%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : RNG026-7 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 12:35:46 PM UTC 2026
% Result : Unsatisfiable 0.31s 0.63s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 14
% Syntax : Number of formulae : 97 ( 97 unt; 0 def)
% Number of atoms : 97 ( 96 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 57 ( 57 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 93 ( 93 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',left_additive_identity) ).
fof(f2,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_additive_identity) ).
fof(f3,axiom,
! [X0] : multiply(additive_identity,X0) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',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/Axioms/RNG003-0.ax',right_multiplicative_zero) ).
fof(f6,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(reorient_equations,[],[f5]) ).
fof(f9,axiom,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',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/Axioms/RNG003-0.ax',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/Axioms/RNG003-0.ax',distribute1) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',distribute2) ).
fof(f14,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).
fof(f15,axiom,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',associativity_for_addition) ).
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/Axioms/RNG003-0.ax',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(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_teichmuller_identity) ).
fof(f31,plain,
additive_identity != add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))),
inference(reorient_equations,[],[f30]) ).
fof(f32,plain,
additive_identity != add(add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))),additive_inverse(add(add(add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d)))),multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d)))))),multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d)))),
inference(definition_unfolding,[],[f31,f18,f18,f18,f18,f18]) ).
fof(f33,plain,
! [X0,X1] : multiply(additive_inverse(X0),X1) = multiply(X0,additive_inverse(X1)),
inference(forward_demodulation,[],[f23,f25]) ).
fof(f54,plain,
additive_identity != add(add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d),add(add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d)))),multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d))))))))),
inference(superposition,[],[f32,f14]) ).
fof(f55,plain,
additive_identity != add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),add(add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d),add(add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d)))),multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d)))))))))),
inference(forward_demodulation,[],[f54,f15]) ).
fof(f61,plain,
additive_identity != add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d),add(add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d)))),multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d))))))))))),
inference(forward_demodulation,[],[f55,f15]) ).
fof(f67,plain,
additive_identity != add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d),add(add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d)))),multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d)))))))))))),
inference(forward_demodulation,[],[f61,f15]) ).
fof(f73,plain,
additive_identity != add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d),add(multiply(multiply(a,multiply(b,c)),d),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d))))))))))))),
inference(forward_demodulation,[],[f67,f15]) ).
fof(f79,plain,
additive_identity != add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d),add(multiply(multiply(a,multiply(b,c)),d),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(a,add(multiply(multiply(b,c),d),multiply(b,additive_inverse(multiply(c,d))))))))))))),
inference(forward_demodulation,[],[f73,f25]) ).
fof(f85,plain,
additive_identity != add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d),add(multiply(multiply(a,multiply(b,c)),d),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(a,add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d))))))))))))),
inference(forward_demodulation,[],[f79,f25]) ).
fof(f91,plain,
additive_identity != add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d),add(multiply(multiply(a,multiply(b,c)),d),add(multiply(a,additive_inverse(multiply(multiply(b,c),d))),multiply(a,add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d))))))))))))),
inference(forward_demodulation,[],[f85,f25]) ).
fof(f97,plain,
additive_identity != add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d),add(multiply(multiply(a,multiply(b,c)),d),multiply(a,add(additive_inverse(multiply(multiply(b,c),d)),add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d))))))))))))),
inference(forward_demodulation,[],[f91,f12]) ).
fof(f103,plain,
additive_identity != add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d),add(multiply(multiply(a,multiply(b,c)),d),multiply(a,add(multiply(multiply(b,c),additive_inverse(d)),add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d))))))))))))),
inference(forward_demodulation,[],[f97,f25]) ).
fof(f109,plain,
additive_identity != add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),multiply(a,additive_inverse(multiply(b,c)))),d),add(multiply(multiply(a,multiply(b,c)),d),multiply(a,add(multiply(multiply(b,c),additive_inverse(d)),add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d))))))))))))),
inference(forward_demodulation,[],[f103,f25]) ).
fof(f115,plain,
additive_identity != add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),d),add(multiply(multiply(a,multiply(b,c)),d),multiply(a,add(multiply(multiply(b,c),additive_inverse(d)),add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d))))))))))))),
inference(forward_demodulation,[],[f109,f25]) ).
