%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG069-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 11:48:01 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 40 unt; 0 def)
% Number of atoms : 40 ( 39 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-4 aty)
% Number of variables : 28 ( 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : ifeq2(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [U] : ifeq(sorti1(U),true,sorti1(sK2_ax3_V(U)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [U] : ifeq2(sorti1(U),true,op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [V] : tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,true),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
sorti2(sK1_ax4_U) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
! [U] : ifeq(sorti1(U),true,sorti2(h(U)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
! [X,W] : ifeq2(sorti1(X),true,ifeq2(sorti1(W),true,op2(h(W),h(X)),h(op1(W,X))),h(op1(W,X))) = h(op1(W,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
! [V] : ifeq(sorti2(V),true,sorti1(j(V)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
! [X1] : ifeq2(sorti2(X1),true,h(j(X1)),X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [X0,X1,X2] : ifeq2(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0] : ifeq(sorti1(X0),true,sorti1(sK2_ax3_V(X0)),true) = true,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f20,plain,
! [X0] : ifeq2(sorti1(X0),true,op1(sK2_ax3_V(X0),sK2_ax3_V(X0)),X0) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
! [X0] : tuple(op2(X0,X0),sorti2(X0)) != tuple(sK1_ax4_U,true),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f22,plain,
sorti2(sK1_ax4_U) = true,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f23,plain,
! [X0] : ifeq(sorti1(X0),true,sorti2(h(X0)),true) = true,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f24,plain,
! [X0,X1] : ifeq2(sorti1(X0),true,ifeq2(sorti1(X1),true,op2(h(X1),h(X0)),h(op1(X1,X0))),h(op1(X1,X0))) = h(op1(X1,X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
! [X0] : ifeq(sorti2(X0),true,sorti1(j(X0)),true) = true,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f28,plain,
! [X0] : ifeq2(sorti2(X0),true,h(j(X0)),X0) = X0,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f34,plain,
ifeq(true,true,sorti1(j(sK1_ax4_U)),true) = true,
inference(paramodulation,[status(thm)],[f22,f26]) ).
fof(f35,plain,
ifeq2(true,true,h(j(sK1_ax4_U)),sK1_ax4_U) = sK1_ax4_U,
inference(paramodulation,[status(thm)],[f22,f28]) ).
fof(f38,plain,
sorti1(j(sK1_ax4_U)) = true,
inference(forward_demodulation,[status(thm)],[f16,f34]) ).
fof(f39,plain,
h(j(sK1_ax4_U)) = sK1_ax4_U,
inference(forward_demodulation,[status(thm)],[f15,f35]) ).
fof(f69,plain,
ifeq(true,true,sorti1(sK2_ax3_V(j(sK1_ax4_U))),true) = true,
inference(paramodulation,[status(thm)],[f38,f19]) ).
fof(f70,plain,
sorti1(sK2_ax3_V(j(sK1_ax4_U))) = true,
inference(forward_demodulation,[status(thm)],[f16,f69]) ).
fof(f71,plain,
ifeq2(true,true,op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))),j(sK1_ax4_U)) = j(sK1_ax4_U),
inference(paramodulation,[status(thm)],[f38,f20]) ).
fof(f72,plain,
op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))) = j(sK1_ax4_U),
inference(forward_demodulation,[status(thm)],[f15,f71]) ).
fof(f84,plain,
ifeq(true,true,sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),true) = true,
inference(paramodulation,[status(thm)],[f70,f23]) ).
fof(f93,plain,
sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))) = true,
inference(forward_demodulation,[status(thm)],[f16,f84]) ).
fof(f627,plain,
ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))))),h(j(sK1_ax4_U))) = h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U)))),
inference(paramodulation,[status(thm)],[f72,f24]) ).
fof(f631,plain,
ifeq2(true,true,ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))))),h(j(sK1_ax4_U))) = h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U)))),
inference(forward_demodulation,[status(thm)],[f70,f627]) ).
fof(f632,plain,
ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))))) = h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U)))),
inference(forward_demodulation,[status(thm)],[f15,f631]) ).
fof(f633,plain,
ifeq2(true,true,op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))))) = h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U)))),
inference(forward_demodulation,[status(thm)],[f70,f632]) ).
fof(f634,plain,
op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))) = h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U)))),
inference(forward_demodulation,[status(thm)],[f15,f633]) ).
fof(f635,plain,
op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))) = h(j(sK1_ax4_U)),
inference(forward_demodulation,[status(thm)],[f72,f634]) ).
fof(f636,plain,
op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))) = sK1_ax4_U,
inference(forward_demodulation,[status(thm)],[f39,f635]) ).
fof(f1957,plain,
tuple(sK1_ax4_U,sorti2(h(sK2_ax3_V(j(sK1_ax4_U))))) != tuple(sK1_ax4_U,true),
inference(paramodulation,[status(thm)],[f636,f21]) ).
fof(f1984,plain,
tuple(sK1_ax4_U,true) != tuple(sK1_ax4_U,true),
inference(forward_demodulation,[status(thm)],[f93,f1957]) ).
fof(f1985,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1984]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG069-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 12:55:03 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.45 % Elapsed time: 0.066526 seconds
% 0.09/0.45 % CPU time: 0.162110 seconds
% 0.09/0.45 % Total memory used: 8.854 MB
% 0.09/0.45 % Net memory used: 8.759 MB
%------------------------------------------------------------------------------