%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG004-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 12:35:04 PM UTC 2026
% Result : Unsatisfiable 19.11s 4.02s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 18
% Syntax : Number of formulae : 126 ( 126 unt; 0 def)
% Number of atoms : 126 ( 125 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 1 ( 1 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 278 ( 278 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
fof(f3,axiom,
! [X0] : sum(additive_identity,X0,X0) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
fof(f4,axiom,
! [X0] : sum(X0,additive_identity,X0) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
fof(f5,plain,
! [X0] : true = sum(X0,additive_identity,X0),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f7,plain,
! [X0,X1] : true = product(X0,X1,multiply(X0,X1)),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X0,X1] : sum(X0,X1,add(X0,X1)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f9,plain,
! [X0,X1] : true = sum(X0,X1,add(X0,X1)),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X0] : sum(additive_inverse(X0),X0,additive_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f11,plain,
! [X0] : true = sum(additive_inverse(X0),X0,additive_identity),
inference(reorient_equations,[],[f10]) ).
fof(f12,axiom,
! [X0] : sum(X0,additive_inverse(X0),additive_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f13,plain,
! [X0] : true = sum(X0,additive_inverse(X0),additive_identity),
inference(reorient_equations,[],[f12]) ).
fof(f16,axiom,
! [X2,X3,X0,X1,X4,X5] : ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X2,X4),true,ifeq(sum(X3,X0,X5),true,sum(X5,X1,X4),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition2) ).
fof(f17,plain,
! [X2,X3,X0,X1,X4,X5] : true = ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X2,X4),true,ifeq(sum(X3,X0,X5),true,sum(X5,X1,X4),true),true),true),
inference(reorient_equations,[],[f16]) ).
fof(f18,axiom,
! [X2,X0,X1] : ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
fof(f19,plain,
! [X2,X0,X1] : true = ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true),
inference(reorient_equations,[],[f18]) ).
fof(f24,axiom,
! [X2,X3,X0,X1,X6,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(product(X0,X5,X6),true,ifeq(sum(X5,X3,X1),true,sum(X6,X4,X2),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
fof(f25,plain,
! [X2,X3,X0,X1,X6,X4,X5] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(product(X0,X5,X6),true,ifeq(sum(X5,X3,X1),true,sum(X6,X4,X2),true),true),true),true),
inference(reorient_equations,[],[f24]) ).
fof(f26,axiom,
! [X2,X3,X0,X1,X6,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(sum(X4,X2,X5),true,ifeq(sum(X3,X1,X6),true,product(X0,X6,X5),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
fof(f27,plain,
! [X2,X3,X0,X1,X6,X4,X5] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(sum(X4,X2,X5),true,ifeq(sum(X3,X1,X6),true,product(X0,X6,X5),true),true),true),true),
inference(reorient_equations,[],[f26]) ).
fof(f30,axiom,
! [X2,X3,X0,X1,X6,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(sum(X4,X2,X5),true,ifeq(sum(X3,X0,X6),true,product(X6,X1,X5),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity4) ).
fof(f31,plain,
! [X2,X3,X0,X1,X6,X4,X5] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(sum(X4,X2,X5),true,ifeq(sum(X3,X0,X6),true,product(X6,X1,X5),true),true),true),true),
inference(reorient_equations,[],[f30]) ).
fof(f32,axiom,
! [X2,X3,X0,X1] : ifeq2(sum(X0,X1,X2),true,ifeq2(sum(X0,X1,X3),true,X3,X2),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f33,axiom,
! [X2,X3,X0,X1] : ifeq2(product(X0,X1,X2),true,ifeq2(product(X0,X1,X3),true,X3,X2),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
fof(f34,axiom,
product(a,b,c) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
fof(f35,plain,
true = product(a,b,c),
inference(reorient_equations,[],[f34]) ).
fof(f36,axiom,
product(additive_inverse(a),additive_inverse(b),d) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_times_b_inverse) ).
fof(f37,plain,
true = product(additive_inverse(a),additive_inverse(b),d),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_equals_d) ).
fof(f41,plain,
! [X2,X0,X1] : multiply(X0,X1) = ifeq2(true,true,ifeq2(product(X0,X1,X2),true,X2,multiply(X0,X1)),multiply(X0,X1)),
inference(superposition,[],[f33,f7]) ).
