%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA133-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 12:02:25 PM UTC 2026
% Result : Unsatisfiable 5.62s 1.19s
% Output : CNFRefutation 5.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 50 ( 50 unt; 2 def)
% Number of atoms : 50 ( 49 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : '+'(X,Y) = '+'(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : '+'(X,'+'(Y,Z)) = '+'('+'(X,Y),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : times(X,Y) = times(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : '+'(zero,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : times(one,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] : '+'(X,minus(X)) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
d(x) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [T,U] : d('+'(T,U)) = '+'(d(T),d(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [T,U] : d(times(T,U)) = '+'(times(T,d(U)),times(U,d(T))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [T] : d(sin(T)) = times(cos(T),d(T)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [T] : d(cos(T)) = minus(times(sin(T),d(T))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
! [T] : d(T) != times(x,cos(x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f19,plain,
! [X0,X1,X2] : '+'(X0,'+'(X1,X2)) = '+'('+'(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
! [X0,X1] : times(X0,X1) = times(X1,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
! [X0] : '+'(zero,X0) = X0,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
! [X0] : times(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
! [X0] : '+'(X0,minus(X0)) = zero,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f29,plain,
d(x) = one,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f30,plain,
! [X0,X1] : d('+'(X0,X1)) = '+'(d(X0),d(X1)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f31,plain,
! [X0,X1] : d(times(X0,X1)) = '+'(times(X0,d(X1)),times(X1,d(X0))),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f32,plain,
! [X0] : d(sin(X0)) = times(cos(X0),d(X0)),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f33,plain,
! [X0] : d(cos(X0)) = minus(times(sin(X0),d(X0))),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f34,plain,
! [X0] : d(X0) != times(x,cos(x)),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f35,definition,
sF1_fnc = cos(x),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f36,definition,
sF0_fnc = times(x,sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f37,plain,
! [X0] : d(X0) != sF0_fnc,
inference(definition_folding,[],[f34,f36,f35]) ).
fof(f154,plain,
! [X0] : times(X0,one) = X0,
inference(paramodulation,[status(thm)],[f20,f24]) ).
fof(f188,plain,
! [X0] : X0 = '+'(X0,zero),
inference(paramodulation,[status(thm)],[f22,f18]) ).
fof(f334,plain,
! [X0,X1] : '+'(X0,'+'(minus(X0),X1)) = '+'(zero,X1),
inference(paramodulation,[status(thm)],[f26,f19]) ).
fof(f335,plain,
! [X0,X1] : '+'(X0,'+'(minus(X0),X1)) = X1,
inference(forward_demodulation,[status(thm)],[f22,f334]) ).
fof(f388,plain,
! [X0,X1] : d('+'(X0,X1)) = '+'(d(X1),d(X0)),
inference(paramodulation,[status(thm)],[f18,f30]) ).
fof(f423,plain,
! [X0] : d(times(x,X0)) = '+'(times(x,d(X0)),times(X0,one)),
inference(paramodulation,[status(thm)],[f29,f31]) ).
fof(f460,plain,
! [X0] : d(times(x,X0)) = '+'(times(x,d(X0)),X0),
inference(forward_demodulation,[status(thm)],[f154,f423]) ).
fof(f721,plain,
! [X0] : '+'(X0,zero) = minus(minus(X0)),
inference(paramodulation,[status(thm)],[f26,f335]) ).
fof(f723,plain,
! [X0,X1] : '+'(X0,'+'(X1,minus(X0))) = X1,
inference(paramodulation,[status(thm)],[f18,f335]) ).
fof(f731,plain,
! [X0] : X0 = minus(minus(X0)),
inference(forward_demodulation,[status(thm)],[f188,f721]) ).
fof(f802,plain,
! [X0,X1] : '+'(minus(X0),'+'(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f731,f723]) ).
fof(f819,plain,
d(sin(x)) = times(sF1_fnc,d(x)),
inference(paramodulation,[status(thm)],[f35,f32]) ).
fof(f840,plain,
d(sin(x)) = times(sF1_fnc,one),
inference(forward_demodulation,[status(thm)],[f29,f819]) ).
fof(f841,plain,
d(sin(x)) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f154,f840]) ).
fof(f854,plain,
d(cos(x)) = minus(times(sin(x),one)),
inference(paramodulation,[status(thm)],[f29,f33]) ).
fof(f866,plain,
d(sF1_fnc) = minus(times(sin(x),one)),
inference(forward_demodulation,[status(thm)],[f35,f854]) ).
fof(f867,plain,
d(sF1_fnc) = minus(sin(x)),
inference(forward_demodulation,[status(thm)],[f154,f866]) ).
fof(f1316,plain,
! [X0] : '+'(d(sF1_fnc),'+'(X0,sin(x))) = X0,
inference(paramodulation,[status(thm)],[f867,f802]) ).
fof(f12510,plain,
'+'(d(sF1_fnc),d(times(x,sin(x)))) = times(x,d(sin(x))),
inference(paramodulation,[status(thm)],[f460,f1316]) ).
fof(f12534,plain,
d('+'(times(x,sin(x)),sF1_fnc)) = times(x,d(sin(x))),
inference(forward_demodulation,[status(thm)],[f388,f12510]) ).
fof(f12535,plain,
d('+'(times(x,sin(x)),sF1_fnc)) = times(x,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f841,f12534]) ).
fof(f12536,plain,
d('+'(times(x,sin(x)),sF1_fnc)) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f36,f12535]) ).
fof(f12537,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f12536,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA133-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 13:33:09 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 5.62/1.19 % Refutation found
% 5.62/1.19 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.62/1.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.62/1.23 % Elapsed time: 0.838555 seconds
% 5.62/1.23 % CPU time: 6.493661 seconds
% 5.62/1.23 % Total memory used: 150.717 MB
% 5.62/1.23 % Net memory used: 144.593 MB
%------------------------------------------------------------------------------