%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ALG171+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 11:49:45 AM UTC 2026
% Result : Theorem 0.14s 15.43s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG171+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/15.39 % Computer : n008.cluster.edu
% 0.11/15.39 % Model : x86_64 x86_64
% 0.11/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.39 % Memory : 8046.5625MB
% 0.11/15.39 % OS : Linux 6.8.0-71-generic
% 0.11/15.39 % CPULimit : 300
% 0.11/15.39 % WCLimit : 300
% 0.11/15.39 % DateTime : Mon Sep 21 13:01:41 UTC 2026
% 0.11/15.39 % CPUTime :
% 0.14/15.41 % Drodi V4.1.1
% 0.14/15.43 % Refutation found
% 0.14/15.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/15.43 % SZS output start CNFRefutation for theBenchmark
% 0.14/15.43 fof(f3,axiom,(
% 0.14/15.43 ( op(op(e0,e0),op(e0,e0)) = e0& op(op(e1,e0),op(e0,e1)) = e0& op(op(e2,e0),op(e0,e2)) = e0& op(op(e3,e0),op(e0,e3)) = e0& op(op(e4,e0),op(e0,e4)) = e0& op(op(e0,e1),op(e1,e0)) = e1& op(op(e1,e1),op(e1,e1)) = e1& op(op(e2,e1),op(e1,e2)) = e1& op(op(e3,e1),op(e1,e3)) = e1& op(op(e4,e1),op(e1,e4)) = e1& op(op(e0,e2),op(e2,e0)) = e2& op(op(e1,e2),op(e2,e1)) = e2& op(op(e2,e2),op(e2,e2)) = e2& op(op(e3,e2),op(e2,e3)) = e2& op(op(e4,e2),op(e2,e4)) = e2& op(op(e0,e3),op(e3,e0)) = e3& op(op(e1,e3),op(e3,e1)) = e3& op(op(e2,e3),op(e3,e2)) = e3& op(op(e3,e3),op(e3,e3)) = e3& op(op(e4,e3),op(e3,e4)) = e3& op(op(e0,e4),op(e4,e0)) = e4& op(op(e1,e4),op(e4,e1)) = e4& op(op(e2,e4),op(e4,e2)) = e4& op(op(e3,e4),op(e4,e3)) = e4& op(op(e4,e4),op(e4,e4)) = e4 ) ),
% 0.14/15.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/15.43 fof(f5,axiom,(
% 0.14/15.43 ( e0 != e1& e0 != e2& e0 != e3& e0 != e4& e1 != e2& e1 != e3& e1 != e4& e2 != e3& e2 != e4& e3 != e4 ) ),
% 0.14/15.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/15.43 fof(f6,axiom,(
% 0.14/15.43 ( e0 = op(e4,op(e4,e4))& e1 = op(e4,e4)& e2 = op(op(e4,op(e4,e4)),op(e4,e4))& e3 = op(op(e4,op(e4,e4)),op(e4,op(e4,e4))) ) ),
% 0.14/15.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/15.43 fof(f7,conjecture,(
