%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : RNG004-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 02:05:05 PM UTC 2026
% Result : Unsatisfiable 188.05s 24.09s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG004-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n001.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Mon Sep 21 04:15:14 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 188.05/24.09 % Refutation found
% 188.05/24.09 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 188.05/24.09 % SZS output start CNFRefutation for theBenchmark
% 188.05/24.09 fof(f1,axiom,(
% 188.05/24.09 (![A,B,C]: (ifeq2(A,A,B,C) = B ))),
% 188.05/24.09 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 188.05/24.09 fof(f2,axiom,(
% 188.05/24.09 (![A,B,C]: (ifeq(A,A,B,C) = B ))),
% 188.05/24.09 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 188.05/24.09 fof(f3,axiom,(
% 188.05/24.09 (![X]: (sum(additive_identity,X,X) = true ))),
% 188.05/24.09 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 188.05/24.09 fof(f4,axiom,(
% 188.05/24.09 (![X]: (sum(X,additive_identity,X) = true ))),
% 188.05/24.09 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 188.05/24.09 fof(f5,axiom,(
% 188.05/24.09 (![X,Y]: (product(X,Y,multiply(X,Y)) = true ))),
% 188.05/24.09 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 188.05/24.09 fof(f6,axiom,(
% 188.05/24.09 (![X,Y]: (sum(X,Y,add(X,Y)) = true ))),
% 188.05/24.09 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 188.05/24.09 fof(f7,axiom,(
% 188.05/24.09 (![X]: (sum(additive_inverse(X),X,additive_identity) = true ))),
% 188.05/24.09 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 188.05/24.09 fof(f8,axiom,(
% 188.05/24.09 (![X]: (sum(X,additive_inverse(X),additive_identity) = true ))),
% 188.05/24.09 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 188.05/24.09 fof(f9,axiom,(
% 188.05/24.09 (![U,Z,W,Y,V,X]: (ifeq(sum(U,Z,W),true,ifeq(sum(Y,Z,V),true,ifeq(sum(X,Y,U),true,sum(X,V,W),true),true),true) = true ))),
% 188.05/24.09 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 188.05/24.09 fof(f11,axiom,(
% 188.05/24.09 (![X,Y,Z]: (ifeq(sum(X,Y,Z),true,sum(Y,X,Z),true) = true ))),
% 188.05/24.09 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 188.05/24.09 fof(f14,axiom,(
% 188.05/24.09 (![X,V3,V4,Z,V2,Y,V1]: (ifeq(product(X,V3,V4),true,ifeq(product(X,Z,V2),true,ifeq(product(X,Y,V1),true,ifeq(sum(Y,Z,V3),true,sum(V1,V2,V4),true),true),true),true) = true ))),
% 188.05/24.09 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 188.05/24.09 fof(f16,axiom,(
% 188.05/24.09 (![V3,X,V4,Z,V2,Y,V1]: (ifeq(product(V3,X,V4),true,ifeq(product(Z,X,V2),true,ifeq(product(Y,X,V1),true,ifeq(sum(Y,Z,V3),true,sum(V1,V2,V4),true),true),true),true) = true ))),
% 188.05/24.09 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 188.05/24.09 fof(f18,axiom,(
% 188.05/24.09 (![X,Y,V,U]: (ifeq2(sum(X,Y,V),true,ifeq2(sum(X,Y,U),true,U,V),V) = V ))),
% 188.05/24.09 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 188.05/24.09 fof(f20,hypothesis,(
% 188.05/24.09 product(a,b,c) = true ),
% 188.05/24.09 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 188.05/24.09 fof(f21,hypothesis,(
% 188.05/24.09 product(additive_inverse(a),additive_inverse(b),d) = true ),
% 188.05/24.09 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 188.05/24.09 fof(f22,negated_conjecture,(
% 188.05/24.09 c != d ),
% 188.05/24.09 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 188.05/24.09 fof(f23,plain,(
% 188.05/24.09 ![X0,X1,X2]: (ifeq2(X0,X0,X1,X2)=X1)),
% 188.05/24.09 inference(cnf_transformation,[status(thm)],[f1])).
% 188.05/24.09 fof(f24,plain,(
% 188.05/24.09 ![X0,X1,X2]: (ifeq(X0,X0,X1,X2)=X1)),
% 188.05/24.09 inference(cnf_transformation,[status(thm)],[f2])).
