%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : BOO004-10 : 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 : n013.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 12:06:42 PM UTC 2026
% Result : Unsatisfiable 1.20s 0.75s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO004-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 13:45:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 1.20/0.75 % Refutation found
% 1.20/0.75 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.20/0.75 % SZS output start CNFRefutation for theBenchmark
% 1.20/0.75 fof(f1,axiom,(
% 1.20/0.75 (![A,B,C]: (ifeq2(A,A,B,C) = B ))),
% 1.20/0.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.75 fof(f2,axiom,(
% 1.20/0.75 (![A,B,C]: (ifeq(A,A,B,C) = B ))),
% 1.20/0.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.75 fof(f3,axiom,(
% 1.20/0.75 (![X,Y]: (sum(X,Y,add(X,Y)) = true ))),
% 1.20/0.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.75 fof(f4,axiom,(
% 1.20/0.75 (![X,Y]: (product(X,Y,multiply(X,Y)) = true ))),
% 1.20/0.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.75 fof(f5,axiom,(
% 1.20/0.75 (![X,Y,Z]: (ifeq(sum(X,Y,Z),true,sum(Y,X,Z),true) = true ))),
% 1.20/0.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.75 fof(f6,axiom,(
% 1.20/0.75 (![X,Y,Z]: (ifeq(product(X,Y,Z),true,product(Y,X,Z),true) = true ))),
% 1.20/0.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.75 fof(f8,axiom,(
% 1.20/0.75 (![X]: (sum(X,additive_identity,X) = true ))),
% 1.20/0.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.75 fof(f10,axiom,(
% 1.20/0.75 (![X]: (product(X,multiplicative_identity,X) = true ))),
% 1.20/0.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.75 fof(f16,axiom,(
% 1.20/0.75 (![V1,V2,V4,Y,Z,V3,X]: (ifeq(product(V1,V2,V4),true,ifeq(product(Y,Z,V3),true,ifeq(sum(X,Z,V2),true,ifeq(sum(X,Y,V1),true,sum(X,V3,V4),true),true),true),true) = true ))),
% 1.20/0.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.75 fof(f20,axiom,(
% 1.20/0.75 (![X]: (sum(X,inverse(X),multiplicative_identity) = true ))),
% 1.20/0.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.75 fof(f21,axiom,(
% 1.20/0.75 (![X]: (product(inverse(X),X,additive_identity) = true ))),
% 1.20/0.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.75 fof(f23,axiom,(
% 1.20/0.75 (![X,Y,V,U]: (ifeq2(sum(X,Y,V),true,ifeq2(sum(X,Y,U),true,U,V),V) = V ))),
% 1.20/0.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.75 fof(f24,axiom,(
% 1.20/0.75 (![X,Y,V,U]: (ifeq2(product(X,Y,V),true,ifeq2(product(X,Y,U),true,U,V),V) = V ))),
% 1.20/0.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.75 fof(f25,negated_conjecture,(
% 1.20/0.75 sum(x,x,x) != true ),
% 1.20/0.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.75 fof(f26,plain,(
% 1.20/0.75 ![X0,X1,X2]: (ifeq2(X0,X0,X1,X2)=X1)),
% 1.20/0.75 inference(cnf_transformation,[status(thm)],[f1])).
% 1.20/0.75 fof(f27,plain,(
% 1.20/0.75 ![X0,X1,X2]: (ifeq(X0,X0,X1,X2)=X1)),
% 1.20/0.75 inference(cnf_transformation,[status(thm)],[f2])).
% 1.20/0.75 fof(f28,plain,(
% 1.20/0.75 ![X0,X1]: (sum(X0,X1,add(X0,X1))=true)),
% 1.20/0.75 inference(cnf_transformation,[status(thm)],[f3])).
% 1.20/0.75 fof(f29,plain,(
% 1.20/0.75 ![X0,X1]: (product(X0,X1,multiply(X0,X1))=true)),
% 1.20/0.75 inference(cnf_transformation,[status(thm)],[f4])).
