%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG025-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:35:10 PM UTC 2026
% Result : Unsatisfiable 1.65s 1.88s
% Output : Refutation 6.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 18
% Syntax : Number of formulae : 117 ( 96 unt; 2 def)
% Number of atoms : 142 ( 107 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 26 ~; 23 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 264 ( 0 sgn 264 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_additive_identity) ).
fof(f2,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_additive_identity) ).
fof(f3,axiom,
! [X0] : multiply(additive_identity,X0) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_multiplicative_zero) ).
fof(f4,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0] : multiply(X0,additive_identity) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_multiplicative_zero) ).
fof(f6,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X0] : add(additive_inverse(X0),X0) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_additive_inverse) ).
fof(f8,plain,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_additive_inverse) ).
fof(f10,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(reorient_equations,[],[f9]) ).
fof(f11,axiom,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
fof(f12,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute1) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute2) ).
fof(f14,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_for_addition) ).
fof(f15,axiom,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_for_addition) ).
fof(f16,axiom,
! [X0,X1] : multiply(multiply(X0,X1),X1) = multiply(X0,multiply(X1,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_alternative) ).
fof(f18,axiom,
! [X2,X0,X1] : associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X1,X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associator) ).
fof(f22,axiom,
! [X0,X1] : multiply(additive_inverse(X0),X1) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product1) ).
fof(f23,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(additive_inverse(X0),X1),
inference(reorient_equations,[],[f22]) ).
fof(f24,axiom,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product2) ).
fof(f25,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(X0,additive_inverse(X1)),
inference(reorient_equations,[],[f24]) ).
fof(f30,negated_conjecture,
add(associator(x,y,z),associator(x,z,y)) != additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
fof(f31,plain,
additive_identity != add(associator(x,y,z),associator(x,z,y)),
inference(reorient_equations,[],[f30]) ).
fof(f33,definition,
( spl0_1
<=> additive_identity = add(associator(x,y,z),associator(x,z,y)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f35,plain,
( additive_identity != add(associator(x,y,z),associator(x,z,y))
| spl0_1 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f36,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f31,f33]) ).
fof(f47,plain,
additive_identity = additive_inverse(additive_identity),
inference(superposition,[],[f2,f8]) ).
fof(f49,definition,
( spl0_2
<=> additive_identity = additive_inverse(additive_identity) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f51,plain,
( additive_identity = additive_inverse(additive_identity)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f52,plain,
spl0_2,
inference(avatar_split_clause,[],[f47,f49]) ).
fof(f96,plain,
! [X0,X1] : add(additive_identity,X1) = add(X0,add(additive_inverse(X0),X1)),
inference(superposition,[],[f15,f10]) ).
fof(f98,plain,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X1,add(X0,X2)),
inference(superposition,[],[f15,f14]) ).
fof(f101,plain,
! [X0,X1] : add(additive_identity,X1) = add(additive_inverse(X0),add(X0,X1)),
inference(superposition,[],[f15,f8]) ).
fof(f110,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(forward_demodulation,[],[f101,f1]) ).
fof(f112,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(X1,add(X0,X2)),
inference(forward_demodulation,[],[f98,f15]) ).
fof(f114,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f96,f1]) ).
fof(f121,plain,
! [X0,X1] : add(additive_inverse(X1),add(X0,X1)) = X0,
inference(superposition,[],[f110,f14]) ).
fof(f135,plain,
! [X0,X1] : add(X1,add(X0,additive_inverse(X1))) = X0,
inference(superposition,[],[f114,f14]) ).
fof(f198,plain,
! [X0,X1] : additive_inverse(X1) = add(additive_inverse(add(X1,X0)),X0),
inference(superposition,[],[f121,f110]) ).
fof(f199,plain,
! [X0,X1] : additive_inverse(X1) = add(additive_inverse(add(X0,X1)),X0),
inference(superposition,[],[f121,f121]) ).
fof(f217,plain,
! [X2,X0,X1] : add(X0,X1) = add(X2,add(X0,add(X1,additive_inverse(X2)))),
inference(superposition,[],[f135,f15]) ).
fof(f256,plain,
! [X0,X1] : additive_inverse(X0) = add(X1,additive_inverse(add(X0,X1))),
inference(superposition,[],[f14,f198]) ).
