%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE169-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 12:58:07 PM UTC 2026
% Result : Unsatisfiable 6.80s 1.68s
% Output : CNFRefutation 9.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 66 ( 66 unt; 7 def)
% Number of atoms : 66 ( 65 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 12 con; 0-4 aty)
% Number of variables : 71 ( 71 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : ifeq3(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : ifeq2(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B] : ifeq2(leq(A,B),true,addition(A,B),B) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B] : ifeq3(addition(A,B),B,leq(A,B),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
sigma = addition(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,plain,
! [X0,X1,X2] : ifeq3(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f24,plain,
! [X0,X1,X2] : ifeq2(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f26,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f27,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f29,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f32,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f33,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f34,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f37,plain,
! [X0,X1] : ifeq2(leq(X0,X1),true,addition(X0,X1),X1) = X1,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f38,plain,
! [X0,X1] : ifeq3(addition(X0,X1),X1,leq(X0,X1),true) = true,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f39,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)) = true,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f43,plain,
sigma = addition(a,b),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f44,plain,
leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))) != true,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f45,definition,
sF2_fnc = multiplication(b,a),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f46,definition,
sF1_fnc = multiplication(a,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f47,definition,
sF4_fnc = star(sigma),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f48,definition,
sF6_fnc = multiplication(sigma,a),
introduced(definition,[new_symbols(definition,[sF6_fnc])],[function_definition]) ).
fof(f49,definition,
sF5_fnc = multiplication(a,sF6_fnc),
introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition]) ).
fof(f50,definition,
sF3_fnc = multiplication(sF4_fnc,sF5_fnc),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f51,definition,
sF0_fnc = leq(sF1_fnc,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f52,plain,
sF0_fnc != true,
inference(definition_folding,[],[f44,f51,f50,f49,f48,f47,f46,f45]) ).
fof(f184,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f190,plain,
! [X0] : addition(a,addition(b,X0)) = addition(sigma,X0),
inference(paramodulation,[status(thm)],[f43,f27]) ).
fof(f194,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f29,f27]) ).
fof(f221,plain,
! [X0] : multiplication(a,addition(sF6_fnc,X0)) = addition(sF5_fnc,multiplication(a,X0)),
inference(paramodulation,[status(thm)],[f49,f33]) ).
fof(f284,plain,
! [X0] : multiplication(addition(sF4_fnc,X0),sF5_fnc) = addition(sF3_fnc,multiplication(X0,sF5_fnc)),
inference(paramodulation,[status(thm)],[f50,f34]) ).
fof(f286,plain,
! [X0] : multiplication(addition(sigma,X0),a) = addition(sF6_fnc,multiplication(X0,a)),
inference(paramodulation,[status(thm)],[f48,f34]) ).
fof(f406,plain,
addition(a,b) = addition(sigma,b),
inference(paramodulation,[status(thm)],[f29,f190]) ).
fof(f411,plain,
sigma = addition(sigma,b),
inference(forward_demodulation,[status(thm)],[f43,f406]) ).
fof(f612,plain,
! [X0,X1] : ifeq2(leq(X0,X1),true,addition(X1,X0),X1) = X1,
inference(paramodulation,[status(thm)],[f26,f37]) ).
fof(f1063,plain,
! [X0,X1] : ifeq3(addition(X0,X1),addition(X0,X1),leq(X0,addition(X0,X1)),true) = true,
inference(paramodulation,[status(thm)],[f194,f38]) ).
fof(f1072,plain,
! [X0,X1] : leq(X0,addition(X0,X1)) = true,
inference(forward_demodulation,[status(thm)],[f23,f1063]) ).
fof(f1080,plain,
! [X0] : ifeq2(true,true,addition(addition(one,multiplication(X0,star(X0))),star(X0)),star(X0)) = star(X0),
inference(paramodulation,[status(thm)],[f39,f37]) ).
fof(f1085,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f24,f1080]) ).
fof(f1086,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f27,f1085]) ).
fof(f1567,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X2,X0))) = true,
inference(paramodulation,[status(thm)],[f184,f1072]) ).
fof(f3729,plain,
multiplication(sigma,a) = addition(sF6_fnc,multiplication(b,a)),
inference(paramodulation,[status(thm)],[f411,f286]) ).
fof(f3760,plain,
sF6_fnc = addition(sF6_fnc,multiplication(b,a)),
inference(forward_demodulation,[status(thm)],[f48,f3729]) ).
fof(f3761,plain,
sF6_fnc = addition(sF6_fnc,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f45,f3760]) ).
fof(f3782,plain,
multiplication(a,sF6_fnc) = addition(sF5_fnc,multiplication(a,sF2_fnc)),
inference(paramodulation,[status(thm)],[f3761,f221]) ).
fof(f3805,plain,
sF5_fnc = addition(sF5_fnc,multiplication(a,sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f49,f3782]) ).
fof(f3806,plain,
sF5_fnc = addition(sF5_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f46,f3805]) ).
fof(f3841,plain,
! [X0] : leq(sF1_fnc,addition(X0,sF5_fnc)) = true,
inference(paramodulation,[status(thm)],[f3806,f1567]) ).
fof(f11698,plain,
! [X0] : leq(one,star(X0)) = true,
inference(paramodulation,[status(thm)],[f1086,f1072]) ).
fof(f11899,plain,
leq(one,sF4_fnc) = true,
inference(paramodulation,[status(thm)],[f47,f11698]) ).
fof(f11907,plain,
ifeq2(true,true,addition(sF4_fnc,one),sF4_fnc) = sF4_fnc,
inference(paramodulation,[status(thm)],[f11899,f612]) ).
fof(f11910,plain,
addition(sF4_fnc,one) = sF4_fnc,
inference(forward_demodulation,[status(thm)],[f24,f11907]) ).
fof(f11914,plain,
multiplication(sF4_fnc,sF5_fnc) = addition(sF3_fnc,multiplication(one,sF5_fnc)),
inference(paramodulation,[status(thm)],[f11910,f284]) ).
fof(f11954,plain,
sF3_fnc = addition(sF3_fnc,multiplication(one,sF5_fnc)),
inference(forward_demodulation,[status(thm)],[f50,f11914]) ).
fof(f11955,plain,
sF3_fnc = addition(sF3_fnc,sF5_fnc),
inference(forward_demodulation,[status(thm)],[f32,f11954]) ).
fof(f12016,plain,
leq(sF1_fnc,sF3_fnc) = true,
inference(paramodulation,[status(thm)],[f11955,f3841]) ).
fof(f12046,plain,
sF0_fnc = true,
inference(forward_demodulation,[status(thm)],[f51,f12016]) ).
fof(f12047,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f12046,f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE169-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n002.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sun Sep 20 22:51:02 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Drodi V4.1.1
% 6.80/1.68 % Refutation found
% 6.80/1.68 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 6.80/1.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.38/1.74 % Elapsed time: 1.292927 seconds
% 9.38/1.74 % CPU time: 9.950254 seconds
% 9.38/1.74 % Total memory used: 126.339 MB
% 9.38/1.74 % Net memory used: 124.285 MB
%------------------------------------------------------------------------------