% 188.05/24.09 fof(f25,plain,(
% 188.05/24.09 ![X0]: (sum(additive_identity,X0,X0)=true)),
% 188.05/24.09 inference(cnf_transformation,[status(thm)],[f3])).
% 188.05/24.09 fof(f26,plain,(
% 188.05/24.09 ![X0]: (sum(X0,additive_identity,X0)=true)),
% 188.05/24.09 inference(cnf_transformation,[status(thm)],[f4])).
% 188.05/24.09 fof(f27,plain,(
% 188.05/24.09 ![X0,X1]: (product(X0,X1,multiply(X0,X1))=true)),
% 188.05/24.09 inference(cnf_transformation,[status(thm)],[f5])).
% 188.05/24.09 fof(f28,plain,(
% 188.05/24.09 ![X0,X1]: (sum(X0,X1,add(X0,X1))=true)),
% 188.05/24.09 inference(cnf_transformation,[status(thm)],[f6])).
% 188.05/24.09 fof(f29,plain,(
% 188.05/24.09 ![X0]: (sum(additive_inverse(X0),X0,additive_identity)=true)),
% 188.05/24.09 inference(cnf_transformation,[status(thm)],[f7])).
% 188.05/24.09 fof(f30,plain,(
% 188.05/24.09 ![X0]: (sum(X0,additive_inverse(X0),additive_identity)=true)),
% 188.05/24.09 inference(cnf_transformation,[status(thm)],[f8])).
% 188.05/24.09 fof(f31,plain,(
% 188.05/24.09 ![X0,X1,X2,X3,X4,X5]: (ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X1,X4),true,ifeq(sum(X5,X3,X0),true,sum(X5,X4,X2),true),true),true)=true)),
% 188.05/24.09 inference(cnf_transformation,[status(thm)],[f9])).
% 188.05/24.09 fof(f33,plain,(
% 188.05/24.09 ![X0,X1,X2]: (ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true)=true)),
% 188.05/24.09 inference(cnf_transformation,[status(thm)],[f11])).
% 188.05/24.09 fof(f36,plain,(
% 188.05/24.09 ![X0,X1,X2,X3,X4,X5,X6]: (ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(product(X0,X5,X6),true,ifeq(sum(X5,X3,X1),true,sum(X6,X4,X2),true),true),true),true)=true)),
% 188.05/24.09 inference(cnf_transformation,[status(thm)],[f14])).
% 188.05/24.09 fof(f38,plain,(
% 188.05/24.09 ![X0,X1,X2,X3,X4,X5,X6]: (ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(product(X5,X1,X6),true,ifeq(sum(X5,X3,X0),true,sum(X6,X4,X2),true),true),true),true)=true)),
% 188.05/24.09 inference(cnf_transformation,[status(thm)],[f16])).
% 188.05/24.09 fof(f40,plain,(
% 188.05/24.09 ![X0,X1,X2,X3]: (ifeq2(sum(X0,X1,X2),true,ifeq2(sum(X0,X1,X3),true,X3,X2),X2)=X2)),
% 188.05/24.09 inference(cnf_transformation,[status(thm)],[f18])).
% 188.05/24.09 fof(f42,plain,(
% 188.05/24.09 product(a,b,c)=true),
% 188.05/24.09 inference(cnf_transformation,[status(thm)],[f20])).
% 188.05/24.09 fof(f43,plain,(
% 188.05/24.09 product(additive_inverse(a),additive_inverse(b),d)=true),
% 188.05/24.09 inference(cnf_transformation,[status(thm)],[f21])).
% 188.05/24.09 fof(f44,plain,(
% 188.05/24.09 ~c=d),
% 188.05/24.09 inference(cnf_transformation,[status(thm)],[f22])).
% 188.05/24.09 fof(f51,plain,(
% 188.05/24.09 ![X0,X1]: (ifeq(true,true,sum(X0,X1,add(X1,X0)),true)=true)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f28,f33])).
% 188.05/24.09 fof(f61,plain,(
% 188.05/24.09 ![X0,X1]: (sum(X0,X1,add(X1,X0))=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f51])).
% 188.05/24.09 fof(f74,plain,(
% 188.05/24.09 ![X0,X1]: (ifeq2(true,true,ifeq2(sum(additive_identity,X0,X1),true,X1,X0),X0)=X0)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f25,f40])).
