%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO008-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 : Thu Sep 24 12:06:19 PM UTC 2026
% Result : Unsatisfiable 1.71s 0.75s
% Output : CNFRefutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 13
% Syntax : Number of formulae : 113 ( 113 unt; 4 def)
% Number of atoms : 113 ( 112 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 : 104 ( 104 !; 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,
add(a,add(b,c)) != add(add(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,
add(a,add(b,c)) != add(add(a,b),c),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f19,definition,
sF1_fnc = add(b,c),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f20,definition,
sF0_fnc = add(a,sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f21,definition,
sF3_fnc = add(a,b),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f22,definition,
sF2_fnc = add(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 = add(c,sF3_fnc),
inference(forward_demodulation,[status(thm)],[f10,f22]) ).
fof(f33,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(paramodulation,[status(thm)],[f10,f14]) ).
fof(f43,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)],[f43,f17]) ).
fof(f61,plain,
! [X0,X1,X2] : multiply(X0,add(X1,X2)) = add(multiply(X0,X2),multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f10,f13]) ).
fof(f64,plain,
! [X0,X1] : multiply(X0,add(inverse(X0),X1)) = add(additive_identity,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f17,f13]) ).
fof(f66,plain,
! [X0,X1,X2] : multiply(X0,add(X1,X2)) = add(multiply(X1,X0),multiply(X0,X2)),
inference(paramodulation,[status(thm)],[f11,f13]) ).
fof(f69,plain,
! [X0,X1] : multiply(X0,add(X1,inverse(X0))) = add(multiply(X0,X1),additive_identity),
inference(paramodulation,[status(thm)],[f17,f13]) ).
fof(f70,plain,
! [X0,X1] : multiply(X0,add(X1,multiplicative_identity)) = add(multiply(X0,X1),X0),
inference(paramodulation,[status(thm)],[f15,f13]) ).
fof(f76,plain,
! [X0,X1] : multiply(X0,add(inverse(X0),X1)) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f33,f64]) ).
fof(f78,plain,
! [X0,X1] : multiply(X0,add(X1,inverse(X0))) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f14,f69]) ).
fof(f79,plain,
! [X0,X1] : multiply(X0,add(X1,multiplicative_identity)) = add(X0,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f10,f70]) ).
fof(f82,plain,
! [X0] : multiply(X0,inverse(X0)) = multiply(X0,additive_identity),
inference(paramodulation,[status(thm)],[f14,f76]) ).
fof(f93,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(forward_demodulation,[status(thm)],[f17,f82]) ).
fof(f101,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(paramodulation,[status(thm)],[f11,f93]) ).
fof(f129,plain,
! [X0,X1,X2] : multiply(X0,add(X1,X2)) = multiply(X0,add(X2,X1)),
inference(paramodulation,[status(thm)],[f13,f61]) ).
fof(f172,plain,
! [X0] : multiply(X0,add(multiplicative_identity,multiplicative_identity)) = add(X0,X0),
inference(paramodulation,[status(thm)],[f15,f79]) ).
fof(f212,plain,
! [X0] : multiply(X0,multiplicative_identity) = multiply(X0,X0),
inference(paramodulation,[status(thm)],[f16,f78]) ).
fof(f228,plain,
! [X0] : X0 = multiply(X0,X0),
inference(forward_demodulation,[status(thm)],[f15,f212]) ).
fof(f250,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = add(multiply(X0,X1),X0),
inference(paramodulation,[status(thm)],[f228,f61]) ).
fof(f251,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = add(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f228,f61]) ).
fof(f254,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = add(X0,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f10,f250]) ).
fof(f297,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = multiply(X0,add(X1,multiplicative_identity)),
inference(paramodulation,[status(thm)],[f79,f254]) ).
fof(f309,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = add(X0,multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f11,f254]) ).
fof(f443,plain,
! [X0] : multiply(inverse(X0),add(inverse(X0),X0)) = add(inverse(X0),additive_identity),
inference(paramodulation,[status(thm)],[f17,f309]) ).
fof(f483,plain,
! [X0] : multiply(inverse(X0),add(X0,multiplicative_identity)) = add(inverse(X0),additive_identity),
inference(forward_demodulation,[status(thm)],[f297,f443]) ).
fof(f484,plain,
! [X0] : multiply(inverse(X0),add(X0,multiplicative_identity)) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f14,f483]) ).
fof(f501,plain,
! [X0] : multiply(inverse(X0),add(multiplicative_identity,X0)) = inverse(X0),
inference(paramodulation,[status(thm)],[f10,f484]) ).
fof(f552,plain,
! [X0] : multiply(add(multiplicative_identity,X0),add(add(multiplicative_identity,X0),inverse(X0))) = add(add(multiplicative_identity,X0),inverse(X0)),
inference(paramodulation,[status(thm)],[f501,f309]) ).
fof(f579,plain,
! [X0] : multiply(add(multiplicative_identity,X0),add(inverse(X0),multiplicative_identity)) = add(add(multiplicative_identity,X0),inverse(X0)),
inference(forward_demodulation,[status(thm)],[f297,f552]) ).
