TSTP Solution File: RNG004-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : RNG004-1 : 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 : n031.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 14:49:55 EDT 2024
% Result : Unsatisfiable 4.48s 0.99s
% Output : Refutation 4.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 28
% Syntax : Number of formulae : 116 ( 75 unt; 0 def)
% Number of atoms : 209 ( 20 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 215 ( 122 ~; 83 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 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 : 261 ( 261 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f62193,plain,
$false,
inference(subsumption_resolution,[],[f62112,f35774]) ).
fof(f35774,plain,
sP7(a,additive_identity,c,multiply(a,additive_inverse(b))),
inference(unit_resulting_resolution,[],[f18,f13393,f35]) ).
fof(f35,plain,
! [X0,X1,X8,X6,X7] :
( ~ sP6(X0,X8,X1,X7)
| ~ product(X0,X1,X6)
| sP7(X0,X8,X6,X7) ),
inference(cnf_transformation,[],[f35_D]) ).
fof(f35_D,plain,
! [X7,X6,X8,X0] :
( ! [X1] :
( ~ sP6(X0,X8,X1,X7)
| ~ product(X0,X1,X6) )
<=> ~ sP7(X0,X8,X6,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP7])]) ).
fof(f13393,plain,
! [X0,X1] : sP6(X0,additive_identity,X1,multiply(X0,additive_inverse(X1))),
inference(unit_resulting_resolution,[],[f6,f3,f33]) ).
fof(f33,plain,
! [X3,X0,X1,X8,X7] :
( ~ product(X0,X3,X7)
| ~ sum(X1,X3,X8)
| sP6(X0,X8,X1,X7) ),
inference(cnf_transformation,[],[f33_D]) ).
fof(f33_D,plain,
! [X7,X1,X8,X0] :
( ! [X3] :
( ~ product(X0,X3,X7)
| ~ sum(X1,X3,X8) )
<=> ~ sP6(X0,X8,X1,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP6])]) ).
fof(f3,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f18,axiom,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
fof(f62112,plain,
~ sP7(a,additive_identity,c,multiply(a,additive_inverse(b))),
inference(unit_resulting_resolution,[],[f39721,f62083,f36]) ).
fof(f36,plain,
! [X0,X8,X6,X9,X7] :
( ~ sP7(X0,X8,X6,X7)
| sum(X6,X7,X9)
| ~ product(X0,X8,X9) ),
inference(general_splitting,[],[f34,f35_D]) ).
fof(f34,plain,
! [X0,X1,X8,X6,X9,X7] :
( ~ product(X0,X1,X6)
| ~ product(X0,X8,X9)
| sum(X6,X7,X9)
| ~ sP6(X0,X8,X1,X7) ),
inference(general_splitting,[],[f12,f33_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/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f62083,plain,
~ sum(c,multiply(a,additive_inverse(b)),additive_identity),
inference(forward_demodulation,[],[f62037,f2882]) ).
fof(f2882,plain,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
inference(forward_demodulation,[],[f2867,f90]) ).
fof(f90,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(unit_resulting_resolution,[],[f2,f49,f16]) ).
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(f49,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(f2,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
fof(f2867,plain,
! [X0] : add(additive_identity,X0) = additive_inverse(additive_inverse(X0)),
inference(unit_resulting_resolution,[],[f2464,f100]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ sum(X2,X1,X0)
| add(X1,X2) = X0 ),
inference(resolution,[],[f16,f49]) ).
fof(f2464,plain,
! [X0] : sum(X0,additive_identity,additive_inverse(additive_inverse(X0))),
inference(unit_resulting_resolution,[],[f6,f2400,f26]) ).
fof(f26,plain,
! [X3,X0,X1,X4,X5] :
( ~ sP2(X5,X0,X3,X1)
| sum(X0,X4,X5)
| ~ sum(X1,X3,X4) ),
inference(general_splitting,[],[f7,f25_D]) ).
fof(f25,plain,
! [X2,X3,X0,X1,X5] :
( ~ sum(X0,X1,X2)
| ~ sum(X2,X3,X5)
| sP2(X5,X0,X3,X1) ),
inference(cnf_transformation,[],[f25_D]) ).
fof(f25_D,plain,
! [X1,X3,X0,X5] :
( ! [X2] :
( ~ sum(X0,X1,X2)
| ~ sum(X2,X3,X5) )
<=> ~ sP2(X5,X0,X3,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).
