%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP685-11 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 12:35:08 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 51 ( 51 unt; 5 def)
% Number of atoms : 51 ( 50 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 57 ( 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] : ld(A,mult(A,A)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A] : rd(mult(A,A),A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : mult(A,ld(A,B)) = ld(A,mult(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : mult(rd(A,B),B) = rd(mult(A,B),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C,D] : rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] : ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
rd(mult(x6,rd(x7,x8)),rd(x7,x8)) != rd(mult(x6,x8),x8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0] : ld(X0,mult(X0,X0)) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0] : rd(mult(X0,X0),X0) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = ld(X0,mult(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f15,plain,
! [X0,X1] : ld(X0,mult(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f16,plain,
rd(mult(x6,rd(x7,x8)),rd(x7,x8)) != rd(mult(x6,x8),x8),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f17,definition,
sF2_fnc = rd(x7,x8),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f18,definition,
sF1_fnc = mult(x6,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f19,definition,
sF0_fnc = rd(sF1_fnc,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f20,definition,
sF4_fnc = mult(x6,x8),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f21,definition,
sF3_fnc = rd(sF4_fnc,x8),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f22,plain,
sF0_fnc != sF3_fnc,
inference(definition_folding,[],[f16,f21,f20,f19,f18,f17]) ).
fof(f49,plain,
! [X0,X1,X2] : rd(mult(mult(X0,X1),X2),rd(mult(X2,X2),X2)) = mult(X0,rd(mult(X1,X2),X2)),
inference(paramodulation,[status(thm)],[f10,f14]) ).
fof(f51,plain,
! [X0,X1] : rd(mult(mult(X0,X1),sF0_fnc),rd(sF1_fnc,sF2_fnc)) = mult(X0,rd(mult(X1,sF2_fnc),sF2_fnc)),
inference(paramodulation,[status(thm)],[f19,f14]) ).
fof(f52,plain,
! [X0,X1] : rd(mult(mult(X0,X1),sF2_fnc),rd(x7,x8)) = mult(X0,rd(mult(X1,x8),x8)),
inference(paramodulation,[status(thm)],[f17,f14]) ).
fof(f80,plain,
! [X0,X1,X2] : rd(mult(mult(X0,X1),X2),X2) = mult(X0,rd(mult(X1,X2),X2)),
inference(forward_demodulation,[status(thm)],[f10,f49]) ).
fof(f82,plain,
! [X0,X1] : rd(mult(mult(X0,X1),sF0_fnc),sF0_fnc) = mult(X0,rd(mult(X1,sF2_fnc),sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f19,f51]) ).
fof(f83,plain,
! [X0,X1] : rd(mult(mult(X0,X1),sF2_fnc),sF2_fnc) = mult(X0,rd(mult(X1,x8),x8)),
inference(forward_demodulation,[status(thm)],[f17,f52]) ).
fof(f113,plain,
! [X0] : rd(mult(mult(X0,x6),x8),x8) = mult(X0,rd(sF4_fnc,x8)),
inference(paramodulation,[status(thm)],[f20,f80]) ).
fof(f114,plain,
! [X0] : rd(mult(mult(X0,x6),sF2_fnc),sF2_fnc) = mult(X0,rd(sF1_fnc,sF2_fnc)),
inference(paramodulation,[status(thm)],[f18,f80]) ).
fof(f124,plain,
! [X0] : rd(mult(mult(X0,x6),x8),x8) = mult(X0,sF3_fnc),
inference(forward_demodulation,[status(thm)],[f21,f113]) ).
fof(f125,plain,
! [X0] : rd(mult(mult(X0,x6),sF2_fnc),sF2_fnc) = mult(X0,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f19,f114]) ).
fof(f505,plain,
! [X0] : ld(X0,mult(X0,ld(X0,X0))) = rd(rd(mult(X0,X0),X0),X0),
inference(paramodulation,[status(thm)],[f12,f15]) ).
