%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : HEN010-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 12:45:29 PM UTC 2026
% Result : Unsatisfiable 10.33s 6.74s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n009.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sun Sep 20 20:46:33 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 10.33/6.74 % Refutation found
% 10.33/6.74 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 10.33/6.74 % SZS output start CNFRefutation for theBenchmark
% 10.33/6.74 fof(f1,axiom,(
% 10.33/6.74 (![A,B,C]: (ifeq2(A,A,B,C) = B ))),
% 10.33/6.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.33/6.74 fof(f2,axiom,(
% 10.33/6.74 (![A,B,C]: (ifeq(A,A,B,C) = B ))),
% 10.33/6.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.33/6.74 fof(f4,axiom,(
% 10.33/6.74 (![X,Y]: (ifeq(quotient(X,Y,zero),true,less_equal(X,Y),true) = true ))),
% 10.33/6.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.33/6.74 fof(f5,axiom,(
% 10.33/6.74 (![X,Y,Z]: (ifeq(quotient(X,Y,Z),true,less_equal(Z,X),true) = true ))),
% 10.33/6.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.33/6.74 fof(f6,axiom,(
% 10.33/6.74 (![V3,V2,V4,V1,Z,V5,Y,X]: (ifeq(quotient(V3,V2,V4),true,ifeq(quotient(V1,Z,V5),true,ifeq(quotient(Y,Z,V2),true,ifeq(quotient(X,Z,V3),true,ifeq(quotient(X,Y,V1),true,less_equal(V4,V5),true),true),true),true),true) = true ))),
% 10.33/6.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.33/6.74 fof(f8,axiom,(
% 10.33/6.74 (![Y,X]: (ifeq2(less_equal(Y,X),true,ifeq2(less_equal(X,Y),true,X,Y),Y) = Y ))),
% 10.33/6.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.33/6.74 fof(f9,axiom,(
% 10.33/6.74 (![X]: (less_equal(X,identity) = true ))),
% 10.33/6.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.33/6.74 fof(f10,axiom,(
% 10.33/6.74 (![X,Y]: (quotient(X,Y,divide(X,Y)) = true ))),
% 10.33/6.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.33/6.74 fof(f14,axiom,(
% 10.33/6.74 (![X]: (quotient(X,X,zero) = true ))),
% 10.33/6.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.33/6.74 fof(f15,axiom,(
% 10.33/6.74 (![X]: (quotient(X,zero,X) = true ))),
% 10.33/6.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.33/6.74 fof(f17,axiom,(
% 10.33/6.74 (![X,Z,W2,Y,W1]: (ifeq(quotient(X,Z,W2),true,ifeq(quotient(X,Y,W1),true,ifeq(less_equal(W1,Z),true,less_equal(W2,Y),true),true),true) = true ))),
% 10.33/6.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.33/6.74 fof(f18,axiom,(
% 10.33/6.74 (![Z,Y,W1,X,W2]: (ifeq(quotient(Z,Y,W1),true,ifeq(quotient(Z,X,W2),true,ifeq(less_equal(X,Y),true,less_equal(W1,W2),true),true),true) = true ))),
% 10.33/6.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.33/6.74 fof(f19,axiom,(
% 10.33/6.74 (![Y,Z,W2,X,W1]: (ifeq(quotient(Y,Z,W2),true,ifeq(quotient(X,Z,W1),true,ifeq(less_equal(X,Y),true,less_equal(W1,W2),true),true),true) = true ))),
% 10.33/6.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.33/6.74 fof(f20,hypothesis,(
% 10.33/6.74 quotient(identity,a,idQa) = true ),
% 10.33/6.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.33/6.74 fof(f21,hypothesis,(
% 10.33/6.74 quotient(identity,idQa,idQ_idQa) = true ),
% 10.33/6.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.33/6.74 fof(f22,hypothesis,(
% 10.33/6.74 quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa) = true ),
% 10.33/6.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.33/6.74 fof(f23,negated_conjecture,(
% 10.33/6.74 idQa != idQa_Q__idQ_idQa ),
% 10.33/6.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.33/6.74 fof(f24,plain,(
% 10.33/6.74 ![X0,X1,X2]: (ifeq2(X0,X0,X1,X2)=X1)),
% 10.33/6.74 inference(cnf_transformation,[status(thm)],[f1])).
