%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO014-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 09:35:52 AM UTC 2026
% Result : Unsatisfiable 40.93s 6.46s
% Output : Refutation 41.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 26
% Syntax : Number of formulae : 242 ( 242 unt; 0 def)
% Number of atoms : 242 ( 241 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 451 ( 451 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
fof(f3,axiom,
! [X0,X1] : sum(X0,X1,add(X0,X1)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f4,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f5,plain,
! [X0,X1] : true = product(X0,X1,multiply(X0,X1)),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X2,X0,X1] : ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
fof(f7,plain,
! [X2,X0,X1] : true = ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X2,X0,X1] : ifeq(product(X0,X1,X2),true,product(X1,X0,X2),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiplication) ).
fof(f9,plain,
! [X2,X0,X1] : true = ifeq(product(X0,X1,X2),true,product(X1,X0,X2),true),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X0] : sum(additive_identity,X0,X0) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
fof(f11,plain,
! [X0] : true = sum(additive_identity,X0,X0),
inference(reorient_equations,[],[f10]) ).
fof(f12,axiom,
! [X0] : sum(X0,additive_identity,X0) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
fof(f13,plain,
! [X0] : true = sum(X0,additive_identity,X0),
inference(reorient_equations,[],[f12]) ).
fof(f14,axiom,
! [X0] : product(multiplicative_identity,X0,X0) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity1) ).
fof(f15,plain,
! [X0] : true = product(multiplicative_identity,X0,X0),
inference(reorient_equations,[],[f14]) ).
fof(f16,axiom,
! [X0] : product(X0,multiplicative_identity,X0) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity2) ).
fof(f17,plain,
! [X0] : true = product(X0,multiplicative_identity,X0),
inference(reorient_equations,[],[f16]) ).
fof(f18,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/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f19,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,[],[f18]) ).
fof(f20,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/sandbox/benchmark/theBenchmark.p',distributivity2) ).
fof(f21,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,[],[f20]) ).
fof(f22,axiom,
! [X2,X3,X0,X1,X6,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(product(X5,X1,X6),true,ifeq(sum(X5,X3,X0),true,sum(X6,X4,X2),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).
fof(f23,plain,
! [X2,X3,X0,X1,X6,X4,X5] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(product(X5,X1,X6),true,ifeq(sum(X5,X3,X0),true,sum(X6,X4,X2),true),true),true),true),
inference(reorient_equations,[],[f22]) ).
fof(f24,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/sandbox/benchmark/theBenchmark.p',distributivity4) ).
fof(f25,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,[],[f24]) ).
fof(f28,axiom,
! [X2,X3,X0,X1,X6,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(product(X3,X4,X5),true,ifeq(sum(X6,X4,X1),true,ifeq(sum(X6,X3,X0),true,sum(X6,X5,X2),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity6) ).
fof(f29,plain,
! [X2,X3,X0,X1,X6,X4,X5] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X3,X4,X5),true,ifeq(sum(X6,X4,X1),true,ifeq(sum(X6,X3,X0),true,sum(X6,X5,X2),true),true),true),true),
inference(reorient_equations,[],[f28]) ).
fof(f30,axiom,
! [X2,X3,X0,X1,X6,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(sum(X2,X3,X4),true,ifeq(sum(X1,X3,X5),true,ifeq(sum(X0,X3,X6),true,product(X6,X5,X4),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity7) ).
fof(f31,plain,
! [X2,X3,X0,X1,X6,X4,X5] : true = ifeq(product(X0,X1,X2),true,ifeq(sum(X2,X3,X4),true,ifeq(sum(X1,X3,X5),true,ifeq(sum(X0,X3,X6),true,product(X6,X5,X4),true),true),true),true),
inference(reorient_equations,[],[f30]) ).
fof(f32,axiom,
! [X2,X3,X0,X1,X6,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(product(X3,X4,X5),true,ifeq(sum(X4,X6,X1),true,ifeq(sum(X3,X6,X0),true,sum(X5,X6,X2),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity8) ).
fof(f33,plain,
! [X2,X3,X0,X1,X6,X4,X5] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X3,X4,X5),true,ifeq(sum(X4,X6,X1),true,ifeq(sum(X3,X6,X0),true,sum(X5,X6,X2),true),true),true),true),
inference(reorient_equations,[],[f32]) ).
fof(f34,axiom,
! [X0] : sum(inverse(X0),X0,multiplicative_identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f35,plain,
! [X0] : true = sum(inverse(X0),X0,multiplicative_identity),
inference(reorient_equations,[],[f34]) ).
fof(f36,axiom,
! [X0] : sum(X0,inverse(X0),multiplicative_identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse2) ).
fof(f37,plain,
! [X0] : true = sum(X0,inverse(X0),multiplicative_identity),
inference(reorient_equations,[],[f36]) ).
fof(f38,axiom,
! [X0] : product(inverse(X0),X0,additive_identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse1) ).
fof(f39,plain,
! [X0] : true = product(inverse(X0),X0,additive_identity),
inference(reorient_equations,[],[f38]) ).
fof(f40,axiom,
! [X0] : product(X0,inverse(X0),additive_identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse2) ).
fof(f41,plain,
! [X0] : true = product(X0,inverse(X0),additive_identity),
inference(reorient_equations,[],[f40]) ).
fof(f42,axiom,
! [X2,X3,X0,X1] : ifeq2(sum(X0,X1,X2),true,ifeq2(sum(X0,X1,X3),true,X3,X2),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f43,axiom,
! [X2,X3,X0,X1] : ifeq2(product(X0,X1,X2),true,ifeq2(product(X0,X1,X3),true,X3,X2),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
fof(f44,negated_conjecture,
sum(x,y,x_plus_y) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_plus_y) ).
fof(f45,plain,
true = sum(x,y,x_plus_y),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
product(inverse(x),inverse(y),x_inverse_times_y_inverse) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_inverse_times_y_inverse) ).
fof(f47,plain,
true = product(inverse(x),inverse(y),x_inverse_times_y_inverse),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
inverse(x_plus_y) != x_inverse_times_y_inverse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
fof(f49,plain,
x_inverse_times_y_inverse != inverse(x_plus_y),
inference(reorient_equations,[],[f48]) ).
fof(f54,plain,
! [X2,X0,X1] : ifeq2(sum(X0,X1,X2),true,ifeq2(true,true,add(X0,X1),X2),X2) = X2,
inference(superposition,[],[f42,f3]) ).
fof(f55,plain,
! [X0,X1] : ifeq2(sum(X0,inverse(X0),X1),true,ifeq2(true,true,multiplicative_identity,X1),X1) = X1,
inference(superposition,[],[f42,f37]) ).
fof(f56,plain,
! [X0,X1] : ifeq2(sum(X0,inverse(X0),X1),true,multiplicative_identity,X1) = X1,
inference(forward_demodulation,[],[f55,f1]) ).
fof(f57,plain,
! [X2,X0,X1] : ifeq2(sum(X0,X1,X2),true,add(X0,X1),X2) = X2,
inference(forward_demodulation,[],[f54,f1]) ).