fof(f42,plain,
! [X0] : ifeq2(product(a,b,X0),true,ifeq2(true,true,c,X0),X0) = X0,
inference(superposition,[],[f33,f35]) ).
fof(f44,plain,
! [X2,X0,X1] : ifeq2(product(X0,X1,X2),true,ifeq2(true,true,multiply(X0,X1),X2),X2) = X2,
inference(superposition,[],[f33,f7]) ).
fof(f45,plain,
! [X2,X0,X1] : ifeq2(product(X0,X1,X2),true,multiply(X0,X1),X2) = X2,
inference(forward_demodulation,[],[f44,f1]) ).
fof(f47,plain,
! [X0] : ifeq2(product(a,b,X0),true,c,X0) = X0,
inference(forward_demodulation,[],[f42,f1]) ).
fof(f48,plain,
! [X2,X0,X1] : multiply(X0,X1) = ifeq2(product(X0,X1,X2),true,X2,multiply(X0,X1)),
inference(forward_demodulation,[],[f41,f1]) ).
fof(f129,plain,
! [X2,X3,X0,X1] : true = ifeq(product(a,X0,X1),true,ifeq(product(a,X2,X3),true,ifeq(true,true,ifeq(sum(b,X2,X0),true,sum(c,X3,X1),true),true),true),true),
inference(superposition,[],[f25,f35]) ).
fof(f140,plain,
! [X2,X3,X0,X1] : true = ifeq(product(a,X0,X1),true,ifeq(product(a,X2,X3),true,ifeq(sum(b,X2,X0),true,sum(c,X3,X1),true),true),true),
inference(forward_demodulation,[],[f129,f2]) ).
fof(f160,plain,
! [X2,X0,X1] : add(X0,X1) = ifeq2(true,true,ifeq2(sum(X0,X1,X2),true,X2,add(X0,X1)),add(X0,X1)),
inference(superposition,[],[f32,f9]) ).
fof(f163,plain,
! [X2,X0,X1] : ifeq2(sum(X0,X1,X2),true,ifeq2(true,true,add(X0,X1),X2),X2) = X2,
inference(superposition,[],[f32,f9]) ).
fof(f168,plain,
! [X2,X0,X1] : ifeq2(sum(X0,X1,X2),true,add(X0,X1),X2) = X2,
inference(forward_demodulation,[],[f163,f1]) ).
fof(f171,plain,
! [X2,X0,X1] : add(X0,X1) = ifeq2(sum(X0,X1,X2),true,X2,add(X0,X1)),
inference(forward_demodulation,[],[f160,f1]) ).
fof(f173,plain,
! [X0,X1] : ifeq2(true,true,ifeq2(sum(additive_identity,X0,X1),true,X1,X0),X0) = X0,
inference(superposition,[],[f32,f3]) ).
fof(f180,plain,
! [X0,X1] : ifeq2(sum(additive_identity,X0,X1),true,X1,X0) = X0,
inference(forward_demodulation,[],[f173,f1]) ).
fof(f182,plain,
! [X0,X1] : true = ifeq(true,true,sum(X1,X0,add(X0,X1)),true),
inference(superposition,[],[f19,f9]) ).
fof(f198,plain,
! [X0,X1] : true = sum(X1,X0,add(X0,X1)),
inference(forward_demodulation,[],[f182,f2]) ).
fof(f210,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(product(additive_identity,X0,X1),true,ifeq(product(X2,X0,X3),true,ifeq(sum(X3,X1,X4),true,ifeq(true,true,product(X2,X0,X4),true),true),true),true),
inference(superposition,[],[f31,f5]) ).
fof(f211,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(product(additive_inverse(X0),X1,X2),true,ifeq(product(X0,X1,X3),true,ifeq(sum(X3,X2,X4),true,ifeq(true,true,product(additive_identity,X1,X4),true),true),true),true),
inference(superposition,[],[f31,f13]) ).
fof(f217,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(product(additive_inverse(X0),X1,X2),true,ifeq(product(X0,X1,X3),true,ifeq(sum(X3,X2,X4),true,product(additive_identity,X1,X4),true),true),true),
inference(forward_demodulation,[],[f211,f2]) ).
fof(f218,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(product(additive_identity,X0,X1),true,ifeq(product(X2,X0,X3),true,ifeq(sum(X3,X1,X4),true,product(X2,X0,X4),true),true),true),
inference(forward_demodulation,[],[f210,f2]) ).