% 188.05/24.09 fof(f78,plain,(
% 188.05/24.09 ![X0,X1,X2]: (ifeq2(true,true,ifeq2(sum(X0,X1,X2),true,X2,add(X0,X1)),add(X0,X1))=add(X0,X1))),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f28,f40])).
% 188.05/24.09 fof(f79,plain,(
% 188.05/24.09 ![X0,X1]: (ifeq2(sum(additive_inverse(X0),X0,X1),true,ifeq2(true,true,additive_identity,X1),X1)=X1)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f29,f40])).
% 188.05/24.09 fof(f82,plain,(
% 188.05/24.09 ![X0,X1]: (ifeq2(sum(X0,additive_identity,X1),true,ifeq2(true,true,X0,X1),X1)=X1)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f26,f40])).
% 188.05/24.09 fof(f83,plain,(
% 188.05/24.09 ![X0,X1,X2]: (ifeq2(sum(X0,X1,X2),true,ifeq2(true,true,add(X1,X0),X2),X2)=X2)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f61,f40])).
% 188.05/24.09 fof(f86,plain,(
% 188.05/24.09 ![X0,X1]: (ifeq2(sum(additive_identity,X0,X1),true,X1,X0)=X0)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f23,f74])).
% 188.05/24.09 fof(f90,plain,(
% 188.05/24.09 ![X0,X1,X2]: (ifeq2(sum(X0,X1,X2),true,X2,add(X0,X1))=add(X0,X1))),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f23,f78])).
% 188.05/24.09 fof(f91,plain,(
% 188.05/24.09 ![X0,X1]: (ifeq2(sum(additive_inverse(X0),X0,X1),true,additive_identity,X1)=X1)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f23,f79])).
% 188.05/24.09 fof(f94,plain,(
% 188.05/24.09 ![X0,X1]: (ifeq2(sum(X0,additive_identity,X1),true,X0,X1)=X1)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f23,f82])).
% 188.05/24.09 fof(f95,plain,(
% 188.05/24.09 ![X0,X1,X2]: (ifeq2(sum(X0,X1,X2),true,add(X1,X0),X2)=X2)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f23,f83])).
% 188.05/24.09 fof(f98,plain,(
% 188.05/24.09 ifeq2(true,true,additive_identity,additive_inverse(additive_identity))=additive_inverse(additive_identity)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f30,f86])).
% 188.05/24.09 fof(f101,plain,(
% 188.05/24.09 ![X0]: (ifeq2(true,true,add(additive_identity,X0),X0)=X0)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f28,f86])).
% 188.05/24.09 fof(f103,plain,(
% 188.05/24.09 additive_identity=additive_inverse(additive_identity)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f23,f98])).
% 188.05/24.09 fof(f105,plain,(
% 188.05/24.09 ![X0]: (add(additive_identity,X0)=X0)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f23,f101])).
% 188.05/24.09 fof(f115,plain,(
% 188.05/24.09 ![X0,X1,X2,X3]: (ifeq(true,true,ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X0,additive_identity),true,sum(X3,X2,X1),true),true),true)=true)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f25,f31])).
% 188.05/24.09 fof(f140,plain,(
% 188.05/24.09 ![X0,X1,X2,X3]: (ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X0,additive_identity),true,sum(X3,X2,X1),true),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f115])).
% 188.05/24.09 fof(f243,plain,(
% 188.05/24.09 ![X0]: (ifeq2(true,true,additive_identity,add(X0,additive_inverse(X0)))=add(X0,additive_inverse(X0)))),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f61,f91])).
% 188.05/24.09 fof(f248,plain,(
% 188.05/24.09 ![X0]: (additive_identity=add(X0,additive_inverse(X0)))),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f23,f243])).
% 188.05/24.09 fof(f274,plain,(
% 188.05/24.09 ![X0,X1]: (ifeq2(true,true,add(X0,X1),add(X1,X0))=add(X1,X0))),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f28,f95])).
% 188.05/24.09 fof(f284,plain,(
% 188.05/24.09 ![X0,X1]: (add(X0,X1)=add(X1,X0))),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f23,f274])).
% 188.05/24.09 fof(f385,plain,(
% 188.05/24.09 ![X0,X1,X2]: (ifeq2(sum(X0,X1,X2),true,X2,add(X1,X0))=add(X0,X1))),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f284,f90])).
% 188.05/24.09 fof(f475,plain,(
% 188.05/24.09 ![X0,X1,X2,X3]: (ifeq(true,true,ifeq(product(a,X0,X1),true,ifeq(product(a,X2,X3),true,ifeq(sum(X2,X0,b),true,sum(X3,X1,c),true),true),true),true)=true)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f42,f36])).