fof(f63,plain,
! [X0,X1] : true = ifeq(true,true,sum(X1,X0,add(X0,X1)),true),
inference(superposition,[],[f7,f3]) ).
fof(f70,plain,
! [X0,X1] : true = sum(X1,X0,add(X0,X1)),
inference(forward_demodulation,[],[f63,f2]) ).
fof(f74,plain,
! [X0] : x_inverse_times_y_inverse = ifeq2(true,true,ifeq2(product(inverse(x),inverse(y),X0),true,X0,x_inverse_times_y_inverse),x_inverse_times_y_inverse),
inference(superposition,[],[f43,f47]) ).
fof(f78,plain,
! [X2,X0,X1] : ifeq2(product(X0,X1,X2),true,ifeq2(true,true,multiply(X0,X1),X2),X2) = X2,
inference(superposition,[],[f43,f5]) ).
fof(f81,plain,
! [X2,X0,X1] : ifeq2(product(X0,X1,X2),true,multiply(X0,X1),X2) = X2,
inference(forward_demodulation,[],[f78,f1]) ).
fof(f85,plain,
! [X0] : x_inverse_times_y_inverse = ifeq2(product(inverse(x),inverse(y),X0),true,X0,x_inverse_times_y_inverse),
inference(forward_demodulation,[],[f74,f1]) ).
fof(f92,plain,
! [X0,X1] : true = ifeq(true,true,product(X1,X0,multiply(X0,X1)),true),
inference(superposition,[],[f9,f5]) ).
fof(f101,plain,
! [X0,X1] : true = product(X1,X0,multiply(X0,X1)),
inference(forward_demodulation,[],[f92,f2]) ).
fof(f133,plain,
! [X0,X1] : ifeq2(true,true,ifeq2(product(X0,multiplicative_identity,X1),true,X1,X0),X0) = X0,
inference(superposition,[],[f43,f17]) ).
fof(f134,plain,
! [X0,X1] : ifeq2(product(X0,multiplicative_identity,X1),true,X1,X0) = X0,
inference(forward_demodulation,[],[f133,f1]) ).
fof(f148,plain,
! [X0,X1] : ifeq2(sum(X0,additive_identity,X1),true,ifeq2(true,true,X0,X1),X1) = X1,
inference(superposition,[],[f42,f13]) ).
fof(f151,plain,
! [X0,X1] : ifeq2(sum(X0,additive_identity,X1),true,X0,X1) = X1,
inference(forward_demodulation,[],[f148,f1]) ).
fof(f175,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(product(inverse(X0),X1,X2),true,ifeq(product(X0,X1,X3),true,ifeq(sum(X3,X2,X4),true,ifeq(true,true,product(multiplicative_identity,X1,X4),true),true),true),true),
inference(superposition,[],[f25,f37]) ).
fof(f190,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(product(inverse(X0),X1,X2),true,ifeq(product(X0,X1,X3),true,ifeq(sum(X3,X2,X4),true,product(multiplicative_identity,X1,X4),true),true),true),
inference(forward_demodulation,[],[f175,f2]) ).
fof(f212,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,ifeq(product(inverse(x),X0,X1),true,ifeq(sum(X1,x_inverse_times_y_inverse,X2),true,ifeq(sum(X0,inverse(y),X3),true,product(inverse(x),X3,X2),true),true),true),true),
inference(superposition,[],[f21,f47]) ).
fof(f269,plain,
! [X2,X3,X0,X1] : true = ifeq(product(inverse(x),X0,X1),true,ifeq(sum(X1,x_inverse_times_y_inverse,X2),true,ifeq(sum(X0,inverse(y),X3),true,product(inverse(x),X3,X2),true),true),true),
inference(forward_demodulation,[],[f212,f2]) ).
fof(f397,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(product(inverse(X0),X1,X2),true,ifeq(true,true,ifeq(product(inverse(X0),X3,X4),true,ifeq(sum(X3,X0,X1),true,sum(X4,additive_identity,X2),true),true),true),true),
inference(superposition,[],[f19,f39]) ).
fof(f440,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(product(inverse(X0),X1,X2),true,ifeq(product(inverse(X0),X3,X4),true,ifeq(sum(X3,X0,X1),true,sum(X4,additive_identity,X2),true),true),true),
inference(forward_demodulation,[],[f397,f2]) ).
fof(f471,plain,
! [X2,X3,X0,X1] : true = ifeq(product(x_plus_y,X0,X1),true,ifeq(product(y,X0,X2),true,ifeq(product(x,X0,X3),true,ifeq(true,true,sum(X3,X2,X1),true),true),true),true),
inference(superposition,[],[f23,f45]) ).
fof(f482,plain,
! [X2,X3,X0,X1] : true = ifeq(product(x_plus_y,X0,X1),true,ifeq(product(y,X0,X2),true,ifeq(product(x,X0,X3),true,sum(X3,X2,X1),true),true),true),
inference(forward_demodulation,[],[f471,f2]) ).
fof(f566,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,ifeq(sum(x_inverse_times_y_inverse,X0,X1),true,ifeq(sum(inverse(y),X0,X2),true,ifeq(sum(inverse(x),X0,X3),true,product(X3,X2,X1),true),true),true),true),
inference(superposition,[],[f31,f47]) ).
fof(f625,plain,
! [X2,X3,X0,X1] : true = ifeq(sum(x_inverse_times_y_inverse,X0,X1),true,ifeq(sum(inverse(y),X0,X2),true,ifeq(sum(inverse(x),X0,X3),true,product(X3,X2,X1),true),true),true),
inference(forward_demodulation,[],[f566,f2]) ).
fof(f678,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(true,true,ifeq(product(X1,X0,X2),true,ifeq(product(X3,X0,X4),true,ifeq(sum(X3,X1,multiplicative_identity),true,sum(X4,X2,X0),true),true),true),true),
inference(superposition,[],[f23,f15]) ).
fof(f686,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(true,true,ifeq(product(X1,X2,X3),true,ifeq(sum(X4,X2,X0),true,ifeq(sum(X4,X1,multiplicative_identity),true,sum(X4,X3,X0),true),true),true),true),
inference(superposition,[],[f29,f15]) ).
fof(f690,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(true,true,ifeq(product(X1,X2,X3),true,ifeq(sum(X2,X4,X0),true,ifeq(sum(X1,X4,multiplicative_identity),true,sum(X3,X4,X0),true),true),true),true),
inference(superposition,[],[f33,f15]) ).
fof(f697,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(product(X1,X2,X3),true,ifeq(sum(X2,X4,X0),true,ifeq(sum(X1,X4,multiplicative_identity),true,sum(X3,X4,X0),true),true),true),
inference(forward_demodulation,[],[f690,f2]) ).
fof(f700,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(product(X1,X2,X3),true,ifeq(sum(X4,X2,X0),true,ifeq(sum(X4,X1,multiplicative_identity),true,sum(X4,X3,X0),true),true),true),
inference(forward_demodulation,[],[f686,f2]) ).