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(f2400,plain,
! [X0,X1] : sP2(X0,X1,X0,additive_inverse(X1)),
inference(forward_demodulation,[],[f2385,f89]) ).
fof(f89,plain,
! [X0] : add(X0,additive_identity) = X0,
inference(unit_resulting_resolution,[],[f1,f49,f16]) ).
fof(f1,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
fof(f2385,plain,
! [X0,X1] : sP2(add(X0,additive_identity),X1,X0,additive_inverse(X1)),
inference(unit_resulting_resolution,[],[f49,f6,f25]) ).
fof(f62037,plain,
~ sum(additive_inverse(additive_inverse(c)),multiply(a,additive_inverse(b)),additive_identity),
inference(unit_resulting_resolution,[],[f7354,f60972,f27]) ).
fof(f27,plain,
! [X2,X3,X0,X1,X5] :
( ~ sum(X0,X1,X2)
| sum(X2,X3,X5)
| sP3(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) )
<=> ~ sP3(X3,X0,X5,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP3])]) ).
fof(f60972,plain,
~ sum(additive_identity,additive_inverse(c),multiply(a,additive_inverse(b))),
inference(forward_demodulation,[],[f60912,f79]) ).
fof(f79,plain,
additive_identity = additive_inverse(additive_identity),
inference(unit_resulting_resolution,[],[f1,f6,f16]) ).
fof(f60912,plain,
~ sum(additive_inverse(additive_identity),additive_inverse(c),multiply(a,additive_inverse(b))),
inference(unit_resulting_resolution,[],[f7354,f59384,f27]) ).
fof(f59384,plain,
~ sum(multiply(a,additive_inverse(b)),additive_identity,additive_inverse(c)),
inference(unit_resulting_resolution,[],[f40130,f59353,f40]) ).
fof(f40,plain,
! [X0,X8,X6,X9,X7] :
( ~ sP9(X0,X8,X6,X7)
| product(X0,X8,X9)
| ~ sum(X6,X7,X9) ),
inference(general_splitting,[],[f38,f39_D]) ).
fof(f39,plain,
! [X0,X1,X8,X6,X7] :
( ~ sP8(X0,X8,X1,X7)
| ~ product(X0,X1,X6)
| sP9(X0,X8,X6,X7) ),
inference(cnf_transformation,[],[f39_D]) ).
fof(f39_D,plain,
! [X7,X6,X8,X0] :
( ! [X1] :
( ~ sP8(X0,X8,X1,X7)
| ~ product(X0,X1,X6) )
<=> ~ sP9(X0,X8,X6,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP9])]) ).
fof(f38,plain,
! [X0,X1,X8,X6,X9,X7] :
( ~ product(X0,X1,X6)
| ~ sum(X6,X7,X9)
| product(X0,X8,X9)
| ~ sP8(X0,X8,X1,X7) ),
inference(general_splitting,[],[f13,f37_D]) ).
fof(f37,plain,
! [X3,X0,X1,X8,X7] :
( ~ product(X0,X3,X7)
| ~ sum(X1,X3,X8)
| sP8(X0,X8,X1,X7) ),
inference(cnf_transformation,[],[f37_D]) ).
fof(f37_D,plain,
! [X7,X1,X8,X0] :
( ! [X3] :
( ~ product(X0,X3,X7)
| ~ sum(X1,X3,X8) )
<=> ~ sP8(X0,X8,X1,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP8])]) ).
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(f59353,plain,
~ product(a,additive_inverse(b),additive_inverse(c)),
inference(unit_resulting_resolution,[],[f22159,f59302,f43]) ).
fof(f43,plain,
! [X0,X1,X8,X6,X7] :
( ~ sP10(X0,X8,X1,X7)
| ~ product(X1,X0,X6)
| sP11(X0,X8,X6,X7) ),
inference(cnf_transformation,[],[f43_D]) ).
fof(f43_D,plain,
! [X7,X6,X8,X0] :
( ! [X1] :
( ~ sP10(X0,X8,X1,X7)
| ~ product(X1,X0,X6) )
<=> ~ sP11(X0,X8,X6,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP11])]) ).