% 188.05/24.09 fof(f478,plain,(
% 188.05/24.09 ![X0,X1,X2,X3]: (ifeq(product(a,X0,X1),true,ifeq(true,true,ifeq(product(a,X2,X3),true,ifeq(sum(X2,b,X0),true,sum(X3,c,X1),true),true),true),true)=true)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f42,f36])).
% 188.05/24.09 fof(f497,plain,(
% 188.05/24.09 ![X0,X1,X2,X3]: (ifeq(product(a,X0,X1),true,ifeq(product(a,X2,X3),true,ifeq(sum(X2,X0,b),true,sum(X3,X1,c),true),true),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f475])).
% 188.05/24.09 fof(f500,plain,(
% 188.05/24.09 ![X0,X1,X2,X3]: (ifeq(product(a,X0,X1),true,ifeq(product(a,X2,X3),true,ifeq(sum(X2,b,X0),true,sum(X3,c,X1),true),true),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f478])).
% 188.05/24.09 fof(f837,plain,(
% 188.05/24.09 ![X0,X1,X2,X3]: (ifeq(true,true,ifeq(product(X0,additive_inverse(b),X1),true,ifeq(product(X2,additive_inverse(b),X3),true,ifeq(sum(X2,X0,additive_inverse(a)),true,sum(X3,X1,d),true),true),true),true)=true)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f43,f38])).
% 188.05/24.09 fof(f841,plain,(
% 188.05/24.09 ![X0,X1,X2,X3]: (ifeq(product(X0,additive_inverse(b),X1),true,ifeq(true,true,ifeq(product(X2,additive_inverse(b),X3),true,ifeq(sum(X2,additive_inverse(a),X0),true,sum(X3,d,X1),true),true),true),true)=true)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f43,f38])).
% 188.05/24.09 fof(f863,plain,(
% 188.05/24.09 ![X0,X1,X2,X3]: (ifeq(product(X0,additive_inverse(b),X1),true,ifeq(product(X2,additive_inverse(b),X3),true,ifeq(sum(X2,X0,additive_inverse(a)),true,sum(X3,X1,d),true),true),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f837])).
% 188.05/24.09 fof(f867,plain,(
% 188.05/24.09 ![X0,X1,X2,X3]: (ifeq(product(X0,additive_inverse(b),X1),true,ifeq(product(X2,additive_inverse(b),X3),true,ifeq(sum(X2,additive_inverse(a),X0),true,sum(X3,d,X1),true),true),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f841])).
% 188.05/24.09 fof(f1314,plain,(
% 188.05/24.09 ![X0,X1,X2]: (ifeq(sum(X0,X1,X2),true,ifeq(true,true,sum(additive_inverse(X0),X2,X1),true),true)=true)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f29,f140])).
% 188.05/24.09 fof(f1316,plain,(
% 188.05/24.09 ![X0,X1,X2]: (ifeq(sum(additive_inverse(X0),X1,X2),true,ifeq(true,true,sum(X0,X2,X1),true),true)=true)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f30,f140])).
% 188.05/24.09 fof(f1333,plain,(
% 188.05/24.09 ![X0,X1,X2]: (ifeq(sum(X0,X1,X2),true,sum(additive_inverse(X0),X2,X1),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f1314])).
% 188.05/24.09 fof(f1335,plain,(
% 188.05/24.09 ![X0,X1,X2]: (ifeq(sum(additive_inverse(X0),X1,X2),true,sum(X0,X2,X1),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f1316])).
% 188.05/24.09 fof(f1603,plain,(
% 188.05/24.09 ![X0]: (ifeq(true,true,sum(additive_inverse(additive_inverse(X0)),additive_identity,X0),true)=true)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f29,f1333])).
% 188.05/24.09 fof(f1607,plain,(
% 188.05/24.09 ![X0,X1]: (ifeq(true,true,sum(additive_inverse(X0),add(X1,X0),X1),true)=true)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f61,f1333])).
% 188.05/24.09 fof(f1618,plain,(
% 188.05/24.09 ![X0]: (sum(additive_inverse(additive_inverse(X0)),additive_identity,X0)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f1603])).
% 188.05/24.09 fof(f1623,plain,(
% 188.05/24.09 ![X0,X1]: (sum(additive_inverse(X0),add(X1,X0),X1)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f1607])).