fof(f706,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(product(X1,X0,X2),true,ifeq(product(X3,X0,X4),true,ifeq(sum(X3,X1,multiplicative_identity),true,sum(X4,X2,X0),true),true),true),
inference(forward_demodulation,[],[f678,f2]) ).
fof(f801,plain,
x_inverse_times_y_inverse = ifeq2(true,true,multiply(inverse(x),inverse(y)),x_inverse_times_y_inverse),
inference(superposition,[],[f85,f5]) ).
fof(f802,plain,
x_inverse_times_y_inverse = ifeq2(true,true,multiply(inverse(y),inverse(x)),x_inverse_times_y_inverse),
inference(superposition,[],[f85,f101]) ).
fof(f804,plain,
x_inverse_times_y_inverse = multiply(inverse(y),inverse(x)),
inference(forward_demodulation,[],[f802,f1]) ).
fof(f805,plain,
x_inverse_times_y_inverse = multiply(inverse(x),inverse(y)),
inference(forward_demodulation,[],[f801,f1]) ).
fof(f818,plain,
! [X2,X0,X1] : true = ifeq(product(x_plus_y,X0,X1),true,ifeq(product(y,X0,X2),true,ifeq(true,true,sum(multiply(x,X0),X2,X1),true),true),true),
inference(superposition,[],[f482,f5]) ).
fof(f833,plain,
! [X2,X0,X1] : true = ifeq(product(x_plus_y,X0,X1),true,ifeq(product(y,X0,X2),true,sum(multiply(x,X0),X2,X1),true),true),
inference(forward_demodulation,[],[f818,f2]) ).
fof(f875,plain,
! [X0,X1] : add(X1,X0) = ifeq2(true,true,add(X0,X1),add(X1,X0)),
inference(superposition,[],[f57,f70]) ).
fof(f876,plain,
! [X0] : multiplicative_identity = ifeq2(true,true,add(X0,inverse(X0)),multiplicative_identity),
inference(superposition,[],[f57,f37]) ).
fof(f877,plain,
! [X0] : ifeq2(true,true,add(X0,additive_identity),X0) = X0,
inference(superposition,[],[f57,f13]) ).
fof(f878,plain,
! [X0] : ifeq2(true,true,add(additive_identity,X0),X0) = X0,
inference(superposition,[],[f57,f11]) ).
fof(f888,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(forward_demodulation,[],[f878,f1]) ).
fof(f889,plain,
! [X0] : add(X0,additive_identity) = X0,
inference(forward_demodulation,[],[f877,f1]) ).
fof(f890,plain,
! [X0] : multiplicative_identity = add(X0,inverse(X0)),
inference(forward_demodulation,[],[f876,f1]) ).
fof(f891,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(forward_demodulation,[],[f875,f1]) ).
fof(f974,plain,
! [X2,X0,X1] : true = ifeq(product(inverse(x),X0,X1),true,ifeq(true,true,ifeq(sum(X0,inverse(y),X2),true,product(inverse(x),X2,add(X1,x_inverse_times_y_inverse)),true),true),true),
inference(superposition,[],[f269,f3]) ).
fof(f1001,plain,
! [X2,X0,X1] : true = ifeq(product(inverse(x),X0,X1),true,ifeq(sum(X0,inverse(y),X2),true,product(inverse(x),X2,add(X1,x_inverse_times_y_inverse)),true),true),
inference(forward_demodulation,[],[f974,f2]) ).
fof(f1087,plain,
! [X0,X1] : multiply(X1,X0) = ifeq2(true,true,multiply(X0,X1),multiply(X1,X0)),
inference(superposition,[],[f81,f101]) ).
fof(f1088,plain,
! [X0] : additive_identity = ifeq2(true,true,multiply(X0,inverse(X0)),additive_identity),
inference(superposition,[],[f81,f41]) ).
fof(f1089,plain,
! [X0] : ifeq2(true,true,multiply(X0,multiplicative_identity),X0) = X0,
inference(superposition,[],[f81,f17]) ).
fof(f1090,plain,
! [X0] : ifeq2(true,true,multiply(multiplicative_identity,X0),X0) = X0,
inference(superposition,[],[f81,f15]) ).
fof(f1094,plain,
! [X0] : multiply(multiplicative_identity,X0) = X0,
inference(forward_demodulation,[],[f1090,f1]) ).
fof(f1095,plain,
! [X0] : multiply(X0,multiplicative_identity) = X0,
inference(forward_demodulation,[],[f1089,f1]) ).
fof(f1096,plain,
! [X0] : additive_identity = multiply(X0,inverse(X0)),
inference(forward_demodulation,[],[f1088,f1]) ).
fof(f1097,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[],[f1087,f1]) ).
fof(f1201,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(product(y,X0,X1),true,sum(multiply(x,X0),X1,multiply(x_plus_y,X0)),true),true),
inference(superposition,[],[f833,f5]) ).
fof(f1223,plain,
! [X0,X1] : true = ifeq(product(y,X0,X1),true,sum(multiply(x,X0),X1,multiply(x_plus_y,X0)),true),
inference(forward_demodulation,[],[f1201,f2]) ).
fof(f1226,plain,
! [X0] : true = ifeq(true,true,sum(multiply(x,X0),multiply(y,X0),multiply(x_plus_y,X0)),true),
inference(superposition,[],[f1223,f5]) ).
fof(f1241,plain,
! [X0] : true = sum(multiply(x,X0),multiply(y,X0),multiply(x_plus_y,X0)),
inference(forward_demodulation,[],[f1226,f2]) ).
fof(f1299,plain,
! [X0] : multiply(x_plus_y,X0) = ifeq2(true,true,add(multiply(x,X0),multiply(y,X0)),multiply(x_plus_y,X0)),
inference(superposition,[],[f57,f1241]) ).
fof(f1303,plain,
! [X0] : multiply(x_plus_y,X0) = add(multiply(x,X0),multiply(y,X0)),
inference(forward_demodulation,[],[f1299,f1]) ).
fof(f1363,plain,
! [X0,X1] : true = ifeq(product(inverse(x),X0,X1),true,ifeq(true,true,product(inverse(x),add(X0,inverse(y)),add(X1,x_inverse_times_y_inverse)),true),true),
inference(superposition,[],[f1001,f3]) ).
fof(f1374,plain,
! [X0,X1] : true = ifeq(product(inverse(x),X0,X1),true,product(inverse(x),add(X0,inverse(y)),add(X1,x_inverse_times_y_inverse)),true),
inference(forward_demodulation,[],[f1363,f2]) ).
fof(f1475,plain,
true = ifeq(true,true,product(inverse(x),add(multiplicative_identity,inverse(y)),add(inverse(x),x_inverse_times_y_inverse)),true),
inference(superposition,[],[f1374,f17]) ).
fof(f1487,plain,
true = product(inverse(x),add(multiplicative_identity,inverse(y)),add(inverse(x),x_inverse_times_y_inverse)),
inference(forward_demodulation,[],[f1475,f2]) ).
fof(f1494,plain,
true = product(inverse(x),add(multiplicative_identity,inverse(y)),add(x_inverse_times_y_inverse,inverse(x))),
inference(forward_demodulation,[],[f1487,f891]) ).
