%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL042-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 01:09:15 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.72s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL042-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.36 % Computer : n005.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Mon Sep 21 00:01:49 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.37 % Drodi V4.1.1
% 0.13/0.72 % Refutation found
% 0.13/0.72 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.72 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.72 fof(f1,axiom,(
% 0.13/0.72 (![A,B,C]: (ifeq(A,A,B,C) = B ))),
% 0.13/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.72 fof(f2,axiom,(
% 0.13/0.72 (![X,Y]: (ifeq(is_a_theorem(implies(X,Y)),true,ifeq(is_a_theorem(X),true,is_a_theorem(Y),true),true) = true ))),
% 0.13/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.72 fof(f3,axiom,(
% 0.13/0.72 (![X,Y]: (is_a_theorem(implies(X,implies(not(X),Y))) = true ))),
% 0.13/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.72 fof(f4,axiom,(
% 0.13/0.72 (![X,Y]: (is_a_theorem(implies(X,implies(Y,X))) = true ))),
% 0.13/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.72 fof(f5,axiom,(
% 0.13/0.72 (![X,Y,Z]: (is_a_theorem(implies(implies(X,implies(Y,Z)),implies(Y,implies(X,Z)))) = true ))),
% 0.13/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.72 fof(f6,axiom,(
% 0.13/0.72 (![Y,Z,X]: (is_a_theorem(implies(implies(Y,Z),implies(implies(X,Y),implies(X,Z)))) = true ))),
% 0.13/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.73 fof(f7,axiom,(
% 0.13/0.73 (![X,Y]: (is_a_theorem(implies(implies(X,Y),implies(implies(not(X),Y),Y))) = true ))),
% 0.13/0.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.73 fof(f8,negated_conjecture,(
% 0.13/0.73 is_a_theorem(implies(implies(a,implies(b,c)),implies(implies(a,b),implies(a,c)))) != true ),
% 0.13/0.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.73 fof(f9,plain,(
% 0.13/0.73 ![X0,X1,X2]: (ifeq(X0,X0,X1,X2)=X1)),
% 0.13/0.73 inference(cnf_transformation,[status(thm)],[f1])).
% 0.13/0.73 fof(f10,plain,(
% 0.13/0.73 ![X0,X1]: (ifeq(is_a_theorem(implies(X0,X1)),true,ifeq(is_a_theorem(X0),true,is_a_theorem(X1),true),true)=true)),
% 0.13/0.73 inference(cnf_transformation,[status(thm)],[f2])).
% 0.13/0.73 fof(f11,plain,(
% 0.13/0.73 ![X0,X1]: (is_a_theorem(implies(X0,implies(not(X0),X1)))=true)),
% 0.13/0.73 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/0.73 fof(f12,plain,(
% 0.13/0.73 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0)))=true)),
% 0.13/0.73 inference(cnf_transformation,[status(thm)],[f4])).
% 0.13/0.73 fof(f13,plain,(
% 0.13/0.73 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2))))=true)),
% 0.13/0.73 inference(cnf_transformation,[status(thm)],[f5])).
% 0.13/0.73 fof(f14,plain,(
% 0.13/0.73 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1))))=true)),
% 0.13/0.73 inference(cnf_transformation,[status(thm)],[f6])).
% 0.13/0.73 fof(f15,plain,(
% 0.13/0.73 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X1),X1)))=true)),
% 0.13/0.73 inference(cnf_transformation,[status(thm)],[f7])).
% 0.13/0.73 fof(f16,plain,(
% 0.13/0.73 ~is_a_theorem(implies(implies(a,implies(b,c)),implies(implies(a,b),implies(a,c))))=true),
% 0.13/0.73 inference(cnf_transformation,[status(thm)],[f8])).
% 0.13/0.73 fof(f17,definition,(
% 0.13/0.73 sF3_fnc=implies(b,c)),
% 0.13/0.73 introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition])).
% 0.13/0.73 fof(f18,definition,(
% 0.13/0.73 sF2_fnc=implies(a,sF3_fnc)),
% 0.13/0.73 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 0.13/0.73 fof(f19,definition,(
% 0.13/0.73 sF5_fnc=implies(a,b)),
% 0.13/0.73 introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition])).