% 1.20/0.75 fof(f30,plain,(
% 1.20/0.75 ![X0,X1,X2]: (ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true)=true)),
% 1.20/0.75 inference(cnf_transformation,[status(thm)],[f5])).
% 1.20/0.75 fof(f31,plain,(
% 1.20/0.75 ![X0,X1,X2]: (ifeq(product(X0,X1,X2),true,product(X1,X0,X2),true)=true)),
% 1.20/0.75 inference(cnf_transformation,[status(thm)],[f6])).
% 1.20/0.75 fof(f33,plain,(
% 1.20/0.75 ![X0]: (sum(X0,additive_identity,X0)=true)),
% 1.20/0.75 inference(cnf_transformation,[status(thm)],[f8])).
% 1.20/0.75 fof(f35,plain,(
% 1.20/0.75 ![X0]: (product(X0,multiplicative_identity,X0)=true)),
% 1.20/0.75 inference(cnf_transformation,[status(thm)],[f10])).
% 1.20/0.75 fof(f41,plain,(
% 1.20/0.75 ![X0,X1,X2,X3,X4,X5,X6]: (ifeq(product(X0,X1,X2),true,ifeq(product(X3,X4,X5),true,ifeq(sum(X6,X4,X1),true,ifeq(sum(X6,X3,X0),true,sum(X6,X5,X2),true),true),true),true)=true)),
% 1.20/0.75 inference(cnf_transformation,[status(thm)],[f16])).
% 1.20/0.75 fof(f45,plain,(
% 1.20/0.75 ![X0]: (sum(X0,inverse(X0),multiplicative_identity)=true)),
% 1.20/0.75 inference(cnf_transformation,[status(thm)],[f20])).
% 1.20/0.75 fof(f46,plain,(
% 1.20/0.75 ![X0]: (product(inverse(X0),X0,additive_identity)=true)),
% 1.20/0.75 inference(cnf_transformation,[status(thm)],[f21])).
% 1.20/0.75 fof(f48,plain,(
% 1.20/0.75 ![X0,X1,X2,X3]: (ifeq2(sum(X0,X1,X2),true,ifeq2(sum(X0,X1,X3),true,X3,X2),X2)=X2)),
% 1.20/0.75 inference(cnf_transformation,[status(thm)],[f23])).
% 1.20/0.75 fof(f49,plain,(
% 1.20/0.75 ![X0,X1,X2,X3]: (ifeq2(product(X0,X1,X2),true,ifeq2(product(X0,X1,X3),true,X3,X2),X2)=X2)),
% 1.20/0.75 inference(cnf_transformation,[status(thm)],[f24])).
% 1.20/0.75 fof(f50,plain,(
% 1.20/0.75 ~sum(x,x,x)=true),
% 1.20/0.75 inference(cnf_transformation,[status(thm)],[f25])).
% 1.20/0.75 fof(f64,plain,(
% 1.20/0.75 ![X0,X1]: (ifeq(true,true,sum(X0,X1,add(X1,X0)),true)=true)),
% 1.20/0.75 inference(paramodulation,[status(thm)],[f28,f30])).
% 1.20/0.75 fof(f66,plain,(
% 1.20/0.75 ![X0,X1]: (sum(X0,X1,add(X1,X0))=true)),
% 1.20/0.75 inference(forward_demodulation,[status(thm)],[f27,f64])).
% 1.20/0.75 fof(f90,plain,(
% 1.20/0.75 ![X0,X1]: (ifeq2(sum(X0,additive_identity,X1),true,ifeq2(true,true,X0,X1),X1)=X1)),
% 1.20/0.75 inference(paramodulation,[status(thm)],[f33,f48])).
% 1.20/0.75 fof(f91,plain,(
% 1.20/0.75 ![X0,X1,X2]: (ifeq2(sum(X0,X1,X2),true,ifeq2(true,true,add(X1,X0),X2),X2)=X2)),
% 1.20/0.75 inference(paramodulation,[status(thm)],[f66,f48])).
