%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ALG172+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/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 0.16s 0.57s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG172+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.52 % Computer : n008.cluster.edu
% 0.09/0.52 % Model : x86_64 x86_64
% 0.09/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.52 % Memory : 8046.5625MB
% 0.09/0.52 % OS : Linux 6.8.0-71-generic
% 0.09/0.52 % CPULimit : 300
% 0.09/0.52 % WCLimit : 300
% 0.09/0.52 % DateTime : Mon Sep 21 13:01:25 UTC 2026
% 0.09/0.52 % CPUTime :
% 0.09/0.54 % Drodi V4.1.1
% 0.16/0.57 % Refutation found
% 0.16/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.57 % SZS output start CNFRefutation for theBenchmark
% 0.16/0.57 fof(f3,axiom,(
% 0.16/0.57 ( 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 ) ),
% 0.16/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.57 fof(f4,axiom,(
% 0.16/0.57 ( op(e0,e0) != op(e1,e0)& op(e0,e0) != op(e2,e0)& op(e0,e0) != op(e3,e0)& op(e0,e0) != op(e4,e0)& op(e1,e0) != op(e2,e0)& op(e1,e0) != op(e3,e0)& op(e1,e0) != op(e4,e0)& op(e2,e0) != op(e3,e0)& op(e2,e0) != op(e4,e0)& op(e3,e0) != op(e4,e0)& op(e0,e1) != op(e1,e1)& op(e0,e1) != op(e2,e1)& op(e0,e1) != op(e3,e1)& op(e0,e1) != op(e4,e1)& op(e1,e1) != op(e2,e1)& op(e1,e1) != op(e3,e1)& op(e1,e1) != op(e4,e1)& op(e2,e1) != op(e3,e1)& op(e2,e1) != op(e4,e1)& op(e3,e1) != op(e4,e1)& op(e0,e2) != op(e1,e2)& op(e0,e2) != op(e2,e2)& op(e0,e2) != op(e3,e2)& op(e0,e2) != op(e4,e2)& op(e1,e2) != op(e2,e2)& op(e1,e2) != op(e3,e2)& op(e1,e2) != op(e4,e2)& op(e2,e2) != op(e3,e2)& op(e2,e2) != op(e4,e2)& op(e3,e2) != op(e4,e2)& op(e0,e3) != op(e1,e3)& op(e0,e3) != op(e2,e3)& op(e0,e3) != op(e3,e3)& op(e0,e3) != op(e4,e3)& op(e1,e3) != op(e2,e3)& op(e1,e3) != op(e3,e3)& op(e1,e3) != op(e4,e3)& op(e2,e3) != op(e3,e3)& op(e2,e3) != op(e4,e3)& op(e3,e3) != op(e4,e3)& op(e0,e4) != op(e1,e4)& op(e0,e4) != op(e2,e4)& op(e0,e4) != op(e3,e4)& op(e0,e4) != op(e4,e4)& op(e1,e4) != op(e2,e4)& op(e1,e4) != op(e3,e4)& op(e1,e4) != op(e4,e4)& op(e2,e4) != op(e3,e4)& op(e2,e4) != op(e4,e4)& op(e3,e4) != op(e4,e4)& op(e0,e0) != op(e0,e1)& op(e0,e0) != op(e0,e2)& op(e0,e0) != op(e0,e3)& op(e0,e0) != op(e0,e4)& op(e0,e1) != op(e0,e2)& op(e0,e1) != op(e0,e3)& op(e0,e1) != op(e0,e4)& op(e0,e2) != op(e0,e3)& op(e0,e2) != op(e0,e4)& op(e0,e3) != op(e0,e4)& op(e1,e0) != op(e1,e1)& op(e1,e0) != op(e1,e2)& op(e1,e0) != op(e1,e3)& op(e1,e0) != op(e1,e4)& op(e1,e1) != op(e1,e2)& op(e1,e1) != op(e1,e3)& op(e1,e1) != op(e1,e4)& op(e1,e2) != op(e1,e3)& op(e1,e2) != op(e1,e4)& op(e1,e3) != op(e1,e4)& op(e2