% 10.33/6.74 fof(f25,plain,(
% 10.33/6.74 ![X0,X1,X2]: (ifeq(X0,X0,X1,X2)=X1)),
% 10.33/6.74 inference(cnf_transformation,[status(thm)],[f2])).
% 10.33/6.74 fof(f27,plain,(
% 10.33/6.74 ![X0,X1]: (ifeq(quotient(X0,X1,zero),true,less_equal(X0,X1),true)=true)),
% 10.33/6.74 inference(cnf_transformation,[status(thm)],[f4])).
% 10.33/6.74 fof(f28,plain,(
% 10.33/6.74 ![X0,X1,X2]: (ifeq(quotient(X0,X1,X2),true,less_equal(X2,X0),true)=true)),
% 10.33/6.74 inference(cnf_transformation,[status(thm)],[f5])).
% 10.33/6.74 fof(f29,plain,(
% 10.33/6.74 ![X0,X1,X2,X3,X4,X5,X6,X7]: (ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X3,X4,X5),true,ifeq(quotient(X6,X4,X1),true,ifeq(quotient(X7,X4,X0),true,ifeq(quotient(X7,X6,X3),true,less_equal(X2,X5),true),true),true),true),true)=true)),
% 10.33/6.74 inference(cnf_transformation,[status(thm)],[f6])).
% 10.33/6.74 fof(f31,plain,(
% 10.33/6.74 ![X0,X1]: (ifeq2(less_equal(X0,X1),true,ifeq2(less_equal(X1,X0),true,X1,X0),X0)=X0)),
% 10.33/6.74 inference(cnf_transformation,[status(thm)],[f8])).
% 10.33/6.74 fof(f32,plain,(
% 10.33/6.74 ![X0]: (less_equal(X0,identity)=true)),
% 10.33/6.74 inference(cnf_transformation,[status(thm)],[f9])).
% 10.33/6.74 fof(f33,plain,(
% 10.33/6.74 ![X0,X1]: (quotient(X0,X1,divide(X0,X1))=true)),
% 10.33/6.74 inference(cnf_transformation,[status(thm)],[f10])).
% 10.33/6.74 fof(f37,plain,(
% 10.33/6.74 ![X0]: (quotient(X0,X0,zero)=true)),
% 10.33/6.74 inference(cnf_transformation,[status(thm)],[f14])).
% 10.33/6.74 fof(f38,plain,(
% 10.33/6.74 ![X0]: (quotient(X0,zero,X0)=true)),
% 10.33/6.74 inference(cnf_transformation,[status(thm)],[f15])).
% 10.33/6.74 fof(f40,plain,(
% 10.33/6.74 ![X0,X1,X2,X3,X4]: (ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X0,X3,X4),true,ifeq(less_equal(X4,X1),true,less_equal(X2,X3),true),true),true)=true)),
% 10.33/6.74 inference(cnf_transformation,[status(thm)],[f17])).
% 10.33/6.74 fof(f41,plain,(
% 10.33/6.74 ![X0,X1,X2,X3,X4]: (ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X0,X3,X4),true,ifeq(less_equal(X3,X1),true,less_equal(X2,X4),true),true),true)=true)),
% 10.33/6.74 inference(cnf_transformation,[status(thm)],[f18])).
% 10.33/6.74 fof(f42,plain,(
% 10.33/6.74 ![X0,X1,X2,X3,X4]: (ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X3,X1,X4),true,ifeq(less_equal(X3,X0),true,less_equal(X4,X2),true),true),true)=true)),
% 10.33/6.74 inference(cnf_transformation,[status(thm)],[f19])).
% 10.33/6.74 fof(f43,plain,(
% 10.33/6.74 quotient(identity,a,idQa)=true),
% 10.33/6.74 inference(cnf_transformation,[status(thm)],[f20])).
% 10.33/6.74 fof(f44,plain,(
% 10.33/6.74 quotient(identity,idQa,idQ_idQa)=true),
% 10.33/6.74 inference(cnf_transformation,[status(thm)],[f21])).