fof(f121,plain,
additive_identity != add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),add(multiply(a,additive_inverse(multiply(b,multiply(c,d)))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),d),add(multiply(multiply(a,multiply(b,c)),d),multiply(a,add(multiply(multiply(b,c),additive_inverse(d)),add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d))))))))))))),
inference(forward_demodulation,[],[f115,f25]) ).
fof(f127,plain,
additive_identity != add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),add(multiply(a,multiply(b,additive_inverse(multiply(c,d)))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),d),add(multiply(multiply(a,multiply(b,c)),d),multiply(a,add(multiply(multiply(b,c),additive_inverse(d)),add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d))))))))))))),
inference(forward_demodulation,[],[f121,f25]) ).
fof(f133,plain,
additive_identity != add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),d),add(multiply(multiply(a,multiply(b,c)),d),multiply(a,add(multiply(multiply(b,c),additive_inverse(d)),add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d))))))))))))),
inference(forward_demodulation,[],[f127,f25]) ).
fof(f139,plain,
additive_identity != add(multiply(multiply(multiply(a,b),c),d),add(multiply(multiply(a,b),additive_inverse(multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),d),add(multiply(multiply(a,multiply(b,c)),d),multiply(a,add(multiply(multiply(b,c),additive_inverse(d)),add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d))))))))))))),
inference(forward_demodulation,[],[f133,f25]) ).
fof(f145,plain,
additive_identity != add(multiply(multiply(multiply(a,b),c),d),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),add(multiply(multiply(a,b),multiply(c,d)),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),d),add(multiply(multiply(a,multiply(b,c)),d),multiply(a,add(multiply(multiply(b,c),additive_inverse(d)),add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d))))))))))))),
inference(forward_demodulation,[],[f139,f25]) ).
fof(f263,plain,
! [X0,X1] : add(additive_identity,X1) = add(X0,add(additive_inverse(X0),X1)),
inference(superposition,[],[f15,f10]) ).
fof(f265,plain,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X1,add(X0,X2)),
inference(superposition,[],[f15,f14]) ).
fof(f276,plain,
! [X0,X1] : additive_identity = add(X0,add(X1,additive_inverse(add(X0,X1)))),
inference(superposition,[],[f10,f15]) ).
fof(f278,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(X2,add(X0,X1)),
inference(superposition,[],[f14,f15]) ).
fof(f284,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f263,f1]) ).
fof(f416,plain,
! [X0,X1] : add(X1,add(X0,additive_inverse(X1))) = X0,
inference(superposition,[],[f284,f14]) ).
fof(f453,plain,
! [X2,X0,X1] : add(multiply(X0,X1),add(X2,multiply(X0,additive_inverse(X1)))) = X2,
inference(superposition,[],[f416,f25]) ).
fof(f511,plain,
! [X2,X3,X0,X1] : add(multiply(X0,X1),add(multiply(X0,X2),X3)) = add(multiply(X0,add(X1,X2)),X3),
inference(superposition,[],[f15,f12]) ).
fof(f551,plain,
! [X2,X0,X1] : multiply(add(X2,additive_inverse(X0)),X1) = add(multiply(X2,X1),multiply(X0,additive_inverse(X1))),
inference(superposition,[],[f13,f33]) ).
fof(f587,plain,
! [X0,X1] : add(X0,additive_identity) = add(X1,additive_inverse(add(additive_inverse(X0),X1))),
inference(superposition,[],[f284,f276]) ).
fof(f588,plain,
! [X0,X1] : add(X1,additive_inverse(add(additive_inverse(X0),X1))) = X0,
inference(forward_demodulation,[],[f587,f2]) ).
fof(f688,plain,
! [X0,X1] : additive_inverse(X0) = add(X1,additive_inverse(add(X0,X1))),
inference(superposition,[],[f588,f11]) ).
fof(f1250,plain,
! [X2,X0,X1] : add(additive_inverse(X0),X2) = add(additive_inverse(add(X0,X1)),add(X1,X2)),
inference(superposition,[],[f265,f688]) ).
fof(f1255,plain,
! [X2,X3,X0,X1] : add(add(X0,add(X1,X2)),X3) = add(X2,add(add(X0,X1),X3)),
inference(superposition,[],[f265,f15]) ).
fof(f1321,plain,
! [X2,X3,X0,X1] : add(add(X0,add(X1,X2)),X3) = add(X2,add(X0,add(X1,X3))),
inference(forward_demodulation,[],[f1255,f15]) ).
