%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE133+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/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 12:58:22 PM UTC 2026
% Result : Theorem 0.17s 0.56s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE133+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n011.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sun Sep 20 22:45:11 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 0.17/0.56 % Refutation found
% 0.17/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.56 % SZS output start CNFRefutation for theBenchmark
% 0.17/0.56 fof(f1,axiom,(
% 0.17/0.56 (! [A,B] : addition(A,B) = addition(B,A) )),
% 0.17/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.56 fof(f3,axiom,(
% 0.17/0.56 (! [A] : addition(A,zero) = A )),
% 0.17/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.56 fof(f6,axiom,(
% 0.17/0.56 (! [A] : multiplication(A,one) = A )),
% 0.17/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.56 fof(f10,axiom,(
% 0.17/0.56 (! [A] : multiplication(A,zero) = zero )),
% 0.17/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.56 fof(f13,axiom,(
% 0.17/0.56 (! [X0] : multiplication(antidomain(X0),X0) = zero )),
% 0.17/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.56 fof(f15,axiom,(
% 0.17/0.56 (! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one )),
% 0.17/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.56 fof(f16,axiom,(
% 0.17/0.56 (! [X0] : domain(X0) = antidomain(antidomain(X0)) )),
% 0.17/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.56 fof(f22,axiom,(
% 0.17/0.56 (! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)) )),
% 0.17/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.56 fof(f23,axiom,(
% 0.17/0.56 (! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))) )),
% 0.17/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.56 fof(f29,conjecture,(
% 0.17/0.56 (! [X0] :( ( (! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))))& (! [X2] : forward_diamond(X0,forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2)) ))=> (! [X3] : addition(forward_diamond(X0,domain(X3)),forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3))))) = forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))) )) )),
% 0.17/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.56 fof(f30,negated_conjecture,(
% 0.17/0.56 ~((! [X0] :( ( (! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))))& (! [X2] : forward_diamond(X0,forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2)) ))=> (! [X3] : addition(forward_diamond(X0,domain(X3)),forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3))))) = forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))) )) ))),
% 0.17/0.56 inference(negated_conjecture,[status(cth)],[f29])).
% 0.17/0.56 fof(f31,plain,(
% 0.17/0.56 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 0.17/0.56 inference(cnf_transformation,[status(thm)],[f1])).
% 0.17/0.56 fof(f33,plain,(
% 0.17/0.56 ![X0]: (addition(X0,zero)=X0)),
% 0.17/0.56 inference(cnf_transformation,[status(thm)],[f3])).
% 0.17/0.56 fof(f36,plain,(
% 0.17/0.56 ![X0]: (multiplication(X0,one)=X0)),
% 0.17/0.56 inference(cnf_transformation,[status(thm)],[f6])).
% 0.17/0.56 fof(f40,plain,(
% 0.17/0.56 ![X0]: (multiplication(X0,zero)=zero)),
% 0.17/0.56 inference(cnf_transformation,[status(thm)],[f10])).
% 0.17/0.56 fof(f46,plain,(
% 0.17/0.56 ![X0]: (multiplication(antidomain(X0),X0)=zero)),
% 0.17/0.56 inference(cnf_transformation,[status(thm)],[f13])).
% 0.17/0.56 fof(f48,plain,(
% 0.17/0.56 ![X0]: (addition(antidomain(antidomain(X0)),antidomain(X0))=one)),
% 0.17/0.56 inference(cnf_transformation,[status(thm)],[f15])).
% 0.17/0.56 fof(f49,plain,(
% 0.17/0.56 ![X0]: (domain(X0)=antidomain(antidomain(X0)))),
% 0.17/0.56 inference(cnf_transformation,[status(thm)],[f16])).
% 0.17/0.56 fof(f55,plain,(
% 0.17/0.56 ![X0,X1]: (domain_difference(X0,X1)=multiplication(domain(X0),antidomain(X1)))),
% 0.17/0.56 inference(cnf_transformation,[status(thm)],[f22])).
% 0.17/0.56 fof(f56,plain,(
% 0.17/0.56 ![X0,X1]: (forward_diamond(X0,X1)=domain(multiplication(X0,domain(X1))))),
% 0.17/0.56 inference(cnf_transformation,[status(thm)],[f23])).