% 188.05/24.09 fof(f1630,plain,(
% 188.05/24.09 ![X0]: (ifeq2(true,true,additive_inverse(additive_inverse(X0)),X0)=X0)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f1618,f94])).
% 188.05/24.09 fof(f1676,plain,(
% 188.05/24.09 ![X0]: (additive_inverse(additive_inverse(X0))=X0)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f23,f1630])).
% 188.05/24.09 fof(f1769,plain,(
% 188.05/24.09 ![X0,X1]: (ifeq2(true,true,X0,add(add(X0,X1),additive_inverse(X1)))=add(additive_inverse(X1),add(X0,X1)))),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f1623,f385])).
% 188.05/24.09 fof(f1820,plain,(
% 188.05/24.09 ![X0,X1]: (X0=add(additive_inverse(X1),add(X0,X1)))),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f23,f1769])).
% 188.05/24.09 fof(f1839,plain,(
% 188.05/24.09 ![X0,X1]: (X0=add(X1,add(X0,additive_inverse(X1))))),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f1676,f1820])).
% 188.05/24.09 fof(f1841,plain,(
% 188.05/24.09 ![X0,X1]: (additive_inverse(X0)=add(additive_inverse(add(X1,X0)),X1))),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f1820,f1820])).
% 188.05/24.09 fof(f1845,plain,(
% 188.05/24.09 ![X0,X1]: (X0=add(additive_inverse(X1),add(X1,X0)))),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f284,f1820])).
% 188.05/24.09 fof(f1861,plain,(
% 188.05/24.09 ![X0,X1]: (additive_inverse(X0)=add(X1,additive_inverse(add(X1,X0))))),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f284,f1841])).
% 188.05/24.09 fof(f2076,plain,(
% 188.05/24.09 ![X0,X1]: (X0=add(X1,add(additive_inverse(X1),X0)))),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f284,f1839])).
% 188.05/24.09 fof(f2121,plain,(
% 188.05/24.09 ![X0,X1]: (additive_inverse(X0)=add(additive_inverse(add(X0,X1)),X1))),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f1845,f1820])).
% 188.05/24.09 fof(f2139,plain,(
% 188.05/24.09 ![X0,X1]: (additive_inverse(X0)=add(X1,additive_inverse(add(X0,X1))))),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f284,f2121])).
% 188.05/24.09 fof(f2176,plain,(
% 188.05/24.09 ![X0,X1]: (sum(add(additive_inverse(X0),X1),X0,X1)=true)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f2076,f61])).
% 188.05/24.09 fof(f2526,plain,(
% 188.05/24.09 ![X0,X1]: (additive_inverse(add(X0,X1))=add(additive_inverse(X0),additive_inverse(X1)))),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f1845,f1861])).
% 188.05/24.09 fof(f2527,plain,(
% 188.05/24.09 ![X0,X1]: (additive_inverse(add(X0,X1))=add(additive_inverse(X1),additive_inverse(X0)))),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f1820,f1861])).
% 188.05/24.09 fof(f2825,plain,(
% 188.05/24.09 ![X0,X1]: (ifeq(true,true,ifeq(product(a,X0,X1),true,ifeq(sum(X0,b,b),true,sum(X1,c,c),true),true),true)=true)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f42,f497])).
% 188.05/24.09 fof(f2846,plain,(
% 188.05/24.09 ![X0,X1]: (ifeq(product(a,X0,X1),true,ifeq(sum(X0,b,b),true,sum(X1,c,c),true),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f2825])).
% 188.05/24.09 fof(f3851,plain,(
% 188.05/24.09 ![X0,X1,X2]: (ifeq(true,true,ifeq(product(a,X0,X1),true,ifeq(sum(X0,b,X2),true,sum(X1,c,multiply(a,X2)),true),true),true)=true)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f27,f500])).
% 188.05/24.09 fof(f3873,plain,(
% 188.05/24.09 ![X0,X1,X2]: (ifeq(product(a,X0,X1),true,ifeq(sum(X0,b,X2),true,sum(X1,c,multiply(a,X2)),true),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f3851])).
% 188.05/24.09 fof(f5860,plain,(
% 188.05/24.09 ![X0,X1]: (additive_inverse(add(X0,additive_inverse(X1)))=add(additive_inverse(X0),X1))),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f1676,f2526])).
