverse(c),additive_identity,multiply(additive_inverse(a),b)),
inference(forward_demodulation,[],[f63747,f92]) ).
fof(f92,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(unit_resulting_resolution,[],[f2,f51,f16]) ).
fof(f16,axiom,
! [X2,X0,X1,X4] :
( ~ sum(X0,X1,X4)
| X2 = X4
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
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/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
fof(f4,axiom,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f2,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
fof(f63747,plain,
~ sum(additive_inverse(add(additive_identity,c)),additive_identity,multiply(additive_inverse(a),b)),
inference(forward_demodulation,[],[f63727,f23560]) ).
fof(f23560,plain,
! [X0,X1] : additive_inverse(add(X0,X1)) = add(additive_inverse(X0),additive_inverse(X1)),
inference(unit_resulting_resolution,[],[f3535,f6404,f19]) ).
fof(f19,axiom,
! [X3,X0,X1,X5] :
( ~ sum(X5,X1,X3)
| X0 = X5
| ~ sum(X0,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation2) ).
fof(f6404,plain,
! [X0,X1] : sum(additive_inverse(add(X0,X1)),X0,additive_inverse(X1)),
inference(unit_resulting_resolution,[],[f3461,f3478,f30]) ).
fof(f3478,plain,
! [X0,X1] : sum(add(X0,X1),additive_inverse(X1),X0),
inference(unit_resulting_resolution,[],[f4,f3191,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(f3191,plain,
! [X0,X1] : ~ sP2(additive_inverse(X0),X1,X1,X0),
inference(forward_demodulation,[],[f2854,f92]) ).
fof(f2854,plain,
! [X0,X1] : ~ sP2(additive_inverse(X0),X1,add(additive_identity,X1),X0),
inference(unit_resulting_resolution,[],[f51,f6,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/sandbox2/benchmark/theBenchmark.p',associativity_of_addition2) ).
fof(f3461,plain,
! [X0,X1] : sP3(X0,additive_inverse(X1),X0,X1),
inference(forward_demodulation,[],[f3438,f91]) ).
fof(f91,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/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
fof(f3438,plain,
! [X0,X1] : sP3(add(X0,additive_identity),additive_inverse(X1),X0,X1),
inference(unit_resulting_resolution,[],[f51,f5,f29]) ).
fof(f3535,plain,
! [X0,X1] : sum(add(additive_inverse(X0),X1),X0,X1),
inference(unit_resulting_resolution,[],[f51,f3194,f27]) ).
fof(f3194,plain,
! [X0,X1] : ~ sP2(X0,X1,X1,additive_inverse(X0)),
inference(forward_demodulation,[],[f2849,f92]) ).
fof(f2849,plain,
! [X0,X1] : ~ sP2(X0,X1,add(additive_identity,X1),additive_inverse(X0)),
inference(unit_resulting_resolution,[],[f51,f5,f28]) ).
fof(f63727,plain,
~ sum(add(additive_inverse(additive_identity),additive_inverse(c)),additive_identity,multiply(additive_inverse(a),b)),
inference(unit_resulting_resolution,[],[f8288,f61912,f30]) ).
fof(f61912,plain,
~ sum(additive_identity,multiply(additive_inverse(a),b),additive_inverse(c)),
inference(unit_resulting_resolution,[],[f46159,f61879,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(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(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/sandbox2/benchmark/theBenchmark.p',distributivity4) ).
fof(f61879,plain,
~ product(additive_inverse(a),b,additive_inverse(c)),
inference(forward_demodulation,[],[f61878,f92]) ).
fof(f61878,plain,
~ product(additive_inverse(a),add(additive_identity,b),additive_inverse(c)),
inference(unit_resulting_resolution,[],[f21331,f61821,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(f61821,plain,
~ sP11(additive_inverse(a),additive_identity,additive_inverse(c),d),
inference(unit_resulting_resolution,[],[f51,f58929,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(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(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/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
fof(f58929,plain,
~ product(additive_inverse(a),additive_identity,add(d,additive_inverse(c))),
inference(unit_resulting_resolution,[],[f53553,f36600,f41]) ).
fof(f36600,plain,
~ sP9(additive_identity,a,add(d,additive_inverse(c)),additive_identity),
inference(unit_resulting_resolution,[],[f2,f36540,f42]) ).
fof(f36540,plain,
~ product(a,additive_identity,add(d,additive_inverse(c))),
inference(forward_demodulation,[],[f36442,f213]) ).
fof(f213,plain,
c = multiply(a,b),
inference(unit_resulting_resolution,[],[f20,f3,f17]) ).
fof(f17,axiom,
! [X2,X0,X1,X4] :
( ~ product(X0,X1,X4)
| X2 = X4
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
fof(f36442,plain,
~ product(a,additive_identity,add(d,additive_inverse(multiply(a,b)))),
inference(unit_resulting_resolution,[],[f10485,f5384,f33]) ).