% 0.13/0.73 fof(f20,definition,(
% 0.13/0.73 sF6_fnc=implies(a,c)),
% 0.13/0.73 introduced(definition,[new_symbols(definition,[sF6_fnc])],[function_definition])).
% 0.13/0.73 fof(f21,definition,(
% 0.13/0.73 sF4_fnc=implies(sF5_fnc,sF6_fnc)),
% 0.13/0.73 introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition])).
% 0.13/0.73 fof(f22,definition,(
% 0.13/0.73 sF1_fnc=implies(sF2_fnc,sF4_fnc)),
% 0.13/0.73 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 0.13/0.73 fof(f23,definition,(
% 0.13/0.73 sF0_fnc=is_a_theorem(sF1_fnc)),
% 0.13/0.73 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 0.13/0.73 fof(f24,plain,(
% 0.13/0.73 ~sF0_fnc=true),
% 0.13/0.73 inference(definition_folding,[],[f16,f23,f22,f21,f20,f19,f18,f17])).
% 0.13/0.73 fof(f29,plain,(
% 0.13/0.73 ![X0]: (ifeq(is_a_theorem(implies(X0,sF1_fnc)),true,ifeq(is_a_theorem(X0),true,sF0_fnc,true),true)=true)),
% 0.13/0.73 inference(paramodulation,[status(thm)],[f23,f10])).
% 0.13/0.73 fof(f40,plain,(
% 0.13/0.73 ![X0,X1]: (ifeq(true,true,ifeq(is_a_theorem(X0),true,is_a_theorem(implies(X1,X0)),true),true)=true)),
% 0.13/0.73 inference(paramodulation,[status(thm)],[f12,f10])).
% 0.13/0.73 fof(f43,plain,(
% 0.13/0.73 ![X0,X1]: (ifeq(is_a_theorem(X0),true,is_a_theorem(implies(X1,X0)),true)=true)),
% 0.13/0.73 inference(forward_demodulation,[status(thm)],[f9,f40])).
% 0.13/0.73 fof(f60,plain,(
% 0.13/0.73 ![X0,X1,X2]: (ifeq(is_a_theorem(implies(implies(X0,implies(not(X0),X1)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true)=true)),
% 0.13/0.73 inference(paramodulation,[status(thm)],[f11,f10])).
% 0.13/0.73 fof(f62,plain,(
% 0.13/0.73 ![X0,X1,X2]: (ifeq(is_a_theorem(implies(implies(X0,implies(not(X0),X1)),X2)),true,is_a_theorem(X2),true)=true)),
% 0.13/0.73 inference(forward_demodulation,[status(thm)],[f9,f60])).
% 0.13/0.73 fof(f93,plain,(
% 0.13/0.73 ![X0]: (is_a_theorem(implies(implies(a,implies(X0,c)),implies(X0,sF6_fnc)))=true)),
% 0.13/0.73 inference(paramodulation,[status(thm)],[f20,f13])).
% 0.13/0.73 fof(f97,plain,(
% 0.13/0.73 ![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)),
% 0.13/0.73 inference(paramodulation,[status(thm)],[f13,f10])).
% 0.13/0.73 fof(f100,plain,(
% 0.13/0.73 ![X0,X1,X2]: (ifeq(is_a_theorem(implies(X0,implies(X1,X2))),true,is_a_theorem(implies(X1,implies(X0,X2))),true)=true)),
% 0.13/0.73 inference(forward_demodulation,[status(thm)],[f9,f97])).
% 0.13/0.73 fof(f179,plain,(
% 0.13/0.73 ![X0]: (is_a_theorem(implies(sF3_fnc,implies(implies(X0,b),implies(X0,c))))=true)),
% 0.13/0.73 inference(paramodulation,[status(thm)],[f17,f14])).
% 0.13/0.73 fof(f194,plain,(
% 0.13/0.73 ![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)),
% 0.13/0.73 inference(paramodulation,[status(thm)],[f14,f10])).
% 0.13/0.73 fof(f198,plain,(
% 0.13/0.73 ![X0,X1,X2]: (ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(implies(implies(X2,X0),implies(X2,X1))),true)=true)),
% 0.13/0.73 inference(forward_demodulation,[status(thm)],[f9,f194])).
