%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : PUZ039-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 01:59:57 PM UTC 2026
% Result : Unsatisfiable 7.89s 1.44s
% Output : CNFRefutation 7.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 14
% Syntax : Number of formulae : 78 ( 78 unt; 5 def)
% Number of atoms : 78 ( 77 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 6 con; 0-12 aty)
% Number of variables : 247 ( 247 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B,V1,V2,V3,V4,H,S1,X,Y,S3,S4,E2] : ifeq(state(B,V1,V2,V3,V4,H,S1,s2(X,Y),S3,S4,e1(s(X),Y),E2),true,state(B,V1,V2,V3,V4,H,S1,s2(s(X),Y),S3,S4,e1(X,Y),E2),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [B,V1,V2,V3,V4,H,S1,S2,S3,X,Y,E2] : ifeq(state(B,V1,V2,V3,V4,H,S1,S2,S3,s4(X,Y),e1(X,s(Y)),E2),true,state(B,V1,V2,V3,V4,H,S1,S2,S3,s4(X,s(Y)),e1(X,Y),E2),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [B,V1,V2,X,Y,V4,H,S1,S2,S3,S4,E2] : ifeq(state(B,V1,V2,v3(X,Y),V4,H,S1,S2,S3,S4,e1(s(s(X)),Y),E2),true,state(B,V1,V2,v3(s(X),Y),V4,H,S1,S2,S3,S4,e1(X,Y),E2),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [B,V1,V2,V3,X,Y,H,S1,S2,S3,S4] : ifeq(state(B,V1,V2,V3,v4(X,s(Y)),H,S1,S2,S3,S4,e1(X,Y),e2(s(X),Y)),true,state(B,V1,V2,V3,v4(X,Y),H,S1,S2,S3,S4,e1(X,s(Y)),e2(s(X),s(Y))),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [B,V1,V2,V3,V4,X,Y,S1,S2,S3,S4,E2] : ifeq(state(B,V1,V2,V3,V4,h(X,s(Y)),S1,S2,S3,S4,e1(X,Y),E2),true,state(B,V1,V2,V3,V4,h(X,Y),S1,S2,S3,S4,e1(X,s(s(Y))),E2),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [B,V1,V2,V3,V4,H,S1,S2,S3,S4,X,Y,Q,W] : ifeq(state(B,V1,V2,V3,V4,H,S1,S2,S3,S4,e1(X,Y),e2(Q,W)),true,state(B,V1,V2,V3,V4,H,S1,S2,S3,S4,e1(Q,W),e2(X,Y)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
! [B,V1,V2,V3,H,S1,S2,S3,S4,E1,E2] : state(B,V1,V2,V3,v4(s(s(o)),s(s(o))),H,S1,S2,S3,S4,E1,E2) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,plain,
! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f52,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] : ifeq(state(X0,X1,X2,X3,X4,X5,X6,s2(X7,X8),X9,X10,e1(s(X7),X8),X11),true,state(X0,X1,X2,X3,X4,X5,X6,s2(s(X7),X8),X9,X10,e1(X7,X8),X11),true) = true,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f58,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] : ifeq(state(X0,X1,X2,X3,X4,X5,X6,X7,X8,s4(X9,X10),e1(X9,s(X10)),X11),true,state(X0,X1,X2,X3,X4,X5,X6,X7,X8,s4(X9,s(X10)),e1(X9,X10),X11),true) = true,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f72,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] : ifeq(state(X0,X1,X2,v3(X3,X4),X5,X6,X7,X8,X9,X10,e1(s(s(X3)),X4),X11),true,state(X0,X1,X2,v3(s(X3),X4),X5,X6,X7,X8,X9,X10,e1(X3,X4),X11),true) = true,
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f75,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] : ifeq(state(X0,X1,X2,X3,v4(X4,s(X5)),X6,X7,X8,X9,X10,e1(X4,X5),e2(s(X4),X5)),true,state(X0,X1,X2,X3,v4(X4,X5),X6,X7,X8,X9,X10,e1(X4,s(X5)),e2(s(X4),s(X5))),true) = true,
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f79,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] : ifeq(state(X0,X1,X2,X3,X4,h(X5,s(X6)),X7,X8,X9,X10,e1(X5,X6),X11),true,state(X0,X1,X2,X3,X4,h(X5,X6),X7,X8,X9,X10,e1(X5,s(s(X6))),X11),true) = true,