fof(f1325,plain,
! [X2,X0,X1] : add(X1,add(X2,additive_inverse(add(X0,X1)))) = add(additive_inverse(X0),X2),
inference(forward_demodulation,[],[f1250,f278]) ).
fof(f1343,plain,
! [X2,X3,X0,X1] : add(X0,add(add(X1,X2),X3)) = add(X2,add(X0,add(X1,X3))),
inference(forward_demodulation,[],[f1321,f15]) ).
fof(f1356,plain,
! [X2,X3,X0,X1] : add(X0,add(X1,add(X2,X3))) = add(X2,add(X0,add(X1,X3))),
inference(forward_demodulation,[],[f1343,f15]) ).
fof(f1476,plain,
! [X2,X3,X0,X1] : add(multiply(X0,X2),add(X3,multiply(X0,X1))) = add(X3,multiply(X0,add(X1,X2))),
inference(superposition,[],[f278,f12]) ).
fof(f1477,plain,
! [X2,X3,X0,X1] : add(multiply(X1,X2),add(X3,multiply(X0,X2))) = add(X3,multiply(add(X0,X1),X2)),
inference(superposition,[],[f278,f13]) ).
fof(f1547,plain,
additive_identity != add(multiply(multiply(multiply(a,b),c),d),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),add(multiply(multiply(a,b),multiply(c,d)),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),additive_inverse(add(multiply(multiply(a,multiply(b,c)),d),add(multiply(a,add(multiply(multiply(b,c),additive_inverse(d)),add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d)))))),multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),d)))))))),
inference(superposition,[],[f145,f278]) ).
fof(f1563,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),additive_inverse(add(multiply(multiply(a,multiply(b,c)),d),add(multiply(a,add(multiply(multiply(b,c),additive_inverse(d)),add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d)))))),multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),d)))))))),
inference(forward_demodulation,[],[f1547,f1356]) ).
fof(f1625,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(additive_inverse(add(multiply(multiply(a,multiply(b,c)),d),add(multiply(a,add(multiply(multiply(b,c),additive_inverse(d)),add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d)))))),multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),d)))),multiply(multiply(a,b),multiply(c,additive_inverse(d))))))),
inference(forward_demodulation,[],[f1563,f278]) ).
fof(f1660,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(multiply(a,multiply(b,c)),d),add(multiply(a,add(multiply(multiply(b,c),additive_inverse(d)),add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d)))))),multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),d)))))))),
inference(forward_demodulation,[],[f1625,f14]) ).
fof(f1678,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(a,add(multiply(multiply(b,c),additive_inverse(d)),add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d)))))),multiply(add(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),multiply(a,multiply(b,c))),d))))))),
inference(forward_demodulation,[],[f1660,f1477]) ).
fof(f1690,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(add(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),multiply(a,multiply(b,c))),d),multiply(a,add(multiply(multiply(b,c),additive_inverse(d)),add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d)))))))))))),
inference(forward_demodulation,[],[f1678,f14]) ).
fof(f1700,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(add(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),multiply(a,multiply(b,c))),d),multiply(a,add(multiply(multiply(b,c),add(additive_inverse(d),d)),multiply(b,multiply(c,additive_inverse(d))))))))))),
inference(forward_demodulation,[],[f1690,f511]) ).
fof(f1708,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(a,add(multiply(multiply(b,c),add(additive_inverse(d),d)),multiply(b,multiply(c,additive_inverse(d))))),multiply(add(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),multiply(a,multiply(b,c))),d))))))),
inference(forward_demodulation,[],[f1700,f14]) ).
fof(f1716,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(a,add(multiply(multiply(b,c),add(additive_inverse(d),d)),multiply(b,multiply(c,additive_inverse(d))))),multiply(add(multiply(multiply(a,b),c),add(multiply(a,multiply(b,additive_inverse(c))),multiply(a,multiply(b,c)))),d))))))),
inference(forward_demodulation,[],[f1708,f15]) ).
fof(f1724,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(a,add(multiply(multiply(b,c),add(additive_inverse(d),d)),multiply(b,multiply(c,additive_inverse(d))))),multiply(add(multiply(a,multiply(b,c)),add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c))))),d))))))),
inference(forward_demodulation,[],[f1716,f278]) ).