fof(f580,plain,
! [X0] : multiply(add(multiplicative_identity,X0),add(multiplicative_identity,inverse(X0))) = add(add(multiplicative_identity,X0),inverse(X0)),
inference(forward_demodulation,[status(thm)],[f129,f579]) ).
fof(f581,plain,
! [X0] : add(multiplicative_identity,multiply(X0,inverse(X0))) = add(add(multiplicative_identity,X0),inverse(X0)),
inference(forward_demodulation,[status(thm)],[f12,f580]) ).
fof(f582,plain,
! [X0] : add(multiplicative_identity,additive_identity) = add(add(multiplicative_identity,X0),inverse(X0)),
inference(forward_demodulation,[status(thm)],[f17,f581]) ).
fof(f583,plain,
! [X0] : multiplicative_identity = add(add(multiplicative_identity,X0),inverse(X0)),
inference(forward_demodulation,[status(thm)],[f14,f582]) ).
fof(f584,plain,
! [X0] : multiplicative_identity = add(inverse(X0),add(multiplicative_identity,X0)),
inference(forward_demodulation,[status(thm)],[f10,f583]) ).
fof(f601,plain,
multiplicative_identity = add(additive_identity,add(multiplicative_identity,multiplicative_identity)),
inference(paramodulation,[status(thm)],[f56,f584]) ).
fof(f612,plain,
! [X0] : multiply(X0,multiplicative_identity) = add(X0,X0),
inference(backward_demodulation,[status(thm)],[f625,f172]) ).
fof(f625,plain,
multiplicative_identity = add(multiplicative_identity,multiplicative_identity),
inference(forward_demodulation,[status(thm)],[f33,f601]) ).
fof(f667,plain,
! [X0] : X0 = add(X0,X0),
inference(forward_demodulation,[status(thm)],[f15,f612]) ).
fof(f871,plain,
! [X0] : add(a,multiply(b,X0)) = multiply(sF3_fnc,add(a,X0)),
inference(paramodulation,[status(thm)],[f21,f12]) ).
fof(f872,plain,
! [X0] : add(a,multiply(sF1_fnc,X0)) = multiply(sF0_fnc,add(a,X0)),
inference(paramodulation,[status(thm)],[f20,f12]) ).
fof(f880,plain,
! [X0,X1] : add(X0,multiply(additive_identity,X1)) = multiply(X0,add(X0,X1)),
inference(paramodulation,[status(thm)],[f14,f12]) ).
fof(f881,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X0,X1)),
inference(paramodulation,[status(thm)],[f667,f12]) ).
fof(f889,plain,
! [X0] : add(c,multiply(X0,sF3_fnc)) = multiply(add(c,X0),sF2_fnc),
inference(paramodulation,[status(thm)],[f24,f12]) ).
fof(f923,plain,
! [X0,X1] : add(X0,additive_identity) = multiply(X0,add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f101,f880]) ).
fof(f925,plain,
! [X0,X1] : X0 = add(X0,multiply(X1,X0)),
inference(backward_demodulation,[status(thm)],[f932,f309]) ).
fof(f932,plain,
! [X0,X1] : X0 = multiply(X0,add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f14,f923]) ).
fof(f933,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = X0,
inference(backward_demodulation,[status(thm)],[f936,f251]) ).
fof(f936,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = X0,
inference(forward_demodulation,[status(thm)],[f932,f881]) ).
fof(f942,plain,
! [X0] : add(c,multiply(X0,sF3_fnc)) = multiply(sF2_fnc,add(c,X0)),
inference(forward_demodulation,[status(thm)],[f11,f889]) ).
fof(f1503,plain,
a = multiply(a,sF3_fnc),
inference(paramodulation,[status(thm)],[f21,f932]) ).
fof(f1505,plain,
b = multiply(b,sF1_fnc),
inference(paramodulation,[status(thm)],[f19,f932]) ).
fof(f1599,plain,
! [X0] : multiply(a,add(X0,sF3_fnc)) = add(multiply(X0,a),a),
inference(paramodulation,[status(thm)],[f1503,f66]) ).
fof(f1610,plain,
! [X0] : multiply(a,add(X0,sF3_fnc)) = add(a,multiply(X0,a)),
inference(forward_demodulation,[status(thm)],[f10,f1599]) ).
fof(f1611,plain,
! [X0] : multiply(a,add(X0,sF3_fnc)) = a,
inference(forward_demodulation,[status(thm)],[f925,f1610]) ).
fof(f1623,plain,
add(a,b) = multiply(sF3_fnc,add(a,sF1_fnc)),
inference(paramodulation,[status(thm)],[f1505,f871]) ).
fof(f1640,plain,
sF3_fnc = multiply(sF3_fnc,add(a,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f21,f1623]) ).
fof(f1641,plain,
sF3_fnc = multiply(sF3_fnc,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f20,f1640]) ).