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f86,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13] : ifeq(state(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,e1(X10,X11),e2(X12,X13)),true,state(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,e1(X12,X13),e2(X10,X11)),true) = true,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f87,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f88,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] : state(X0,X1,X2,X3,v4(s(s(o)),s(s(o))),X4,X5,X6,X7,X8,X9,X10) != true,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f89,definition,
sF3_fnc = s(o),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f90,definition,
sF2_fnc = s(sF3_fnc),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f91,definition,
sF4_fnc = s(sF3_fnc),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f92,definition,
sF1_fnc = v4(sF2_fnc,sF4_fnc),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f93,definition,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] : sF0_fnc(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10) = state(X0,X1,X2,X3,sF1_fnc,X4,X5,X6,X7,X8,X9,X10),
introduced(definition,[new_symbols(definition,[sF0_fnc(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10)])],[function_definition]) ).
fof(f94,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] : sF0_fnc(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10) != true,
inference(definition_folding,[],[f88,f93,f92,f91,f90,f89]) ).
fof(f95,plain,
sF4_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f90,f91]) ).
fof(f96,plain,
sF1_fnc = v4(sF2_fnc,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f95,f92]) ).
fof(f153,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] : ifeq(state(X0,X1,X2,X3,v4(sF2_fnc,s(sF2_fnc)),X4,X5,X6,X7,X8,e1(sF2_fnc,sF2_fnc),e2(s(sF2_fnc),sF2_fnc)),true,state(X0,X1,X2,X3,sF1_fnc,X4,X5,X6,X7,X8,e1(sF2_fnc,s(sF2_fnc)),e2(s(sF2_fnc),s(sF2_fnc))),true) = true,
inference(paramodulation,[status(thm)],[f96,f75]) ).
fof(f166,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] : ifeq(state(X0,X1,X2,X3,v4(sF2_fnc,s(sF2_fnc)),X4,X5,X6,X7,X8,e1(sF2_fnc,sF2_fnc),e2(s(sF2_fnc),sF2_fnc)),true,sF0_fnc(X0,X1,X2,X3,X4,X5,X6,X7,X8,e1(sF2_fnc,s(sF2_fnc)),e2(s(sF2_fnc),s(sF2_fnc))),true) = true,
inference(forward_demodulation,[status(thm)],[f93,f153]) ).
fof(f1035,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] : ifeq(state(X0,X1,X2,X3,X4,h(X5,sF3_fnc),X6,X7,X8,X9,e1(X5,o),X10),true,state(X0,X1,X2,X3,X4,h(X5,o),X6,X7,X8,X9,e1(X5,s(s(o))),X10),true) = true,
inference(paramodulation,[status(thm)],[f89,f79]) ).
fof(f1041,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] : ifeq(state(X0,X1,X2,X3,X4,h(X5,sF3_fnc),X6,X7,X8,X9,e1(X5,o),X10),true,state(X0,X1,X2,X3,X4,h(X5,o),X6,X7,X8,X9,e1(X5,s(sF3_fnc)),X10),true) = true,
inference(forward_demodulation,[status(thm)],[f89,f1035]) ).
fof(f1042,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] : ifeq(state(X0,X1,X2,X3,X4,h(X5,sF3_fnc),X6,X7,X8,X9,e1(X5,o),X10),true,state(X0,X1,X2,X3,X4,h(X5,o),X6,X7,X8,X9,e1(X5,sF2_fnc),X10),true) = true,
inference(forward_demodulation,[status(thm)],[f90,f1041]) ).
fof(f1381,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f89,f87]) ).
fof(f1382,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(s(sF3_fnc))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f89,f1381]) ).
fof(f1383,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f90,f1382]) ).