% 188.05/24.09 fof(f5939,plain,(
% 188.05/24.09 ![X0,X1]: (additive_inverse(add(X0,X1))=additive_inverse(add(X1,X0)))),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f2526,f2527])).
% 188.05/24.09 fof(f6085,plain,(
% 188.05/24.09 ![X0,X1,X2]: (X0=add(add(X1,X2),add(additive_inverse(add(X2,X1)),X0)))),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f5939,f2076])).
% 188.05/24.09 fof(f6102,plain,(
% 188.05/24.09 ![X0,X1]: (additive_identity=add(add(X0,X1),additive_inverse(add(X1,X0))))),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f5939,f248])).
% 188.05/24.09 fof(f7480,plain,(
% 188.05/24.09 ![X0,X1]: (ifeq(true,true,ifeq(product(X0,additive_inverse(b),X1),true,ifeq(sum(X0,additive_inverse(a),additive_inverse(a)),true,sum(X1,d,d),true),true),true)=true)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f43,f863])).
% 188.05/24.09 fof(f7513,plain,(
% 188.05/24.09 ![X0,X1]: (ifeq(product(X0,additive_inverse(b),X1),true,ifeq(sum(X0,additive_inverse(a),additive_inverse(a)),true,sum(X1,d,d),true),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f7480])).
% 188.05/24.09 fof(f8311,plain,(
% 188.05/24.09 ![X0,X1,X2]: (ifeq(true,true,ifeq(product(X0,additive_inverse(b),X1),true,ifeq(sum(X0,additive_inverse(a),X2),true,sum(X1,d,multiply(X2,additive_inverse(b))),true),true),true)=true)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f27,f867])).
% 188.05/24.09 fof(f8340,plain,(
% 188.05/24.09 ![X0,X1,X2]: (ifeq(product(X0,additive_inverse(b),X1),true,ifeq(sum(X0,additive_inverse(a),X2),true,sum(X1,d,multiply(X2,additive_inverse(b))),true),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f8311])).
% 188.05/24.09 fof(f10690,plain,(
% 188.05/24.09 ![X0,X1,X2]: (add(X0,add(X1,X2))=add(add(X2,X1),X0))),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f1820,f6085])).
% 188.05/24.09 fof(f21206,plain,(
% 188.05/24.09 ![X0]: (ifeq(product(a,add(additive_inverse(b),b),X0),true,ifeq(true,true,sum(X0,c,c),true),true)=true)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f2176,f2846])).
% 188.05/24.09 fof(f21220,plain,(
% 188.05/24.09 ![X0]: (ifeq(product(a,add(b,additive_inverse(b)),X0),true,ifeq(true,true,sum(X0,c,c),true),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f284,f21206])).
% 188.05/24.09 fof(f21221,plain,(
% 188.05/24.09 ![X0]: (ifeq(product(a,additive_identity,X0),true,ifeq(true,true,sum(X0,c,c),true),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f248,f21220])).
% 188.05/24.09 fof(f21222,plain,(
% 188.05/24.09 ![X0]: (ifeq(product(a,additive_identity,X0),true,sum(X0,c,c),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f21221])).
% 188.05/24.09 fof(f21230,plain,(
% 188.05/24.09 ifeq(true,true,sum(multiply(a,additive_identity),c,c),true)=true),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f27,f21222])).
% 188.05/24.09 fof(f21238,plain,(
% 188.05/24.09 sum(multiply(a,additive_identity),c,c)=true),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f21230])).
% 188.05/24.09 fof(f21340,plain,(
% 188.05/24.09 ifeq2(true,true,c,add(c,multiply(a,additive_identity)))=add(multiply(a,additive_identity),c)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f21238,f385])).
% 188.05/24.09 fof(f21429,plain,(
% 188.05/24.09 c=add(multiply(a,additive_identity),c)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f23,f21340])).
% 188.05/24.09 fof(f21430,plain,(
% 188.05/24.09 c=add(c,multiply(a,additive_identity))),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f284,f21429])).
% 188.05/24.09 fof(f21489,plain,(
% 188.05/24.09 additive_identity=add(add(multiply(a,additive_identity),c),additive_inverse(c))),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f21430,f6102])).
% 188.05/24.09 fof(f21571,plain,(
% 188.05/24.09 additive_identity=add(additive_inverse(c),add(c,multiply(a,additive_identity)))),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f10690,f21489])).
% 188.05/24.09 fof(f21572,plain,(
% 188.05/24.09 additive_identity=multiply(a,additive_identity)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f1845,f21571])).
