%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG030-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 11:47:49 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.57s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 65 ( 65 unt; 2 def)
% Number of atoms : 65 ( 64 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 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(f3,axiom,
! [V,U] : ifeq(sorti1(V),true,ifeq(sorti1(U),true,sorti1(op1(U,V)),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
op1(sK2_ax3_U,sK1_ax3_V) != op1(sK1_ax3_V,sK2_ax3_U),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
sorti1(sK1_ax3_V) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
sorti1(sK2_ax3_U) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [V,U] : ifeq2(sorti2(V),true,ifeq2(sorti2(U),true,op2(U,V),op2(V,U)),op2(V,U)) = op2(V,U),
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(f11,negated_conjecture,
! [X2] : ifeq2(sorti1(X2),true,j(h(X2)),X2) = X2,
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(f17,plain,
! [X0,X1] : ifeq(sorti1(X0),true,ifeq(sorti1(X1),true,sorti1(op1(X1,X0)),true),true) = true,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f19,plain,
op1(sK2_ax3_U,sK1_ax3_V) != op1(sK1_ax3_V,sK2_ax3_U),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f20,plain,
sorti1(sK1_ax3_V) = true,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
sorti1(sK2_ax3_U) = true,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f22,plain,
! [X0,X1] : ifeq2(sorti2(X0),true,ifeq2(sorti2(X1),true,op2(X1,X0),op2(X0,X1)),op2(X0,X1)) = op2(X0,X1),
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(f25,plain,
! [X0] : ifeq2(sorti1(X0),true,j(h(X0)),X0) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f29,definition,
sF0_fnc = op1(sK2_ax3_U,sK1_ax3_V),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f30,definition,
sF1_fnc = op1(sK1_ax3_V,sK2_ax3_U),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f31,plain,
sF0_fnc != sF1_fnc,
inference(definition_folding,[],[f19,f30,f29]) ).
fof(f32,plain,
ifeq2(sorti1(sK2_ax3_U),true,ifeq2(sorti1(sK1_ax3_V),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(sF1_fnc)),h(op1(sK1_ax3_V,sK2_ax3_U))) = h(op1(sK1_ax3_V,sK2_ax3_U)),
inference(paramodulation,[status(thm)],[f30,f24]) ).
fof(f33,plain,
ifeq2(sorti1(sK1_ax3_V),true,ifeq2(sorti1(sK2_ax3_U),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(sF0_fnc)),h(op1(sK2_ax3_U,sK1_ax3_V))) = h(op1(sK2_ax3_U,sK1_ax3_V)),
inference(paramodulation,[status(thm)],[f29,f24]) ).
fof(f36,plain,
ifeq2(sorti1(sK2_ax3_U),true,ifeq2(sorti1(sK1_ax3_V),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(sF1_fnc)),h(sF1_fnc)) = h(op1(sK1_ax3_V,sK2_ax3_U)),
inference(forward_demodulation,[status(thm)],[f30,f32]) ).
fof(f37,plain,
ifeq2(sorti1(sK2_ax3_U),true,ifeq2(sorti1(sK1_ax3_V),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(sF1_fnc)),h(sF1_fnc)) = h(sF1_fnc),
inference(forward_demodulation,[status(thm)],[f30,f36]) ).
fof(f38,plain,
ifeq2(sorti1(sK1_ax3_V),true,ifeq2(sorti1(sK2_ax3_U),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(sF0_fnc)),h(sF0_fnc)) = h(op1(sK2_ax3_U,sK1_ax3_V)),
inference(forward_demodulation,[status(thm)],[f29,f33]) ).
fof(f39,plain,
ifeq2(sorti1(sK1_ax3_V),true,ifeq2(sorti1(sK2_ax3_U),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(sF0_fnc)),h(sF0_fnc)) = h(sF0_fnc),
inference(forward_demodulation,[status(thm)],[f29,f38]) ).