fof(f59302,plain,
~ sP11(additive_inverse(b),additive_identity,additive_inverse(c),d),
inference(unit_resulting_resolution,[],[f49,f52370,f44]) ).
fof(f44,plain,
! [X0,X8,X6,X9,X7] :
( ~ sP11(X0,X8,X6,X7)
| product(X8,X0,X9)
| ~ sum(X6,X7,X9) ),
inference(general_splitting,[],[f42,f43_D]) ).
fof(f42,plain,
! [X0,X1,X8,X6,X9,X7] :
( ~ product(X1,X0,X6)
| ~ sum(X6,X7,X9)
| product(X8,X0,X9)
| ~ sP10(X0,X8,X1,X7) ),
inference(general_splitting,[],[f15,f41_D]) ).
fof(f41,plain,
! [X3,X0,X1,X8,X7] :
( ~ product(X3,X0,X7)
| ~ sum(X1,X3,X8)
| sP10(X0,X8,X1,X7) ),
inference(cnf_transformation,[],[f41_D]) ).
fof(f41_D,plain,
! [X7,X1,X8,X0] :
( ! [X3] :
( ~ product(X3,X0,X7)
| ~ sum(X1,X3,X8) )
<=> ~ sP10(X0,X8,X1,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP10])]) ).
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(f52370,plain,
~ product(additive_identity,additive_inverse(b),add(d,additive_inverse(c))),
inference(unit_resulting_resolution,[],[f48260,f34098,f39]) ).
fof(f34098,plain,
~ sP9(additive_identity,b,add(d,additive_inverse(c)),additive_identity),
inference(forward_demodulation,[],[f34089,f2882]) ).
fof(f34089,plain,
~ sP9(additive_identity,b,additive_inverse(additive_inverse(add(d,additive_inverse(c)))),additive_identity),
inference(unit_resulting_resolution,[],[f2483,f33974,f40]) ).
fof(f33974,plain,
~ product(additive_identity,b,add(d,additive_inverse(c))),
inference(unit_resulting_resolution,[],[f11239,f5922,f31]) ).
fof(f31,plain,
! [X0,X1,X8,X6,X7] :
( ~ sP4(X0,X8,X1,X7)
| ~ product(X1,X0,X6)
| sP5(X0,X8,X6,X7) ),
inference(cnf_transformation,[],[f31_D]) ).
fof(f31_D,plain,
! [X7,X6,X8,X0] :
( ! [X1] :
( ~ sP4(X0,X8,X1,X7)
| ~ product(X1,X0,X6) )
<=> ~ sP5(X0,X8,X6,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP5])]) ).
fof(f5922,plain,
sP4(b,a,additive_identity,c),
inference(unit_resulting_resolution,[],[f1,f18,f29]) ).
fof(f29,plain,
! [X3,X0,X1,X8,X7] :
( ~ product(X3,X0,X7)
| ~ sum(X1,X3,X8)
| sP4(X0,X8,X1,X7) ),
inference(cnf_transformation,[],[f29_D]) ).
fof(f29_D,plain,
! [X7,X1,X8,X0] :
( ! [X3] :
( ~ product(X3,X0,X7)
| ~ sum(X1,X3,X8) )
<=> ~ sP4(X0,X8,X1,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP4])]) ).
fof(f11239,plain,
! [X0] : ~ sP5(b,a,add(d,additive_inverse(X0)),X0),
inference(unit_resulting_resolution,[],[f18,f2653,f32]) ).
fof(f32,plain,
! [X0,X8,X6,X9,X7] :
( ~ sP5(X0,X8,X6,X7)
| sum(X6,X7,X9)
| ~ product(X8,X0,X9) ),
inference(general_splitting,[],[f30,f31_D]) ).
fof(f30,plain,
! [X0,X1,X8,X6,X9,X7] :
( ~ product(X1,X0,X6)
| ~ product(X8,X0,X9)
| sum(X6,X7,X9)
| ~ sP4(X0,X8,X1,X7) ),
inference(general_splitting,[],[f14,f29_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/sandbox/benchmark/theBenchmark.p',distributivity3) ).
fof(f2653,plain,
! [X0] : ~ sum(add(d,additive_inverse(X0)),X0,c),
inference(forward_demodulation,[],[f2651,f93]) ).