% 188.05/24.09 fof(f35395,plain,(
% 188.05/24.09 ![X0]: (ifeq(product(a,additive_inverse(b),X0),true,ifeq(true,true,sum(X0,c,multiply(a,additive_identity)),true),true)=true)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f29,f3873])).
% 188.05/24.09 fof(f35421,plain,(
% 188.05/24.09 ![X0]: (ifeq(product(a,additive_inverse(b),X0),true,sum(X0,c,multiply(a,additive_identity)),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f35395])).
% 188.05/24.09 fof(f35422,plain,(
% 188.05/24.09 ![X0]: (ifeq(product(a,additive_inverse(b),X0),true,sum(X0,c,additive_identity),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f21572,f35421])).
% 188.05/24.09 fof(f68429,plain,(
% 188.05/24.09 ifeq(true,true,sum(multiply(a,additive_inverse(b)),c,additive_identity),true)=true),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f27,f35422])).
% 188.05/24.09 fof(f68448,plain,(
% 188.05/24.09 sum(multiply(a,additive_inverse(b)),c,additive_identity)=true),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f68429])).
% 188.05/24.09 fof(f68639,plain,(
% 188.05/24.09 ifeq2(true,true,additive_identity,add(c,multiply(a,additive_inverse(b))))=add(multiply(a,additive_inverse(b)),c)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f68448,f385])).
% 188.05/24.09 fof(f68810,plain,(
% 188.05/24.09 additive_identity=add(multiply(a,additive_inverse(b)),c)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f23,f68639])).
% 188.05/24.09 fof(f68811,plain,(
% 188.05/24.09 additive_identity=add(c,multiply(a,additive_inverse(b)))),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f284,f68810])).
% 188.05/24.09 fof(f68951,plain,(
% 188.05/24.09 additive_inverse(c)=add(multiply(a,additive_inverse(b)),additive_inverse(additive_identity))),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f68811,f2139])).
% 188.05/24.09 fof(f69174,plain,(
% 188.05/24.09 additive_inverse(c)=add(additive_inverse(additive_identity),multiply(a,additive_inverse(b)))),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f284,f68951])).
% 188.05/24.09 fof(f69175,plain,(
% 188.05/24.09 additive_inverse(c)=add(additive_identity,multiply(a,additive_inverse(b)))),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f103,f69174])).
% 188.05/24.09 fof(f69176,plain,(
% 188.05/24.09 additive_inverse(c)=multiply(a,additive_inverse(b))),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f105,f69175])).
% 188.05/24.09 fof(f69238,plain,(
% 188.05/24.09 product(a,additive_inverse(b),additive_inverse(c))=true),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f69176,f27])).
% 188.05/24.09 fof(f98372,plain,(
% 188.05/24.09 ![X0]: (ifeq(product(add(additive_inverse(additive_inverse(a)),additive_inverse(a)),additive_inverse(b),X0),true,ifeq(true,true,sum(X0,d,d),true),true)=true)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f2176,f7513])).
% 188.05/24.09 fof(f98391,plain,(
% 188.05/24.09 ![X0]: (ifeq(product(additive_inverse(add(a,additive_inverse(a))),additive_inverse(b),X0),true,ifeq(true,true,sum(X0,d,d),true),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f2527,f98372])).
% 188.05/24.09 fof(f98392,plain,(
% 188.05/24.09 ![X0]: (ifeq(product(add(additive_inverse(a),a),additive_inverse(b),X0),true,ifeq(true,true,sum(X0,d,d),true),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f5860,f98391])).
% 188.05/24.09 fof(f98393,plain,(
% 188.05/24.09 ![X0]: (ifeq(product(add(a,additive_inverse(a)),additive_inverse(b),X0),true,ifeq(true,true,sum(X0,d,d),true),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f284,f98392])).
% 188.05/24.09 fof(f98394,plain,(
% 188.05/24.09 ![X0]: (ifeq(product(additive_identity,additive_inverse(b),X0),true,ifeq(true,true,sum(X0,d,d),true),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f248,f98393])).
% 188.05/24.09 fof(f98395,plain,(
% 188.05/24.09 ![X0]: (ifeq(product(additive_identity,additive_inverse(b),X0),true,sum(X0,d,d),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f98394])).