% 0.14/15.43 ~ ( ( ( op(e0,e0) != e0& op(e1,e0) != e1& op(e2,e0) != e2& op(e3,e0) != e3& op(e4,e0) != e4 )| ( op(e0,e1) != e0& op(e1,e1) != e1& op(e2,e1) != e2& op(e3,e1) != e3& op(e4,e1) != e4 )| ( op(e0,e2) != e0& op(e1,e2) != e1& op(e2,e2) != e2& op(e3,e2) != e3& op(e4,e2) != e4 )| ( op(e0,e3) != e0& op(e1,e3) != e1& op(e2,e3) != e2& op(e3,e3) != e3& op(e4,e3) != e4 )| ( op(e0,e4) != e0& op(e1,e4) != e1& op(e2,e4) != e2& op(e3,e4) != e3& op(e4,e4) != e4 ) )& op(e0,op(e0,e0)) = e0& op(e0,op(e0,e1)) = e1& op(e0,op(e0,e2)) = e2& op(e0,op(e0,e3)) = e3& op(e0,op(e0,e4)) = e4& op(e1,op(e1,e0)) = e0& op(e1,op(e1,e1)) = e1& op(e1,op(e1,e2)) = e2& op(e1,op(e1,e3)) = e3& op(e1,op(e1,e4)) = e4& op(e2,op(e2,e0)) = e0& op(e2,op(e2,e1)) = e1& op(e2,op(e2,e2)) = e2& op(e2,op(e2,e3)) = e3& op(e2,op(e2,e4)) = e4& op(e3,op(e3,e0)) = e0& op(e3,op(e3,e1)) = e1& op(e3,op(e3,e2)) = e2& op(e3,op(e3,e3)) = e3& op(e3,op(e3,e4)) = e4& op(e4,op(e4,e0)) = e0& op(e4,op(e4,e1)) = e1& op(e4,op(e4,e2)) = e2& op(e4,op(e4,e3)) = e3& op(e4,op(e4,e4)) = e4 ) ),
% 0.14/15.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/15.43 fof(f8,negated_conjecture,(
% 0.14/15.43 ~(~ ( ( ( op(e0,e0) != e0& op(e1,e0) != e1& op(e2,e0) != e2& op(e3,e0) != e3& op(e4,e0) != e4 )| ( op(e0,e1) != e0& op(e1,e1) != e1& op(e2,e1) != e2& op(e3,e1) != e3& op(e4,e1) != e4 )| ( op(e0,e2) != e0& op(e1,e2) != e1& op(e2,e2) != e2& op(e3,e2) != e3& op(e4,e2) != e4 )| ( op(e0,e3) != e0& op(e1,e3) != e1& op(e2,e3) != e2& op(e3,e3) != e3& op(e4,e3) != e4 )| ( op(e0,e4) != e0& op(e1,e4) != e1& op(e2,e4) != e2& op(e3,e4) != e3& op(e4,e4) != e4 ) )& op(e0,op(e0,e0)) = e0& op(e0,op(e0,e1)) = e1& op(e0,op(e0,e2)) = e2& op(e0,op(e0,e3)) = e3& op(e0,op(e0,e4)) = e4& op(e1,op(e1,e0)) = e0& op(e1,op(e1,e1)) = e1& op(e1,op(e1,e2)) = e2& op(e1,op(e1,e3)) = e3& op(e1,op(e1,e4)) = e4& op(e2,op(e2,e0)) = e0& op(e2,op(e2,e1)) = e1& op(e2,op(e2,e2)) = e2& op(e2,op(e2,e3)) = e3& op(e2,op(e2,e4)) = e4& op(e3,op(e3,e0)) = e0& op(e3,op(e3,e1)) = e1& op(e3,op(e3,e2)) = e2& op(e3,op(e3,e3)) = e3& op(e3,op(e3,e4)) = e4& op(e4,op(e4,e0)) = e0& op(e4,op(e4,e1)) = e1& op(e4,op(e4,e2)) = e2& op(e4,op(e4,e3)) = e3& op(e4,op(e4,e4)) = e4 ) )),
% 0.14/15.43 inference(negated_conjecture,[status(cth)],[f7])).
% 0.14/15.43 fof(f105,plain,(
% 0.14/15.43 op(op(e1,e4),op(e4,e1))=e4),
% 0.14/15.43 inference(cnf_transformation,[status(thm)],[f3])).
% 0.14/15.43 fof(f108,plain,(
% 0.14/15.43 op(op(e4,e4),op(e4,e4))=e4),
% 0.14/15.43 inference(cnf_transformation,[status(thm)],[f3])).
% 0.14/15.43 fof(f215,plain,(
% 0.14/15.43 ~e1=e4),
% 0.14/15.43 inference(cnf_transformation,[status(thm)],[f5])).
% 0.14/15.43 fof(f220,plain,(
% 0.14/15.43 e1=op(e4,e4)),
% 0.14/15.43 inference(cnf_transformation,[status(thm)],[f6])).