,e0) != op(e2,e1)& op(e2,e0) != op(e2,e2)& op(e2,e0) != op(e2,e3)& op(e2,e0) != op(e2,e4)& op(e2,e1) != op(e2,e2)& op(e2,e1) != op(e2,e3)& op(e2,e1) != op(e2,e4)& op(e2,e2) != op(e2,e3)& op(e2,e2) != op(e2,e4)& op(e2,e3) != op(e2,e4)& op(e3,e0) != op(e3,e1)& op(e3,e0) != op(e3,e2)& op(e3,e0) != op(e3,e3)& op(e3,e0) != op(e3,e4)& op(e3,e1) != op(e3,e2)& op(e3,e1) != op(e3,e3)& op(e3,e1) != op(e3,e4)& op(e3,e2) != op(e3,e3)& op(e3,e2) != op(e3,e4)& op(e3,e3) != op(e3,e4)& op(e4,e0) != op(e4,e1)& op(e4,e0) != op(e4,e2)& op(e4,e0) != op(e4,e3)& op(e4,e0) != op(e4,e4)& op(e4,e1) != op(e4,e2)& op(e4,e1) != op(e4,e3)& op(e4,e1) != op(e4,e4)& op(e4,e2) != op(e4,e3)& op(e4,e2) != op(e4,e4)& op(e4,e3) != op(e4,e4) ) ),
% 0.16/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.57 fof(f6,axiom,(
% 0.16/0.57 ( 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))) ) ),
% 0.16/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.57 fof(f7,conjecture,(
% 0.16/0.57 ~ ( ( ( 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(op(e0,e0),e0) = e0& op(op(e0,e1),e1) = e0& op(op(e0,e2),e2) = e0& op(op(e0,e3),e3) = e0& op(op(e0,e4),e4) = e0& op(op(e1,e0),e0) = e1& op(op(e1,e1),e1) = e1& op(op(e1,e2),e2) = e1& op(op(e1,e3),e3) = e1& op(op(e1,e4),e4) = e1& op(op(e2,e0),e0) = e2& op(op(e2,e1),e1) = e2& op(op(e2,e2),e2) = e2& op(op(e2,e3),e3) = e2& op(op(e2,e4),e4) = e2& op(op(e3,e0),e0) = e3& op(op(e3,e1),e1) = e3& op(op(e3,e2),e2) = e3& op(op(e3,e3),e3) = e3& op(op(e3,e4),e4) = e3& op(op(e4,e0),e0) = e4& op(op(e4,e1),e1) = e4& op(op(e4,e2),e2) = e4& op(op(e4,e3),e3) = e4& op(op(e4,e4),e4) = e4 ) ),
% 0.16/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.57 fof(f8,negated_conjecture,(
% 0.16/0.57 ~(~ ( ( ( 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(op(e0,e0),e0) = e0& op(op(e0,e1),e1) = e0& op(op(e0,e2),e2) = e0& op(op(e0,e3),e3) = e0& op(op(e0,e4),e4) = e0& op(op(e1,e0),e0) = e1& op(op(e1,e1),e1) = e1& op(op(e1,e2),e2) = e1& op(op(e1,e3),e3) = e1& op(op(e1,e4),e4) = e1& op(op(e2,e0),e0) = e2& op(op(e2,e1),e1) = e2& op(op(e2,e2),e2) = e2& op(op(e2,e3),e3) = e2& op(op(e2,e4),e4) = e2& op(op(e3,e0),e0) = e3& op(op(e3,e1),e1) = e3& op(op(e3,e2),e2) = e3& op(op(e3,e3),e3) = e3& op(op(e3,e4),e4) = e3& op(op(e4,e0),e0) = e4& op(op(e4,e1),e1) = e4& op(op(e4,e2),e2) = e4& op(op(e4,e3),e3) = e4& op(op(e4,e4),e4) = e4 ) )),
% 0.16/0.57 inference(negated_conjecture,[status(cth)],[f7])).
% 0.16/0.57 fof(f84,plain,(
% 0.16/0.57 op(op(e0,e0),op(e0,e0))=e0),
% 0.16/0.57 inference(cnf_transformation,[status(thm)],[f3])).
% 0.16/0.57 fof(f191,plain,(
% 0.16/0.57 ~op(e3,e0)=op(e3,e3)),
% 0.16/0.57 inference(cnf_transformation,[status(thm)],[f4])).