% 10.33/6.74 fof(f45,plain,(
% 10.33/6.74 quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa)=true),
% 10.33/6.74 inference(cnf_transformation,[status(thm)],[f22])).
% 10.33/6.74 fof(f46,plain,(
% 10.33/6.74 ~idQa=idQa_Q__idQ_idQa),
% 10.33/6.74 inference(cnf_transformation,[status(thm)],[f23])).
% 10.33/6.74 fof(f57,plain,(
% 10.33/6.74 ![X0]: (ifeq(true,true,less_equal(X0,X0),true)=true)),
% 10.33/6.74 inference(paramodulation,[status(thm)],[f37,f27])).
% 10.33/6.74 fof(f59,plain,(
% 10.33/6.74 ![X0]: (less_equal(X0,X0)=true)),
% 10.33/6.74 inference(forward_demodulation,[status(thm)],[f25,f57])).
% 10.33/6.74 fof(f62,plain,(
% 10.33/6.74 ifeq(true,true,less_equal(idQa_Q__idQ_idQa,idQa),true)=true),
% 10.33/6.74 inference(paramodulation,[status(thm)],[f45,f28])).
% 10.33/6.74 fof(f67,plain,(
% 10.33/6.74 less_equal(idQa_Q__idQ_idQa,idQa)=true),
% 10.33/6.74 inference(forward_demodulation,[status(thm)],[f25,f62])).
% 10.33/6.74 fof(f71,plain,(
% 10.33/6.74 ![X0,X1,X2,X3,X4]: (ifeq(quotient(X0,X1,X2),true,ifeq(true,true,ifeq(quotient(X3,idQ_idQa,X1),true,ifeq(quotient(X4,idQ_idQa,X0),true,ifeq(quotient(X4,X3,idQa),true,less_equal(X2,idQa_Q__idQ_idQa),true),true),true),true),true)=true)),
% 10.33/6.74 inference(paramodulation,[status(thm)],[f45,f29])).
% 10.33/6.74 fof(f86,plain,(
% 10.33/6.74 ![X0,X1,X2,X3,X4]: (ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X3,idQ_idQa,X1),true,ifeq(quotient(X4,idQ_idQa,X0),true,ifeq(quotient(X4,X3,idQa),true,less_equal(X2,idQa_Q__idQ_idQa),true),true),true),true)=true)),
% 10.33/6.74 inference(forward_demodulation,[status(thm)],[f25,f71])).
% 10.33/6.74 fof(f118,plain,(
% 10.33/6.74 ifeq2(true,true,ifeq2(less_equal(idQa,idQa_Q__idQ_idQa),true,idQa,idQa_Q__idQ_idQa),idQa_Q__idQ_idQa)=idQa_Q__idQ_idQa),
% 10.33/6.74 inference(paramodulation,[status(thm)],[f67,f31])).
% 10.33/6.74 fof(f124,plain,(
% 10.33/6.74 ifeq2(less_equal(idQa,idQa_Q__idQ_idQa),true,idQa,idQa_Q__idQ_idQa)=idQa_Q__idQ_idQa),
% 10.33/6.74 inference(forward_demodulation,[status(thm)],[f24,f118])).
% 10.33/6.74 fof(f133,plain,(
% 10.33/6.74 ![X0,X1,X2]: (ifeq(quotient(X0,zero,X1),true,ifeq(true,true,ifeq(quotient(X2,idQ_idQa,X0),true,ifeq(quotient(X2,idQ_idQa,idQa),true,less_equal(X1,idQa_Q__idQ_idQa),true),true),true),true)=true)),
% 10.33/6.74 inference(paramodulation,[status(thm)],[f37,f86])).
% 10.33/6.74 fof(f145,plain,(
% 10.33/6.74 ![X0,X1,X2]: (ifeq(quotient(X0,zero,X1),true,ifeq(quotient(X2,idQ_idQa,X0),true,ifeq(quotient(X2,idQ_idQa,idQa),true,less_equal(X1,idQa_Q__idQ_idQa),true),true),true)=true)),
% 10.33/6.74 inference(forward_demodulation,[status(thm)],[f25,f133])).