fof(f311,plain,
! [X0,X1] : add(additive_inverse(X0),X1) = additive_inverse(add(X0,additive_inverse(X1))),
inference(superposition,[],[f199,f135]) ).
fof(f1064,plain,
! [X2,X0,X1] : add(X1,add(X2,additive_inverse(add(X0,X1)))) = add(X2,additive_inverse(X0)),
inference(superposition,[],[f112,f256]) ).
fof(f1374,plain,
! [X2,X0,X1] : associator(X0,additive_inverse(X1),X2) = add(multiply(additive_inverse(multiply(X0,X1)),X2),additive_inverse(multiply(X0,multiply(additive_inverse(X1),X2)))),
inference(superposition,[],[f18,f25]) ).
fof(f1375,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(multiply(add(multiply(X0,X1),multiply(X0,X2)),X3),additive_inverse(multiply(X0,multiply(add(X1,X2),X3)))),
inference(superposition,[],[f18,f12]) ).
fof(f1381,plain,
! [X0,X1] : associator(X0,X1,X1) = add(multiply(X0,multiply(X1,X1)),additive_inverse(multiply(X0,multiply(X1,X1)))),
inference(superposition,[],[f18,f16]) ).
fof(f1387,plain,
! [X2,X0,X1] : associator(X2,X0,additive_inverse(X1)) = add(multiply(multiply(X2,X0),additive_inverse(X1)),additive_inverse(multiply(X2,additive_inverse(multiply(X0,X1))))),
inference(superposition,[],[f18,f25]) ).
fof(f1388,plain,
! [X2,X3,X0,X1] : associator(X3,X0,add(X1,X2)) = add(multiply(multiply(X3,X0),add(X1,X2)),additive_inverse(multiply(X3,add(multiply(X0,X1),multiply(X0,X2))))),
inference(superposition,[],[f18,f12]) ).
fof(f1389,plain,
! [X0,X1] : associator(X0,additive_identity,X1) = add(multiply(multiply(X0,additive_identity),X1),additive_inverse(multiply(X0,additive_identity))),
inference(superposition,[],[f18,f4]) ).
fof(f1404,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = add(multiply(X0,multiply(X1,X2)),associator(X0,X1,X2)),
inference(superposition,[],[f135,f18]) ).
fof(f1457,plain,
! [X0,X1] : associator(X0,additive_identity,X1) = add(multiply(additive_identity,X1),additive_inverse(additive_identity)),
inference(forward_demodulation,[],[f1389,f6]) ).
fof(f1458,plain,
! [X2,X3,X0,X1] : associator(X3,X0,add(X1,X2)) = add(multiply(multiply(X3,X0),add(X1,X2)),additive_inverse(add(multiply(X3,multiply(X0,X1)),multiply(X3,multiply(X0,X2))))),
inference(forward_demodulation,[],[f1388,f12]) ).
fof(f1459,plain,
! [X2,X0,X1] : associator(X2,X0,additive_inverse(X1)) = add(multiply(multiply(X2,X0),additive_inverse(X1)),additive_inverse(additive_inverse(multiply(X2,multiply(X0,X1))))),
inference(forward_demodulation,[],[f1387,f25]) ).
fof(f1465,plain,
! [X0,X1] : additive_identity = associator(X0,X1,X1),
inference(forward_demodulation,[],[f1381,f10]) ).
fof(f1471,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(multiply(add(multiply(X0,X1),multiply(X0,X2)),X3),additive_inverse(multiply(X0,add(multiply(X1,X3),multiply(X2,X3))))),
inference(forward_demodulation,[],[f1375,f13]) ).
fof(f1472,plain,
! [X2,X0,X1] : associator(X0,additive_inverse(X1),X2) = add(multiply(additive_inverse(multiply(X0,X1)),X2),additive_inverse(multiply(X0,additive_inverse(multiply(X1,X2))))),
inference(forward_demodulation,[],[f1374,f23]) ).
fof(f1508,plain,
( ! [X0,X1] : associator(X0,additive_identity,X1) = add(multiply(additive_identity,X1),additive_identity)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1457,f51]) ).