% 188.05/24.09 fof(f100172,plain,(
% 188.05/24.09 ifeq(true,true,sum(multiply(additive_identity,additive_inverse(b)),d,d),true)=true),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f27,f98395])).
% 188.05/24.09 fof(f100186,plain,(
% 188.05/24.09 sum(multiply(additive_identity,additive_inverse(b)),d,d)=true),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f100172])).
% 188.05/24.09 fof(f100395,plain,(
% 188.05/24.09 ifeq2(true,true,d,add(d,multiply(additive_identity,additive_inverse(b))))=add(multiply(additive_identity,additive_inverse(b)),d)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f100186,f385])).
% 188.05/24.09 fof(f100581,plain,(
% 188.05/24.09 d=add(multiply(additive_identity,additive_inverse(b)),d)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f23,f100395])).
% 188.05/24.09 fof(f100582,plain,(
% 188.05/24.09 d=add(d,multiply(additive_identity,additive_inverse(b)))),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f284,f100581])).
% 188.05/24.09 fof(f100750,plain,(
% 188.05/24.09 additive_inverse(multiply(additive_identity,additive_inverse(b)))=add(d,additive_inverse(d))),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f100582,f1861])).
% 188.05/24.09 fof(f100869,plain,(
% 188.05/24.09 additive_inverse(multiply(additive_identity,additive_inverse(b)))=additive_identity),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f248,f100750])).
% 188.05/24.09 fof(f101009,plain,(
% 188.05/24.09 additive_inverse(additive_identity)=multiply(additive_identity,additive_inverse(b))),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f100869,f1676])).
% 188.05/24.09 fof(f101069,plain,(
% 188.05/24.09 additive_identity=multiply(additive_identity,additive_inverse(b))),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f103,f101009])).
% 188.05/24.09 fof(f118026,plain,(
% 188.05/24.09 ![X0]: (ifeq(product(additive_inverse(additive_inverse(a)),additive_inverse(b),X0),true,ifeq(true,true,sum(X0,d,multiply(additive_identity,additive_inverse(b))),true),true)=true)),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f29,f8340])).
% 188.05/24.09 fof(f118070,plain,(
% 188.05/24.09 ![X0]: (ifeq(product(a,additive_inverse(b),X0),true,ifeq(true,true,sum(X0,d,multiply(additive_identity,additive_inverse(b))),true),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f1676,f118026])).
% 188.05/24.09 fof(f118071,plain,(
% 188.05/24.09 ![X0]: (ifeq(product(a,additive_inverse(b),X0),true,sum(X0,d,multiply(additive_identity,additive_inverse(b))),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f118070])).
% 188.05/24.09 fof(f118072,plain,(
% 188.05/24.09 ![X0]: (ifeq(product(a,additive_inverse(b),X0),true,sum(X0,d,additive_identity),true)=true)),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f101069,f118071])).
% 188.05/24.09 fof(f186191,plain,(
% 188.05/24.09 ifeq(true,true,sum(additive_inverse(c),d,additive_identity),true)=true),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f69238,f118072])).
% 188.05/24.09 fof(f186211,plain,(
% 188.05/24.09 sum(additive_inverse(c),d,additive_identity)=true),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f186191])).
% 188.05/24.09 fof(f186229,plain,(
% 188.05/24.09 ifeq(true,true,sum(c,additive_identity,d),true)=true),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f186211,f1335])).
% 188.05/24.09 fof(f186488,plain,(
% 188.05/24.09 sum(c,additive_identity,d)=true),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f24,f186229])).
% 188.05/24.09 fof(f186800,plain,(
% 188.05/24.09 ifeq2(true,true,c,d)=d),
% 188.05/24.09 inference(paramodulation,[status(thm)],[f186488,f94])).
% 188.05/24.09 fof(f187050,plain,(
% 188.05/24.09 c=d),
% 188.05/24.09 inference(forward_demodulation,[status(thm)],[f23,f186800])).
% 188.05/24.09 fof(f187051,plain,(
% 188.05/24.09 $false),
% 166.55/24.31 inference(forward_subsumption_resolution,[status(thm)],[f187050,f44])).
% 166.55/24.31 % SZS output end CNFRefutation for theBenchmark.p
% 11.38/24.53 % Elapsed time: 24.156342 seconds
% 11.38/24.53 % CPU time: 191.042676 seconds
% 11.38/24.53 % Total memory used: 1.367 GB
% 11.38/24.53 % Net memory used: 1.346 GB
%------------------------------------------------------------------------------