% 10.33/6.74 fof(f598,plain,(
% 10.33/6.74 ![X0,X1,X2,X3]: (ifeq(quotient(X0,X1,X2),true,ifeq(true,true,ifeq(less_equal(divide(X0,X3),X1),true,less_equal(X2,X3),true),true),true)=true)),
% 10.33/6.74 inference(paramodulation,[status(thm)],[f33,f40])).
% 10.33/6.74 fof(f604,plain,(
% 10.33/6.74 ![X0,X1,X2,X3]: (ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X0,X3,X1),true,ifeq(true,true,less_equal(X2,X3),true),true),true)=true)),
% 10.33/6.74 inference(paramodulation,[status(thm)],[f59,f40])).
% 10.33/6.74 fof(f703,plain,(
% 10.33/6.74 ![X0,X1,X2,X3]: (ifeq(quotient(X0,X1,X2),true,ifeq(less_equal(divide(X0,X3),X1),true,less_equal(X2,X3),true),true)=true)),
% 10.33/6.74 inference(forward_demodulation,[status(thm)],[f25,f598])).
% 10.33/6.74 fof(f711,plain,(
% 10.33/6.74 ![X0,X1,X2,X3]: (ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X0,X3,X1),true,less_equal(X2,X3),true),true)=true)),
% 10.33/6.74 inference(forward_demodulation,[status(thm)],[f25,f604])).
% 10.33/6.74 fof(f802,plain,(
% 10.33/6.74 ![X0,X1]: (ifeq(true,true,ifeq(quotient(identity,X0,X1),true,ifeq(less_equal(X0,a),true,less_equal(idQa,X1),true),true),true)=true)),
% 10.33/6.74 inference(paramodulation,[status(thm)],[f43,f41])).
% 10.33/6.74 fof(f829,plain,(
% 10.33/6.74 ![X0,X1]: (ifeq(quotient(identity,X0,X1),true,ifeq(less_equal(X0,a),true,less_equal(idQa,X1),true),true)=true)),
% 10.33/6.74 inference(forward_demodulation,[status(thm)],[f25,f802])).
% 10.33/6.74 fof(f1005,plain,(
% 10.33/6.74 ![X0,X1]: (ifeq(true,true,ifeq(quotient(X0,idQa,X1),true,ifeq(less_equal(X0,identity),true,less_equal(X1,idQ_idQa),true),true),true)=true)),
% 10.33/6.74 inference(paramodulation,[status(thm)],[f44,f42])).
% 10.33/6.74 fof(f1037,plain,(
% 10.33/6.74 ![X0,X1]: (ifeq(quotient(X0,idQa,X1),true,ifeq(less_equal(X0,identity),true,less_equal(X1,idQ_idQa),true),true)=true)),
% 10.33/6.74 inference(forward_demodulation,[status(thm)],[f25,f1005])).
% 10.33/6.74 fof(f1038,plain,(
% 10.33/6.74 ![X0,X1]: (ifeq(quotient(X0,idQa,X1),true,ifeq(true,true,less_equal(X1,idQ_idQa),true),true)=true)),
% 10.33/6.74 inference(forward_demodulation,[status(thm)],[f32,f1037])).
% 10.33/6.74 fof(f1040,plain,(
% 10.33/6.74 ![X0,X1]: (ifeq(quotient(X0,idQa,X1),true,less_equal(X1,idQ_idQa),true)=true)),
% 10.33/6.74 inference(forward_demodulation,[status(thm)],[f25,f1038])).
% 10.33/6.74 fof(f2967,plain,(
% 10.33/6.74 ![X0,X1]: (ifeq(true,true,ifeq(quotient(X0,idQ_idQa,X1),true,ifeq(quotient(X0,idQ_idQa,idQa),true,less_equal(X1,idQa_Q__idQ_idQa),true),true),true)=true)),
% 10.33/6.74 inference(paramodulation,[status(thm)],[f38,f145])).
% 10.33/6.74 fof(f2982,plain,(
% 10.33/6.74 ![X0,X1]: (ifeq(quotient(X0,idQ_idQa,X1),true,ifeq(quotient(X0,idQ_idQa,idQa),true,less_equal(X1,idQa_Q__idQ_idQa),true),true)=true)),
% 10.33/6.74 inference(forward_demodulation,[status(thm)],[f25,f2967])).