fof(f1509,plain,
! [X2,X3,X0,X1] : associator(X3,X0,add(X1,X2)) = add(add(multiply(multiply(X3,X0),X1),multiply(multiply(X3,X0),X2)),additive_inverse(add(multiply(X3,multiply(X0,X1)),multiply(X3,multiply(X0,X2))))),
inference(forward_demodulation,[],[f1458,f12]) ).
fof(f1510,plain,
! [X2,X0,X1] : associator(X2,X0,additive_inverse(X1)) = add(multiply(multiply(X2,X0),additive_inverse(X1)),multiply(X2,multiply(X0,X1))),
inference(forward_demodulation,[],[f1459,f11]) ).
fof(f1520,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(multiply(add(multiply(X0,X1),multiply(X0,X2)),X3),additive_inverse(add(multiply(X0,multiply(X1,X3)),multiply(X0,multiply(X2,X3))))),
inference(forward_demodulation,[],[f1471,f12]) ).
fof(f1521,plain,
! [X2,X0,X1] : associator(X0,additive_inverse(X1),X2) = add(multiply(additive_inverse(multiply(X0,X1)),X2),additive_inverse(additive_inverse(multiply(X0,multiply(X1,X2))))),
inference(forward_demodulation,[],[f1472,f25]) ).
fof(f1553,plain,
( ! [X0,X1] : multiply(additive_identity,X1) = associator(X0,additive_identity,X1)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1508,f2]) ).
fof(f1554,plain,
! [X2,X3,X0,X1] : associator(X3,X0,add(X1,X2)) = add(multiply(multiply(X3,X0),X1),add(multiply(multiply(X3,X0),X2),additive_inverse(add(multiply(X3,multiply(X0,X1)),multiply(X3,multiply(X0,X2)))))),
inference(forward_demodulation,[],[f1509,f15]) ).
fof(f1555,plain,
! [X2,X0,X1] : associator(X2,X0,additive_inverse(X1)) = add(additive_inverse(multiply(multiply(X2,X0),X1)),multiply(X2,multiply(X0,X1))),
inference(forward_demodulation,[],[f1510,f25]) ).
fof(f1565,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(add(multiply(multiply(X0,X1),X3),multiply(multiply(X0,X2),X3)),additive_inverse(add(multiply(X0,multiply(X1,X3)),multiply(X0,multiply(X2,X3))))),
inference(forward_demodulation,[],[f1520,f13]) ).
fof(f1566,plain,
! [X2,X0,X1] : associator(X0,additive_inverse(X1),X2) = add(multiply(additive_inverse(multiply(X0,X1)),X2),multiply(X0,multiply(X1,X2))),
inference(forward_demodulation,[],[f1521,f11]) ).
fof(f1589,plain,
( ! [X0,X1] : additive_identity = associator(X0,additive_identity,X1)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1553,f4]) ).
fof(f1590,plain,
! [X2,X3,X0,X1] : associator(X3,X0,add(X1,X2)) = add(multiply(multiply(X3,X0),X1),add(add(multiply(X3,multiply(X0,X2)),associator(X3,X0,X2)),additive_inverse(add(multiply(X3,multiply(X0,X1)),multiply(X3,multiply(X0,X2)))))),
inference(forward_demodulation,[],[f1554,f1404]) ).
fof(f1591,plain,
! [X2,X0,X1] : associator(X2,X0,additive_inverse(X1)) = additive_inverse(add(multiply(multiply(X2,X0),X1),additive_inverse(multiply(X2,multiply(X0,X1))))),
inference(forward_demodulation,[],[f1555,f311]) ).
fof(f1601,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(multiply(multiply(X0,X1),X3),add(multiply(multiply(X0,X2),X3),additive_inverse(add(multiply(X0,multiply(X1,X3)),multiply(X0,multiply(X2,X3)))))),
inference(forward_demodulation,[],[f1565,f15]) ).
fof(f1602,plain,
! [X2,X0,X1] : associator(X0,additive_inverse(X1),X2) = add(additive_inverse(multiply(multiply(X0,X1),X2)),multiply(X0,multiply(X1,X2))),
inference(forward_demodulation,[],[f1566,f23]) ).