% 0.17/0.56 fof(f63,plain,(
% 0.17/0.56 (?[X0]: (((![X1]: addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))))=forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))))&(![X2]: forward_diamond(X0,forward_diamond(X0,domain(X2)))=forward_diamond(X0,domain(X2))))&(?[X3]: ~addition(forward_diamond(X0,domain(X3)),forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))))=forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))))))),
% 0.17/0.56 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 0.17/0.56 fof(f64,plain,(
% 0.17/0.56 (((![X1]: addition(domain(X1),forward_diamond(star(sK0_skl),domain_difference(domain(X1),forward_diamond(sK0_skl,domain(X1)))))=forward_diamond(star(sK0_skl),domain_difference(domain(X1),forward_diamond(sK0_skl,domain(X1)))))&(![X2]: forward_diamond(sK0_skl,forward_diamond(sK0_skl,domain(X2)))=forward_diamond(sK0_skl,domain(X2))))&~addition(forward_diamond(sK0_skl,domain(sK1_skl)),forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),forward_diamond(sK0_skl,domain(sK1_skl)))))=forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),forward_diamond(sK0_skl,domain(sK1_skl)))))),
% 0.17/0.56 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X3,sK1_skl)],[f63])).
% 0.17/0.56 fof(f65,plain,(
% 0.17/0.56 ![X0]: (addition(domain(X0),forward_diamond(star(sK0_skl),domain_difference(domain(X0),forward_diamond(sK0_skl,domain(X0)))))=forward_diamond(star(sK0_skl),domain_difference(domain(X0),forward_diamond(sK0_skl,domain(X0)))))),
% 0.17/0.56 inference(cnf_transformation,[status(thm)],[f64])).
% 0.17/0.56 fof(f66,plain,(
% 0.17/0.56 ![X0]: (forward_diamond(sK0_skl,forward_diamond(sK0_skl,domain(X0)))=forward_diamond(sK0_skl,domain(X0)))),
% 0.17/0.56 inference(cnf_transformation,[status(thm)],[f64])).
% 0.17/0.56 fof(f67,plain,(
% 0.17/0.56 ~addition(forward_diamond(sK0_skl,domain(sK1_skl)),forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),forward_diamond(sK0_skl,domain(sK1_skl)))))=forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),forward_diamond(sK0_skl,domain(sK1_skl))))),
% 0.17/0.56 inference(cnf_transformation,[status(thm)],[f64])).
% 0.17/0.56 fof(f131,plain,(
% 0.17/0.56 ![X0,X1]: (addition(domain(multiplication(X0,domain(X1))),forward_diamond(star(sK0_skl),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sK0_skl,forward_diamond(X0,X1)))))=forward_diamond(star(sK0_skl),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sK0_skl,domain(multiplication(X0,domain(X1)))))))),
% 0.17/0.56 inference(paramodulation,[status(thm)],[f56,f65])).
% 0.17/0.56 fof(f135,plain,(
% 0.17/0.56 ![X0,X1]: (addition(forward_diamond(X0,X1),forward_diamond(star(sK0_skl),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sK0_skl,forward_diamond(X0,X1)))))=forward_diamond(star(sK0_skl),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sK0_skl,domain(multiplication(X0,domain(X1)))))))),
% 0.17/0.56 inference(forward_demodulation,[status(thm)],[f56,f131])).
% 0.17/0.56 fof(f136,plain,(
% 0.17/0.56 ![X0,X1]: (addition(forward_diamond(X0,X1),forward_diamond(star(sK0_skl),domain_difference(forward_diamond(X0,X1),forward_diamond(sK0_skl,forward_diamond(X0,X1)))))=forward_diamond(star(sK0_skl),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sK0_skl,domain(multiplication(X0,domain(X1)))))))),
% 0.17/0.56 inference(forward_demodulation,[status(thm)],[f56,f135])).
% 0.17/0.56 fof(f137,plain,(
% 0.17/0.56 ![X0,X1]: (addition(forward_diamond(X0,X1),forward_diamond(star(sK0_skl),domain_difference(forward_diamond(X0,X1),forward_diamond(sK0_skl,forward_diamond(X0,X1)))))=forward_diamond(star(sK0_skl),domain_difference(forward_diamond(X0,X1),forward_diamond(sK0_skl,domain(multiplication(X0,domain(X1)))))))),
% 0.17/0.56 inference(forward_demodulation,[status(thm)],[f56,f136])).