% 1.20/0.75 fof(f102,plain,(
% 1.20/0.75 ![X0,X1]: (ifeq2(sum(X0,additive_identity,X1),true,X0,X1)=X1)),
% 1.20/0.75 inference(forward_demodulation,[status(thm)],[f26,f90])).
% 1.20/0.75 fof(f103,plain,(
% 1.20/0.75 ![X0,X1,X2]: (ifeq2(sum(X0,X1,X2),true,add(X1,X0),X2)=X2)),
% 1.20/0.75 inference(forward_demodulation,[status(thm)],[f26,f91])).
% 1.20/0.75 fof(f107,plain,(
% 1.20/0.75 ![X0]: (ifeq2(true,true,add(inverse(X0),X0),multiplicative_identity)=multiplicative_identity)),
% 1.20/0.75 inference(paramodulation,[status(thm)],[f45,f103])).
% 1.20/0.75 fof(f114,plain,(
% 1.20/0.75 ![X0]: (add(inverse(X0),X0)=multiplicative_identity)),
% 1.20/0.75 inference(forward_demodulation,[status(thm)],[f26,f107])).
% 1.20/0.75 fof(f331,plain,(
% 1.20/0.75 ![X0,X1]: (ifeq(true,true,product(X0,X1,multiply(X1,X0)),true)=true)),
% 1.20/0.75 inference(paramodulation,[status(thm)],[f29,f31])).
% 1.20/0.75 fof(f341,plain,(
% 1.20/0.75 ![X0,X1]: (product(X0,X1,multiply(X1,X0))=true)),
% 1.20/0.75 inference(forward_demodulation,[status(thm)],[f27,f331])).
% 1.20/0.75 fof(f421,plain,(
% 1.20/0.75 ![X0,X1]: (ifeq2(product(inverse(X0),X0,X1),true,ifeq2(true,true,additive_identity,X1),X1)=X1)),
% 1.20/0.75 inference(paramodulation,[status(thm)],[f46,f49])).
% 1.20/0.75 fof(f433,plain,(
% 1.20/0.75 ![X0,X1]: (ifeq2(product(inverse(X0),X0,X1),true,additive_identity,X1)=X1)),
% 1.20/0.75 inference(forward_demodulation,[status(thm)],[f26,f421])).
% 1.20/0.75 fof(f1071,plain,(
% 1.20/0.75 ![X0]: (ifeq2(true,true,additive_identity,multiply(inverse(X0),X0))=multiply(inverse(X0),X0))),
% 1.20/0.75 inference(paramodulation,[status(thm)],[f29,f433])).
% 1.20/0.75 fof(f1077,plain,(
% 1.20/0.75 ![X0]: (additive_identity=multiply(inverse(X0),X0))),
% 1.20/0.75 inference(forward_demodulation,[status(thm)],[f26,f1071])).
% 1.20/0.75 fof(f1405,plain,(
% 1.20/0.75 ![X0,X1,X2,X3,X4,X5]: (ifeq(product(X0,add(X1,X2),X3),true,ifeq(product(X4,X1,X5),true,ifeq(true,true,ifeq(sum(X2,X4,X0),true,sum(X2,X5,X3),true),true),true),true)=true)),
% 1.20/0.75 inference(paramodulation,[status(thm)],[f66,f41])).
% 1.20/0.75 fof(f1436,plain,(
% 1.20/0.75 ![X0,X1,X2,X3,X4,X5]: (ifeq(product(X0,add(X1,X2),X3),true,ifeq(product(X4,X1,X5),true,ifeq(sum(X2,X4,X0),true,sum(X2,X5,X3),true),true),true)=true)),
% 1.20/0.75 inference(forward_demodulation,[status(thm)],[f27,f1405])).
% 1.20/0.75 fof(f1458,plain,(
% 1.20/0.75 ![X0,X1,X2,X3,X4]: (ifeq(product(X0,add(X1,X2),X3),true,ifeq(true,true,ifeq(sum(X2,X4,X0),true,sum(X2,multiply(X1,X4),X3),true),true),true)=true)),
% 1.20/0.75 inference(paramodulation,[status(thm)],[f341,f1436])).