% 10.33/6.74 fof(f3081,plain,(
% 10.33/6.74 ![X0]: (ifeq(true,true,less_equal(divide(X0,idQa),idQ_idQa),true)=true)),
% 10.33/6.74 inference(paramodulation,[status(thm)],[f33,f1040])).
% 10.33/6.74 fof(f3105,plain,(
% 10.33/6.74 ![X0]: (less_equal(divide(X0,idQa),idQ_idQa)=true)),
% 10.33/6.74 inference(forward_demodulation,[status(thm)],[f25,f3081])).
% 10.33/6.74 fof(f10272,plain,(
% 10.33/6.74 ![X0]: (ifeq(true,true,ifeq(quotient(identity,X0,idQa),true,less_equal(idQ_idQa,X0),true),true)=true)),
% 10.33/6.74 inference(paramodulation,[status(thm)],[f44,f711])).
% 10.33/6.74 fof(f10346,plain,(
% 10.33/6.74 ![X0]: (ifeq(quotient(identity,X0,idQa),true,less_equal(idQ_idQa,X0),true)=true)),
% 10.33/6.74 inference(forward_demodulation,[status(thm)],[f25,f10272])).
% 10.33/6.74 fof(f10845,plain,(
% 10.33/6.74 ![X0]: (ifeq(true,true,ifeq(quotient(X0,idQ_idQa,idQa),true,less_equal(divide(X0,idQ_idQa),idQa_Q__idQ_idQa),true),true)=true)),
% 10.33/6.74 inference(paramodulation,[status(thm)],[f33,f2982])).
% 10.33/6.74 fof(f10876,plain,(
% 10.33/6.74 ![X0]: (ifeq(quotient(X0,idQ_idQa,idQa),true,less_equal(divide(X0,idQ_idQa),idQa_Q__idQ_idQa),true)=true)),
% 10.33/6.74 inference(forward_demodulation,[status(thm)],[f25,f10845])).
% 10.33/6.74 fof(f11101,plain,(
% 10.33/6.74 ifeq(true,true,less_equal(idQ_idQa,a),true)=true),
% 10.33/6.74 inference(paramodulation,[status(thm)],[f43,f10346])).
% 10.33/6.74 fof(f11135,plain,(
% 10.33/6.74 less_equal(idQ_idQa,a)=true),
% 10.33/6.74 inference(forward_demodulation,[status(thm)],[f25,f11101])).
% 10.33/6.74 fof(f14633,plain,(
% 10.33/6.74 ![X0,X1]: (ifeq(quotient(X0,idQ_idQa,X1),true,ifeq(true,true,less_equal(X1,idQa),true),true)=true)),
% 10.33/6.74 inference(paramodulation,[status(thm)],[f3105,f703])).
% 10.33/6.74 fof(f14676,plain,(
% 10.33/6.74 ![X0,X1]: (ifeq(quotient(X0,idQ_idQa,X1),true,less_equal(X1,idQa),true)=true)),
% 10.33/6.74 inference(forward_demodulation,[status(thm)],[f25,f14633])).
% 10.33/6.74 fof(f15671,plain,(
% 10.33/6.74 ![X0]: (ifeq(true,true,less_equal(divide(X0,idQ_idQa),idQa),true)=true)),
% 10.33/6.74 inference(paramodulation,[status(thm)],[f33,f14676])).
% 10.33/6.74 fof(f15729,plain,(
% 10.33/6.74 ![X0]: (less_equal(divide(X0,idQ_idQa),idQa)=true)),
% 10.33/6.74 inference(forward_demodulation,[status(thm)],[f25,f15671])).
% 10.33/6.74 fof(f15978,plain,(
% 10.33/6.74 ![X0]: (ifeq(quotient(identity,idQ_idQa,X0),true,ifeq(true,true,less_equal(idQa,X0),true),true)=true)),
% 10.33/6.74 inference(paramodulation,[status(thm)],[f11135,f829])).