fof(f1617,plain,
! [X2,X3,X0,X1] : associator(X3,X0,add(X1,X2)) = add(multiply(multiply(X3,X0),X1),add(multiply(X3,multiply(X0,X2)),add(associator(X3,X0,X2),additive_inverse(add(multiply(X3,multiply(X0,X1)),multiply(X3,multiply(X0,X2))))))),
inference(forward_demodulation,[],[f1590,f15]) ).
fof(f1618,plain,
! [X2,X0,X1] : associator(X2,X0,additive_inverse(X1)) = additive_inverse(add(add(multiply(X2,multiply(X0,X1)),associator(X2,X0,X1)),additive_inverse(multiply(X2,multiply(X0,X1))))),
inference(forward_demodulation,[],[f1591,f1404]) ).
fof(f1625,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(multiply(multiply(X0,X1),X3),add(add(multiply(X0,multiply(X2,X3)),associator(X0,X2,X3)),additive_inverse(add(multiply(X0,multiply(X1,X3)),multiply(X0,multiply(X2,X3)))))),
inference(forward_demodulation,[],[f1601,f1404]) ).
fof(f1626,plain,
! [X2,X0,X1] : associator(X0,additive_inverse(X1),X2) = additive_inverse(add(multiply(multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X1,X2))))),
inference(forward_demodulation,[],[f1602,f311]) ).
fof(f1634,plain,
! [X2,X3,X0,X1] : associator(X3,X0,add(X1,X2)) = add(multiply(multiply(X3,X0),X1),add(associator(X3,X0,X2),additive_inverse(multiply(X3,multiply(X0,X1))))),
inference(forward_demodulation,[],[f1617,f1064]) ).
fof(f1635,plain,
! [X2,X0,X1] : associator(X2,X0,additive_inverse(X1)) = additive_inverse(add(multiply(X2,multiply(X0,X1)),add(associator(X2,X0,X1),additive_inverse(multiply(X2,multiply(X0,X1)))))),
inference(forward_demodulation,[],[f1618,f15]) ).
fof(f1642,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(multiply(multiply(X0,X1),X3),add(multiply(X0,multiply(X2,X3)),add(associator(X0,X2,X3),additive_inverse(add(multiply(X0,multiply(X1,X3)),multiply(X0,multiply(X2,X3))))))),
inference(forward_demodulation,[],[f1625,f15]) ).
fof(f1643,plain,
! [X2,X0,X1] : associator(X0,additive_inverse(X1),X2) = additive_inverse(add(add(multiply(X0,multiply(X1,X2)),associator(X0,X1,X2)),additive_inverse(multiply(X0,multiply(X1,X2))))),
inference(forward_demodulation,[],[f1626,f1404]) ).
fof(f1650,plain,
! [X2,X3,X0,X1] : associator(X3,X0,add(X1,X2)) = add(add(multiply(X3,multiply(X0,X1)),associator(X3,X0,X1)),add(associator(X3,X0,X2),additive_inverse(multiply(X3,multiply(X0,X1))))),
inference(forward_demodulation,[],[f1634,f1404]) ).
fof(f1651,plain,
! [X2,X0,X1] : associator(X2,X0,additive_inverse(X1)) = additive_inverse(associator(X2,X0,X1)),
inference(forward_demodulation,[],[f1635,f135]) ).
fof(f1657,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(multiply(multiply(X0,X1),X3),add(associator(X0,X2,X3),additive_inverse(multiply(X0,multiply(X1,X3))))),
inference(forward_demodulation,[],[f1642,f1064]) ).
fof(f1658,plain,
! [X2,X0,X1] : associator(X0,additive_inverse(X1),X2) = additive_inverse(add(multiply(X0,multiply(X1,X2)),add(associator(X0,X1,X2),additive_inverse(multiply(X0,multiply(X1,X2)))))),
inference(forward_demodulation,[],[f1643,f15]) ).
fof(f1663,plain,
! [X2,X3,X0,X1] : associator(X3,X0,add(X1,X2)) = add(multiply(X3,multiply(X0,X1)),add(associator(X3,X0,X1),add(associator(X3,X0,X2),additive_inverse(multiply(X3,multiply(X0,X1)))))),
inference(forward_demodulation,[],[f1650,f15]) ).