fof(f93,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(unit_resulting_resolution,[],[f4,f49,f16]) ).
fof(f2651,plain,
! [X0] : ~ sum(add(additive_inverse(X0),d),X0,c),
inference(unit_resulting_resolution,[],[f49,f2446,f25]) ).
fof(f2446,plain,
! [X0] : ~ sP2(c,d,X0,additive_inverse(X0)),
inference(unit_resulting_resolution,[],[f5,f68,f26]) ).
fof(f68,plain,
~ sum(d,additive_identity,c),
inference(unit_resulting_resolution,[],[f20,f2,f16]) ).
fof(f20,axiom,
c != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
fof(f5,axiom,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f2483,plain,
! [X0] : sum(additive_inverse(additive_inverse(X0)),additive_identity,X0),
inference(unit_resulting_resolution,[],[f5,f2403,f26]) ).
fof(f2403,plain,
! [X0,X1] : sP2(X0,additive_inverse(X1),X0,X1),
inference(forward_demodulation,[],[f2380,f89]) ).
fof(f2380,plain,
! [X0,X1] : sP2(add(X0,additive_identity),additive_inverse(X1),X0,X1),
inference(unit_resulting_resolution,[],[f49,f5,f25]) ).
fof(f48260,plain,
sP8(additive_identity,b,additive_inverse(b),additive_identity),
inference(unit_resulting_resolution,[],[f2486,f48089,f37]) ).
fof(f48089,plain,
product(additive_identity,add(b,b),additive_identity),
inference(forward_demodulation,[],[f48087,f2882]) ).
fof(f48087,plain,
product(additive_identity,add(b,b),additive_inverse(additive_inverse(additive_identity))),
inference(unit_resulting_resolution,[],[f2464,f46755,f40]) ).
fof(f46755,plain,
sP9(additive_identity,add(b,b),additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f38247,f38435,f39]) ).
fof(f38435,plain,
! [X0] : sP8(additive_identity,add(X0,b),X0,additive_identity),
inference(unit_resulting_resolution,[],[f4,f38247,f37]) ).
fof(f38247,plain,
product(additive_identity,b,additive_identity),
inference(superposition,[],[f3,f38194]) ).
fof(f38194,plain,
additive_identity = multiply(additive_identity,b),
inference(forward_demodulation,[],[f38181,f92]) ).
fof(f92,plain,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
inference(unit_resulting_resolution,[],[f6,f49,f16]) ).
fof(f38181,plain,
add(additive_inverse(c),c) = multiply(additive_identity,b),
inference(superposition,[],[f8597,f34331]) ).
fof(f34331,plain,
c = add(multiply(additive_identity,b),c),
inference(unit_resulting_resolution,[],[f34150,f99]) ).
fof(f99,plain,
! [X2,X0,X1] :
( ~ sum(X1,X2,X0)
| add(X1,X2) = X0 ),
inference(resolution,[],[f16,f4]) ).
fof(f34150,plain,
sum(multiply(additive_identity,b),c,c),
inference(forward_demodulation,[],[f34145,f211]) ).
fof(f211,plain,
c = multiply(a,b),
inference(unit_resulting_resolution,[],[f18,f3,f17]) ).
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(f34145,plain,
sum(multiply(additive_identity,b),c,multiply(a,b)),
inference(unit_resulting_resolution,[],[f3,f33973,f32]) ).
fof(f33973,plain,
sP5(b,a,multiply(additive_identity,b),c),
inference(unit_resulting_resolution,[],[f3,f5922,f31]) ).
fof(f8597,plain,
! [X0,X1] : add(additive_inverse(X0),add(X1,X0)) = X1,
inference(unit_resulting_resolution,[],[f2486,f99]) ).
fof(f2486,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1),
inference(unit_resulting_resolution,[],[f49,f2403,f26]) ).
fof(f22159,plain,
sP10(additive_inverse(b),additive_identity,a,d),
inference(unit_resulting_resolution,[],[f6,f19,f41]) ).
fof(f19,axiom,
product(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_inverse_times_b_inverse) ).
fof(f40130,plain,
! [X0] : sP9(a,X0,multiply(a,X0),additive_identity),
inference(unit_resulting_resolution,[],[f3,f39719,f39]) ).
