%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO007-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 12:06:19 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.49s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 13
% Syntax : Number of formulae : 112 ( 112 unt; 4 def)
% Number of atoms : 112 ( 111 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 : 4 ( 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 : 103 ( 103 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : add(X,Y) = add(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = multiply(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] : multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : add(X,additive_identity) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : multiply(X,multiplicative_identity) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : add(X,inverse(X)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] : multiply(X,inverse(X)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
multiply(a,multiply(b,c)) != multiply(multiply(a,b),c),
file('/export/starexec/sandbox/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,
multiply(a,multiply(b,c)) != multiply(multiply(a,b),c),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f19,definition,
sF1_fnc = multiply(b,c),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f20,definition,
sF0_fnc = multiply(a,sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f21,definition,
sF3_fnc = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f22,definition,
sF2_fnc = multiply(sF3_fnc,c),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f23,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f18,f22,f21,f20,f19]) ).
fof(f24,plain,
sF2_fnc = multiply(c,sF3_fnc),
inference(forward_demodulation,[status(thm)],[f11,f22]) ).
fof(f37,plain,
! [X0] : multiply(multiplicative_identity,X0) = X0,
inference(paramodulation,[status(thm)],[f11,f15]) ).
fof(f56,plain,
inverse(multiplicative_identity) = additive_identity,
inference(paramodulation,[status(thm)],[f37,f17]) ).
fof(f61,plain,
! [X0,X1,X2] : add(X0,multiply(X1,X2)) = multiply(add(X0,X2),add(X0,X1)),
inference(paramodulation,[status(thm)],[f11,f12]) ).
fof(f64,plain,
! [X0,X1] : add(X0,multiply(inverse(X0),X1)) = multiply(multiplicative_identity,add(X0,X1)),
inference(paramodulation,[status(thm)],[f16,f12]) ).
fof(f66,plain,
! [X0,X1,X2] : add(X0,multiply(X1,X2)) = multiply(add(X1,X0),add(X0,X2)),
inference(paramodulation,[status(thm)],[f10,f12]) ).
fof(f69,plain,
! [X0,X1] : add(X0,multiply(X1,inverse(X0))) = multiply(add(X0,X1),multiplicative_identity),
inference(paramodulation,[status(thm)],[f16,f12]) ).
fof(f70,plain,
! [X0,X1] : add(X0,multiply(X1,additive_identity)) = multiply(add(X0,X1),X0),
inference(paramodulation,[status(thm)],[f14,f12]) ).
fof(f76,plain,
! [X0,X1] : add(X0,multiply(inverse(X0),X1)) = add(X0,X1),
inference(forward_demodulation,[status(thm)],[f37,f64]) ).
fof(f78,plain,
! [X0,X1] : add(X0,multiply(X1,inverse(X0))) = add(X0,X1),
inference(forward_demodulation,[status(thm)],[f15,f69]) ).
fof(f79,plain,
! [X0,X1] : add(X0,multiply(X1,additive_identity)) = multiply(X0,add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f11,f70]) ).
fof(f82,plain,
! [X0] : add(X0,inverse(X0)) = add(X0,multiplicative_identity),
inference(paramodulation,[status(thm)],[f15,f76]) ).
fof(f93,plain,
! [X0] : multiplicative_identity = add(X0,multiplicative_identity),
inference(forward_demodulation,[status(thm)],[f16,f82]) ).
fof(f101,plain,
! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
inference(paramodulation,[status(thm)],[f10,f93]) ).
fof(f129,plain,
! [X0,X1,X2] : add(X0,multiply(X1,X2)) = add(X0,multiply(X2,X1)),
inference(paramodulation,[status(thm)],[f12,f61]) ).
fof(f172,plain,
! [X0] : add(X0,multiply(additive_identity,additive_identity)) = multiply(X0,X0),
inference(paramodulation,[status(thm)],[f14,f79]) ).
