%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO014-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 : Thu Sep 24 12:06:22 PM UTC 2026
% Result : Unsatisfiable 14.35s 2.23s
% Output : CNFRefutation 14.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 14
% Syntax : Number of formulae : 121 ( 121 unt; 5 def)
% Number of atoms : 121 ( 120 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 110 ( 110 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : add(X,Y) = add(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = multiply(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] : multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : add(X,additive_identity) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : multiply(X,multiplicative_identity) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : add(X,inverse(X)) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] : multiply(X,inverse(X)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
inverse(add(a,b)) != multiply(inverse(a),inverse(b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1,X2] : add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
! [X0,X1,X2] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0] : add(X0,additive_identity) = X0,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [X0] : multiply(X0,multiplicative_identity) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f17,plain,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f18,plain,
inverse(add(a,b)) != multiply(inverse(a),inverse(b)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f19,definition,
sF1_fnc = add(a,b),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f20,definition,
sF0_fnc = inverse(sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f21,definition,
sF3_fnc = inverse(a),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f22,definition,
sF4_fnc = inverse(b),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f23,definition,
sF2_fnc = multiply(sF3_fnc,sF4_fnc),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f24,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f18,f23,f22,f21,f20,f19]) ).
fof(f25,plain,
! [X0] : X0 = add(additive_identity,X0),
inference(paramodulation,[status(thm)],[f14,f10]) ).
fof(f39,plain,
multiply(b,sF4_fnc) = additive_identity,
inference(paramodulation,[status(thm)],[f22,f17]) ).
fof(f40,plain,
multiply(a,sF3_fnc) = additive_identity,
inference(paramodulation,[status(thm)],[f21,f17]) ).
fof(f43,plain,
! [X0] : X0 = multiply(multiplicative_identity,X0),
inference(paramodulation,[status(thm)],[f15,f11]) ).
fof(f65,plain,
add(b,sF4_fnc) = multiplicative_identity,
inference(paramodulation,[status(thm)],[f22,f16]) ).
fof(f66,plain,
add(a,sF3_fnc) = multiplicative_identity,
inference(paramodulation,[status(thm)],[f21,f16]) ).
fof(f73,plain,
! [X0] : add(a,multiply(b,X0)) = multiply(sF1_fnc,add(a,X0)),
inference(paramodulation,[status(thm)],[f19,f12]) ).
fof(f75,plain,
! [X0,X1] : add(X0,multiply(inverse(X0),X1)) = multiply(multiplicative_identity,add(X0,X1)),
inference(paramodulation,[status(thm)],[f16,f12]) ).
fof(f77,plain,
! [X0,X1,X2] : add(X0,multiply(X1,X2)) = multiply(add(X1,X0),add(X0,X2)),
inference(paramodulation,[status(thm)],[f10,f12]) ).
fof(f90,plain,
! [X0,X1] : add(X0,multiply(inverse(X0),X1)) = add(X0,X1),
inference(forward_demodulation,[status(thm)],[f43,f75]) ).
fof(f116,plain,
! [X0] : add(X0,additive_identity) = add(X0,inverse(inverse(X0))),
inference(paramodulation,[status(thm)],[f17,f90]) ).
fof(f117,plain,
! [X0] : add(X0,inverse(X0)) = add(X0,multiplicative_identity),
inference(paramodulation,[status(thm)],[f15,f90]) ).
fof(f130,plain,
! [X0] : X0 = add(X0,inverse(inverse(X0))),
inference(forward_demodulation,[status(thm)],[f14,f116]) ).
fof(f131,plain,
! [X0] : multiplicative_identity = add(X0,multiplicative_identity),
inference(forward_demodulation,[status(thm)],[f16,f117]) ).
fof(f139,plain,
! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
inference(paramodulation,[status(thm)],[f10,f131]) ).
fof(f155,plain,
! [X0] : multiply(a,add(sF3_fnc,X0)) = add(additive_identity,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f40,f13]) ).
fof(f156,plain,
! [X0] : multiply(b,add(sF4_fnc,X0)) = add(additive_identity,multiply(b,X0)),
inference(paramodulation,[status(thm)],[f39,f13]) ).
fof(f158,plain,
! [X0,X1] : multiply(X0,add(inverse(X0),X1)) = add(additive_identity,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f17,f13]) ).