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(f5384,plain,
! [X0,X1] : sP4(X0,X1,additive_identity,multiply(X0,X1)),
inference(unit_resulting_resolution,[],[f1,f3,f31]) ).
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(f10485,plain,
! [X0] : ~ sP5(a,b,add(d,additive_inverse(X0)),X0),
inference(unit_resulting_resolution,[],[f20,f3484,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(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(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/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
fof(f3484,plain,
! [X0] : ~ sum(add(d,additive_inverse(X0)),X0,c),
inference(unit_resulting_resolution,[],[f300,f3191,f27]) ).
fof(f300,plain,
! [X0] : ~ sum(c,X0,add(d,X0)),
inference(unit_resulting_resolution,[],[f268,f9]) ).
fof(f268,plain,
! [X0] : ~ sum(X0,c,add(d,X0)),
inference(unit_resulting_resolution,[],[f22,f51,f18]) ).
fof(f22,axiom,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_equals_d) ).
fof(f53553,plain,
sP8(additive_identity,a,additive_inverse(a),additive_identity),
inference(unit_resulting_resolution,[],[f4617,f53385,f39]) ).
fof(f53385,plain,
product(add(a,a),additive_identity,additive_identity),
inference(forward_demodulation,[],[f53383,f91]) ).
fof(f53383,plain,
product(add(a,a),additive_identity,add(additive_identity,additive_identity)),
inference(unit_resulting_resolution,[],[f51,f48528,f42]) ).
fof(f48528,plain,
sP9(additive_identity,add(a,a),additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f36999,f37174,f41]) ).
fof(f37174,plain,
! [X0] : sP8(additive_identity,add(X0,a),X0,additive_identity),
inference(unit_resulting_resolution,[],[f4,f36999,f39]) ).
fof(f36999,plain,
product(a,additive_identity,additive_identity),
inference(superposition,[],[f3,f36957]) ).
fof(f36957,plain,
additive_identity = multiply(a,additive_identity),
inference(forward_demodulation,[],[f36956,f81]) ).
fof(f81,plain,
additive_identity = additive_inverse(additive_identity),
inference(unit_resulting_resolution,[],[f1,f6,f16]) ).
fof(f36956,plain,
additive_inverse(additive_identity) = multiply(a,additive_identity),
inference(forward_demodulation,[],[f36705,f93]) ).
fof(f93,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(unit_resulting_resolution,[],[f5,f51,f16]) ).
fof(f36705,plain,
additive_inverse(add(c,additive_inverse(c))) = multiply(a,additive_identity),
inference(unit_resulting_resolution,[],[f7273,f36673,f19]) ).
fof(f36673,plain,
sum(multiply(a,additive_identity),c,c),
inference(forward_demodulation,[],[f36668,f213]) ).
fof(f36668,plain,
sum(multiply(a,additive_identity),c,multiply(a,b)),
inference(unit_resulting_resolution,[],[f3,f36432,f34]) ).
fof(f36432,plain,
sP5(a,b,multiply(a,additive_identity),c),
inference(unit_resulting_resolution,[],[f3,f5442,f33]) ).
fof(f5442,plain,
sP4(a,b,additive_identity,c),
inference(unit_resulting_resolution,[],[f1,f20,f31]) ).
fof(f7273,plain,
! [X0,X1] : sum(additive_inverse(add(X0,additive_inverse(X1))),X0,X1),
inference(unit_resulting_resolution,[],[f3461,f3534,f30]) ).
fof(f3534,plain,
! [X0,X1] : sum(add(X0,additive_inverse(X1)),X1,X0),
inference(unit_resulting_resolution,[],[f4,f3194,f27]) ).
fof(f4617,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1),
inference(unit_resulting_resolution,[],[f51,f3461,f30]) ).
fof(f21331,plain,
! [X0] : sP10(additive_inverse(a),X0,add(X0,b),d),
inference(forward_demodulation,[],[f21276,f259]) ).
fof(f21276,plain,
! [X0] : sP10(additive_inverse(a),X0,add(X0,additive_inverse(additive_inverse(b))),d),
inference(unit_resulting_resolution,[],[f3534,f21,f43]) ).
fof(f21,axiom,
product(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_times_b_inverse) ).
fof(f46159,plain,
! [X0] : sP9(b,X0,additive_identity,multiply(X0,b)),
inference(unit_resulting_resolution,[],[f42197,f17186,f41]) ).
