%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL003-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 12:08:25 PM UTC 2026
% Result : Unsatisfiable 5.71s 1.21s
% Output : CNFRefutation 5.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 44 ( 44 unt; 9 def)
% Number of atoms : 44 ( 43 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 : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 13 con; 0-4 aty)
% Number of variables : 48 ( 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : apply(apply(w,X),Y) = apply(apply(X,Y),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [Strong_fixed_point] : ifeq(apply(Strong_fixed_point,fixed_pt),apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)),fixed_point(Strong_fixed_point),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1,X2] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0,X1] : apply(apply(w,X0),X1) = apply(apply(X0,X1),X1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
! [X0] : ifeq(apply(X0,fixed_pt),apply(fixed_pt,apply(X0,fixed_pt)),fixed_point(X0),true) = true,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)) != true,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,definition,
sF5_fnc = apply(w,w),
introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition]) ).
fof(f12,definition,
sF4_fnc = apply(b,sF5_fnc),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f13,definition,
sF8_fnc = apply(b,w),
introduced(definition,[new_symbols(definition,[sF8_fnc])],[function_definition]) ).
fof(f14,definition,
sF7_fnc = apply(b,sF8_fnc),
introduced(definition,[new_symbols(definition,[sF7_fnc])],[function_definition]) ).
fof(f15,definition,
sF6_fnc = apply(sF7_fnc,b),
introduced(definition,[new_symbols(definition,[sF6_fnc])],[function_definition]) ).
fof(f16,definition,
sF3_fnc = apply(sF4_fnc,sF6_fnc),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f17,definition,
sF2_fnc = apply(b,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f18,definition,
sF1_fnc = apply(sF2_fnc,b),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f19,definition,
sF0_fnc = fixed_point(sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f20,plain,
sF0_fnc != true,
inference(definition_folding,[],[f10,f19,f18,f17,f16,f15,f14,f13,f12,f11]) ).
fof(f22,plain,
! [X0] : apply(apply(w,w),X0) = apply(apply(X0,X0),X0),
inference(paramodulation,[status(thm)],[f8,f8]) ).
fof(f23,plain,
! [X0] : apply(sF5_fnc,X0) = apply(apply(w,X0),X0),
inference(paramodulation,[status(thm)],[f11,f8]) ).
fof(f35,plain,
! [X0] : apply(sF5_fnc,X0) = apply(apply(X0,X0),X0),
inference(forward_demodulation,[status(thm)],[f11,f22]) ).
fof(f56,plain,
! [X0,X1] : apply(apply(sF2_fnc,X0),X1) = apply(sF3_fnc,apply(X0,X1)),
inference(paramodulation,[status(thm)],[f17,f7]) ).
fof(f57,plain,
! [X0,X1] : apply(apply(sF7_fnc,X0),X1) = apply(sF8_fnc,apply(X0,X1)),
inference(paramodulation,[status(thm)],[f14,f7]) ).
fof(f59,plain,
! [X0,X1] : apply(apply(sF4_fnc,X0),X1) = apply(sF5_fnc,apply(X0,X1)),
inference(paramodulation,[status(thm)],[f12,f7]) ).
fof(f63,plain,
! [X0,X1,X2] : apply(apply(w,apply(apply(b,X0),X1)),X2) = apply(apply(X0,apply(X1,X2)),X2),
inference(paramodulation,[status(thm)],[f7,f8]) ).
fof(f74,plain,
ifeq(apply(sF1_fnc,fixed_pt),apply(fixed_pt,apply(sF1_fnc,fixed_pt)),sF0_fnc,true) = true,
inference(paramodulation,[status(thm)],[f19,f9]) ).
fof(f87,plain,
! [X0] : apply(sF1_fnc,X0) = apply(sF3_fnc,apply(b,X0)),
inference(paramodulation,[status(thm)],[f18,f56]) ).
fof(f107,plain,
! [X0] : apply(sF6_fnc,X0) = apply(sF8_fnc,apply(b,X0)),
inference(paramodulation,[status(thm)],[f15,f57]) ).
fof(f330,plain,
! [X0] : apply(sF3_fnc,X0) = apply(sF5_fnc,apply(sF6_fnc,X0)),
inference(paramodulation,[status(thm)],[f16,f59]) ).
fof(f752,plain,
! [X0,X1] : apply(apply(w,apply(apply(b,w),apply(b,X0))),X1) = apply(apply(X0,apply(X1,X1)),X1),
inference(paramodulation,[status(thm)],[f63,f63]) ).
fof(f870,plain,
! [X0,X1] : apply(apply(w,apply(sF8_fnc,apply(b,X0))),X1) = apply(apply(X0,apply(X1,X1)),X1),
inference(forward_demodulation,[status(thm)],[f13,f752]) ).
fof(f871,plain,
! [X0,X1] : apply(apply(w,apply(sF6_fnc,X0)),X1) = apply(apply(X0,apply(X1,X1)),X1),
inference(forward_demodulation,[status(thm)],[f107,f870]) ).
fof(f2934,plain,
! [X0,X1] : apply(apply(w,apply(sF6_fnc,apply(b,X0))),X1) = apply(X0,apply(apply(X1,X1),X1)),
inference(paramodulation,[status(thm)],[f7,f871]) ).
fof(f3065,plain,
! [X0,X1] : apply(apply(w,apply(sF6_fnc,apply(b,X0))),X1) = apply(X0,apply(sF5_fnc,X1)),
inference(forward_demodulation,[status(thm)],[f35,f2934]) ).
fof(f11345,plain,
! [X0] : apply(sF5_fnc,apply(sF6_fnc,apply(b,X0))) = apply(X0,apply(sF5_fnc,apply(sF6_fnc,apply(b,X0)))),
inference(paramodulation,[status(thm)],[f23,f3065]) ).
fof(f11438,plain,
! [X0] : apply(sF3_fnc,apply(b,X0)) = apply(X0,apply(sF5_fnc,apply(sF6_fnc,apply(b,X0)))),
inference(forward_demodulation,[status(thm)],[f330,f11345]) ).
fof(f11439,plain,
! [X0] : apply(sF1_fnc,X0) = apply(X0,apply(sF5_fnc,apply(sF6_fnc,apply(b,X0)))),
inference(forward_demodulation,[status(thm)],[f87,f11438]) ).
fof(f11440,plain,
! [X0] : apply(sF1_fnc,X0) = apply(X0,apply(sF3_fnc,apply(b,X0))),
inference(forward_demodulation,[status(thm)],[f330,f11439]) ).
fof(f11441,plain,
! [X0] : apply(sF1_fnc,X0) = apply(X0,apply(sF1_fnc,X0)),
inference(forward_demodulation,[status(thm)],[f87,f11440]) ).
fof(f11515,plain,
ifeq(apply(sF1_fnc,fixed_pt),apply(sF1_fnc,fixed_pt),sF0_fnc,true) = true,
inference(backward_demodulation,[status(thm)],[f11441,f74]) ).
fof(f11662,plain,
sF0_fnc = true,
inference(forward_demodulation,[status(thm)],[f6,f11515]) ).
fof(f11663,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f11662,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL003-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 14:03:25 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 5.71/1.21 % Refutation found
% 5.71/1.21 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.71/1.21 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.71/1.26 % Elapsed time: 0.887200 seconds
% 5.71/1.26 % CPU time: 6.882242 seconds
% 5.71/1.26 % Total memory used: 172.800 MB
% 5.71/1.26 % Net memory used: 169.765 MB
%------------------------------------------------------------------------------