fof(f1732,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(a,add(multiply(multiply(b,c),add(additive_inverse(d),d)),multiply(b,multiply(c,additive_inverse(d))))),multiply(add(multiply(multiply(a,b),c),multiply(a,add(multiply(b,additive_inverse(c)),multiply(b,c)))),d))))))),
inference(forward_demodulation,[],[f1724,f1476]) ).
fof(f1739,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(a,add(multiply(multiply(b,c),add(additive_inverse(d),d)),multiply(b,multiply(c,additive_inverse(d))))),multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,add(additive_inverse(c),c)))),d))))))),
inference(forward_demodulation,[],[f1732,f12]) ).
fof(f1745,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,add(additive_inverse(c),c)))),d),multiply(a,add(multiply(multiply(b,c),add(additive_inverse(d),d)),multiply(b,multiply(c,additive_inverse(d))))))))))),
inference(forward_demodulation,[],[f1739,f14]) ).
fof(f1750,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,add(additive_inverse(c),c)))),d),multiply(a,add(multiply(b,multiply(c,additive_inverse(d))),multiply(multiply(b,c),add(additive_inverse(d),d)))))))))),
inference(forward_demodulation,[],[f1745,f14]) ).
fof(f1755,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,add(additive_inverse(c),c)))),d),multiply(a,add(multiply(b,multiply(c,additive_inverse(d))),multiply(multiply(b,c),add(d,additive_inverse(d))))))))))),
inference(forward_demodulation,[],[f1750,f14]) ).
fof(f1760,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,add(additive_inverse(c),c)))),d),multiply(a,add(multiply(b,multiply(c,additive_inverse(d))),multiply(multiply(b,c),additive_identity))))))))),
inference(forward_demodulation,[],[f1755,f10]) ).
fof(f1764,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(a,add(multiply(b,multiply(c,additive_inverse(d))),multiply(multiply(b,c),additive_identity))),multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,add(additive_inverse(c),c)))),d))))))),
inference(forward_demodulation,[],[f1760,f14]) ).
fof(f1768,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(a,add(multiply(b,multiply(c,additive_inverse(d))),multiply(multiply(b,c),additive_identity))),multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,add(c,additive_inverse(c))))),d))))))),
inference(forward_demodulation,[],[f1764,f14]) ).
fof(f1772,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(a,add(multiply(b,multiply(c,additive_inverse(d))),multiply(multiply(b,c),additive_identity))),multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_identity))),d))))))),
inference(forward_demodulation,[],[f1768,f10]) ).
fof(f1776,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_identity))),d),multiply(a,add(multiply(b,multiply(c,additive_inverse(d))),multiply(multiply(b,c),additive_identity))))))))),
inference(forward_demodulation,[],[f1772,f14]) ).
fof(f1780,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_identity))),d),multiply(a,add(multiply(multiply(b,c),additive_identity),multiply(b,multiply(c,additive_inverse(d))))))))))),
inference(forward_demodulation,[],[f1776,f14]) ).
fof(f1784,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_identity))),d),multiply(a,add(additive_identity,multiply(b,multiply(c,additive_inverse(d))))))))))),
inference(forward_demodulation,[],[f1780,f6]) ).
fof(f1788,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(a,add(additive_identity,multiply(b,multiply(c,additive_inverse(d))))),multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_identity))),d))))))),
inference(forward_demodulation,[],[f1784,f14]) ).
fof(f1792,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(a,add(additive_identity,multiply(b,multiply(c,additive_inverse(d))))),multiply(add(multiply(a,multiply(b,additive_identity)),multiply(multiply(a,b),c)),d))))))),
inference(forward_demodulation,[],[f1788,f14]) ).
fof(f1796,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(a,add(additive_identity,multiply(b,multiply(c,additive_inverse(d))))),multiply(add(multiply(a,additive_identity),multiply(multiply(a,b),c)),d))))))),
inference(forward_demodulation,[],[f1792,f6]) ).
fof(f1800,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(a,add(additive_identity,multiply(b,multiply(c,additive_inverse(d))))),multiply(add(additive_identity,multiply(multiply(a,b),c)),d))))))),
inference(forward_demodulation,[],[f1796,f6]) ).
fof(f1804,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(add(additive_identity,multiply(multiply(a,b),c)),d),multiply(a,add(additive_identity,multiply(b,multiply(c,additive_inverse(d))))))))))),
inference(forward_demodulation,[],[f1800,f14]) ).