fof(f39719,plain,
! [X0] : sP8(a,X0,X0,additive_identity),
inference(superposition,[],[f17940,f39667]) ).
fof(f39667,plain,
additive_identity = multiply(a,additive_identity),
inference(forward_demodulation,[],[f39654,f92]) ).
fof(f39654,plain,
add(additive_inverse(c),c) = multiply(a,additive_identity),
inference(superposition,[],[f8597,f36148]) ).
fof(f36148,plain,
c = add(multiply(a,additive_identity),c),
inference(unit_resulting_resolution,[],[f35957,f99]) ).
fof(f35957,plain,
sum(multiply(a,additive_identity),c,c),
inference(forward_demodulation,[],[f35952,f211]) ).
fof(f35952,plain,
sum(multiply(a,additive_identity),c,multiply(a,b)),
inference(unit_resulting_resolution,[],[f3,f35732,f36]) ).
fof(f35732,plain,
sP7(a,b,multiply(a,additive_identity),c),
inference(unit_resulting_resolution,[],[f3,f13485,f35]) ).
fof(f13485,plain,
sP6(a,b,additive_identity,c),
inference(unit_resulting_resolution,[],[f1,f18,f33]) ).
fof(f17940,plain,
! [X0,X1] : sP8(X0,X1,X1,multiply(X0,additive_identity)),
inference(forward_demodulation,[],[f17767,f2882]) ).
fof(f17767,plain,
! [X0,X1] : sP8(X0,additive_inverse(additive_inverse(X1)),X1,multiply(X0,additive_identity)),
inference(unit_resulting_resolution,[],[f2464,f3,f37]) ).
fof(f7354,plain,
! [X0,X1] : ~ sP3(X0,additive_inverse(X0),X1,X1),
inference(superposition,[],[f7002,f2882]) ).
fof(f7002,plain,
! [X0,X1] : ~ sP3(additive_inverse(X0),X0,X1,X1),
inference(unit_resulting_resolution,[],[f49,f2465,f28]) ).
fof(f28,plain,
! [X3,X0,X1,X4,X5] :
( ~ sP3(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(f2465,plain,
! [X0,X1] : sum(X0,add(additive_inverse(X0),X1),X1),
inference(unit_resulting_resolution,[],[f4,f2400,f26]) ).
fof(f39721,plain,
product(a,additive_identity,additive_identity),
inference(superposition,[],[f3,f39667]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : RNG004-1 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.32 % Computer : n031.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Apr 30 02:43:13 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.13/0.33 % (18418)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.34 % (18423)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)
% 0.13/0.34 % (18424)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)
% 0.13/0.34 % (18421)WARNING: value z3 for option sas not known
% 0.13/0.35 % (18419)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.35 % (18420)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.35 % (18422)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.35 % (18421)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 % (18425)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 TRYING [1]
% 0.13/0.35 TRYING [2]
% 0.13/0.35 TRYING [1]
% 0.18/0.35 TRYING [3]
% 0.18/0.35 TRYING [2]
% 0.18/0.37 TRYING [3]
% 0.18/0.37 TRYING [4]
% 0.18/0.42 TRYING [4]
% 0.18/0.43 TRYING [5]
% 0.18/0.53 TRYING [6]
% 1.63/0.55 TRYING [5]
% 3.20/0.78 TRYING [7]
% 4.48/0.98 % (18425)First to succeed.
% 4.48/0.99 % (18425)Refutation found. Thanks to Tanya!
% 4.48/0.99 % SZS status Unsatisfiable for theBenchmark
% 4.48/0.99 % SZS output start Proof for theBenchmark
% See solution above
% 4.48/0.99 % (18425)------------------------------
% 4.48/0.99 % (18425)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 4.48/0.99 % (18425)Termination reason: Refutation
% 4.48/0.99
% 4.48/0.99 % (18425)Memory used [KB]: 8970
% 4.48/0.99 % (18425)Time elapsed: 0.642 s
% 4.48/0.99 % (18425)Instructions burned: 1975 (million)
% 4.48/0.99 % (18425)------------------------------
% 4.48/0.99 % (18425)------------------------------
% 4.48/0.99 % (18418)Success in time 0.647 s
%------------------------------------------------------------------------------