%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL042-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 01:06:39 PM UTC 2026
% Result : Unsatisfiable 0.13s 5.79s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of formulae : 63 ( 63 unt; 7 def)
% Number of atoms : 63 ( 62 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 : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-4 aty)
% Number of variables : 70 ( 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : ifeq(is_a_theorem(implies(X,Y)),true,ifeq(is_a_theorem(X),true,is_a_theorem(Y),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(not(X),Y))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(X,implies(Y,Z)),implies(Y,implies(X,Z)))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Y,Z,X] : is_a_theorem(implies(implies(Y,Z),implies(implies(X,Y),implies(X,Z)))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(not(X),Y),Y))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
is_a_theorem(implies(implies(a,implies(b,c)),implies(implies(a,b),implies(a,c)))) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0,X1] : ifeq(is_a_theorem(implies(X0,X1)),true,ifeq(is_a_theorem(X0),true,is_a_theorem(X1),true),true) = true,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) = true,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) = true,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))) = true,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))) = true,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f15,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X1),X1))) = true,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f16,plain,
is_a_theorem(implies(implies(a,implies(b,c)),implies(implies(a,b),implies(a,c)))) != true,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f17,definition,
sF3_fnc = implies(b,c),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f18,definition,
sF2_fnc = implies(a,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f19,definition,
sF5_fnc = implies(a,b),
introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition]) ).
fof(f20,definition,
sF6_fnc = implies(a,c),
introduced(definition,[new_symbols(definition,[sF6_fnc])],[function_definition]) ).
fof(f21,definition,
sF4_fnc = implies(sF5_fnc,sF6_fnc),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f22,definition,
sF1_fnc = implies(sF2_fnc,sF4_fnc),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f23,definition,
sF0_fnc = is_a_theorem(sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f24,plain,
sF0_fnc != true,
inference(definition_folding,[],[f16,f23,f22,f21,f20,f19,f18,f17]) ).
fof(f49,plain,
! [X0] : is_a_theorem(implies(sF3_fnc,implies(implies(X0,b),implies(X0,c)))) = true,
inference(paramodulation,[status(thm)],[f17,f14]) ).
fof(f92,plain,
! [X0,X1,X2] : ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(X1,X2))),true,is_a_theorem(implies(X1,implies(X0,X2))),true),true) = true,
inference(paramodulation,[status(thm)],[f13,f10]) ).
fof(f93,plain,
! [X0,X1] : ifeq(true,true,ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(implies(implies(not(X0),X1),X1)),true),true) = true,
inference(paramodulation,[status(thm)],[f15,f10]) ).
fof(f94,plain,
! [X0,X1,X2] : ifeq(true,true,ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(implies(implies(X2,X0),implies(X2,X1))),true),true) = true,
inference(paramodulation,[status(thm)],[f14,f10]) ).
fof(f103,plain,
! [X0,X1] : ifeq(true,true,ifeq(is_a_theorem(X0),true,is_a_theorem(implies(X1,X0)),true),true) = true,
inference(paramodulation,[status(thm)],[f12,f10]) ).
fof(f159,plain,
! [X0] : ifeq(is_a_theorem(implies(X0,sF1_fnc)),true,ifeq(is_a_theorem(X0),true,sF0_fnc,true),true) = true,
inference(paramodulation,[status(thm)],[f23,f10]) ).
fof(f173,plain,
! [X0,X1,X2] : ifeq(is_a_theorem(implies(X0,implies(X1,X2))),true,is_a_theorem(implies(X1,implies(X0,X2))),true) = true,
inference(forward_demodulation,[status(thm)],[f9,f92]) ).
fof(f174,plain,
! [X0,X1] : ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(implies(implies(not(X0),X1),X1)),true) = true,
inference(forward_demodulation,[status(thm)],[f9,f93]) ).
fof(f175,plain,
! [X0,X1,X2] : ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(implies(implies(X2,X0),implies(X2,X1))),true) = true,
inference(forward_demodulation,[status(thm)],[f9,f94]) ).
fof(f185,plain,
! [X0,X1] : ifeq(is_a_theorem(X0),true,is_a_theorem(implies(X1,X0)),true) = true,
inference(forward_demodulation,[status(thm)],[f9,f103]) ).
fof(f1122,plain,
is_a_theorem(implies(sF3_fnc,implies(sF5_fnc,implies(a,c)))) = true,
inference(paramodulation,[status(thm)],[f19,f49]) ).
fof(f1132,plain,
is_a_theorem(implies(sF3_fnc,implies(sF5_fnc,sF6_fnc))) = true,
inference(forward_demodulation,[status(thm)],[f20,f1122]) ).
fof(f1133,plain,
is_a_theorem(implies(sF3_fnc,sF4_fnc)) = true,
inference(forward_demodulation,[status(thm)],[f21,f1132]) ).
fof(f5837,plain,
! [X0,X1] : ifeq(true,true,is_a_theorem(implies(not(X0),implies(X0,X1))),true) = true,
inference(paramodulation,[status(thm)],[f11,f173]) ).
fof(f6110,plain,
! [X0,X1] : is_a_theorem(implies(not(X0),implies(X0,X1))) = true,
inference(forward_demodulation,[status(thm)],[f9,f5837]) ).