fof(f233,plain,
! [X2,X3,X0,X1] : true = ifeq(product(a,X0,X1),true,ifeq(true,true,ifeq(sum(c,X1,X2),true,ifeq(sum(b,X0,X3),true,product(a,X3,X2),true),true),true),true),
inference(superposition,[],[f27,f35]) ).
fof(f257,plain,
! [X2,X3,X0,X1] : true = ifeq(product(a,X0,X1),true,ifeq(sum(c,X1,X2),true,ifeq(sum(b,X0,X3),true,product(a,X3,X2),true),true),true),
inference(forward_demodulation,[],[f233,f2]) ).
fof(f272,plain,
! [X0,X1] : ifeq2(sum(additive_inverse(X0),X0,X1),true,ifeq2(true,true,additive_identity,X1),X1) = X1,
inference(superposition,[],[f32,f11]) ).
fof(f273,plain,
! [X0,X1] : ifeq2(sum(additive_inverse(X0),X0,X1),true,additive_identity,X1) = X1,
inference(forward_demodulation,[],[f272,f1]) ).
fof(f292,plain,
! [X2,X0,X1] : true = ifeq(product(a,X0,X1),true,ifeq(true,true,ifeq(sum(b,X2,X0),true,sum(c,multiply(a,X2),X1),true),true),true),
inference(superposition,[],[f140,f7]) ).
fof(f305,plain,
! [X2,X0,X1] : true = ifeq(product(a,X0,X1),true,ifeq(sum(b,X2,X0),true,sum(c,multiply(a,X2),X1),true),true),
inference(forward_demodulation,[],[f292,f2]) ).
fof(f311,plain,
! [X2,X0,X1] : true = ifeq(product(a,X0,X1),true,ifeq(true,true,ifeq(sum(b,X0,X2),true,product(a,X2,add(c,X1)),true),true),true),
inference(superposition,[],[f257,f9]) ).
fof(f326,plain,
! [X2,X0,X1] : true = ifeq(product(a,X0,X1),true,ifeq(sum(b,X0,X2),true,product(a,X2,add(c,X1)),true),true),
inference(forward_demodulation,[],[f311,f2]) ).
fof(f547,plain,
d = ifeq2(true,true,multiply(additive_inverse(a),additive_inverse(b)),d),
inference(superposition,[],[f45,f37]) ).
fof(f551,plain,
d = multiply(additive_inverse(a),additive_inverse(b)),
inference(forward_demodulation,[],[f547,f1]) ).
fof(f609,plain,
! [X2,X3,X0,X1] : true = ifeq(sum(X0,X1,additive_identity),true,ifeq(true,true,ifeq(sum(X2,X0,X3),true,sum(X3,X1,X2),true),true),true),
inference(superposition,[],[f17,f5]) ).
fof(f635,plain,
! [X2,X3,X0,X1] : true = ifeq(sum(X0,X1,additive_identity),true,ifeq(sum(X2,X0,X3),true,sum(X3,X1,X2),true),true),
inference(forward_demodulation,[],[f609,f2]) ).
fof(f650,plain,
! [X0] : ifeq2(true,true,add(X0,additive_identity),X0) = X0,
inference(superposition,[],[f180,f198]) ).
fof(f655,plain,
! [X0] : add(X0,additive_identity) = X0,
inference(forward_demodulation,[],[f650,f1]) ).
fof(f884,plain,
! [X0] : add(additive_inverse(X0),X0) = ifeq2(true,true,additive_identity,add(additive_inverse(X0),X0)),
inference(superposition,[],[f273,f9]) ).
fof(f885,plain,
! [X0] : add(X0,additive_inverse(X0)) = ifeq2(true,true,additive_identity,add(X0,additive_inverse(X0))),
inference(superposition,[],[f273,f198]) ).
fof(f889,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(forward_demodulation,[],[f885,f1]) ).
fof(f890,plain,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
inference(forward_demodulation,[],[f884,f1]) ).
fof(f992,plain,
! [X0,X1] : add(X1,X0) = ifeq2(true,true,add(X0,X1),add(X1,X0)),
inference(superposition,[],[f168,f198]) ).
fof(f1006,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(forward_demodulation,[],[f992,f1]) ).