% 0.14/15.43 fof(f223,definition,(
% 0.14/15.43 sP0_prd<=>(((((((~op(e0,e0)=e0&~op(e1,e0)=e1)&~op(e2,e0)=e2)&~op(e3,e0)=e3)&~op(e4,e0)=e4)|((((~op(e0,e1)=e0&~op(e1,e1)=e1)&~op(e2,e1)=e2)&~op(e3,e1)=e3)&~op(e4,e1)=e4))|((((~op(e0,e2)=e0&~op(e1,e2)=e1)&~op(e2,e2)=e2)&~op(e3,e2)=e3)&~op(e4,e2)=e4))|((((~op(e0,e3)=e0&~op(e1,e3)=e1)&~op(e2,e3)=e2)&~op(e3,e3)=e3)&~op(e4,e3)=e4))),
% 0.14/15.43 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.14/15.43 fof(f224,plain,(
% 0.14/15.43 (((((((((((((((((((((((((sP0_prd|((((~op(e0,e4)=e0&~op(e1,e4)=e1)&~op(e2,e4)=e2)&~op(e3,e4)=e3)&~op(e4,e4)=e4))&op(e0,op(e0,e0))=e0)&op(e0,op(e0,e1))=e1)&op(e0,op(e0,e2))=e2)&op(e0,op(e0,e3))=e3)&op(e0,op(e0,e4))=e4)&op(e1,op(e1,e0))=e0)&op(e1,op(e1,e1))=e1)&op(e1,op(e1,e2))=e2)&op(e1,op(e1,e3))=e3)&op(e1,op(e1,e4))=e4)&op(e2,op(e2,e0))=e0)&op(e2,op(e2,e1))=e1)&op(e2,op(e2,e2))=e2)&op(e2,op(e2,e3))=e3)&op(e2,op(e2,e4))=e4)&op(e3,op(e3,e0))=e0)&op(e3,op(e3,e1))=e1)&op(e3,op(e3,e2))=e2)&op(e3,op(e3,e3))=e3)&op(e3,op(e3,e4))=e4)&op(e4,op(e4,e0))=e0)&op(e4,op(e4,e1))=e1)&op(e4,op(e4,e2))=e2)&op(e4,op(e4,e3))=e3)&op(e4,op(e4,e4))=e4),
% 0.14/15.43 inference(formula_renaming,[status(thm)],[f8,f223])).
% 0.14/15.43 fof(f236,plain,(
% 0.14/15.43 op(e1,op(e1,e1))=e1),
% 0.14/15.43 inference(cnf_transformation,[status(thm)],[f224])).
% 0.14/15.43 fof(f254,plain,(
% 0.14/15.43 op(e4,op(e4,e4))=e4),
% 0.14/15.43 inference(cnf_transformation,[status(thm)],[f224])).
% 0.14/15.43 fof(f786,plain,(
% 0.14/15.43 op(e4,e1)=e4),
% 0.14/15.43 inference(backward_demodulation,[status(thm)],[f220,f254])).
% 0.14/15.43 fof(f787,plain,(
% 0.14/15.43 op(op(e1,e4),e4)=e4),
% 0.14/15.43 inference(backward_demodulation,[status(thm)],[f786,f105])).
% 0.14/15.43 fof(f790,plain,(
% 0.14/15.43 op(e1,op(e4,e4))=e4),
% 0.14/15.43 inference(forward_demodulation,[status(thm)],[f220,f108])).
% 0.14/15.43 fof(f791,plain,(
% 0.14/15.43 op(e1,e4)=e1),
% 0.14/15.43 inference(backward_demodulation,[status(thm)],[f793,f236])).
% 0.14/15.43 fof(f793,plain,(
% 0.14/15.43 op(e1,e1)=e4),
% 0.14/15.43 inference(forward_demodulation,[status(thm)],[f220,f790])).
% 0.14/15.43 fof(f796,plain,(
% 0.14/15.43 op(e1,e4)=e4),
% 0.14/15.43 inference(backward_demodulation,[status(thm)],[f791,f787])).
% 0.14/15.43 fof(f798,plain,(
% 0.14/15.43 e1=e4),
% 0.14/15.43 inference(forward_demodulation,[status(thm)],[f791,f796])).
% 0.14/15.43 fof(f799,plain,(
% 0.14/15.43 $false),
% 0.14/15.43 inference(forward_subsumption_resolution,[status(thm)],[f798,f215])).
% 0.14/15.43 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/15.46 % Elapsed time: 0.056558 seconds
% 0.14/15.46 % CPU time: 0.177864 seconds
% 0.14/15.46 % Total memory used: 115.566 MB
% 0.14/15.46 % Net memory used: 115.499 MB
%------------------------------------------------------------------------------