fof(f1816,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(sum(inverse(y),X0,X1),true,ifeq(sum(inverse(x),X0,X2),true,product(X2,X1,add(x_inverse_times_y_inverse,X0)),true),true),true),
inference(superposition,[],[f625,f3]) ).
fof(f1856,plain,
! [X2,X0,X1] : true = ifeq(sum(inverse(y),X0,X1),true,ifeq(sum(inverse(x),X0,X2),true,product(X2,X1,add(x_inverse_times_y_inverse,X0)),true),true),
inference(forward_demodulation,[],[f1816,f2]) ).
fof(f2138,plain,
! [X2,X3,X0,X1] : true = ifeq(product(inverse(X0),X1,X2),true,ifeq(product(X0,X1,X3),true,ifeq(true,true,product(multiplicative_identity,X1,add(X3,X2)),true),true),true),
inference(superposition,[],[f190,f3]) ).
fof(f2167,plain,
! [X2,X3,X0,X1] : true = ifeq(product(inverse(X0),X1,X2),true,ifeq(product(X0,X1,X3),true,product(multiplicative_identity,X1,add(X3,X2)),true),true),
inference(forward_demodulation,[],[f2138,f2]) ).
fof(f2760,plain,
! [X0,X1] : true = ifeq(sum(inverse(y),X0,X1),true,ifeq(true,true,product(add(inverse(x),X0),X1,add(x_inverse_times_y_inverse,X0)),true),true),
inference(superposition,[],[f1856,f3]) ).
fof(f2779,plain,
! [X0,X1] : true = ifeq(sum(inverse(y),X0,X1),true,product(add(inverse(x),X0),X1,add(x_inverse_times_y_inverse,X0)),true),
inference(forward_demodulation,[],[f2760,f2]) ).
fof(f2791,plain,
! [X0] : true = ifeq(true,true,product(add(inverse(x),X0),add(inverse(y),X0),add(x_inverse_times_y_inverse,X0)),true),
inference(superposition,[],[f2779,f3]) ).
fof(f2814,plain,
! [X0] : true = product(add(inverse(x),X0),add(inverse(y),X0),add(x_inverse_times_y_inverse,X0)),
inference(forward_demodulation,[],[f2791,f2]) ).
fof(f2897,plain,
! [X0] : add(x_inverse_times_y_inverse,X0) = ifeq2(true,true,multiply(add(inverse(x),X0),add(inverse(y),X0)),add(x_inverse_times_y_inverse,X0)),
inference(superposition,[],[f81,f2814]) ).
fof(f2901,plain,
! [X0] : add(x_inverse_times_y_inverse,X0) = multiply(add(inverse(x),X0),add(inverse(y),X0)),
inference(forward_demodulation,[],[f2897,f1]) ).
fof(f3733,plain,
! [X2,X0,X1] : true = ifeq(product(inverse(X0),X1,X2),true,ifeq(true,true,product(multiplicative_identity,X1,add(multiply(X0,X1),X2)),true),true),
inference(superposition,[],[f2167,f5]) ).
fof(f3771,plain,
! [X2,X0,X1] : true = ifeq(product(inverse(X0),X1,X2),true,product(multiplicative_identity,X1,add(multiply(X0,X1),X2)),true),
inference(forward_demodulation,[],[f3733,f2]) ).
fof(f3789,plain,
! [X0] : true = ifeq(true,true,product(multiplicative_identity,X0,add(multiply(X0,X0),additive_identity)),true),
inference(superposition,[],[f3771,f39]) ).
fof(f3823,plain,
! [X0] : true = product(multiplicative_identity,X0,add(multiply(X0,X0),additive_identity)),
inference(forward_demodulation,[],[f3789,f2]) ).
fof(f3831,plain,
! [X0] : true = product(multiplicative_identity,X0,multiply(X0,X0)),
inference(forward_demodulation,[],[f3823,f889]) ).
fof(f3864,plain,
! [X0] : multiply(X0,X0) = ifeq2(true,true,multiply(multiplicative_identity,X0),multiply(X0,X0)),
inference(superposition,[],[f81,f3831]) ).
fof(f3883,plain,
! [X0] : multiply(X0,X0) = multiply(multiplicative_identity,X0),
inference(forward_demodulation,[],[f3864,f1]) ).
fof(f3906,plain,
! [X0] : multiply(X0,X0) = X0,
inference(forward_demodulation,[],[f3883,f1094]) ).
fof(f4040,plain,
multiply(x_plus_y,x) = add(x,multiply(y,x)),
inference(superposition,[],[f1303,f3906]) ).
fof(f4049,plain,
multiply(x_plus_y,y) = add(multiply(x,y),y),
inference(superposition,[],[f1303,f3906]) ).
fof(f4058,plain,
multiply(x_plus_y,y) = add(y,multiply(x,y)),
inference(forward_demodulation,[],[f4049,f891]) ).
fof(f4063,plain,
multiply(x_plus_y,x) = add(x,multiply(x,y)),
inference(forward_demodulation,[],[f4040,f1097]) ).
fof(f4065,plain,
multiply(y,x_plus_y) = add(y,multiply(x,y)),
inference(forward_demodulation,[],[f4058,f1097]) ).
fof(f4067,plain,
multiply(x,x_plus_y) = add(x,multiply(x,y)),
inference(forward_demodulation,[],[f4063,f1097]) ).
fof(f4712,plain,
! [X2,X0,X1] : true = ifeq(product(X0,X1,X2),true,ifeq(true,true,ifeq(sum(multiplicative_identity,X0,multiplicative_identity),true,sum(X1,X2,X1),true),true),true),
inference(superposition,[],[f706,f15]) ).
fof(f4719,plain,
! [X2,X3,X0,X1] : true = ifeq(product(inverse(X0),X1,X2),true,ifeq(product(X0,X1,X3),true,ifeq(true,true,sum(X3,X2,X1),true),true),true),
inference(superposition,[],[f706,f37]) ).
fof(f4744,plain,
! [X2,X3,X0,X1] : true = ifeq(product(inverse(X0),X1,X2),true,ifeq(product(X0,X1,X3),true,sum(X3,X2,X1),true),true),
inference(forward_demodulation,[],[f4719,f2]) ).
fof(f4751,plain,
! [X2,X0,X1] : true = ifeq(product(X0,X1,X2),true,ifeq(sum(multiplicative_identity,X0,multiplicative_identity),true,sum(X1,X2,X1),true),true),
inference(forward_demodulation,[],[f4712,f2]) ).
fof(f4785,plain,
! [X2,X0,X1] : true = ifeq(product(inverse(X0),X1,X2),true,ifeq(true,true,sum(multiply(X0,X1),X2,X1),true),true),
inference(superposition,[],[f4744,f5]) ).
fof(f4821,plain,
! [X2,X0,X1] : true = ifeq(product(inverse(X0),X1,X2),true,sum(multiply(X0,X1),X2,X1),true),
inference(forward_demodulation,[],[f4785,f2]) ).