fof(f1091,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(sum(b,X0,X1),true,product(a,X1,add(c,multiply(a,X0))),true),true),
inference(superposition,[],[f326,f7]) ).
fof(f1107,plain,
! [X0,X1] : true = ifeq(sum(b,X0,X1),true,product(a,X1,add(c,multiply(a,X0))),true),
inference(forward_demodulation,[],[f1091,f2]) ).
fof(f1134,plain,
true = ifeq(true,true,product(a,b,add(c,multiply(a,additive_identity))),true),
inference(superposition,[],[f1107,f5]) ).
fof(f1149,plain,
true = product(a,b,add(c,multiply(a,additive_identity))),
inference(forward_demodulation,[],[f1134,f2]) ).
fof(f1153,plain,
add(c,multiply(a,additive_identity)) = ifeq2(true,true,c,add(c,multiply(a,additive_identity))),
inference(superposition,[],[f47,f1149]) ).
fof(f1248,plain,
c = add(c,multiply(a,additive_identity)),
inference(forward_demodulation,[],[f1153,f1]) ).
fof(f1380,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(sum(b,X1,X0),true,sum(c,multiply(a,X1),multiply(a,X0)),true),true),
inference(superposition,[],[f305,f7]) ).
fof(f1403,plain,
! [X0,X1] : true = ifeq(sum(b,X1,X0),true,sum(c,multiply(a,X1),multiply(a,X0)),true),
inference(forward_demodulation,[],[f1380,f2]) ).
fof(f1411,plain,
! [X0] : true = ifeq(true,true,sum(c,multiply(a,X0),multiply(a,add(b,X0))),true),
inference(superposition,[],[f1403,f9]) ).
fof(f1431,plain,
! [X0] : true = sum(c,multiply(a,X0),multiply(a,add(b,X0))),
inference(forward_demodulation,[],[f1411,f2]) ).
fof(f1834,plain,
! [X2,X3,X0,X1] : true = ifeq(product(additive_identity,X0,X1),true,ifeq(product(X2,X0,X3),true,ifeq(true,true,product(X2,X0,add(X3,X1)),true),true),true),
inference(superposition,[],[f218,f9]) ).
fof(f1858,plain,
! [X2,X3,X0,X1] : true = ifeq(product(additive_identity,X0,X1),true,ifeq(product(X2,X0,X3),true,product(X2,X0,add(X3,X1)),true),true),
inference(forward_demodulation,[],[f1834,f2]) ).
fof(f2503,plain,
! [X2,X3,X0,X1] : true = ifeq(product(additive_inverse(X0),X1,X2),true,ifeq(product(X0,X1,X3),true,ifeq(true,true,product(additive_identity,X1,add(X3,X2)),true),true),true),
inference(superposition,[],[f217,f9]) ).
fof(f2517,plain,
! [X2,X3,X0,X1] : true = ifeq(product(additive_inverse(X0),X1,X2),true,ifeq(product(X0,X1,X3),true,product(additive_identity,X1,add(X3,X2)),true),true),
inference(forward_demodulation,[],[f2503,f2]) ).
fof(f2962,plain,
! [X2,X0,X1] : true = ifeq(product(additive_inverse(X0),X1,X2),true,ifeq(true,true,product(additive_identity,X1,add(multiply(X0,X1),X2)),true),true),
inference(superposition,[],[f2517,f7]) ).
fof(f2975,plain,
! [X2,X0,X1] : true = ifeq(product(additive_inverse(X0),X1,X2),true,product(additive_identity,X1,add(multiply(X0,X1),X2)),true),
inference(forward_demodulation,[],[f2962,f2]) ).
fof(f2993,plain,
! [X0,X1] : true = ifeq(true,true,product(additive_identity,X1,add(multiply(X0,X1),multiply(additive_inverse(X0),X1))),true),
inference(superposition,[],[f2975,f7]) ).
fof(f3010,plain,
! [X0,X1] : true = product(additive_identity,X1,add(multiply(X0,X1),multiply(additive_inverse(X0),X1))),
inference(forward_demodulation,[],[f2993,f2]) ).
fof(f3371,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(sum(X1,additive_inverse(X0),X2),true,sum(X2,X0,X1),true),true),
inference(superposition,[],[f635,f11]) ).
fof(f3403,plain,
! [X2,X0,X1] : true = ifeq(sum(X1,additive_inverse(X0),X2),true,sum(X2,X0,X1),true),
inference(forward_demodulation,[],[f3371,f2]) ).