% 0.17/0.56 fof(f138,plain,(
% 0.17/0.56 ![X0,X1]: (addition(forward_diamond(X0,X1),forward_diamond(star(sK0_skl),domain_difference(forward_diamond(X0,X1),forward_diamond(sK0_skl,forward_diamond(X0,X1)))))=forward_diamond(star(sK0_skl),domain_difference(forward_diamond(X0,X1),forward_diamond(sK0_skl,forward_diamond(X0,X1)))))),
% 0.17/0.56 inference(forward_demodulation,[status(thm)],[f56,f137])).
% 0.17/0.56 fof(f341,plain,(
% 0.17/0.56 ![X0]: (addition(zero,X0)=X0)),
% 0.17/0.56 inference(paramodulation,[status(thm)],[f31,f33])).
% 0.17/0.56 fof(f407,plain,(
% 0.17/0.56 antidomain(one)=zero),
% 0.17/0.56 inference(paramodulation,[status(thm)],[f36,f46])).
% 0.17/0.56 fof(f415,plain,(
% 0.17/0.56 domain(one)=antidomain(zero)),
% 0.17/0.56 inference(paramodulation,[status(thm)],[f407,f49])).
% 0.17/0.56 fof(f416,plain,(
% 0.17/0.56 ![X0]: (multiplication(domain(X0),antidomain(X0))=zero)),
% 0.17/0.56 inference(paramodulation,[status(thm)],[f49,f46])).
% 0.17/0.56 fof(f418,plain,(
% 0.17/0.56 ![X0]: (domain_difference(X0,X0)=zero)),
% 0.17/0.56 inference(forward_demodulation,[status(thm)],[f55,f416])).
% 0.17/0.56 fof(f595,plain,(
% 0.17/0.56 ![X0]: (addition(forward_diamond(sK0_skl,domain(X0)),forward_diamond(star(sK0_skl),domain_difference(forward_diamond(sK0_skl,domain(X0)),forward_diamond(sK0_skl,domain(X0)))))=forward_diamond(star(sK0_skl),domain_difference(forward_diamond(sK0_skl,domain(X0)),forward_diamond(sK0_skl,forward_diamond(sK0_skl,domain(X0))))))),
% 0.17/0.56 inference(paramodulation,[status(thm)],[f66,f138])).
% 0.17/0.56 fof(f640,plain,(
% 0.17/0.56 ![X0]: (addition(forward_diamond(sK0_skl,domain(X0)),forward_diamond(star(sK0_skl),zero))=forward_diamond(star(sK0_skl),domain_difference(forward_diamond(sK0_skl,domain(X0)),forward_diamond(sK0_skl,forward_diamond(sK0_skl,domain(X0))))))),
% 0.17/0.56 inference(forward_demodulation,[status(thm)],[f418,f595])).
% 0.17/0.56 fof(f641,plain,(
% 0.17/0.56 ![X0]: (addition(forward_diamond(sK0_skl,domain(X0)),forward_diamond(star(sK0_skl),zero))=forward_diamond(star(sK0_skl),domain_difference(forward_diamond(sK0_skl,domain(X0)),forward_diamond(sK0_skl,domain(X0)))))),
% 0.17/0.56 inference(forward_demodulation,[status(thm)],[f66,f640])).
% 0.17/0.56 fof(f642,plain,(
% 0.17/0.56 ![X0]: (addition(forward_diamond(sK0_skl,domain(X0)),forward_diamond(star(sK0_skl),zero))=forward_diamond(star(sK0_skl),zero))),
% 0.17/0.56 inference(forward_demodulation,[status(thm)],[f418,f641])).
% 0.17/0.56 fof(f1173,plain,(
% 0.17/0.56 ![X0]: (addition(domain(X0),antidomain(X0))=one)),
% 0.17/0.56 inference(forward_demodulation,[status(thm)],[f49,f48])).
% 0.17/0.56 fof(f1176,plain,(
% 0.17/0.56 addition(antidomain(zero),antidomain(one))=one),
% 0.17/0.56 inference(paramodulation,[status(thm)],[f415,f1173])).