fof(f6217,plain,
! [X0] : ifeq(true,true,is_a_theorem(implies(implies(X0,sF3_fnc),implies(X0,sF4_fnc))),true) = true,
inference(paramodulation,[status(thm)],[f1133,f175]) ).
fof(f6440,plain,
! [X0] : is_a_theorem(implies(implies(X0,sF3_fnc),implies(X0,sF4_fnc))) = true,
inference(forward_demodulation,[status(thm)],[f9,f6217]) ).
fof(f7138,plain,
is_a_theorem(implies(not(a),sF6_fnc)) = true,
inference(paramodulation,[status(thm)],[f20,f6110]) ).
fof(f7624,plain,
! [X0] : ifeq(true,true,is_a_theorem(implies(X0,implies(not(a),sF6_fnc))),true) = true,
inference(paramodulation,[status(thm)],[f7138,f185]) ).
fof(f7631,plain,
! [X0] : is_a_theorem(implies(X0,implies(not(a),sF6_fnc))) = true,
inference(forward_demodulation,[status(thm)],[f9,f7624]) ).
fof(f9510,plain,
! [X0] : ifeq(true,true,is_a_theorem(implies(not(a),implies(X0,sF6_fnc))),true) = true,
inference(paramodulation,[status(thm)],[f7631,f173]) ).
fof(f9521,plain,
! [X0] : is_a_theorem(implies(not(a),implies(X0,sF6_fnc))) = true,
inference(forward_demodulation,[status(thm)],[f9,f9510]) ).
fof(f13443,plain,
is_a_theorem(implies(not(a),sF4_fnc)) = true,
inference(paramodulation,[status(thm)],[f21,f9521]) ).
fof(f13502,plain,
! [X0] : ifeq(true,true,is_a_theorem(implies(X0,implies(not(a),sF4_fnc))),true) = true,
inference(paramodulation,[status(thm)],[f13443,f185]) ).
fof(f13511,plain,
! [X0] : is_a_theorem(implies(X0,implies(not(a),sF4_fnc))) = true,
inference(forward_demodulation,[status(thm)],[f9,f13502]) ).
fof(f13950,plain,
! [X0] : ifeq(true,true,is_a_theorem(implies(not(a),implies(X0,sF4_fnc))),true) = true,
inference(paramodulation,[status(thm)],[f13511,f173]) ).
fof(f13975,plain,
! [X0] : is_a_theorem(implies(not(a),implies(X0,sF4_fnc))) = true,
inference(forward_demodulation,[status(thm)],[f9,f13950]) ).
fof(f14561,plain,
is_a_theorem(implies(not(a),sF1_fnc)) = true,
inference(paramodulation,[status(thm)],[f22,f13975]) ).
fof(f15611,plain,
is_a_theorem(implies(sF2_fnc,implies(a,sF4_fnc))) = true,
inference(paramodulation,[status(thm)],[f18,f6440]) ).
fof(f15661,plain,
ifeq(true,true,is_a_theorem(implies(a,implies(sF2_fnc,sF4_fnc))),true) = true,
inference(paramodulation,[status(thm)],[f15611,f173]) ).
fof(f15680,plain,
is_a_theorem(implies(a,implies(sF2_fnc,sF4_fnc))) = true,
inference(forward_demodulation,[status(thm)],[f9,f15661]) ).
fof(f15681,plain,
is_a_theorem(implies(a,sF1_fnc)) = true,
inference(forward_demodulation,[status(thm)],[f22,f15680]) ).
fof(f15694,plain,
ifeq(true,true,is_a_theorem(implies(implies(not(a),sF1_fnc),sF1_fnc)),true) = true,
inference(paramodulation,[status(thm)],[f15681,f174]) ).
fof(f15713,plain,
is_a_theorem(implies(implies(not(a),sF1_fnc),sF1_fnc)) = true,
inference(forward_demodulation,[status(thm)],[f9,f15694]) ).
fof(f25118,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(not(a),sF1_fnc)),true,sF0_fnc,true),true) = true,
inference(paramodulation,[status(thm)],[f15713,f159]) ).
fof(f25146,plain,
ifeq(is_a_theorem(implies(not(a),sF1_fnc)),true,sF0_fnc,true) = true,
inference(forward_demodulation,[status(thm)],[f9,f25118]) ).
fof(f25147,plain,
ifeq(true,true,sF0_fnc,true) = true,
inference(forward_demodulation,[status(thm)],[f14561,f25146]) ).
fof(f25148,plain,
sF0_fnc = true,
inference(forward_demodulation,[status(thm)],[f9,f25147]) ).
fof(f25149,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f25148,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL042-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n011.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Mon Sep 21 00:02:01 UTC 2026
% 0.10/5.36 % CPUTime :
% 0.10/5.37 % Drodi V4.1.1
% 0.13/5.79 % Refutation found
% 0.13/5.79 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/5.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.83 % Elapsed time: 0.449779 seconds
% 0.13/5.83 % CPU time: 3.462027 seconds
% 0.13/5.83 % Total memory used: 103.201 MB
% 0.13/5.83 % Net memory used: 101.171 MB
%------------------------------------------------------------------------------