fof(f44,plain,
ifeq(sorti1(sK2_ax3_U),true,ifeq(sorti1(sK1_ax3_V),true,sorti1(sF1_fnc),true),true) = true,
inference(paramodulation,[status(thm)],[f30,f17]) ).
fof(f45,plain,
ifeq(sorti1(sK1_ax3_V),true,ifeq(sorti1(sK2_ax3_U),true,sorti1(sF0_fnc),true),true) = true,
inference(paramodulation,[status(thm)],[f29,f17]) ).
fof(f46,plain,
ifeq2(true,true,ifeq2(sorti1(sK2_ax3_U),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(sF0_fnc)),h(sF0_fnc)) = h(sF0_fnc),
inference(backward_demodulation,[status(thm)],[f20,f39]) ).
fof(f47,plain,
ifeq2(sorti1(sK2_ax3_U),true,ifeq2(true,true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(sF1_fnc)),h(sF1_fnc)) = h(sF1_fnc),
inference(backward_demodulation,[status(thm)],[f20,f37]) ).
fof(f48,plain,
ifeq(true,true,ifeq(sorti1(sK2_ax3_U),true,sorti1(sF0_fnc),true),true) = true,
inference(backward_demodulation,[status(thm)],[f20,f45]) ).
fof(f49,plain,
ifeq(sorti1(sK2_ax3_U),true,ifeq(true,true,sorti1(sF1_fnc),true),true) = true,
inference(backward_demodulation,[status(thm)],[f20,f44]) ).
fof(f54,plain,
ifeq(true,true,sorti2(h(sK1_ax3_V)),true) = true,
inference(paramodulation,[status(thm)],[f20,f23]) ).
fof(f56,plain,
ifeq2(sorti1(sK2_ax3_U),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(sF0_fnc)) = h(sF0_fnc),
inference(forward_demodulation,[status(thm)],[f15,f46]) ).
fof(f57,plain,
ifeq2(sorti1(sK2_ax3_U),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(sF1_fnc)) = h(sF1_fnc),
inference(forward_demodulation,[status(thm)],[f15,f47]) ).
fof(f58,plain,
ifeq(sorti1(sK2_ax3_U),true,sorti1(sF0_fnc),true) = true,
inference(forward_demodulation,[status(thm)],[f16,f48]) ).
fof(f59,plain,
ifeq(sorti1(sK2_ax3_U),true,sorti1(sF1_fnc),true) = true,
inference(forward_demodulation,[status(thm)],[f16,f49]) ).
fof(f64,plain,
sorti2(h(sK1_ax3_V)) = true,
inference(forward_demodulation,[status(thm)],[f16,f54]) ).
fof(f70,plain,
ifeq(true,true,sorti2(h(sK2_ax3_U)),true) = true,
inference(paramodulation,[status(thm)],[f21,f23]) ).
fof(f76,plain,
sorti2(h(sK2_ax3_U)) = true,
inference(forward_demodulation,[status(thm)],[f16,f70]) ).
fof(f142,plain,
ifeq(true,true,sorti1(sF0_fnc),true) = true,
inference(forward_demodulation,[status(thm)],[f21,f58]) ).
fof(f143,plain,
sorti1(sF0_fnc) = true,
inference(forward_demodulation,[status(thm)],[f16,f142]) ).
fof(f149,plain,
ifeq2(true,true,j(h(sF0_fnc)),sF0_fnc) = sF0_fnc,
inference(paramodulation,[status(thm)],[f143,f25]) ).
fof(f155,plain,
j(h(sF0_fnc)) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f15,f149]) ).
fof(f188,plain,
ifeq(true,true,sorti1(sF1_fnc),true) = true,
inference(forward_demodulation,[status(thm)],[f21,f59]) ).
fof(f189,plain,
sorti1(sF1_fnc) = true,
inference(forward_demodulation,[status(thm)],[f16,f188]) ).
fof(f195,plain,
ifeq2(true,true,j(h(sF1_fnc)),sF1_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f189,f25]) ).