fof(f213,plain,
! [X0] : add(X0,additive_identity) = add(X0,X0),
inference(paramodulation,[status(thm)],[f17,f78]) ).
fof(f229,plain,
! [X0] : X0 = add(X0,X0),
inference(forward_demodulation,[status(thm)],[f14,f213]) ).
fof(f251,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(add(X0,X1),X0),
inference(paramodulation,[status(thm)],[f229,f61]) ).
fof(f252,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = multiply(X0,add(X0,X1)),
inference(paramodulation,[status(thm)],[f229,f61]) ).
fof(f255,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f11,f251]) ).
fof(f298,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = add(X0,multiply(X1,additive_identity)),
inference(paramodulation,[status(thm)],[f79,f255]) ).
fof(f310,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X1,X0)),
inference(paramodulation,[status(thm)],[f10,f255]) ).
fof(f444,plain,
! [X0] : add(inverse(X0),multiply(inverse(X0),X0)) = multiply(inverse(X0),multiplicative_identity),
inference(paramodulation,[status(thm)],[f16,f310]) ).
fof(f484,plain,
! [X0] : add(inverse(X0),multiply(X0,additive_identity)) = multiply(inverse(X0),multiplicative_identity),
inference(forward_demodulation,[status(thm)],[f298,f444]) ).
fof(f485,plain,
! [X0] : add(inverse(X0),multiply(X0,additive_identity)) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f15,f484]) ).
fof(f502,plain,
! [X0] : add(inverse(X0),multiply(additive_identity,X0)) = inverse(X0),
inference(paramodulation,[status(thm)],[f11,f485]) ).
fof(f553,plain,
! [X0] : add(multiply(additive_identity,X0),multiply(multiply(additive_identity,X0),inverse(X0))) = multiply(multiply(additive_identity,X0),inverse(X0)),
inference(paramodulation,[status(thm)],[f502,f310]) ).
fof(f580,plain,
! [X0] : add(multiply(additive_identity,X0),multiply(inverse(X0),additive_identity)) = multiply(multiply(additive_identity,X0),inverse(X0)),
inference(forward_demodulation,[status(thm)],[f298,f553]) ).
fof(f581,plain,
! [X0] : add(multiply(additive_identity,X0),multiply(additive_identity,inverse(X0))) = multiply(multiply(additive_identity,X0),inverse(X0)),
inference(forward_demodulation,[status(thm)],[f129,f580]) ).
fof(f582,plain,
! [X0] : multiply(additive_identity,add(X0,inverse(X0))) = multiply(multiply(additive_identity,X0),inverse(X0)),
inference(forward_demodulation,[status(thm)],[f13,f581]) ).
fof(f583,plain,
! [X0] : multiply(additive_identity,multiplicative_identity) = multiply(multiply(additive_identity,X0),inverse(X0)),
inference(forward_demodulation,[status(thm)],[f16,f582]) ).
fof(f584,plain,
! [X0] : additive_identity = multiply(multiply(additive_identity,X0),inverse(X0)),
inference(forward_demodulation,[status(thm)],[f15,f583]) ).
fof(f585,plain,
! [X0] : additive_identity = multiply(inverse(X0),multiply(additive_identity,X0)),
inference(forward_demodulation,[status(thm)],[f11,f584]) ).
fof(f602,plain,
additive_identity = multiply(additive_identity,multiply(additive_identity,multiplicative_identity)),
inference(paramodulation,[status(thm)],[f56,f585]) ).
fof(f613,plain,
! [X0] : add(X0,additive_identity) = multiply(X0,X0),
inference(backward_demodulation,[status(thm)],[f626,f172]) ).
fof(f626,plain,
additive_identity = multiply(additive_identity,additive_identity),
inference(forward_demodulation,[status(thm)],[f15,f602]) ).
fof(f668,plain,
! [X0] : X0 = multiply(X0,X0),
inference(forward_demodulation,[status(thm)],[f14,f613]) ).