fof(f516,plain,
! [X0] : ld(X0,ld(X0,mult(X0,X0))) = rd(rd(mult(X0,X0),X0),X0),
inference(forward_demodulation,[status(thm)],[f11,f505]) ).
fof(f517,plain,
! [X0] : ld(X0,X0) = rd(rd(mult(X0,X0),X0),X0),
inference(forward_demodulation,[status(thm)],[f9,f516]) ).
fof(f518,plain,
! [X0] : ld(X0,X0) = rd(X0,X0),
inference(forward_demodulation,[status(thm)],[f10,f517]) ).
fof(f864,plain,
! [X0] : mult(ld(X0,X0),X0) = rd(mult(X0,X0),X0),
inference(paramodulation,[status(thm)],[f518,f12]) ).
fof(f873,plain,
! [X0] : mult(ld(X0,X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f10,f864]) ).
fof(f880,plain,
rd(mult(x6,sF2_fnc),sF2_fnc) = mult(ld(x6,x6),sF0_fnc),
inference(paramodulation,[status(thm)],[f873,f125]) ).
fof(f881,plain,
rd(mult(x6,x8),x8) = mult(ld(x6,x6),sF3_fnc),
inference(paramodulation,[status(thm)],[f873,f124]) ).
fof(f892,plain,
rd(sF1_fnc,sF2_fnc) = mult(ld(x6,x6),sF0_fnc),
inference(forward_demodulation,[status(thm)],[f18,f880]) ).
fof(f893,plain,
sF0_fnc = mult(ld(x6,x6),sF0_fnc),
inference(forward_demodulation,[status(thm)],[f19,f892]) ).
fof(f894,plain,
rd(sF4_fnc,x8) = mult(ld(x6,x6),sF3_fnc),
inference(forward_demodulation,[status(thm)],[f20,f881]) ).
fof(f895,plain,
sF3_fnc = mult(ld(x6,x6),sF3_fnc),
inference(forward_demodulation,[status(thm)],[f21,f894]) ).
fof(f1746,plain,
! [X0] : rd(mult(mult(X0,x6),sF0_fnc),sF0_fnc) = mult(X0,sF0_fnc),
inference(backward_demodulation,[status(thm)],[f1747,f125]) ).
fof(f1747,plain,
! [X0,X1] : rd(mult(mult(X0,X1),sF0_fnc),sF0_fnc) = rd(mult(mult(X0,X1),sF2_fnc),sF2_fnc),
inference(forward_demodulation,[status(thm)],[f80,f82]) ).
fof(f1835,plain,
! [X0,X1] : rd(mult(mult(X0,X1),sF0_fnc),sF0_fnc) = mult(X0,rd(mult(X1,x8),x8)),
inference(forward_demodulation,[status(thm)],[f1747,f83]) ).
fof(f1838,plain,
! [X0,X1] : rd(mult(mult(X0,X1),sF0_fnc),sF0_fnc) = rd(mult(mult(X0,X1),x8),x8),
inference(forward_demodulation,[status(thm)],[f80,f1835]) ).
fof(f2177,plain,
! [X0] : rd(mult(mult(X0,x6),x8),x8) = mult(X0,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f1838,f1746]) ).
fof(f2178,plain,
sF3_fnc = mult(ld(x6,x6),sF0_fnc),
inference(backward_demodulation,[status(thm)],[f2184,f895]) ).
fof(f2184,plain,
! [X0] : mult(X0,sF3_fnc) = mult(X0,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f124,f2177]) ).
fof(f2205,plain,
sF3_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f893,f2178]) ).
fof(f2206,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2205,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP685-11 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:32:50 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.49/1.62 % Elapsed time: 1.037952 seconds
% 1.49/1.62 % CPU time: 0.242628 seconds
% 1.49/1.62 % Total memory used: 11.159 MB
% 1.49/1.62 % Net memory used: 10.646 MB
%------------------------------------------------------------------------------