fof(f4842,plain,
! [X0,X1] : true = ifeq(true,true,sum(multiply(X0,X1),multiply(inverse(X0),X1),X1),true),
inference(superposition,[],[f4821,f5]) ).
fof(f4866,plain,
! [X0,X1] : true = sum(multiply(X0,X1),multiply(inverse(X0),X1),X1),
inference(forward_demodulation,[],[f4842,f2]) ).
fof(f4925,plain,
! [X0,X1] : ifeq2(true,true,add(multiply(X0,X1),multiply(inverse(X0),X1)),X1) = X1,
inference(superposition,[],[f57,f4866]) ).
fof(f4959,plain,
! [X0,X1] : add(multiply(X0,X1),multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f4925,f1]) ).
fof(f5001,plain,
! [X0,X1] : add(multiply(X0,X1),multiply(inverse(X1),X0)) = X0,
inference(superposition,[],[f4959,f1097]) ).
fof(f5018,plain,
! [X0] : inverse(inverse(X0)) = add(multiply(X0,inverse(inverse(X0))),additive_identity),
inference(superposition,[],[f4959,f1096]) ).
fof(f5027,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,inverse(inverse(X0))),
inference(forward_demodulation,[],[f5018,f889]) ).
fof(f5124,plain,
! [X0] : add(additive_identity,multiply(inverse(inverse(X0)),X0)) = X0,
inference(superposition,[],[f5001,f1096]) ).
fof(f5161,plain,
! [X0] : multiply(inverse(inverse(X0)),X0) = X0,
inference(forward_demodulation,[],[f5124,f888]) ).
fof(f5169,plain,
! [X0] : multiply(X0,inverse(inverse(X0))) = X0,
inference(forward_demodulation,[],[f5161,f1097]) ).
fof(f5172,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(backward_demodulation,[],[f5027,f5169]) ).
fof(f8044,plain,
! [X2,X3,X0,X1] : true = ifeq(product(inverse(X0),X1,X2),true,ifeq(sum(X1,X0,X3),true,ifeq(true,true,sum(X2,X0,X3),true),true),true),
inference(superposition,[],[f697,f35]) ).
fof(f8066,plain,
! [X2,X3,X0,X1] : true = ifeq(product(inverse(X0),X1,X2),true,ifeq(sum(X1,X0,X3),true,sum(X2,X0,X3),true),true),
inference(forward_demodulation,[],[f8044,f2]) ).
fof(f8118,plain,
! [X2,X0,X1] : true = ifeq(product(inverse(X0),X1,X2),true,ifeq(true,true,sum(X2,X0,add(X1,X0)),true),true),
inference(superposition,[],[f8066,f3]) ).
fof(f8169,plain,
! [X2,X0,X1] : true = ifeq(product(inverse(X0),X1,X2),true,sum(X2,X0,add(X1,X0)),true),
inference(forward_demodulation,[],[f8118,f2]) ).
fof(f8191,plain,
! [X0,X1] : true = ifeq(true,true,sum(multiply(inverse(X0),X1),X0,add(X1,X0)),true),
inference(superposition,[],[f8169,f5]) ).
fof(f8223,plain,
! [X0,X1] : true = sum(multiply(inverse(X0),X1),X0,add(X1,X0)),
inference(forward_demodulation,[],[f8191,f2]) ).
fof(f8288,plain,
! [X0,X1] : add(X1,X0) = ifeq2(true,true,add(multiply(inverse(X0),X1),X0),add(X1,X0)),
inference(superposition,[],[f57,f8223]) ).
fof(f8384,plain,
! [X0,X1] : add(X1,X0) = add(multiply(inverse(X0),X1),X0),
inference(forward_demodulation,[],[f8288,f1]) ).
fof(f8435,plain,
! [X0,X1] : add(X1,X0) = add(X0,multiply(inverse(X0),X1)),
inference(forward_demodulation,[],[f8384,f891]) ).
fof(f8460,plain,
! [X0] : add(X0,inverse(X0)) = add(multiplicative_identity,X0),
inference(superposition,[],[f8435,f1095]) ).
fof(f8518,plain,
! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
inference(forward_demodulation,[],[f8460,f890]) ).
fof(f8587,plain,
true = product(inverse(x),multiplicative_identity,add(x_inverse_times_y_inverse,inverse(x))),
inference(backward_demodulation,[],[f1494,f8518]) ).
fof(f8781,plain,
inverse(x) = ifeq2(true,true,add(x_inverse_times_y_inverse,inverse(x)),inverse(x)),
inference(superposition,[],[f134,f8587]) ).
fof(f8881,plain,
inverse(x) = add(x_inverse_times_y_inverse,inverse(x)),
inference(forward_demodulation,[],[f8781,f1]) ).
fof(f9961,plain,
! [X2,X3,X0,X1] : true = ifeq(product(inverse(X0),X1,X2),true,ifeq(sum(X0,X1,X3),true,ifeq(true,true,sum(X0,X2,X3),true),true),true),
inference(superposition,[],[f700,f37]) ).
fof(f9995,plain,
! [X2,X3,X0,X1] : true = ifeq(product(inverse(X0),X1,X2),true,ifeq(sum(X0,X1,X3),true,sum(X0,X2,X3),true),true),
inference(forward_demodulation,[],[f9961,f2]) ).
fof(f10047,plain,
! [X2,X0,X1] : true = ifeq(product(inverse(X0),X1,X2),true,ifeq(true,true,sum(X0,X2,add(X0,X1)),true),true),
inference(superposition,[],[f9995,f3]) ).
fof(f10103,plain,
! [X2,X0,X1] : true = ifeq(product(inverse(X0),X1,X2),true,sum(X0,X2,add(X0,X1)),true),
inference(forward_demodulation,[],[f10047,f2]) ).
fof(f10127,plain,
! [X0] : true = ifeq(true,true,sum(X0,inverse(X0),add(X0,multiplicative_identity)),true),
inference(superposition,[],[f10103,f17]) ).
fof(f10157,plain,
! [X0] : true = sum(X0,inverse(X0),add(X0,multiplicative_identity)),
inference(forward_demodulation,[],[f10127,f2]) ).
fof(f10182,plain,
! [X0] : add(X0,multiplicative_identity) = ifeq2(true,true,multiplicative_identity,add(X0,multiplicative_identity)),
inference(superposition,[],[f56,f10157]) ).
fof(f10360,plain,
! [X0] : multiplicative_identity = add(X0,multiplicative_identity),
inference(forward_demodulation,[],[f10182,f1]) ).
fof(f10600,plain,
! [X0] : true = sum(multiplicative_identity,X0,multiplicative_identity),
inference(superposition,[],[f70,f10360]) ).
fof(f10667,plain,
! [X2,X0,X1] : true = ifeq(product(X0,X1,X2),true,ifeq(true,true,sum(X1,X2,X1),true),true),
inference(backward_demodulation,[],[f4751,f10600]) ).
fof(f10707,plain,
! [X2,X0,X1] : true = ifeq(product(X0,X1,X2),true,sum(X1,X2,X1),true),
inference(forward_demodulation,[],[f10667,f2]) ).