fof(f872,plain,
! [X0] : multiply(a,add(b,X0)) = add(sF3_fnc,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f21,f13]) ).
fof(f873,plain,
! [X0] : multiply(a,add(sF1_fnc,X0)) = add(sF0_fnc,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f20,f13]) ).
fof(f881,plain,
! [X0,X1] : multiply(X0,add(multiplicative_identity,X1)) = add(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f15,f13]) ).
fof(f882,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = add(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f668,f13]) ).
fof(f890,plain,
! [X0] : multiply(c,add(X0,sF3_fnc)) = add(multiply(c,X0),sF2_fnc),
inference(paramodulation,[status(thm)],[f24,f13]) ).
fof(f924,plain,
! [X0,X1] : multiply(X0,multiplicative_identity) = add(X0,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f101,f881]) ).
fof(f926,plain,
! [X0,X1] : X0 = multiply(X0,add(X1,X0)),
inference(backward_demodulation,[status(thm)],[f933,f310]) ).
fof(f933,plain,
! [X0,X1] : X0 = add(X0,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f15,f924]) ).
fof(f934,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = X0,
inference(backward_demodulation,[status(thm)],[f937,f252]) ).
fof(f937,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = X0,
inference(forward_demodulation,[status(thm)],[f933,f882]) ).
fof(f943,plain,
! [X0] : multiply(c,add(X0,sF3_fnc)) = add(sF2_fnc,multiply(c,X0)),
inference(forward_demodulation,[status(thm)],[f10,f890]) ).
fof(f1504,plain,
a = add(a,sF3_fnc),
inference(paramodulation,[status(thm)],[f21,f933]) ).
fof(f1506,plain,
b = add(b,sF1_fnc),
inference(paramodulation,[status(thm)],[f19,f933]) ).
fof(f1600,plain,
! [X0] : add(a,multiply(X0,sF3_fnc)) = multiply(add(X0,a),a),
inference(paramodulation,[status(thm)],[f1504,f66]) ).
fof(f1611,plain,
! [X0] : add(a,multiply(X0,sF3_fnc)) = multiply(a,add(X0,a)),
inference(forward_demodulation,[status(thm)],[f11,f1600]) ).
fof(f1612,plain,
! [X0] : add(a,multiply(X0,sF3_fnc)) = a,
inference(forward_demodulation,[status(thm)],[f926,f1611]) ).
fof(f1624,plain,
multiply(a,b) = add(sF3_fnc,multiply(a,sF1_fnc)),
inference(paramodulation,[status(thm)],[f1506,f872]) ).
fof(f1641,plain,
sF3_fnc = add(sF3_fnc,multiply(a,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f21,f1624]) ).
fof(f1642,plain,
sF3_fnc = add(sF3_fnc,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f20,f1641]) ).
fof(f1643,plain,
sF3_fnc = add(sF0_fnc,sF3_fnc),
inference(forward_demodulation,[status(thm)],[f10,f1642]) ).
fof(f1693,plain,
multiply(c,sF3_fnc) = add(sF2_fnc,multiply(c,sF0_fnc)),
inference(paramodulation,[status(thm)],[f1643,f943]) ).
fof(f1704,plain,
sF2_fnc = add(sF2_fnc,multiply(c,sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f24,f1693]) ).
fof(f1734,plain,
add(sF3_fnc,sF2_fnc) = sF3_fnc,
inference(paramodulation,[status(thm)],[f24,f934]) ).
fof(f1739,plain,
add(b,sF3_fnc) = b,
inference(paramodulation,[status(thm)],[f21,f934]) ).
fof(f1740,plain,
add(sF1_fnc,sF0_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f20,f934]) ).
fof(f1742,plain,
add(c,sF1_fnc) = c,
inference(paramodulation,[status(thm)],[f19,f934]) ).