fof(f159,plain,
! [X0,X1] : multiply(X0,add(multiplicative_identity,X1)) = add(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f15,f13]) ).
fof(f168,plain,
! [X0] : multiply(sF3_fnc,add(X0,sF4_fnc)) = add(multiply(sF3_fnc,X0),sF2_fnc),
inference(paramodulation,[status(thm)],[f23,f13]) ).
fof(f169,plain,
! [X0,X1] : multiply(X0,add(X1,inverse(X0))) = add(multiply(X0,X1),additive_identity),
inference(paramodulation,[status(thm)],[f17,f13]) ).
fof(f170,plain,
! [X0,X1] : multiply(X0,add(X1,multiplicative_identity)) = add(multiply(X0,X1),X0),
inference(paramodulation,[status(thm)],[f15,f13]) ).
fof(f182,plain,
! [X0] : multiply(a,add(sF3_fnc,X0)) = multiply(a,X0),
inference(forward_demodulation,[status(thm)],[f25,f155]) ).
fof(f183,plain,
! [X0] : multiply(b,add(sF4_fnc,X0)) = multiply(b,X0),
inference(forward_demodulation,[status(thm)],[f25,f156]) ).
fof(f184,plain,
! [X0,X1] : multiply(X0,add(inverse(X0),X1)) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f25,f158]) ).
fof(f185,plain,
! [X0,X1] : multiply(X0,multiplicative_identity) = add(X0,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f139,f159]) ).
fof(f186,plain,
! [X0,X1] : X0 = add(X0,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f15,f185]) ).
fof(f192,plain,
! [X0,X1] : multiply(X0,add(X1,inverse(X0))) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f14,f169]) ).
fof(f193,plain,
! [X0,X1] : multiply(X0,multiplicative_identity) = add(multiply(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f131,f170]) ).
fof(f194,plain,
! [X0,X1] : X0 = add(multiply(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f15,f193]) ).
fof(f216,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(paramodulation,[status(thm)],[f25,f186]) ).
fof(f223,plain,
sF3_fnc = add(sF3_fnc,sF2_fnc),
inference(paramodulation,[status(thm)],[f23,f186]) ).
fof(f225,plain,
! [X0] : X0 = add(X0,X0),
inference(paramodulation,[status(thm)],[f15,f186]) ).
fof(f226,plain,
! [X0,X1] : X0 = add(X0,multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f11,f186]) ).
fof(f251,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X0,X1)),
inference(paramodulation,[status(thm)],[f225,f12]) ).
fof(f256,plain,
! [X0,X1] : X0 = multiply(X0,add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f186,f251]) ).
fof(f261,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(paramodulation,[status(thm)],[f11,f216]) ).
fof(f289,plain,
sF3_fnc = add(sF2_fnc,sF3_fnc),
inference(paramodulation,[status(thm)],[f10,f223]) ).
fof(f415,plain,
! [X0,X1] : X0 = add(multiply(X1,X0),X0),
inference(paramodulation,[status(thm)],[f11,f194]) ).
fof(f437,plain,
add(a,multiply(b,additive_identity)) = multiply(sF1_fnc,a),
inference(paramodulation,[status(thm)],[f14,f73]) ).
fof(f456,plain,
add(a,additive_identity) = multiply(sF1_fnc,a),
inference(forward_demodulation,[status(thm)],[f261,f437]) ).
fof(f458,plain,
a = multiply(sF1_fnc,a),
inference(forward_demodulation,[status(thm)],[f14,f456]) ).
fof(f461,plain,
a = multiply(a,sF1_fnc),
inference(paramodulation,[status(thm)],[f11,f458]) ).
fof(f512,plain,
sF4_fnc = add(sF2_fnc,sF4_fnc),
inference(paramodulation,[status(thm)],[f23,f415]) ).
fof(f548,plain,
! [X0] : add(sF4_fnc,multiply(b,X0)) = multiply(multiplicative_identity,add(sF4_fnc,X0)),
inference(paramodulation,[status(thm)],[f65,f77]) ).
fof(f551,plain,
! [X0] : add(sF3_fnc,multiply(a,X0)) = multiply(multiplicative_identity,add(sF3_fnc,X0)),
inference(paramodulation,[status(thm)],[f66,f77]) ).