fof(f3409,plain,
! [X0,X1] : true = ifeq(true,true,sum(add(X0,additive_inverse(X1)),X1,X0),true),
inference(superposition,[],[f3403,f9]) ).
fof(f3447,plain,
! [X0,X1] : true = sum(add(X0,additive_inverse(X1)),X1,X0),
inference(forward_demodulation,[],[f3409,f2]) ).
fof(f3482,plain,
! [X0,X1] : add(add(X0,additive_inverse(X1)),X1) = ifeq2(true,true,X0,add(add(X0,additive_inverse(X1)),X1)),
inference(superposition,[],[f171,f3447]) ).
fof(f3579,plain,
! [X0,X1] : add(add(X0,additive_inverse(X1)),X1) = X0,
inference(forward_demodulation,[],[f3482,f1]) ).
fof(f3609,plain,
! [X0,X1] : add(X1,add(X0,additive_inverse(X1))) = X0,
inference(forward_demodulation,[],[f3579,f1006]) ).
fof(f3617,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(superposition,[],[f3609,f1006]) ).
fof(f3619,plain,
! [X0] : add(X0,additive_identity) = additive_inverse(additive_inverse(X0)),
inference(superposition,[],[f3609,f890]) ).
fof(f3644,plain,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
inference(forward_demodulation,[],[f3619,f655]) ).
fof(f3682,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(superposition,[],[f3617,f3644]) ).
fof(f3765,plain,
multiply(a,additive_identity) = add(additive_inverse(c),c),
inference(superposition,[],[f3682,f1248]) ).
fof(f3784,plain,
multiply(a,additive_identity) = add(c,additive_inverse(c)),
inference(forward_demodulation,[],[f3765,f1006]) ).
fof(f3789,plain,
additive_identity = multiply(a,additive_identity),
inference(forward_demodulation,[],[f3784,f889]) ).
fof(f6460,plain,
! [X0] : add(c,multiply(a,X0)) = ifeq2(true,true,multiply(a,add(b,X0)),add(c,multiply(a,X0))),
inference(superposition,[],[f171,f1431]) ).
fof(f6521,plain,
! [X0] : add(c,multiply(a,X0)) = multiply(a,add(b,X0)),
inference(forward_demodulation,[],[f6460,f1]) ).
fof(f11286,plain,
! [X2,X0,X1] : true = ifeq(product(additive_identity,X0,X1),true,ifeq(true,true,product(X2,X0,add(multiply(X2,X0),X1)),true),true),
inference(superposition,[],[f1858,f7]) ).
fof(f11328,plain,
! [X2,X0,X1] : true = ifeq(product(additive_identity,X0,X1),true,product(X2,X0,add(multiply(X2,X0),X1)),true),
inference(forward_demodulation,[],[f11286,f2]) ).
fof(f11341,plain,
! [X0,X1] : true = ifeq(true,true,product(X1,X0,add(multiply(X1,X0),multiply(additive_identity,X0))),true),
inference(superposition,[],[f11328,f7]) ).
fof(f11378,plain,
! [X0,X1] : true = product(X1,X0,add(multiply(X1,X0),multiply(additive_identity,X0))),
inference(forward_demodulation,[],[f11341,f2]) ).
fof(f11423,plain,
! [X0,X1] : multiply(X0,X1) = ifeq2(true,true,add(multiply(X0,X1),multiply(additive_identity,X1)),multiply(X0,X1)),
inference(superposition,[],[f48,f11378]) ).
fof(f11754,plain,
! [X0,X1] : multiply(X0,X1) = add(multiply(X0,X1),multiply(additive_identity,X1)),
inference(forward_demodulation,[],[f11423,f1]) ).
fof(f12102,plain,
! [X0,X1] : multiply(additive_identity,X1) = add(additive_inverse(multiply(X0,X1)),multiply(X0,X1)),
inference(superposition,[],[f3682,f11754]) ).
fof(f12108,plain,
! [X0,X1] : multiply(additive_identity,X1) = add(multiply(X0,X1),additive_inverse(multiply(X0,X1))),
inference(forward_demodulation,[],[f12102,f1006]) ).
fof(f12112,plain,
! [X1] : additive_identity = multiply(additive_identity,X1),
inference(forward_demodulation,[],[f12108,f889]) ).