fof(f1772,plain,
add(sF2_fnc,sF3_fnc) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f10,f1734]) ).
fof(f1773,plain,
add(sF0_fnc,sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f10,f1740]) ).
fof(f1793,plain,
multiply(sF0_fnc,sF1_fnc) = sF0_fnc,
inference(paramodulation,[status(thm)],[f1773,f937]) ).
fof(f1810,plain,
! [X0] : multiply(sF0_fnc,add(X0,sF1_fnc)) = add(multiply(sF0_fnc,X0),sF0_fnc),
inference(paramodulation,[status(thm)],[f1793,f13]) ).
fof(f1813,plain,
! [X0] : multiply(sF0_fnc,add(X0,sF1_fnc)) = add(sF0_fnc,multiply(sF0_fnc,X0)),
inference(forward_demodulation,[status(thm)],[f10,f1810]) ).
fof(f1814,plain,
! [X0] : multiply(sF0_fnc,add(X0,sF1_fnc)) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f933,f1813]) ).
fof(f1844,plain,
multiply(sF2_fnc,sF3_fnc) = sF2_fnc,
inference(paramodulation,[status(thm)],[f1772,f937]) ).
fof(f1870,plain,
multiply(c,b) = add(sF2_fnc,multiply(c,b)),
inference(paramodulation,[status(thm)],[f1739,f943]) ).
fof(f1882,plain,
multiply(b,c) = add(sF2_fnc,multiply(c,b)),
inference(forward_demodulation,[status(thm)],[f11,f1870]) ).
fof(f1883,plain,
sF1_fnc = add(sF2_fnc,multiply(c,b)),
inference(forward_demodulation,[status(thm)],[f19,f1882]) ).
fof(f1884,plain,
sF1_fnc = add(sF2_fnc,multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f129,f1883]) ).
fof(f1885,plain,
sF1_fnc = add(sF2_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f19,f1884]) ).
fof(f1886,plain,
sF1_fnc = add(sF1_fnc,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f10,f1885]) ).
fof(f1903,plain,
multiply(a,sF1_fnc) = add(sF0_fnc,multiply(a,sF2_fnc)),
inference(paramodulation,[status(thm)],[f1886,f873]) ).
fof(f1914,plain,
sF0_fnc = add(sF0_fnc,multiply(a,sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f20,f1903]) ).
fof(f2966,plain,
add(a,sF2_fnc) = a,
inference(paramodulation,[status(thm)],[f1844,f1612]) ).
fof(f3065,plain,
sF2_fnc = multiply(sF2_fnc,a),
inference(paramodulation,[status(thm)],[f2966,f926]) ).
fof(f3077,plain,
sF0_fnc = add(sF0_fnc,sF2_fnc),
inference(backward_demodulation,[status(thm)],[f3078,f1914]) ).
fof(f3078,plain,
sF2_fnc = multiply(a,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f11,f3065]) ).
fof(f4599,plain,
multiply(sF0_fnc,c) = sF0_fnc,
inference(paramodulation,[status(thm)],[f1742,f1814]) ).
fof(f4624,plain,
sF2_fnc = add(sF2_fnc,sF0_fnc),
inference(backward_demodulation,[status(thm)],[f4625,f1704]) ).
fof(f4625,plain,
multiply(c,sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f11,f4599]) ).
fof(f4642,plain,
sF2_fnc = add(sF0_fnc,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f10,f4624]) ).
fof(f4643,plain,
sF2_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f3077,f4642]) ).
fof(f4644,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4643,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO007-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 13:52:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.16/0.36 % Drodi V4.1.1
% 0.16/0.49 % Refutation found
% 0.16/0.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.52 % Elapsed time: 0.156511 seconds
% 0.16/0.52 % CPU time: 0.988683 seconds
% 0.16/0.52 % Total memory used: 23.244 MB
% 0.16/0.52 % Net memory used: 22.794 MB
%------------------------------------------------------------------------------