fof(f590,plain,
! [X0,X1] : add(X0,multiply(X1,additive_identity)) = multiply(add(X1,X0),X0),
inference(paramodulation,[status(thm)],[f14,f77]) ).
fof(f614,plain,
! [X0] : add(sF4_fnc,multiply(b,X0)) = add(sF4_fnc,X0),
inference(forward_demodulation,[status(thm)],[f43,f548]) ).
fof(f616,plain,
! [X0] : add(sF3_fnc,multiply(a,X0)) = add(sF3_fnc,X0),
inference(forward_demodulation,[status(thm)],[f43,f551]) ).
fof(f649,plain,
! [X0,X1] : add(X0,additive_identity) = multiply(add(X1,X0),X0),
inference(forward_demodulation,[status(thm)],[f261,f590]) ).
fof(f654,plain,
! [X0,X1] : X0 = multiply(add(X1,X0),X0),
inference(forward_demodulation,[status(thm)],[f14,f649]) ).
fof(f760,plain,
! [X0,X1] : add(X0,inverse(X0)) = add(X0,add(inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f256,f90]) ).
fof(f774,plain,
! [X0,X1] : multiplicative_identity = add(X0,add(inverse(X0),X1)),
inference(forward_demodulation,[status(thm)],[f16,f760]) ).
fof(f973,plain,
b = multiply(sF1_fnc,b),
inference(paramodulation,[status(thm)],[f19,f654]) ).
fof(f981,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,inverse(inverse(X0))),
inference(paramodulation,[status(thm)],[f130,f654]) ).
fof(f1010,plain,
b = multiply(b,sF1_fnc),
inference(paramodulation,[status(thm)],[f11,f973]) ).
fof(f3509,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(X0,multiply(X1,inverse(X0))),
inference(paramodulation,[status(thm)],[f226,f184]) ).
fof(f3514,plain,
! [X0] : multiply(X0,multiplicative_identity) = multiply(X0,inverse(inverse(X0))),
inference(paramodulation,[status(thm)],[f16,f184]) ).
fof(f3560,plain,
! [X0,X1] : additive_identity = multiply(X0,multiply(X1,inverse(X0))),
inference(forward_demodulation,[status(thm)],[f17,f3509]) ).
fof(f3565,plain,
! [X0] : X0 = multiply(X0,inverse(inverse(X0))),
inference(forward_demodulation,[status(thm)],[f15,f3514]) ).
fof(f3577,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f981,f3565]) ).
fof(f3609,plain,
sF1_fnc = inverse(sF0_fnc),
inference(paramodulation,[status(thm)],[f20,f3577]) ).
fof(f3612,plain,
! [X0,X1] : multiplicative_identity = add(inverse(X0),add(X0,X1)),
inference(paramodulation,[status(thm)],[f3577,f774]) ).
fof(f6990,plain,
! [X0] : additive_identity = multiply(sF0_fnc,multiply(X0,sF1_fnc)),
inference(paramodulation,[status(thm)],[f3609,f3560]) ).
fof(f7192,plain,
multiplicative_identity = add(inverse(sF2_fnc),sF4_fnc),
inference(paramodulation,[status(thm)],[f512,f3612]) ).
fof(f7193,plain,
multiplicative_identity = add(inverse(sF2_fnc),sF3_fnc),
inference(paramodulation,[status(thm)],[f289,f3612]) ).
fof(f7210,plain,
! [X0,X1] : multiplicative_identity = add(inverse(multiply(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f415,f3612]) ).
fof(f8072,plain,
multiplicative_identity = add(sF3_fnc,inverse(sF2_fnc)),
inference(paramodulation,[status(thm)],[f10,f7193]) ).
fof(f8125,plain,
multiplicative_identity = add(sF4_fnc,inverse(sF2_fnc)),
inference(paramodulation,[status(thm)],[f10,f7192]) ).
fof(f10756,plain,
additive_identity = multiply(sF0_fnc,a),
inference(paramodulation,[status(thm)],[f461,f6990]) ).
fof(f10757,plain,
additive_identity = multiply(sF0_fnc,b),
inference(paramodulation,[status(thm)],[f1010,f6990]) ).
fof(f10825,plain,
additive_identity = multiply(a,sF0_fnc),
inference(paramodulation,[status(thm)],[f11,f10756]) ).