% 0.16/0.57 fof(f219,plain,(
% 0.16/0.57 e0=op(e4,op(e4,e4))),
% 0.16/0.57 inference(cnf_transformation,[status(thm)],[f6])).
% 0.16/0.57 fof(f222,plain,(
% 0.16/0.57 e3=op(op(e4,op(e4,e4)),op(e4,op(e4,e4)))),
% 0.16/0.57 inference(cnf_transformation,[status(thm)],[f6])).
% 0.16/0.57 fof(f223,definition,(
% 0.16/0.57 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))),
% 0.16/0.57 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.16/0.57 fof(f224,plain,(
% 0.16/0.57 (((((((((((((((((((((((((sP0_prd|((((~op(e0,e4)=e0&~op(e1,e4)=e1)&~op(e2,e4)=e2)&~op(e3,e4)=e3)&~op(e4,e4)=e4))&op(op(e0,e0),e0)=e0)&op(op(e0,e1),e1)=e0)&op(op(e0,e2),e2)=e0)&op(op(e0,e3),e3)=e0)&op(op(e0,e4),e4)=e0)&op(op(e1,e0),e0)=e1)&op(op(e1,e1),e1)=e1)&op(op(e1,e2),e2)=e1)&op(op(e1,e3),e3)=e1)&op(op(e1,e4),e4)=e1)&op(op(e2,e0),e0)=e2)&op(op(e2,e1),e1)=e2)&op(op(e2,e2),e2)=e2)&op(op(e2,e3),e3)=e2)&op(op(e2,e4),e4)=e2)&op(op(e3,e0),e0)=e3)&op(op(e3,e1),e1)=e3)&op(op(e3,e2),e2)=e3)&op(op(e3,e3),e3)=e3)&op(op(e3,e4),e4)=e3)&op(op(e4,e0),e0)=e4)&op(op(e4,e1),e1)=e4)&op(op(e4,e2),e2)=e4)&op(op(e4,e3),e3)=e4)&op(op(e4,e4),e4)=e4),
% 0.16/0.57 inference(formula_renaming,[status(thm)],[f8,f223])).
% 0.16/0.57 fof(f230,plain,(
% 0.16/0.57 op(op(e0,e0),e0)=e0),
% 0.16/0.57 inference(cnf_transformation,[status(thm)],[f224])).
% 0.16/0.57 fof(f336,plain,(
% 0.16/0.57 e3=op(e0,op(e4,op(e4,e4)))),
% 0.16/0.57 inference(forward_demodulation,[status(thm)],[f219,f222])).
% 0.16/0.57 fof(f344,plain,(
% 0.16/0.57 op(op(e0,e0),e3)=e0),
% 0.16/0.57 inference(backward_demodulation,[status(thm)],[f351,f84])).
% 0.16/0.57 fof(f351,plain,(
% 0.16/0.57 e3=op(e0,e0)),
% 0.16/0.57 inference(forward_demodulation,[status(thm)],[f219,f336])).
% 0.16/0.57 fof(f354,plain,(
% 0.16/0.57 ~e0=op(e3,e3)),
% 0.16/0.57 inference(backward_demodulation,[status(thm)],[f368,f191])).
% 0.16/0.57 fof(f368,plain,(
% 0.16/0.57 op(e3,e0)=e0),
% 0.16/0.57 inference(forward_demodulation,[status(thm)],[f351,f230])).
% 0.16/0.57 fof(f508,plain,(
% 0.16/0.57 op(e3,e3)=e0),
% 0.16/0.57 inference(forward_demodulation,[status(thm)],[f351,f344])).
% 0.16/0.57 fof(f519,plain,(
% 0.16/0.57 ~e0=e0),
% 0.16/0.57 inference(forward_demodulation,[status(thm)],[f508,f354])).
% 0.16/0.57 fof(f520,plain,(
% 0.16/0.57 $false),
% 0.16/0.57 inference(trivial_equality_resolution,[status(thm)],[f519])).
% 0.16/0.57 % SZS output end CNFRefutation for theBenchmark.p
% 0.16/0.60 % Elapsed time: 0.073032 seconds
% 0.16/0.60 % CPU time: 0.207921 seconds
% 0.16/0.60 % Total memory used: 116.053 MB
% 0.16/0.60 % Net memory used: 115.984 MB
%------------------------------------------------------------------------------