%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ALG174+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 : n002.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 0.12s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG174+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36 % Computer : n002.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 21 13:03:18 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.39 fof(f3,axiom,(
% 0.12/0.39 ( 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 ) ),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f5,axiom,(
% 0.12/0.39 ( e0 != e1& e0 != e2& e0 != e3& e0 != e4& e1 != e2& e1 != e3& e1 != e4& e2 != e3& e2 != e4& e3 != e4 ) ),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f6,axiom,(
% 0.12/0.39 ( e0 = op(op(e3,op(e3,e3)),op(e3,op(e3,e3)))& e1 = op(e3,op(e3,op(e3,e3)))& e2 = op(e3,e3)& e4 = op(e3,op(e3,e3)) ) ),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f7,conjecture,(
% 0.12/0.39 ~ ( ( ( op(e0,e0) != e0& op(e0,e1) != e1& op(e0,e2) != e2& op(e0,e3) != e3& op(e0,e4) != e4 )| ( op(e1,e0) != e0& op(e1,e1) != e1& op(e1,e2) != e2& op(e1,e3) != e3& op(e1,e4) != e4 )| ( op(e2,e0) != e0& op(e2,e1) != e1& op(e2,e2) != e2& op(e2,e3) != e3& op(e2,e4) != e4 )| ( op(e3,e0) != e0& op(e3,e1) != e1& op(e3,e2) != e2& op(e3,e3) != e3& op(e3,e4) != e4 )| ( op(e4,e0) != e0& op(e4,e1) != e1& op(e4,e2) != e2& op(e4,e3) != 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 ) ),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f8,negated_conjecture,(
% 0.12/0.39 ~(~ ( ( ( op(e0,e0) != e0& op(e0,e1) != e1& op(e0,e2) != e2& op(e0,e3) != e3& op(e0,e4) != e4 )| ( op(e1,e0) != e0& op(e1,e1) != e1& op(e1,e2) != e2& op(e1,e3) != e3& op(e1,e4) != e4 )| ( op(e2,e0) != e0& op(e2,e1) != e1& op(e2,e2) != e2& op(e2,e3) != e3& op(e2,e4) != e4 )| ( op(e3,e0) != e0& op(e3,e1) != e1& op(e3,e2) != e2& op(e3,e3) != e3& op(e3,e4) != e4 )| ( op(e4,e0) != e0& op(e4,e1) != e1& op(e4,e2) != e2& op(e4,e3) != 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 ) )),
% 0.12/0.39 inference(negated_conjecture,[status(cth)],[f7])).
% 0.12/0.39 fof(f101,plain,(
% 0.12/0.39 op(op(e2,e3),op(e3,e2))=e3),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.12/0.39 fof(f214,plain,(
% 0.12/0.39 ~e1=e3),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.12/0.39 fof(f220,plain,(
% 0.12/0.39 e1=op(e3,op(e3,op(e3,e3)))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f6])).
% 0.12/0.39 fof(f221,plain,(
% 0.12/0.39 e2=op(e3,e3)),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f6])).
% 0.12/0.39 fof(f222,plain,(
% 0.12/0.39 e4=op(e3,op(e3,e3))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f6])).
% 0.12/0.39 fof(f223,definition,(
% 0.12/0.39 sP0_prd<=>(((((((~op(e0,e0)=e0&~op(e0,e1)=e1)&~op(e0,e2)=e2)&~op(e0,e3)=e3)&~op(e0,e4)=e4)|((((~op(e1,e0)=e0&~op(e1,e1)=e1)&~op(e1,e2)=e2)&~op(e1,e3)=e3)&~op(e1,e4)=e4))|((((~op(e2,e0)=e0&~op(e2,e1)=e1)&~op(e2,e2)=e2)&~op(e2,e3)=e3)&~op(e2,e4)=e4))|((((~op(e3,e0)=e0&~op(e3,e1)=e1)&~op(e3,e2)=e2)&~op(e3,e3)=e3)&~op(e3,e4)=e4))),
% 0.12/0.40 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.12/0.40 fof(f224,plain,(
% 0.12/0.40 (((((((((((((((((((((((((sP0_prd|((((~op(e4,e0)=e0&~op(e4,e1)=e1)&~op(e4,e2)=e2)&~op(e4,e3)=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),
% 0.12/0.40 inference(formula_renaming,[status(thm)],[f8,f223])).
% 0.12/0.40 fof(f248,plain,(
% 0.12/0.40 op(op(e3,e3),e3)=e3),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f224])).
% 0.12/0.40 fof(f292,plain,(
% 0.12/0.40 e1=op(e3,op(e3,e2))),
% 0.12/0.40 inference(backward_demodulation,[status(thm)],[f221,f220])).
% 0.12/0.40 fof(f321,plain,(
% 0.12/0.40 op(op(e2,e3),e4)=e3),
% 0.12/0.40 inference(backward_demodulation,[status(thm)],[f329,f101])).
% 0.12/0.40 fof(f329,plain,(
% 0.12/0.40 e4=op(e3,e2)),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f221,f222])).
% 0.12/0.40 fof(f361,plain,(
% 0.12/0.40 op(e2,e3)=e3),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f221,f248])).
% 0.12/0.40 fof(f387,plain,(
% 0.12/0.40 e1=op(e3,e4)),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f329,f292])).
% 0.12/0.40 fof(f446,plain,(
% 0.12/0.40 op(e3,e4)=e3),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f361,f321])).
% 0.12/0.40 fof(f447,plain,(
% 0.12/0.40 e1=e3),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f387,f446])).
% 0.12/0.40 fof(f448,plain,(
% 0.12/0.40 $false),
% 0.12/0.40 inference(forward_subsumption_resolution,[status(thm)],[f447,f214])).
% 0.12/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.43 % Elapsed time: 0.056450 seconds
% 0.12/0.43 % CPU time: 0.189168 seconds
% 0.12/0.43 % Total memory used: 115.973 MB
% 0.12/0.43 % Net memory used: 115.894 MB
%------------------------------------------------------------------------------