fof(f10894,plain,
additive_identity = multiply(b,sF0_fnc),
inference(paramodulation,[status(thm)],[f11,f10757]) ).
fof(f12937,plain,
! [X0,X1] : multiply(X0,multiplicative_identity) = multiply(X0,inverse(multiply(X1,inverse(X0)))),
inference(paramodulation,[status(thm)],[f7210,f192]) ).
fof(f13014,plain,
! [X0,X1] : X0 = multiply(X0,inverse(multiply(X1,inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f15,f12937]) ).
fof(f17423,plain,
multiply(a,multiplicative_identity) = multiply(a,inverse(sF2_fnc)),
inference(paramodulation,[status(thm)],[f8072,f182]) ).
fof(f17487,plain,
a = multiply(a,inverse(sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f15,f17423]) ).
fof(f17550,plain,
inverse(sF2_fnc) = add(a,inverse(sF2_fnc)),
inference(paramodulation,[status(thm)],[f17487,f415]) ).
fof(f18173,plain,
multiply(b,multiplicative_identity) = multiply(b,inverse(sF2_fnc)),
inference(paramodulation,[status(thm)],[f8125,f183]) ).
fof(f18238,plain,
b = multiply(b,inverse(sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f15,f18173]) ).
fof(f24593,plain,
add(a,multiply(b,inverse(sF2_fnc))) = multiply(sF1_fnc,inverse(sF2_fnc)),
inference(paramodulation,[status(thm)],[f17550,f73]) ).
fof(f24625,plain,
add(a,b) = multiply(sF1_fnc,inverse(sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f18238,f24593]) ).
fof(f24626,plain,
sF1_fnc = multiply(sF1_fnc,inverse(sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f19,f24625]) ).
fof(f25444,plain,
sF2_fnc = multiply(sF2_fnc,inverse(sF1_fnc)),
inference(paramodulation,[status(thm)],[f24626,f13014]) ).
fof(f25474,plain,
sF2_fnc = multiply(sF2_fnc,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f20,f25444]) ).
fof(f25667,plain,
sF0_fnc = add(sF0_fnc,sF2_fnc),
inference(paramodulation,[status(thm)],[f25474,f226]) ).
fof(f33433,plain,
add(sF4_fnc,additive_identity) = add(sF4_fnc,sF0_fnc),
inference(paramodulation,[status(thm)],[f10894,f614]) ).
fof(f33522,plain,
sF4_fnc = add(sF4_fnc,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f14,f33433]) ).
fof(f33596,plain,
sF4_fnc = add(sF0_fnc,sF4_fnc),
inference(paramodulation,[status(thm)],[f10,f33522]) ).
fof(f33673,plain,
multiply(sF3_fnc,sF4_fnc) = add(multiply(sF3_fnc,sF0_fnc),sF2_fnc),
inference(paramodulation,[status(thm)],[f33596,f168]) ).
fof(f33702,plain,
sF2_fnc = add(multiply(sF3_fnc,sF0_fnc),sF2_fnc),
inference(forward_demodulation,[status(thm)],[f23,f33673]) ).
fof(f34086,plain,
add(sF3_fnc,additive_identity) = add(sF3_fnc,sF0_fnc),
inference(paramodulation,[status(thm)],[f10825,f616]) ).
fof(f34174,plain,
sF3_fnc = add(sF3_fnc,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f14,f34086]) ).
fof(f34281,plain,
sF0_fnc = multiply(sF3_fnc,sF0_fnc),
inference(paramodulation,[status(thm)],[f34174,f654]) ).
fof(f34310,plain,
sF2_fnc = add(sF0_fnc,sF2_fnc),
inference(backward_demodulation,[status(thm)],[f34281,f33702]) ).
fof(f34315,plain,
sF2_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f25667,f34310]) ).
fof(f34316,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f34315,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO014-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 13:48:06 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 14.35/2.23 % Refutation found
% 14.35/2.23 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 14.35/2.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 12.00/7.82 % Elapsed time: 7.454360 seconds
% 12.00/7.82 % CPU time: 47.215857 seconds
% 12.00/7.82 % Total memory used: 18.323 GB
% 12.00/7.82 % Net memory used: 18.320 GB
%------------------------------------------------------------------------------