fof(f201,plain,
j(h(sF1_fnc)) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f15,f195]) ).
fof(f234,plain,
ifeq2(true,true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(sF0_fnc)) = h(sF0_fnc),
inference(forward_demodulation,[status(thm)],[f21,f56]) ).
fof(f235,plain,
op2(h(sK2_ax3_U),h(sK1_ax3_V)) = h(sF0_fnc),
inference(forward_demodulation,[status(thm)],[f15,f234]) ).
fof(f281,plain,
ifeq2(true,true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(sF1_fnc)) = h(sF1_fnc),
inference(forward_demodulation,[status(thm)],[f21,f57]) ).
fof(f282,plain,
op2(h(sK1_ax3_V),h(sK2_ax3_U)) = h(sF1_fnc),
inference(forward_demodulation,[status(thm)],[f15,f281]) ).
fof(f286,plain,
ifeq2(sorti2(h(sK1_ax3_V)),true,ifeq2(sorti2(h(sK2_ax3_U)),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),op2(h(sK1_ax3_V),h(sK2_ax3_U))),h(sF1_fnc)) = op2(h(sK1_ax3_V),h(sK2_ax3_U)),
inference(paramodulation,[status(thm)],[f282,f22]) ).
fof(f310,plain,
ifeq2(true,true,ifeq2(sorti2(h(sK2_ax3_U)),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),op2(h(sK1_ax3_V),h(sK2_ax3_U))),h(sF1_fnc)) = op2(h(sK1_ax3_V),h(sK2_ax3_U)),
inference(forward_demodulation,[status(thm)],[f64,f286]) ).
fof(f311,plain,
ifeq2(sorti2(h(sK2_ax3_U)),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),op2(h(sK1_ax3_V),h(sK2_ax3_U))) = op2(h(sK1_ax3_V),h(sK2_ax3_U)),
inference(forward_demodulation,[status(thm)],[f15,f310]) ).
fof(f312,plain,
ifeq2(true,true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),op2(h(sK1_ax3_V),h(sK2_ax3_U))) = op2(h(sK1_ax3_V),h(sK2_ax3_U)),
inference(forward_demodulation,[status(thm)],[f76,f311]) ).
fof(f313,plain,
op2(h(sK2_ax3_U),h(sK1_ax3_V)) = op2(h(sK1_ax3_V),h(sK2_ax3_U)),
inference(forward_demodulation,[status(thm)],[f15,f312]) ).
fof(f314,plain,
h(sF0_fnc) = op2(h(sK1_ax3_V),h(sK2_ax3_U)),
inference(forward_demodulation,[status(thm)],[f235,f313]) ).
fof(f315,plain,
h(sF0_fnc) = h(sF1_fnc),
inference(forward_demodulation,[status(thm)],[f282,f314]) ).
fof(f346,plain,
j(h(sF0_fnc)) = sF1_fnc,
inference(backward_demodulation,[status(thm)],[f315,f201]) ).
fof(f352,plain,
sF0_fnc = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f155,f346]) ).
fof(f353,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f352,f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG030-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.55 % Computer : n007.cluster.edu
% 0.09/0.55 % Model : x86_64 x86_64
% 0.09/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.55 % Memory : 8046.5625MB
% 0.09/0.55 % OS : Linux 6.8.0-71-generic
% 0.09/0.55 % CPULimit : 300
% 0.09/0.55 % WCLimit : 300
% 0.09/0.55 % DateTime : Mon Sep 21 12:51:36 UTC 2026
% 0.09/0.56 % CPUTime :
% 0.13/0.56 % Drodi V4.1.1
% 0.13/0.57 % Refutation found
% 0.13/0.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.60 % Elapsed time: 0.034962 seconds
% 0.13/0.60 % CPU time: 0.049726 seconds
% 0.13/0.60 % Total memory used: 2.555 MB
% 0.13/0.60 % Net memory used: 2.543 MB
%------------------------------------------------------------------------------