fof(f11064,plain,
! [X0,X1] : true = ifeq(true,true,sum(X1,multiply(X0,X1),X1),true),
inference(superposition,[],[f10707,f5]) ).
fof(f11103,plain,
! [X0,X1] : true = sum(X1,multiply(X0,X1),X1),
inference(forward_demodulation,[],[f11064,f2]) ).
fof(f11148,plain,
! [X0,X1] : ifeq2(true,true,add(X0,multiply(X1,X0)),X0) = X0,
inference(superposition,[],[f57,f11103]) ).
fof(f11301,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = X0,
inference(forward_demodulation,[],[f11148,f1]) ).
fof(f11340,plain,
y = multiply(y,x_plus_y),
inference(backward_demodulation,[],[f4065,f11301]) ).
fof(f11350,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = X0,
inference(superposition,[],[f11301,f1097]) ).
fof(f11355,plain,
inverse(y) = add(inverse(y),x_inverse_times_y_inverse),
inference(superposition,[],[f11301,f805]) ).
fof(f11419,plain,
inverse(y) = add(x_inverse_times_y_inverse,inverse(y)),
inference(forward_demodulation,[],[f11355,f891]) ).
fof(f11421,plain,
x = multiply(x,x_plus_y),
inference(backward_demodulation,[],[f4067,f11350]) ).
fof(f12367,plain,
x_plus_y = add(x_plus_y,x),
inference(superposition,[],[f11301,f11421]) ).
fof(f12370,plain,
x_plus_y = add(x,x_plus_y),
inference(forward_demodulation,[],[f12367,f891]) ).
fof(f12556,plain,
x_plus_y = add(x_plus_y,y),
inference(superposition,[],[f11301,f11340]) ).
fof(f12559,plain,
x_plus_y = add(y,x_plus_y),
inference(forward_demodulation,[],[f12556,f891]) ).
fof(f16769,plain,
! [X2,X3,X0,X1] : true = ifeq(product(inverse(X0),X1,X2),true,ifeq(true,true,ifeq(sum(X3,X0,X1),true,sum(multiply(inverse(X0),X3),additive_identity,X2),true),true),true),
inference(superposition,[],[f440,f5]) ).
fof(f16869,plain,
! [X2,X3,X0,X1] : true = ifeq(product(inverse(X0),X1,X2),true,ifeq(sum(X3,X0,X1),true,sum(multiply(inverse(X0),X3),additive_identity,X2),true),true),
inference(forward_demodulation,[],[f16769,f2]) ).
fof(f16899,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(sum(X2,X0,X1),true,sum(multiply(inverse(X0),X2),additive_identity,multiply(inverse(X0),X1)),true),true),
inference(superposition,[],[f16869,f5]) ).
fof(f16995,plain,
! [X2,X0,X1] : true = ifeq(sum(X2,X0,X1),true,sum(multiply(inverse(X0),X2),additive_identity,multiply(inverse(X0),X1)),true),
inference(forward_demodulation,[],[f16899,f2]) ).
fof(f17035,plain,
! [X0,X1] : true = ifeq(true,true,sum(multiply(inverse(X1),X0),additive_identity,multiply(inverse(X1),add(X0,X1))),true),
inference(superposition,[],[f16995,f3]) ).
fof(f17161,plain,
! [X0,X1] : true = sum(multiply(inverse(X1),X0),additive_identity,multiply(inverse(X1),add(X0,X1))),
inference(forward_demodulation,[],[f17035,f2]) ).
fof(f17252,plain,
! [X0,X1] : multiply(inverse(X0),add(X1,X0)) = ifeq2(true,true,multiply(inverse(X0),X1),multiply(inverse(X0),add(X1,X0))),
inference(superposition,[],[f151,f17161]) ).
fof(f17387,plain,
! [X0,X1] : multiply(inverse(X0),X1) = multiply(inverse(X0),add(X1,X0)),
inference(forward_demodulation,[],[f17252,f1]) ).
fof(f17586,plain,
multiply(inverse(x_plus_y),x) = multiply(inverse(x_plus_y),x_plus_y),
inference(superposition,[],[f17387,f12370]) ).
fof(f17589,plain,
multiply(inverse(x_plus_y),y) = multiply(inverse(x_plus_y),x_plus_y),
inference(superposition,[],[f17387,f12559]) ).
fof(f17591,plain,
multiply(inverse(inverse(x)),x_inverse_times_y_inverse) = multiply(inverse(inverse(x)),inverse(x)),
inference(superposition,[],[f17387,f8881]) ).
fof(f17592,plain,
multiply(inverse(inverse(y)),x_inverse_times_y_inverse) = multiply(inverse(inverse(y)),inverse(y)),
inference(superposition,[],[f17387,f11419]) ).
fof(f17654,plain,
multiply(inverse(inverse(y)),x_inverse_times_y_inverse) = multiply(inverse(y),inverse(inverse(y))),
inference(forward_demodulation,[],[f17592,f1097]) ).
fof(f17655,plain,
multiply(inverse(x),inverse(inverse(x))) = multiply(inverse(inverse(x)),x_inverse_times_y_inverse),
inference(forward_demodulation,[],[f17591,f1097]) ).
fof(f17657,plain,
multiply(x_plus_y,inverse(x_plus_y)) = multiply(inverse(x_plus_y),y),
inference(forward_demodulation,[],[f17589,f1097]) ).
fof(f17660,plain,
multiply(x_plus_y,inverse(x_plus_y)) = multiply(inverse(x_plus_y),x),
inference(forward_demodulation,[],[f17586,f1097]) ).
fof(f17685,plain,
additive_identity = multiply(inverse(inverse(y)),x_inverse_times_y_inverse),
inference(forward_demodulation,[],[f17654,f1096]) ).
fof(f17686,plain,
multiply(inverse(x),inverse(inverse(x))) = multiply(x_inverse_times_y_inverse,inverse(inverse(x))),
inference(forward_demodulation,[],[f17655,f1097]) ).
fof(f17688,plain,
multiply(x_plus_y,inverse(x_plus_y)) = multiply(y,inverse(x_plus_y)),
inference(forward_demodulation,[],[f17657,f1097]) ).
fof(f17691,plain,
multiply(x,inverse(x_plus_y)) = multiply(x_plus_y,inverse(x_plus_y)),
inference(forward_demodulation,[],[f17660,f1097]) ).
fof(f17710,plain,
additive_identity = multiply(x_inverse_times_y_inverse,inverse(inverse(y))),
inference(forward_demodulation,[],[f17685,f1097]) ).
fof(f17711,plain,
multiply(x_inverse_times_y_inverse,x) = multiply(inverse(x),x),
inference(forward_demodulation,[],[f17686,f5172]) ).
fof(f17715,plain,
additive_identity = multiply(y,inverse(x_plus_y)),
inference(forward_demodulation,[],[f17688,f1096]) ).
fof(f17716,plain,
additive_identity = multiply(x,inverse(x_plus_y)),
inference(forward_demodulation,[],[f17691,f1096]) ).
fof(f17744,plain,
additive_identity = multiply(x_inverse_times_y_inverse,y),
inference(forward_demodulation,[],[f17710,f5172]) ).
