%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE151-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:58:05 PM UTC 2026
% Result : Unsatisfiable 4.11s 1.00s
% Output : CNFRefutation 4.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 47 ( 47 unt; 7 def)
% Number of atoms : 47 ( 46 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 : 17 ( 17 usr; 11 con; 0-4 aty)
% Number of variables : 48 ( 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : ifeq3(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C] : ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [C,A,B] : ifeq(leq(C,addition(multiplication(A,C),B)),true,leq(C,multiplication(strong_iteration(A),B)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A,B] : ifeq3(addition(A,B),B,leq(A,B),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
leq(multiplication(sK2_goals_X0,strong_iteration(multiplication(sK1_goals_X1,sK2_goals_X0))),multiplication(strong_iteration(multiplication(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0)) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [X0,X1,X2] : ifeq3(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f26,plain,
! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f30,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f31,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f32,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f34,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f41,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f42,plain,
! [X0,X1,X2] : ifeq(leq(X0,addition(multiplication(X1,X0),X2)),true,leq(X0,multiplication(strong_iteration(X1),X2)),true) = true,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f45,plain,
! [X0,X1] : ifeq3(addition(X0,X1),X1,leq(X0,X1),true) = true,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f46,plain,
leq(multiplication(sK2_goals_X0,strong_iteration(multiplication(sK1_goals_X1,sK2_goals_X0))),multiplication(strong_iteration(multiplication(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0)) != true,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f47,definition,
sF3_fnc = multiplication(sK1_goals_X1,sK2_goals_X0),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f48,definition,
sF2_fnc = strong_iteration(sF3_fnc),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f49,definition,
sF1_fnc = multiplication(sK2_goals_X0,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f50,definition,
sF6_fnc = multiplication(sK2_goals_X0,sK1_goals_X1),
introduced(definition,[new_symbols(definition,[sF6_fnc])],[function_definition]) ).
fof(f51,definition,
sF5_fnc = strong_iteration(sF6_fnc),
introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition]) ).
fof(f52,definition,
sF4_fnc = multiplication(sF5_fnc,sK2_goals_X0),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f53,definition,
sF0_fnc = leq(sF1_fnc,sF4_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f54,plain,
sF0_fnc != true,
inference(definition_folding,[],[f46,f53,f52,f51,f50,f49,f48,f47]) ).
fof(f57,plain,
! [X0] : multiplication(sK2_goals_X0,multiplication(sK1_goals_X1,X0)) = multiplication(sF6_fnc,X0),
inference(paramodulation,[status(thm)],[f50,f31]) ).
fof(f59,plain,
! [X0] : multiplication(sK1_goals_X1,multiplication(sK2_goals_X0,X0)) = multiplication(sF3_fnc,X0),
inference(paramodulation,[status(thm)],[f47,f31]) ).
fof(f85,plain,
multiplication(sK1_goals_X1,sF1_fnc) = multiplication(sF3_fnc,sF2_fnc),
inference(paramodulation,[status(thm)],[f49,f59]) ).
fof(f178,plain,
! [X0,X1] : multiplication(sK2_goals_X0,addition(multiplication(sK1_goals_X1,X0),X1)) = addition(multiplication(sF6_fnc,X0),multiplication(sK2_goals_X0,X1)),
inference(paramodulation,[status(thm)],[f57,f34]) ).
fof(f613,plain,
strong_iteration(sF3_fnc) = addition(multiplication(sF3_fnc,sF2_fnc),one),
inference(paramodulation,[status(thm)],[f48,f41]) ).
fof(f621,plain,
sF2_fnc = addition(multiplication(sF3_fnc,sF2_fnc),one),
inference(forward_demodulation,[status(thm)],[f48,f613]) ).
fof(f622,plain,
sF2_fnc = addition(multiplication(sK1_goals_X1,sF1_fnc),one),
inference(forward_demodulation,[status(thm)],[f85,f621]) ).
fof(f793,plain,
! [X0,X1] : ifeq(leq(X0,addition(multiplication(sF6_fnc,X0),X1)),true,leq(X0,multiplication(sF5_fnc,X1)),true) = true,
inference(paramodulation,[status(thm)],[f51,f42]) ).
fof(f1224,plain,
! [X0] : ifeq3(X0,X0,leq(X0,X0),true) = true,
inference(paramodulation,[status(thm)],[f30,f45]) ).
fof(f1238,plain,
! [X0] : leq(X0,X0) = true,
inference(forward_demodulation,[status(thm)],[f24,f1224]) ).
fof(f16143,plain,
multiplication(sK2_goals_X0,sF2_fnc) = addition(multiplication(sF6_fnc,sF1_fnc),multiplication(sK2_goals_X0,one)),
inference(paramodulation,[status(thm)],[f622,f178]) ).
fof(f16239,plain,
sF1_fnc = addition(multiplication(sF6_fnc,sF1_fnc),multiplication(sK2_goals_X0,one)),
inference(forward_demodulation,[status(thm)],[f49,f16143]) ).
fof(f16240,plain,
sF1_fnc = addition(multiplication(sF6_fnc,sF1_fnc),sK2_goals_X0),
inference(forward_demodulation,[status(thm)],[f32,f16239]) ).
fof(f19260,plain,
ifeq(leq(sF1_fnc,sF1_fnc),true,leq(sF1_fnc,multiplication(sF5_fnc,sK2_goals_X0)),true) = true,
inference(paramodulation,[status(thm)],[f16240,f793]) ).
fof(f19303,plain,
ifeq(true,true,leq(sF1_fnc,multiplication(sF5_fnc,sK2_goals_X0)),true) = true,
inference(forward_demodulation,[status(thm)],[f1238,f19260]) ).
fof(f19304,plain,
leq(sF1_fnc,multiplication(sF5_fnc,sK2_goals_X0)) = true,
inference(forward_demodulation,[status(thm)],[f26,f19303]) ).
fof(f19305,plain,
leq(sF1_fnc,sF4_fnc) = true,
inference(forward_demodulation,[status(thm)],[f52,f19304]) ).
fof(f19306,plain,
sF0_fnc = true,
inference(forward_demodulation,[status(thm)],[f53,f19305]) ).
fof(f19307,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f19306,f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE151-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.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 : Sun Sep 20 22:46:51 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 4.11/1.00 % Refutation found
% 4.11/1.00 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.11/1.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.80/1.05 % Elapsed time: 0.678229 seconds
% 4.80/1.05 % CPU time: 5.217401 seconds
% 4.80/1.05 % Total memory used: 148.620 MB
% 4.80/1.05 % Net memory used: 146.746 MB
%------------------------------------------------------------------------------