% 0.17/0.56 fof(f1193,plain,(
% 0.17/0.56 addition(antidomain(zero),zero)=one),
% 0.17/0.56 inference(forward_demodulation,[status(thm)],[f407,f1176])).
% 0.17/0.56 fof(f1194,plain,(
% 0.17/0.56 antidomain(zero)=one),
% 0.17/0.56 inference(forward_demodulation,[status(thm)],[f33,f1193])).
% 0.17/0.56 fof(f1299,plain,(
% 0.17/0.56 domain(zero)=antidomain(one)),
% 0.17/0.56 inference(paramodulation,[status(thm)],[f1194,f49])).
% 0.17/0.56 fof(f1303,plain,(
% 0.17/0.56 domain(zero)=zero),
% 0.17/0.56 inference(forward_demodulation,[status(thm)],[f407,f1299])).
% 0.17/0.56 fof(f1382,plain,(
% 0.17/0.56 ![X0]: (forward_diamond(X0,zero)=domain(multiplication(X0,zero)))),
% 0.17/0.56 inference(paramodulation,[status(thm)],[f1303,f56])).
% 0.17/0.56 fof(f1416,plain,(
% 0.17/0.56 ![X0]: (forward_diamond(X0,zero)=domain(zero))),
% 0.17/0.56 inference(forward_demodulation,[status(thm)],[f40,f1382])).
% 0.17/0.56 fof(f1417,plain,(
% 0.17/0.56 ![X0]: (forward_diamond(X0,zero)=zero)),
% 0.17/0.56 inference(forward_demodulation,[status(thm)],[f1303,f1416])).
% 0.17/0.56 fof(f1454,plain,(
% 0.17/0.56 ![X0]: (addition(forward_diamond(sK0_skl,domain(X0)),forward_diamond(star(sK0_skl),zero))=zero)),
% 0.17/0.56 inference(backward_demodulation,[status(thm)],[f1417,f642])).
% 0.17/0.56 fof(f1461,plain,(
% 0.17/0.56 ![X0]: (addition(forward_diamond(sK0_skl,domain(X0)),zero)=zero)),
% 0.17/0.56 inference(forward_demodulation,[status(thm)],[f1417,f1454])).
% 0.17/0.56 fof(f1462,plain,(
% 0.17/0.56 ![X0]: (forward_diamond(sK0_skl,domain(X0))=zero)),
% 0.17/0.56 inference(forward_demodulation,[status(thm)],[f33,f1461])).
% 0.17/0.56 fof(f1572,plain,(
% 0.17/0.56 ~addition(forward_diamond(sK0_skl,domain(sK1_skl)),forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),forward_diamond(sK0_skl,domain(sK1_skl)))))=forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),zero))),
% 0.17/0.56 inference(backward_demodulation,[status(thm)],[f1462,f67])).
% 0.17/0.56 fof(f1585,plain,(
% 0.17/0.56 ~addition(zero,forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),forward_diamond(sK0_skl,domain(sK1_skl)))))=forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),zero))),
% 0.17/0.56 inference(forward_demodulation,[status(thm)],[f1462,f1572])).
% 0.17/0.56 fof(f1586,plain,(
% 0.17/0.56 ~forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),forward_diamond(sK0_skl,domain(sK1_skl))))=forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),zero))),
% 0.17/0.56 inference(forward_demodulation,[status(thm)],[f341,f1585])).
% 0.17/0.56 fof(f1587,plain,(
% 0.17/0.56 ~forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),zero))=forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),zero))),
% 0.17/0.56 inference(forward_demodulation,[status(thm)],[f1462,f1586])).
% 0.22/0.58 fof(f1588,plain,(
% 0.22/0.58 $false),
% 0.22/0.58 inference(trivial_equality_resolution,[status(thm)],[f1587])).
% 0.22/0.58 % SZS output end CNFRefutation for theBenchmark.p
% 0.22/0.59 % Elapsed time: 0.123141 seconds
% 0.22/0.59 % CPU time: 0.732173 seconds
% 0.22/0.59 % Total memory used: 77.962 MB
% 0.22/0.59 % Net memory used: 77.530 MB
%------------------------------------------------------------------------------