fof(f17153,plain,
! [X0,X1] : multiply(additive_identity,X0) = ifeq2(true,true,add(multiply(X1,X0),multiply(additive_inverse(X1),X0)),multiply(additive_identity,X0)),
inference(superposition,[],[f48,f3010]) ).
fof(f17364,plain,
! [X0,X1] : multiply(additive_identity,X0) = add(multiply(X1,X0),multiply(additive_inverse(X1),X0)),
inference(forward_demodulation,[],[f17153,f1]) ).
fof(f17451,plain,
! [X0,X1] : additive_identity = add(multiply(X1,X0),multiply(additive_inverse(X1),X0)),
inference(forward_demodulation,[],[f17364,f12112]) ).
fof(f17507,plain,
additive_identity = add(multiply(a,additive_inverse(b)),d),
inference(superposition,[],[f17451,f551]) ).
fof(f17579,plain,
additive_identity = add(d,multiply(a,additive_inverse(b))),
inference(forward_demodulation,[],[f17507,f1006]) ).
fof(f17903,plain,
multiply(a,additive_inverse(b)) = add(additive_inverse(d),additive_identity),
inference(superposition,[],[f3682,f17579]) ).
fof(f17925,plain,
additive_inverse(d) = multiply(a,additive_inverse(b)),
inference(forward_demodulation,[],[f17903,f655]) ).
fof(f17967,plain,
multiply(a,add(b,additive_inverse(b))) = add(c,additive_inverse(d)),
inference(superposition,[],[f6521,f17925]) ).
fof(f18018,plain,
multiply(a,additive_identity) = add(c,additive_inverse(d)),
inference(forward_demodulation,[],[f17967,f889]) ).
fof(f18032,plain,
additive_identity = add(c,additive_inverse(d)),
inference(forward_demodulation,[],[f18018,f3789]) ).
fof(f18047,plain,
c = add(d,additive_identity),
inference(superposition,[],[f3609,f18032]) ).
fof(f18108,plain,
c = d,
inference(forward_demodulation,[],[f18047,f655]) ).
fof(f18126,plain,
$false,
inference(forward_subsumption_resolution,[],[f18108,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG004-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.47 % Computer : n020.cluster.edu
% 0.21/0.47 % Model : x86_64 x86_64
% 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.47 % Memory : 8046.5625MB
% 0.21/0.47 % OS : Linux 6.8.0-71-generic
% 0.21/0.47 % CPULimit : 300
% 0.21/0.47 % WCLimit : 300
% 0.21/0.47 % DateTime : Sun Sep 27 22:58:34 UTC 2026
% 0.21/0.48 % CPUTime :
% 0.21/0.48 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.53 Running first-order theorem proving
% 0.26/0.53 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
% 19.11/4.02 % (3865509)Detected a unit-equality problem, will run specialized UEQ schedule.
% 19.11/4.02 % (3865515)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=2581196200:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 19.11/4.02 % (3865514)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=2454975677:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 19.11/4.02 % (3865516)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3081967466:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 19.11/4.02 % (3865517)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=46537512:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 19.11/4.02 % (3865518)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=575424761:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 19.11/4.02 % (3865519)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4120417610:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 19.11/4.02 % (3865520)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3255977849:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 19.11/4.02 % (3865517)Instruction limit reached!
% 19.11/4.02 % (3865517)------------------------------
% 19.11/4.02 % (3865517)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.11/4.02 % (3865517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.11/4.02 % (3865517)CaDiCaL version: 2.1.3
% 19.11/4.02 % (3865517)Termination reason: Instruction limit
% 19.11/4.02 % (3865517)Termination phase: Saturation
% 19.11/4.02 % (3865517)Time elapsed: 0.136 s
% 19.11/4.02 % (3865517)Peak memory usage: 89 MB
% 19.11/4.02 % (3865517)Instructions burned: 136 (million)
% 19.11/4.02 % (3865518)Instruction limit reached!
% 19.11/4.02 % (3865518)------------------------------
% 19.11/4.02 % (3865518)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.11/4.02 % (3865518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.11/4.02 % (3865518)CaDiCaL version: 2.1.3
% 19.11/4.02 % (3865518)Termination reason: Instruction limit
% 19.11/4.02 % (3865518)Termination phase: Saturation
% 19.11/4.02 % (3865518)Time elapsed: 0.175 s
% 19.11/4.02 % (3865518)Peak memory usage: 89 MB
% 19.11/4.02 % (3865518)Instructions burned: 181 (million)
% 19.11/4.02 % (3865519)Instruction limit reached!