fof(f1668,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(add(multiply(X0,multiply(X1,X3)),associator(X0,X1,X3)),add(associator(X0,X2,X3),additive_inverse(multiply(X0,multiply(X1,X3))))),
inference(forward_demodulation,[],[f1657,f1404]) ).
fof(f1669,plain,
! [X2,X0,X1] : associator(X0,additive_inverse(X1),X2) = additive_inverse(associator(X0,X1,X2)),
inference(forward_demodulation,[],[f1658,f135]) ).
fof(f1672,plain,
! [X2,X3,X0,X1] : associator(X3,X0,add(X1,X2)) = add(associator(X3,X0,X1),associator(X3,X0,X2)),
inference(forward_demodulation,[],[f1663,f217]) ).
fof(f1676,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(multiply(X0,multiply(X1,X3)),add(associator(X0,X1,X3),add(associator(X0,X2,X3),additive_inverse(multiply(X0,multiply(X1,X3)))))),
inference(forward_demodulation,[],[f1668,f15]) ).
fof(f1677,plain,
! [X2,X0,X1] : associator(X0,additive_inverse(X1),X2) = associator(X0,X1,additive_inverse(X2)),
inference(forward_demodulation,[],[f1669,f1651]) ).
fof(f1678,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(associator(X0,X1,X3),associator(X0,X2,X3)),
inference(forward_demodulation,[],[f1676,f217]) ).
fof(f1702,plain,
! [X2,X0,X1] : add(associator(X0,X1,X1),X2) = X2,
inference(superposition,[],[f1,f1465]) ).
fof(f1703,plain,
! [X2,X0,X1] : add(X2,associator(X0,X1,X1)) = X2,
inference(superposition,[],[f2,f1465]) ).
fof(f1706,plain,
( ! [X0,X1] : associator(X0,X1,X1) = additive_inverse(associator(X0,X1,X1))
| ~ spl0_2 ),
inference(superposition,[],[f51,f1465]) ).
fof(f1709,plain,
( ! [X0,X1] : associator(X0,X1,X1) = associator(X0,X1,additive_inverse(X1))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1706,f1651]) ).
fof(f2178,plain,
! [X2,X0,X1] : associator(X1,X2,X0) = associator(X1,additive_inverse(X2),additive_inverse(X0)),
inference(superposition,[],[f1677,f11]) ).
fof(f2655,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = associator(X0,X1,add(X2,X1)),
inference(superposition,[],[f1703,f1672]) ).
fof(f2756,plain,
( ! [X0,X1] : associator(X1,additive_inverse(X0),additive_inverse(X0)) = associator(X1,additive_inverse(X0),X0)
| ~ spl0_2 ),
inference(superposition,[],[f1709,f11]) ).
fof(f2792,plain,
( ! [X0,X1] : associator(X1,additive_inverse(X0),X0) = associator(X1,X0,X0)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f2756,f2178]) ).
fof(f3548,plain,
( ! [X2,X0,X1] : associator(X0,add(X2,additive_inverse(X1)),X1) = add(associator(X0,X2,X1),associator(X0,X1,X1))
| ~ spl0_2 ),
inference(superposition,[],[f1678,f2792]) ).
fof(f3573,plain,
! [X2,X0,X1] : associator(X0,X2,X1) = associator(X0,add(X1,X2),X1),
inference(superposition,[],[f1702,f1678]) ).
fof(f3614,plain,
( ! [X2,X0,X1] : associator(X0,X2,X1) = associator(X0,add(X2,additive_inverse(X1)),X1)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f3548,f1703]) ).
fof(f3810,plain,
! [X2,X0,X1] : associator(X1,add(X0,additive_inverse(X2)),X2) = associator(X1,add(X0,additive_inverse(X2)),X0),
inference(superposition,[],[f2655,f135]) ).
fof(f3886,plain,
! [X2,X0,X1] : associator(X1,additive_inverse(X2),X0) = associator(X1,add(X0,additive_inverse(X2)),X2),
inference(forward_demodulation,[],[f3810,f3573]) ).
fof(f3894,plain,
( ! [X2,X0,X1] : associator(X1,X0,X2) = associator(X1,additive_inverse(X2),X0)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f3886,f3614]) ).