fof(f17745,plain,
multiply(x,inverse(x)) = multiply(x_inverse_times_y_inverse,x),
inference(forward_demodulation,[],[f17711,f1097]) ).
fof(f17830,plain,
additive_identity = multiply(y,x_inverse_times_y_inverse),
inference(forward_demodulation,[],[f17744,f1097]) ).
fof(f17831,plain,
multiply(x,inverse(x)) = multiply(x,x_inverse_times_y_inverse),
inference(forward_demodulation,[],[f17745,f1097]) ).
fof(f17901,plain,
additive_identity = multiply(x,x_inverse_times_y_inverse),
inference(forward_demodulation,[],[f17831,f1096]) ).
fof(f18142,plain,
multiply(x_plus_y,x_inverse_times_y_inverse) = add(multiply(x,x_inverse_times_y_inverse),additive_identity),
inference(superposition,[],[f1303,f17830]) ).
fof(f18170,plain,
multiply(x,x_inverse_times_y_inverse) = multiply(x_plus_y,x_inverse_times_y_inverse),
inference(forward_demodulation,[],[f18142,f889]) ).
fof(f18176,plain,
additive_identity = multiply(x_plus_y,x_inverse_times_y_inverse),
inference(forward_demodulation,[],[f18170,f17901]) ).
fof(f18195,plain,
x_inverse_times_y_inverse = add(additive_identity,multiply(inverse(x_plus_y),x_inverse_times_y_inverse)),
inference(superposition,[],[f4959,f18176]) ).
fof(f18209,plain,
x_inverse_times_y_inverse = multiply(inverse(x_plus_y),x_inverse_times_y_inverse),
inference(forward_demodulation,[],[f18195,f888]) ).
fof(f18217,plain,
x_inverse_times_y_inverse = multiply(x_inverse_times_y_inverse,inverse(x_plus_y)),
inference(forward_demodulation,[],[f18209,f1097]) ).
fof(f18302,plain,
inverse(x_plus_y) = add(inverse(x_plus_y),x_inverse_times_y_inverse),
inference(superposition,[],[f11301,f18217]) ).
fof(f18307,plain,
inverse(x_plus_y) = add(x_inverse_times_y_inverse,inverse(x_plus_y)),
inference(forward_demodulation,[],[f18302,f891]) ).
fof(f18384,plain,
inverse(x_plus_y) = add(additive_identity,multiply(inverse(y),inverse(x_plus_y))),
inference(superposition,[],[f4959,f17715]) ).
fof(f18397,plain,
inverse(x_plus_y) = multiply(inverse(y),inverse(x_plus_y)),
inference(forward_demodulation,[],[f18384,f888]) ).
fof(f18428,plain,
inverse(x_plus_y) = add(additive_identity,multiply(inverse(x),inverse(x_plus_y))),
inference(superposition,[],[f4959,f17716]) ).
fof(f18441,plain,
inverse(x_plus_y) = multiply(inverse(x),inverse(x_plus_y)),
inference(forward_demodulation,[],[f18428,f888]) ).
fof(f18516,plain,
inverse(y) = add(inverse(y),inverse(x_plus_y)),
inference(superposition,[],[f11350,f18397]) ).
fof(f18566,plain,
inverse(x) = add(inverse(x),inverse(x_plus_y)),
inference(superposition,[],[f11350,f18441]) ).
fof(f19094,plain,
add(x_inverse_times_y_inverse,inverse(x_plus_y)) = multiply(add(inverse(x),inverse(x_plus_y)),inverse(y)),
inference(superposition,[],[f2901,f18516]) ).
fof(f19140,plain,
add(x_inverse_times_y_inverse,inverse(x_plus_y)) = multiply(inverse(y),add(inverse(x),inverse(x_plus_y))),
inference(forward_demodulation,[],[f19094,f1097]) ).
fof(f19150,plain,
multiply(inverse(y),inverse(x)) = add(x_inverse_times_y_inverse,inverse(x_plus_y)),
inference(forward_demodulation,[],[f19140,f18566]) ).
fof(f19155,plain,
inverse(x_plus_y) = multiply(inverse(y),inverse(x)),
inference(forward_demodulation,[],[f19150,f18307]) ).
fof(f19158,plain,
x_inverse_times_y_inverse = inverse(x_plus_y),
inference(forward_demodulation,[],[f19155,f804]) ).
fof(f19159,plain,
$false,
inference(forward_subsumption_resolution,[],[f19158,f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO014-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n003.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 21:05:42 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 40.93/6.46 % (2017666)Detected a unit-equality problem, will run specialized UEQ schedule.
% 40.93/6.46 % (2017733)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2405106254:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 40.93/6.46 % (2017732)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=2505976796:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 40.93/6.46 % (2017734)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=614194397:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 40.93/6.46 % (2017738)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2347278388:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 40.93/6.46 % (2017736)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1731273243:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 40.93/6.46 % (2017731)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=2517700579:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 40.93/6.46 % (2017735)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2983287268:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 40.93/6.46 % (2017734)Instruction limit reached!
% 40.93/6.46 % (2017734)------------------------------
% 40.93/6.46 % (2017734)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 40.93/6.46 % (2017734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.93/6.46 % (2017734)CaDiCaL version: 2.1.3
% 40.93/6.46 % (2017734)Termination reason: Instruction limit
% 40.93/6.46 % (2017734)Termination phase: Saturation
% 40.93/6.46 % (2017734)Time elapsed: 0.078 s
% 40.93/6.46 % (2017734)Peak memory usage: 89 MB
% 40.93/6.46 % (2017734)Instructions burned: 137 (million)
% 40.93/6.46 % (2017735)Instruction limit reached!
% 40.93/6.46 % (2017735)------------------------------
% 40.93/6.46 % (2017735)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 40.93/6.46 % (2017735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.93/6.46 % (2017735)CaDiCaL version: 2.1.3
% 40.93/6.46 % (2017735)Termination reason: Instruction limit
% 40.93/6.46 % (2017735)Termination phase: Saturation
% 40.93/6.46 % (2017735)Time elapsed: 0.105 s
% 40.93/6.46 % (2017735)Peak memory usage: 89 MB
% 40.93/6.46 % (2017735)Instructions burned: 181 (million)
% 40.93/6.46 % (2017736)Instruction limit reached!
% 40.93/6.46 % (2017736)------------------------------
% 40.93/6.46 % (2017736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 40.93/6.46 % (2017736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.93/6.46 % (2017736)CaDiCaL version: 2.1.3
% 40.93/6.46 % (2017736)Termination reason: Instruction limit
% 40.93/6.46 % (2017736)Termination phase: Saturation
% 40.93/6.46 % (2017736)Time elapsed: 0.157 s
% 40.93/6.46 % (2017736)Peak memory usage: 91 MB
% 40.93/6.46 % (2017736)Instructions burned: 259 (million)
% 40.93/6.46 % (2017795)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1993016234:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 40.93/6.46 % (2017807)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2411191659:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 40.93/6.46 % (2017817)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2866571993:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 40.93/6.46 % (2017817)Instruction limit reached!