fof(f1642,plain,
sF3_fnc = multiply(sF0_fnc,sF3_fnc),
inference(forward_demodulation,[status(thm)],[f11,f1641]) ).
fof(f1692,plain,
add(c,sF3_fnc) = multiply(sF2_fnc,add(c,sF0_fnc)),
inference(paramodulation,[status(thm)],[f1642,f942]) ).
fof(f1703,plain,
sF2_fnc = multiply(sF2_fnc,add(c,sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f24,f1692]) ).
fof(f1733,plain,
multiply(sF3_fnc,sF2_fnc) = sF3_fnc,
inference(paramodulation,[status(thm)],[f24,f933]) ).
fof(f1738,plain,
multiply(b,sF3_fnc) = b,
inference(paramodulation,[status(thm)],[f21,f933]) ).
fof(f1739,plain,
multiply(sF1_fnc,sF0_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f20,f933]) ).
fof(f1741,plain,
multiply(c,sF1_fnc) = c,
inference(paramodulation,[status(thm)],[f19,f933]) ).
fof(f1771,plain,
multiply(sF2_fnc,sF3_fnc) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f11,f1733]) ).
fof(f1772,plain,
multiply(sF0_fnc,sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f11,f1739]) ).
fof(f1792,plain,
add(sF0_fnc,sF1_fnc) = sF0_fnc,
inference(paramodulation,[status(thm)],[f1772,f936]) ).
fof(f1809,plain,
! [X0] : add(sF0_fnc,multiply(X0,sF1_fnc)) = multiply(add(sF0_fnc,X0),sF0_fnc),
inference(paramodulation,[status(thm)],[f1792,f12]) ).
fof(f1812,plain,
! [X0] : add(sF0_fnc,multiply(X0,sF1_fnc)) = multiply(sF0_fnc,add(sF0_fnc,X0)),
inference(forward_demodulation,[status(thm)],[f11,f1809]) ).
fof(f1813,plain,
! [X0] : add(sF0_fnc,multiply(X0,sF1_fnc)) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f932,f1812]) ).
fof(f1843,plain,
add(sF2_fnc,sF3_fnc) = sF2_fnc,
inference(paramodulation,[status(thm)],[f1771,f936]) ).
fof(f1869,plain,
add(c,b) = multiply(sF2_fnc,add(c,b)),
inference(paramodulation,[status(thm)],[f1738,f942]) ).
fof(f1881,plain,
add(b,c) = multiply(sF2_fnc,add(c,b)),
inference(forward_demodulation,[status(thm)],[f10,f1869]) ).
fof(f1882,plain,
sF1_fnc = multiply(sF2_fnc,add(c,b)),
inference(forward_demodulation,[status(thm)],[f19,f1881]) ).
fof(f1883,plain,
sF1_fnc = multiply(sF2_fnc,add(b,c)),
inference(forward_demodulation,[status(thm)],[f129,f1882]) ).
fof(f1884,plain,
sF1_fnc = multiply(sF2_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f19,f1883]) ).
fof(f1885,plain,
sF1_fnc = multiply(sF1_fnc,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f11,f1884]) ).
fof(f1902,plain,
add(a,sF1_fnc) = multiply(sF0_fnc,add(a,sF2_fnc)),
inference(paramodulation,[status(thm)],[f1885,f872]) ).
fof(f1913,plain,
sF0_fnc = multiply(sF0_fnc,add(a,sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f20,f1902]) ).
fof(f2965,plain,
multiply(a,sF2_fnc) = a,
inference(paramodulation,[status(thm)],[f1843,f1611]) ).
fof(f3064,plain,
sF2_fnc = add(sF2_fnc,a),
inference(paramodulation,[status(thm)],[f2965,f925]) ).
fof(f3076,plain,
sF0_fnc = multiply(sF0_fnc,sF2_fnc),
inference(backward_demodulation,[status(thm)],[f3077,f1913]) ).
fof(f3077,plain,
sF2_fnc = add(a,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f10,f3064]) ).
fof(f4598,plain,
add(sF0_fnc,c) = sF0_fnc,
inference(paramodulation,[status(thm)],[f1741,f1813]) ).
fof(f4623,plain,
sF2_fnc = multiply(sF2_fnc,sF0_fnc),
inference(backward_demodulation,[status(thm)],[f4624,f1703]) ).
fof(f4624,plain,
add(c,sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f10,f4598]) ).
fof(f4641,plain,
sF2_fnc = multiply(sF0_fnc,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f11,f4623]) ).
fof(f4642,plain,
sF2_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f3076,f4641]) ).
fof(f4643,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4642,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO008-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n020.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 13:48:32 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 1.71/0.75 % Refutation found
% 1.71/0.75 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.71/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.71/0.76 % Elapsed time: 0.411571 seconds
% 1.71/0.76 % CPU time: 3.125309 seconds
% 1.71/0.76 % Total memory used: 61.328 MB
% 1.71/0.76 % Net memory used: 59.590 MB
%------------------------------------------------------------------------------