% 19.11/4.02 % (3865519)------------------------------
% 19.11/4.02 % (3865519)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.11/4.02 % (3865519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.11/4.02 % (3865519)CaDiCaL version: 2.1.3
% 19.11/4.02 % (3865519)Termination reason: Instruction limit
% 19.11/4.02 % (3865519)Termination phase: Saturation
% 19.11/4.02 % (3865519)Time elapsed: 0.246 s
% 19.11/4.02 % (3865519)Peak memory usage: 91 MB
% 19.11/4.02 % (3865519)Instructions burned: 257 (million)
% 19.11/4.02 % (3865528)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2365199711:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 19.11/4.02 % (3865529)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1930507822:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 19.11/4.02 % (3865530)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2445299675:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 19.11/4.02 % (3865530)Instruction limit reached!
% 19.11/4.02 % (3865530)------------------------------
% 19.11/4.02 % (3865530)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.11/4.02 % (3865530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.11/4.02 % (3865530)CaDiCaL version: 2.1.3
% 19.11/4.02 % (3865530)Termination reason: Instruction limit
% 19.11/4.02 % (3865530)Termination phase: Saturation
% 19.11/4.02 % (3865530)Time elapsed: 0.178 s
% 19.11/4.02 % (3865530)Peak memory usage: 91 MB
% 19.11/4.02 % (3865530)Instructions burned: 216 (million)
% 19.11/4.02 % (3865534)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=122399647:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2989 on theBenchmark for (2989ds/317Mi)
% 19.11/4.02 % (3865520)Instruction limit reached!
% 19.11/4.02 % (3865520)------------------------------
% 19.11/4.02 % (3865520)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.11/4.02 % (3865520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.11/4.02 % (3865520)CaDiCaL version: 2.1.3
% 19.11/4.02 % (3865520)Termination reason: Instruction limit
% 19.11/4.02 % (3865520)Termination phase: Saturation
% 19.11/4.02 % (3865520)Time elapsed: 1.101 s
% 19.11/4.02 % (3865520)Peak memory usage: 100 MB
% 19.11/4.02 % (3865520)Instructions burned: 1188 (million)
% 19.11/4.02 % (3865534)Instruction limit reached!
% 19.11/4.02 % (3865534)------------------------------
% 19.11/4.02 % (3865534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.11/4.02 % (3865534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.11/4.02 % (3865534)CaDiCaL version: 2.1.3
% 19.11/4.02 % (3865534)Termination reason: Instruction limit
% 19.11/4.02 % (3865534)Termination phase: Saturation
% 19.11/4.02 % (3865534)Time elapsed: 0.331 s
% 19.11/4.02 % (3865534)Peak memory usage: 93 MB
% 19.11/4.02 % (3865534)Instructions burned: 317 (million)
% 19.11/4.02 % (3865536)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=3990950496:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2985 on theBenchmark for (2985ds/12125Mi)
% 19.11/4.02 % (3865537)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=3126230020:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2983 on theBenchmark for (2983ds/2836Mi)
% 19.11/4.02 % (3865515)First to succeed.
% 19.11/4.02 % (3865515)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3865509"
% 19.11/4.02 % (3865515)Refutation found. Thanks to Tanya!
% 19.11/4.02 % SZS status Unsatisfiable for theBenchmark
% 19.11/4.02 % SZS output start Proof for theBenchmark
% See solution above
% 0.30/4.41 % (3865515)------------------------------
% 0.30/4.41 % (3865515)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/4.41 % (3865515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/4.41 % (3865515)CaDiCaL version: 2.1.3
% 0.30/4.41 % (3865515)Termination reason: Refutation
% 0.30/4.41 % (3865515)Time elapsed: 2.207 s
% 0.30/4.41 % (3865515)Peak memory usage: 158 MB
% 0.30/4.41 % (3865515)Instructions burned: 3892 (million)
% 0.30/4.41 % (3865515)------------------------------
% 0.30/4.41 % (3865515)------------------------------
% 0.30/4.41 % (3865509)Success in time 2.714 s
% 0.30/4.41 % Vampire exiting
%------------------------------------------------------------------------------