% 40.93/6.46 % (2017817)------------------------------
% 40.93/6.46 % (2017817)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 40.93/6.46 % (2017817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.93/6.46 % (2017817)CaDiCaL version: 2.1.3
% 40.93/6.46 % (2017817)Termination reason: Instruction limit
% 40.93/6.46 % (2017817)Termination phase: Saturation
% 40.93/6.46 % (2017817)Time elapsed: 0.060 s
% 40.93/6.46 % (2017817)Peak memory usage: 90 MB
% 40.93/6.46 % (2017817)Instructions burned: 219 (million)
% 40.93/6.46 % (2017821)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=3473713059:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 40.93/6.46 % (2017738)Instruction limit reached!
% 40.93/6.46 % (2017738)------------------------------
% 40.93/6.46 % (2017738)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 40.93/6.46 % (2017738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.93/6.46 % (2017738)CaDiCaL version: 2.1.3
% 40.93/6.46 % (2017738)Termination reason: Instruction limit
% 40.93/6.46 % (2017738)Termination phase: Saturation
% 40.93/6.46 % (2017738)Time elapsed: 0.649 s
% 40.93/6.46 % (2017738)Peak memory usage: 99 MB
% 40.93/6.46 % (2017738)Instructions burned: 1187 (million)
% 40.93/6.46 % (2017821)Instruction limit reached!
% 40.93/6.46 % (2017821)------------------------------
% 40.93/6.46 % (2017821)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 40.93/6.46 % (2017821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.93/6.46 % (2017821)CaDiCaL version: 2.1.3
% 40.93/6.46 % (2017821)Termination reason: Instruction limit
% 40.93/6.46 % (2017821)Termination phase: Saturation
% 40.93/6.46 % (2017821)Time elapsed: 0.096 s
% 40.93/6.46 % (2017821)Peak memory usage: 94 MB
% 40.93/6.46 % (2017821)Instructions burned: 321 (million)
% 40.93/6.46 % (2017824)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=565742495:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2991 on theBenchmark for (2991ds/2836Mi)
% 40.93/6.46 % (2017823)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=3165322791:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 40.93/6.46 % (2017795)Instruction limit reached!
% 40.93/6.46 % (2017795)------------------------------
% 40.93/6.46 % (2017795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 40.93/6.46 % (2017795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.93/6.46 % (2017795)CaDiCaL version: 2.1.3
% 40.93/6.46 % (2017795)Termination reason: Instruction limit
% 40.93/6.46 % (2017795)Termination phase: Saturation
% 40.93/6.46 % (2017795)Time elapsed: 1.444 s
% 40.93/6.46 % (2017795)Peak memory usage: 141 MB
% 40.93/6.46 % (2017795)Instructions burned: 2052 (million)
% 40.93/6.46 % (2017895)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=770956067:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2981 on theBenchmark for (2981ds/14534Mi)
% 40.93/6.46 % (2017824)Instruction limit reached!
% 40.93/6.46 % (2017824)------------------------------
% 40.93/6.46 % (2017824)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 40.93/6.46 % (2017824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.93/6.46 % (2017824)CaDiCaL version: 2.1.3
% 40.93/6.46 % (2017824)Termination reason: Instruction limit
% 40.93/6.46 % (2017824)Termination phase: Saturation
% 40.93/6.46 % (2017824)Time elapsed: 1.114 s
% 40.93/6.46 % (2017824)Peak memory usage: 132 MB
% 40.93/6.46 % (2017824)Instructions burned: 2837 (million)
% 40.93/6.46 % (2017951)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:sas=cadical:sp=reverse_frequency:bsr=on:alpa=false:sac=on:random_seed=914291040:i=11832:s2at=3:bs=on:bd=preordered:fsd=on_2979 on theBenchmark for (2979ds/11832Mi)
% 40.93/6.46 % (2017807)Instruction limit reached!
% 40.93/6.46 % (2017807)------------------------------
% 40.93/6.46 % (2017807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 40.93/6.46 % (2017807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.93/6.46 % (2017807)CaDiCaL version: 2.1.3
% 40.93/6.46 % (2017807)Termination reason: Instruction limit
% 40.93/6.46 % (2017807)Termination phase: Saturation
% 40.93/6.46 % (2017807)Time elapsed: 3.032 s
% 40.93/6.46 % (2017807)Peak memory usage: 169 MB
% 40.93/6.46 % (2017807)Instructions burned: 4949 (million)
% 40.93/6.46 % (2018000)lrs+10_1_to=lpo:ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:drc=off:fde=unused:sp=const_min:spb=goal:fd=preordered:random_seed=3102131417:i=2279:fgj=on:bd=all_2964 on theBenchmark for (2964ds/2279Mi)
% 40.93/6.46 % (2018000)Instruction limit reached!
% 40.93/6.46 % (2018000)------------------------------
% 40.93/6.46 % (2018000)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 40.93/6.46 % (2018000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.93/6.46 % (2018000)CaDiCaL version: 2.1.3
% 40.93/6.46 % (2018000)Termination reason: Instruction limit
% 40.93/6.46 % (2018000)Termination phase: Saturation
% 40.93/6.46 % (2018000)Time elapsed: 1.382 s
% 40.93/6.46 % (2018000)Peak memory usage: 142 MB
% 40.93/6.46 % (2018000)Instructions burned: 2279 (million)
% 40.93/6.46 % (2018002)lrs-1010_1_to=lpo:ncem=casc2026/models/loop8.pt:sil=32000:tgt=ground:npcc=on:drc=off:fde=none:sp=reverse_arity:urr=ec_only:gs=on:s2agt=16:random_seed=291004451:st=3:i=6225:bd=all:gtg=exists_all:ss=included:er=filter:sgt=10_2949 on theBenchmark for (2949ds/6225Mi)
% 40.93/6.46 % (2017895)First to succeed.
% 40.93/6.46 % (2017895)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2017666"
% 40.93/6.46 % (2017731)Also succeeded, but the first one will report.
% 40.93/6.46 % (2017951)Also succeeded, but the first one will report.
% 40.93/6.46 % (2017895)Refutation found. Thanks to Tanya!
% 40.93/6.46 % SZS status Unsatisfiable for theBenchmark
% 40.93/6.46 % SZS output start Proof for theBenchmark
% See solution above
% 41.44/6.56 % (2017895)------------------------------
% 41.44/6.56 % (2017895)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 41.44/6.56 % (2017895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.44/6.56 % (2017895)CaDiCaL version: 2.1.3
% 41.44/6.56 % (2017895)Termination reason: Refutation
% 41.44/6.56 % (2017895)Time elapsed: 3.492 s
% 41.44/6.56 % (2017895)Peak memory usage: 175 MB
% 41.44/6.56 % (2017895)Instructions burned: 5874 (million)
% 41.44/6.56 % (2017895)------------------------------
% 41.44/6.56 % (2017895)------------------------------
% 41.44/6.56 % (2017666)Success in time 5.785 s
% 41.44/6.56 % Vampire exiting
%------------------------------------------------------------------------------