fof(f17186,plain,
! [X0,X1] : sP8(X0,X1,additive_identity,multiply(X1,X0)),
inference(unit_resulting_resolution,[],[f1,f3,f39]) ).
fof(f8288,plain,
! [X0,X1] : sP3(X0,X1,additive_identity,add(additive_inverse(X1),X0)),
inference(unit_resulting_resolution,[],[f2,f4568,f29]) ).
fof(f4568,plain,
! [X0,X1] : sum(X0,add(additive_inverse(X0),X1),X1),
inference(unit_resulting_resolution,[],[f4,f3458,f30]) ).
fof(f3458,plain,
! [X0,X1] : sP3(X0,X1,X0,additive_inverse(X1)),
inference(forward_demodulation,[],[f3443,f91]) ).
fof(f3443,plain,
! [X0,X1] : sP3(add(X0,additive_identity),X1,X0,additive_inverse(X1)),
inference(unit_resulting_resolution,[],[f51,f6,f29]) ).
fof(f6342,plain,
! [X0,X1] : sP3(X0,X1,additive_inverse(X1),X0),
inference(unit_resulting_resolution,[],[f51,f3478,f29]) ).
fof(f42197,plain,
product(additive_identity,b,additive_identity),
inference(superposition,[],[f3,f42172]) ).
fof(f42172,plain,
additive_identity = multiply(additive_identity,b),
inference(forward_demodulation,[],[f42171,f81]) ).
fof(f42171,plain,
additive_inverse(additive_identity) = multiply(additive_identity,b),
inference(forward_demodulation,[],[f42170,f93]) ).
fof(f42170,plain,
additive_inverse(add(c,additive_inverse(c))) = multiply(additive_identity,b),
inference(forward_demodulation,[],[f41868,f95]) ).
fof(f95,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(unit_resulting_resolution,[],[f4,f51,f16]) ).
fof(f41868,plain,
additive_inverse(add(additive_inverse(c),c)) = multiply(additive_identity,b),
inference(unit_resulting_resolution,[],[f8180,f41846,f18]) ).
fof(f41846,plain,
sum(c,multiply(additive_identity,b),c),
inference(forward_demodulation,[],[f41841,f213]) ).
fof(f41841,plain,
sum(c,multiply(additive_identity,b),multiply(a,b)),
inference(unit_resulting_resolution,[],[f3,f41595,f38]) ).
fof(f41595,plain,
sP7(b,a,c,multiply(additive_identity,b)),
inference(unit_resulting_resolution,[],[f20,f12973,f37]) ).
fof(f12973,plain,
! [X0,X1] : sP6(X0,X1,X1,multiply(additive_identity,X0)),
inference(unit_resulting_resolution,[],[f2,f3,f35]) ).
fof(f8180,plain,
! [X0,X1] : sum(X0,additive_inverse(add(additive_inverse(X1),X0)),X1),
inference(unit_resulting_resolution,[],[f3191,f4568,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : RNG004-2 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.30 % Computer : n025.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri May 3 18:21:08 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.10/0.30 % (24639)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.32 % (24641)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.32 % (24646)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)
% 0.14/0.32 % (24642)WARNING: value z3 for option sas not known
% 0.14/0.32 % (24644)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)
% 0.14/0.32 % (24645)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)
% 0.14/0.32 % (24640)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.32 % (24643)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.32 % (24642)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)
% 0.14/0.32 TRYING [1]
% 0.14/0.32 TRYING [2]
% 0.14/0.32 TRYING [3]
% 0.14/0.33 TRYING [1]
% 0.14/0.33 TRYING [2]
% 0.14/0.34 TRYING [4]
% 0.14/0.34 TRYING [3]
% 0.14/0.38 TRYING [5]
% 0.14/0.39 TRYING [4]
% 0.14/0.50 TRYING [6]
% 1.76/0.58 TRYING [5]
% 3.29/0.78 TRYING [7]
% 5.85/1.16 % (24646)First to succeed.
% 5.85/1.16 % (24646)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-24639"
% 6.07/1.16 % (24646)Refutation found. Thanks to Tanya!
% 6.07/1.16 % SZS status Unsatisfiable for theBenchmark
% 6.07/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 6.07/1.16 % (24646)------------------------------
% 6.07/1.16 % (24646)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 6.07/1.16 % (24646)Termination reason: Refutation
% 6.07/1.16
% 6.07/1.16 % (24646)Memory used [KB]: 8132
% 6.07/1.16 % (24646)Time elapsed: 0.842 s
% 6.07/1.16 % (24646)Instructions burned: 2054 (million)
% 6.07/1.16 % (24639)Success in time 0.842 s
%------------------------------------------------------------------------------