% 0.13/0.73 fof(f288,plain,(
% 0.13/0.73 ![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)),
% 0.13/0.73 inference(paramodulation,[status(thm)],[f15,f10])).
% 0.13/0.73 fof(f292,plain,(
% 0.13/0.73 ![X0,X1]: (ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(implies(implies(not(X0),X1),X1)),true)=true)),
% 0.13/0.73 inference(forward_demodulation,[status(thm)],[f9,f288])).
% 0.13/0.73 fof(f1487,plain,(
% 0.13/0.73 is_a_theorem(implies(sF3_fnc,implies(sF5_fnc,implies(a,c))))=true),
% 0.13/0.73 inference(paramodulation,[status(thm)],[f19,f179])).
% 0.13/0.73 fof(f1498,plain,(
% 0.13/0.73 is_a_theorem(implies(sF3_fnc,implies(sF5_fnc,sF6_fnc)))=true),
% 0.13/0.73 inference(forward_demodulation,[status(thm)],[f20,f1487])).
% 0.13/0.73 fof(f1499,plain,(
% 0.13/0.73 is_a_theorem(implies(sF3_fnc,sF4_fnc))=true),
% 0.13/0.73 inference(forward_demodulation,[status(thm)],[f21,f1498])).
% 0.13/0.73 fof(f2790,plain,(
% 0.13/0.73 ifeq(true,true,is_a_theorem(implies(not(a),sF6_fnc)),true)=true),
% 0.13/0.73 inference(paramodulation,[status(thm)],[f93,f62])).
% 0.13/0.73 fof(f2907,plain,(
% 0.13/0.73 is_a_theorem(implies(not(a),sF6_fnc))=true),
% 0.13/0.73 inference(forward_demodulation,[status(thm)],[f9,f2790])).
% 0.13/0.73 fof(f3014,plain,(
% 0.13/0.73 ![X0]: (ifeq(true,true,is_a_theorem(implies(X0,implies(not(a),sF6_fnc))),true)=true)),
% 0.13/0.73 inference(paramodulation,[status(thm)],[f2907,f43])).
% 0.13/0.73 fof(f3021,plain,(
% 0.13/0.73 ![X0]: (is_a_theorem(implies(X0,implies(not(a),sF6_fnc)))=true)),
% 0.13/0.73 inference(forward_demodulation,[status(thm)],[f9,f3014])).
% 0.13/0.73 fof(f4862,plain,(
% 0.13/0.73 ![X0]: (ifeq(true,true,is_a_theorem(implies(not(a),implies(X0,sF6_fnc))),true)=true)),
% 0.13/0.73 inference(paramodulation,[status(thm)],[f3021,f100])).
% 0.13/0.73 fof(f4882,plain,(
% 0.13/0.73 ![X0]: (is_a_theorem(implies(not(a),implies(X0,sF6_fnc)))=true)),
% 0.13/0.73 inference(forward_demodulation,[status(thm)],[f9,f4862])).
% 0.13/0.73 fof(f6030,plain,(
% 0.13/0.73 is_a_theorem(implies(not(a),sF4_fnc))=true),
% 0.13/0.73 inference(paramodulation,[status(thm)],[f21,f4882])).
% 0.13/0.73 fof(f6071,plain,(
% 0.13/0.73 ![X0]: (ifeq(true,true,is_a_theorem(implies(X0,implies(not(a),sF4_fnc))),true)=true)),
% 0.13/0.73 inference(paramodulation,[status(thm)],[f6030,f43])).
% 0.13/0.73 fof(f6078,plain,(
% 0.13/0.73 ![X0]: (is_a_theorem(implies(X0,implies(not(a),sF4_fnc)))=true)),
% 0.13/0.73 inference(forward_demodulation,[status(thm)],[f9,f6071])).
% 0.13/0.73 fof(f6324,plain,(
% 0.13/0.73 ![X0]: (ifeq(true,true,is_a_theorem(implies(not(a),implies(X0,sF4_fnc))),true)=true)),
% 0.13/0.73 inference(paramodulation,[status(thm)],[f6078,f100])).
% 0.13/0.73 fof(f6344,plain,(
% 0.13/0.73 ![X0]: (is_a_theorem(implies(not(a),implies(X0,sF4_fnc)))=true)),
% 0.13/0.73 inference(forward_demodulation,[status(thm)],[f9,f6324])).