fof(f4106,plain,
( ! [X2,X3,X0,X1] : add(associator(X0,X3,X1),associator(X0,X1,X2)) = associator(X0,add(X3,additive_inverse(X2)),X1)
| ~ spl0_2 ),
inference(superposition,[],[f1678,f3894]) ).
fof(f4154,plain,
( additive_identity != associator(x,add(y,additive_inverse(y)),z)
| spl0_1
| ~ spl0_2 ),
inference(backward_demodulation,[],[f35,f4106]) ).
fof(f4226,plain,
( additive_identity != associator(x,additive_identity,z)
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f4154,f10]) ).
fof(f4236,plain,
( additive_identity != additive_identity
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f4226,f1589]) ).
fof(f4237,plain,
( $false
| spl0_1
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f4236]) ).
fof(f4238,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f4237]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f36]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f52]) ).
cnf(s4,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f4238]) ).
cnf(s5,plain,
spl0_1,
inference(rat,[],[s4,s2]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s5]) ).
fof(f4243,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG025-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.44 % Computer : n007.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sun Sep 27 22:57:55 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.51 Running first-order theorem proving
% 0.22/0.51 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.65/1.88 % (1873557)Detected a unit-equality problem, will run specialized UEQ schedule.
% 1.65/1.88 % (1873566)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=893265196:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 1.65/1.88 % (1873566)Refutation not found, incomplete strategy
% 1.65/1.88 % (1873566)------------------------------
% 1.65/1.88 % (1873566)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.65/1.88 % (1873566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/1.88 % (1873566)CaDiCaL version: 2.1.3
% 1.65/1.88 % (1873566)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.88 % (1873566)Time elapsed: 0.002 s
% 1.65/1.88 % (1873566)Peak memory usage: 88 MB
% 1.65/1.88 % (1873566)Instructions burned: 2 (million)
% 1.65/1.88 % (1873563)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3633336892:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 1.65/1.88 % (1873562)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=4151279747:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 1.65/1.88 % (1873565)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3761517467:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 1.65/1.88 % (1873564)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=953438172:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 1.65/1.88 % (1873567)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2674481568:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 1.65/1.88 % (1873568)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3679357301:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 1.65/1.88 % (1873565)Instruction limit reached!
% 1.65/1.88 % (1873565)------------------------------
% 1.65/1.88 % (1873565)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.65/1.88 % (1873565)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/1.88 % (1873565)CaDiCaL version: 2.1.3
% 1.65/1.88 % (1873565)Termination reason: Instruction limit
% 1.65/1.88 % (1873565)Termination phase: Saturation
% 1.65/1.88 % (1873565)Time elapsed: 0.118 s
% 1.65/1.88 % (1873565)Peak memory usage: 88 MB
% 1.65/1.88 % (1873565)Instructions burned: 137 (million)
% 1.65/1.88 % (1873567)First to succeed.
% 1.65/1.88 % (1873567)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1873557"
% 1.65/1.88 % (1873566)------------------------------
% 1.65/1.88 % (1873566)------------------------------
% 1.65/1.88 % (1873576)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3166408764:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 1.65/1.88 % (1873577)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3883457680:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 1.65/1.88 % (1873567)Refutation found. Thanks to Tanya!
% 1.65/1.88 % SZS status Unsatisfiable for theBenchmark
% 1.65/1.88 % SZS output start Proof for theBenchmark
% See solution above
% 6.92/2.16 % (1873567)------------------------------
% 6.92/2.16 % (1873567)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.92/2.16 % (1873567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.92/2.16 % (1873567)CaDiCaL version: 2.1.3
% 6.92/2.16 % (1873567)Termination reason: Refutation
% 6.92/2.16 % (1873567)Time elapsed: 0.144 s
% 6.92/2.16 % (1873567)Peak memory usage: 90 MB
% 6.92/2.16 % (1873567)Instructions burned: 136 (million)
% 6.92/2.16 % (1873567)------------------------------
% 6.92/2.16 % (1873567)------------------------------
% 6.92/2.16 % (1873557)Success in time 0.845 s
% 6.92/2.16 % Vampire exiting
%------------------------------------------------------------------------------