fof(f1808,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(add(additive_identity,multiply(multiply(a,b),c)),d),multiply(a,multiply(b,multiply(c,additive_inverse(d)))))))))),
inference(forward_demodulation,[],[f1804,f1]) ).
fof(f1812,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(add(additive_identity,multiply(multiply(a,b),c)),d)),multiply(multiply(a,b),multiply(c,additive_inverse(d)))))),
inference(forward_demodulation,[],[f1808,f1325]) ).
fof(f1816,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(multiply(add(additive_identity,multiply(multiply(a,b),c)),d))))),
inference(forward_demodulation,[],[f1812,f14]) ).
fof(f1820,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),multiply(add(additive_identity,multiply(multiply(a,b),c)),additive_inverse(d))))),
inference(forward_demodulation,[],[f1816,f25]) ).
fof(f1824,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),multiply(multiply(multiply(a,b),c),additive_inverse(d))))),
inference(forward_demodulation,[],[f1820,f1]) ).
fof(f1828,plain,
additive_identity != add(multiply(multiply(a,b),multiply(c,d)),multiply(multiply(a,b),multiply(c,additive_inverse(d)))),
inference(forward_demodulation,[],[f1824,f453]) ).
fof(f1832,plain,
additive_identity != multiply(multiply(a,b),add(multiply(c,d),multiply(c,additive_inverse(d)))),
inference(forward_demodulation,[],[f1828,f12]) ).
fof(f1836,plain,
additive_identity != multiply(multiply(a,b),multiply(add(c,additive_inverse(c)),d)),
inference(forward_demodulation,[],[f1832,f551]) ).
fof(f1840,plain,
additive_identity != multiply(multiply(a,b),multiply(additive_identity,d)),
inference(forward_demodulation,[],[f1836,f10]) ).
fof(f1844,plain,
additive_identity != multiply(multiply(a,b),additive_identity),
inference(forward_demodulation,[],[f1840,f4]) ).
fof(f1848,plain,
$false,
inference(forward_subsumption_resolution,[],[f1844,f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG026-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.20/0.48 % Computer : n002.cluster.edu
% 0.20/0.48 % Model : x86_64 x86_64
% 0.20/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.48 % Memory : 8046.5625MB
% 0.20/0.48 % OS : Linux 6.8.0-71-generic
% 0.20/0.49 % CPULimit : 300
% 0.20/0.49 % WCLimit : 300
% 0.20/0.49 % DateTime : Sun Sep 27 23:02:07 UTC 2026
% 0.20/0.49 % CPUTime :
% 0.20/0.49 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.27/0.53 Running first-order model finding
% 0.27/0.53 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.31/0.63 % (3990643)Will run a generic schedule for satisfiability detection.
% 0.31/0.63 % (3990652)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=404463517:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.31/0.63 % (3990649)% WARNING: option uhcvi not known.
% 0.31/0.63 % (3990648)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=131125542_2999 on theBenchmark for (2999ds/0Mi)
% 0.31/0.63 % (3990651)dis+10_1_sil=32000:sp=arity:random_seed=3384287575:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.31/0.63 % (3990650)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2290960374:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.31/0.63 % (3990654)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=759772331:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.31/0.63 % (3990649)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2359753541:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.31/0.63 % (3990653)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1998927426:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.31/0.63 % TRYING [1]
% 0.31/0.63 % TRYING [2]
% 0.31/0.63 % TRYING [3]
% 0.31/0.63 % (3990652) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3990643-3990652"...
% 0.31/0.63 % (3990652)...printing done.
% 0.31/0.63 % (3990652)Refutation found. Thanks to Tanya!
% 0.31/0.63 % SZS status Unsatisfiable for theBenchmark
% 0.31/0.63 % SZS output start Proof for theBenchmark
% See solution above
% 0.31/0.64 % (3990652)------------------------------
% 0.31/0.64 % (3990652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.64 % (3990652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.64 % (3990652)CaDiCaL version: 2.1.3
% 0.31/0.64 % (3990652)Termination reason: Refutation
% 0.31/0.64 % (3990652)Time elapsed: 0.044 s
% 0.31/0.64 % (3990652)Peak memory usage: 12 MB
% 0.31/0.64 % (3990652)Instructions burned: 92 (million)
% 0.31/0.64 % (3990643)Success in time 0.09 s
% 0.31/0.64 % Vampire exiting
%------------------------------------------------------------------------------