% 1.20/0.75 fof(f1482,plain,(
% 1.20/0.75 ![X0,X1,X2,X3,X4]: (ifeq(product(X0,add(X1,X2),X3),true,ifeq(sum(X2,X4,X0),true,sum(X2,multiply(X1,X4),X3),true),true)=true)),
% 1.20/0.75 inference(forward_demodulation,[status(thm)],[f27,f1458])).
% 1.20/0.75 fof(f1668,plain,(
% 1.20/0.75 ![X0,X1,X2,X3]: (ifeq(product(X0,multiplicative_identity,X1),true,ifeq(sum(X2,X3,X0),true,sum(X2,multiply(inverse(X2),X3),X1),true),true)=true)),
% 1.20/0.75 inference(paramodulation,[status(thm)],[f114,f1482])).
% 1.20/0.75 fof(f1739,plain,(
% 1.20/0.75 ![X0,X1,X2]: (ifeq(true,true,ifeq(sum(X0,X1,X2),true,sum(X0,multiply(inverse(X0),X1),X2),true),true)=true)),
% 1.20/0.75 inference(paramodulation,[status(thm)],[f35,f1668])).
% 1.20/0.75 fof(f1766,plain,(
% 1.20/0.75 ![X0,X1,X2]: (ifeq(sum(X0,X1,X2),true,sum(X0,multiply(inverse(X0),X1),X2),true)=true)),
% 1.20/0.75 inference(forward_demodulation,[status(thm)],[f27,f1739])).
% 1.20/0.75 fof(f1791,plain,(
% 1.20/0.75 ![X0,X1]: (ifeq(sum(X0,X0,X1),true,sum(X0,additive_identity,X1),true)=true)),
% 1.20/0.75 inference(paramodulation,[status(thm)],[f1077,f1766])).
% 1.20/0.75 fof(f2101,plain,(
% 1.20/0.75 ![X0]: (ifeq(true,true,sum(X0,additive_identity,add(X0,X0)),true)=true)),
% 1.20/0.75 inference(paramodulation,[status(thm)],[f66,f1791])).
% 1.20/0.75 fof(f2121,plain,(
% 1.20/0.75 ![X0]: (sum(X0,additive_identity,add(X0,X0))=true)),
% 1.20/0.75 inference(forward_demodulation,[status(thm)],[f27,f2101])).
% 1.20/0.75 fof(f2149,plain,(
% 1.20/0.75 ![X0]: (ifeq2(true,true,X0,add(X0,X0))=add(X0,X0))),
% 1.20/0.75 inference(paramodulation,[status(thm)],[f2121,f102])).
% 1.20/0.75 fof(f2211,plain,(
% 1.20/0.75 ![X0]: (X0=add(X0,X0))),
% 1.20/0.77 inference(forward_demodulation,[status(thm)],[f26,f2149])).
% 1.20/0.77 fof(f2307,plain,(
% 1.20/0.77 ![X0]: (sum(X0,X0,X0)=true)),
% 1.20/0.77 inference(paramodulation,[status(thm)],[f2211,f66])).
% 1.20/0.77 fof(f2313,plain,(
% 1.20/0.77 ~true=true),
% 1.20/0.77 inference(backward_demodulation,[status(thm)],[f2307,f50])).
% 1.20/0.77 fof(f2315,plain,(
% 1.20/0.77 $false),
% 1.20/0.77 inference(trivial_equality_resolution,[status(thm)],[f2313])).
% 1.20/0.77 % SZS output end CNFRefutation for theBenchmark.p
% 2.01/0.78 % Elapsed time: 0.407048 seconds
% 2.01/0.78 % CPU time: 3.052485 seconds
% 2.01/0.78 % Total memory used: 109.572 MB
% 2.01/0.78 % Net memory used: 108.598 MB
%------------------------------------------------------------------------------