% 10.33/6.74 fof(f15998,plain,(
% 10.33/6.74 ![X0]: (ifeq(quotient(identity,idQ_idQa,X0),true,less_equal(idQa,X0),true)=true)),
% 10.33/6.74 inference(forward_demodulation,[status(thm)],[f25,f15978])).
% 10.33/6.74 fof(f18526,plain,(
% 10.33/6.74 ifeq(true,true,less_equal(idQa,divide(identity,idQ_idQa)),true)=true),
% 10.33/6.74 inference(paramodulation,[status(thm)],[f33,f15998])).
% 10.33/6.74 fof(f18560,plain,(
% 10.33/6.74 less_equal(idQa,divide(identity,idQ_idQa))=true),
% 10.33/6.74 inference(forward_demodulation,[status(thm)],[f25,f18526])).
% 10.33/6.74 fof(f18708,plain,(
% 10.33/6.74 ifeq2(less_equal(divide(identity,idQ_idQa),idQa),true,ifeq2(true,true,idQa,divide(identity,idQ_idQa)),divide(identity,idQ_idQa))=divide(identity,idQ_idQa)),
% 10.33/6.78 inference(paramodulation,[status(thm)],[f18560,f31])).
% 10.33/6.78 fof(f18876,plain,(
% 10.33/6.78 ifeq2(true,true,ifeq2(true,true,idQa,divide(identity,idQ_idQa)),divide(identity,idQ_idQa))=divide(identity,idQ_idQa)),
% 10.33/6.78 inference(forward_demodulation,[status(thm)],[f15729,f18708])).
% 10.33/6.78 fof(f18877,plain,(
% 10.33/6.78 ifeq2(true,true,idQa,divide(identity,idQ_idQa))=divide(identity,idQ_idQa)),
% 10.33/6.78 inference(forward_demodulation,[status(thm)],[f24,f18876])).
% 10.33/6.78 fof(f18911,plain,(
% 10.33/6.78 idQa=divide(identity,idQ_idQa)),
% 10.33/6.78 inference(forward_demodulation,[status(thm)],[f24,f18877])).
% 10.33/6.78 fof(f19750,plain,(
% 10.33/6.78 ifeq(quotient(identity,idQ_idQa,idQa),true,less_equal(idQa,idQa_Q__idQ_idQa),true)=true),
% 10.33/6.78 inference(paramodulation,[status(thm)],[f18911,f10876])).
% 10.33/6.78 fof(f19773,plain,(
% 10.33/6.78 quotient(identity,idQ_idQa,idQa)=true),
% 10.33/6.78 inference(paramodulation,[status(thm)],[f18911,f33])).
% 10.33/6.78 fof(f19779,plain,(
% 10.33/6.78 ifeq(true,true,less_equal(idQa,idQa_Q__idQ_idQa),true)=true),
% 10.33/6.78 inference(backward_demodulation,[status(thm)],[f19773,f19750])).
% 10.33/6.78 fof(f19782,plain,(
% 10.33/6.78 ifeq2(true,true,idQa,idQa_Q__idQ_idQa)=idQa_Q__idQ_idQa),
% 10.33/6.78 inference(backward_demodulation,[status(thm)],[f19788,f124])).
% 10.33/6.78 fof(f19788,plain,(
% 10.33/6.78 less_equal(idQa,idQa_Q__idQ_idQa)=true),
% 10.33/6.78 inference(forward_demodulation,[status(thm)],[f25,f19779])).
% 10.33/6.78 fof(f19790,plain,(
% 10.33/6.78 idQa=idQa_Q__idQ_idQa),
% 10.33/6.78 inference(forward_demodulation,[status(thm)],[f24,f19782])).
% 10.33/6.78 fof(f19791,plain,(
% 10.33/6.78 $false),
% 10.33/6.78 inference(forward_subsumption_resolution,[status(thm)],[f19790,f46])).
% 10.33/6.78 % SZS output end CNFRefutation for theBenchmark.p
% 2.58/6.82 % Elapsed time: 1.430587 seconds
% 2.58/6.82 % CPU time: 11.236879 seconds
% 2.58/6.82 % Total memory used: 311.130 MB
% 2.58/6.82 % Net memory used: 306.934 MB
%------------------------------------------------------------------------------