% 0.13/0.74 fof(f6478,plain,(
% 0.13/0.74 is_a_theorem(implies(not(a),sF1_fnc))=true),
% 0.13/0.74 inference(paramodulation,[status(thm)],[f22,f6344])).
% 0.13/0.74 fof(f6521,plain,(
% 0.13/0.74 ifeq(is_a_theorem(implies(implies(not(a),sF1_fnc),sF1_fnc)),true,ifeq(true,true,sF0_fnc,true),true)=true),
% 0.13/0.74 inference(paramodulation,[status(thm)],[f6478,f29])).
% 0.13/0.74 fof(f6531,plain,(
% 0.13/0.74 ifeq(is_a_theorem(implies(implies(not(a),sF1_fnc),sF1_fnc)),true,sF0_fnc,true)=true),
% 0.13/0.74 inference(forward_demodulation,[status(thm)],[f9,f6521])).
% 0.13/0.74 fof(f8531,plain,(
% 0.13/0.74 ![X0]: (ifeq(true,true,is_a_theorem(implies(implies(X0,sF3_fnc),implies(X0,sF4_fnc))),true)=true)),
% 0.13/0.74 inference(paramodulation,[status(thm)],[f1499,f198])).
% 0.13/0.74 fof(f8795,plain,(
% 0.13/0.74 ![X0]: (is_a_theorem(implies(implies(X0,sF3_fnc),implies(X0,sF4_fnc)))=true)),
% 0.13/0.74 inference(forward_demodulation,[status(thm)],[f9,f8531])).
% 0.13/0.74 fof(f10307,plain,(
% 0.13/0.74 is_a_theorem(implies(sF2_fnc,implies(a,sF4_fnc)))=true),
% 0.13/0.74 inference(paramodulation,[status(thm)],[f18,f8795])).
% 0.13/0.74 fof(f10343,plain,(
% 0.13/0.74 ifeq(true,true,is_a_theorem(implies(a,implies(sF2_fnc,sF4_fnc))),true)=true),
% 0.13/0.74 inference(paramodulation,[status(thm)],[f10307,f100])).
% 0.13/0.74 fof(f10358,plain,(
% 0.13/0.74 is_a_theorem(implies(a,implies(sF2_fnc,sF4_fnc)))=true),
% 0.13/0.74 inference(forward_demodulation,[status(thm)],[f9,f10343])).
% 0.13/0.74 fof(f10360,plain,(
% 0.13/0.74 is_a_theorem(implies(a,sF1_fnc))=true),
% 0.13/0.74 inference(forward_demodulation,[status(thm)],[f22,f10358])).
% 0.13/0.74 fof(f11797,plain,(
% 0.13/0.74 ifeq(true,true,is_a_theorem(implies(implies(not(a),sF1_fnc),sF1_fnc)),true)=true),
% 0.13/0.74 inference(paramodulation,[status(thm)],[f10360,f292])).
% 0.13/0.74 fof(f12084,plain,(
% 0.13/0.74 ifeq(true,true,sF0_fnc,true)=true),
% 0.13/0.74 inference(backward_demodulation,[status(thm)],[f12085,f6531])).
% 0.13/0.74 fof(f12085,plain,(
% 0.13/0.74 is_a_theorem(implies(implies(not(a),sF1_fnc),sF1_fnc))=true),
% 0.13/0.74 inference(forward_demodulation,[status(thm)],[f9,f11797])).
% 0.13/0.74 fof(f12302,plain,(
% 0.13/0.74 sF0_fnc=true),
% 0.13/0.74 inference(forward_demodulation,[status(thm)],[f9,f12084])).
% 0.13/0.74 fof(f12303,plain,(
% 0.13/0.74 $false),
% 0.13/0.74 inference(forward_subsumption_resolution,[status(thm)],[f12302,f24])).
% 0.13/0.74 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.78 % Elapsed time: 0.403693 seconds
% 0.13/0.78 % CPU time: 2.503937 seconds
% 0.13/0.78 % Total memory used: 65.496 MB
% 0.13/0.78 % Net memory used: 63.917 MB
%------------------------------------------------------------------------------