fof(f1384,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(s(sF3_fnc),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f89,f1383]) ).
fof(f1385,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f90,f1384]) ).
fof(f1386,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(s(sF3_fnc),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f89,f1385]) ).
fof(f1387,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f90,f1386]) ).
fof(f1388,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(s(sF3_fnc))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f89,f1387]) ).
fof(f1389,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f90,f1388]) ).
fof(f1390,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(s(sF3_fnc),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f89,f1389]) ).
fof(f1391,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f90,f1390]) ).
fof(f1392,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f89,f1391]) ).
fof(f1393,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(s(sF3_fnc)),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f89,f1392]) ).
fof(f1394,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(sF2_fnc),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f90,f1393]) ).
fof(f1395,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(sF2_fnc),sF3_fnc),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f89,f1394]) ).
fof(f1396,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(sF2_fnc),sF3_fnc),s2(s(s(sF3_fnc)),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f89,f1395]) ).
fof(f1397,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f90,f1396]) ).
fof(f1398,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),s(sF3_fnc)),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f89,f1397]) ).
fof(f1399,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f90,f1398]) ).
fof(f1400,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(s(sF3_fnc))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f89,f1399]) ).
fof(f1401,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(sF2_fnc)),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f90,f1400]) ).
fof(f1402,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f89,f1401]) ).
fof(f1403,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(s(sF3_fnc))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f89,f1402]) ).
fof(f1404,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f90,f1403]) ).
fof(f1405,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),s(sF3_fnc)),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f89,f1404]) ).
fof(f1406,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),sF2_fnc),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f90,f1405]) ).
fof(f1407,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),sF2_fnc),e1(s(s(s(sF3_fnc))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f89,f1406]) ).
fof(f1408,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),sF2_fnc),e1(s(s(sF2_fnc)),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f90,f1407]) ).
fof(f1409,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),sF2_fnc),e1(s(s(sF2_fnc)),o),e2(s(s(s(sF3_fnc))),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f89,f1408]) ).
fof(f1410,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),sF2_fnc),e1(s(s(sF2_fnc)),o),e2(s(s(sF2_fnc)),s(s(s(o))))) = true,
inference(forward_demodulation,[status(thm)],[f90,f1409]) ).
fof(f1411,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),sF2_fnc),e1(s(s(sF2_fnc)),o),e2(s(s(sF2_fnc)),s(s(sF3_fnc)))) = true,
inference(forward_demodulation,[status(thm)],[f89,f1410]) ).
fof(f1412,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(sF2_fnc,o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),sF2_fnc),e1(s(s(sF2_fnc)),o),e2(s(s(sF2_fnc)),s(sF2_fnc))) = true,
inference(forward_demodulation,[status(thm)],[f90,f1411]) ).
fof(f1414,plain,
ifeq(true,true,state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(s(sF2_fnc),o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),sF2_fnc),e1(sF2_fnc,o),e2(s(s(sF2_fnc)),s(sF2_fnc))),true) = true,
inference(paramodulation,[status(thm)],[f1412,f72]) ).
fof(f1419,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(s(sF2_fnc),o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,sF3_fnc),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),sF2_fnc),e1(sF2_fnc,o),e2(s(s(sF2_fnc)),s(sF2_fnc))) = true,
inference(forward_demodulation,[status(thm)],[f45,f1414]) ).
fof(f3075,plain,
ifeq(true,true,state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(s(sF2_fnc),o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,o),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),sF2_fnc),e1(sF2_fnc,sF2_fnc),e2(s(s(sF2_fnc)),s(sF2_fnc))),true) = true,
inference(paramodulation,[status(thm)],[f1419,f1042]) ).
fof(f3082,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(s(sF2_fnc),o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,o),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),sF2_fnc),e1(sF2_fnc,sF2_fnc),e2(s(s(sF2_fnc)),s(sF2_fnc))) = true,
inference(forward_demodulation,[status(thm)],[f45,f3075]) ).
fof(f3537,plain,
ifeq(true,true,state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(s(sF2_fnc),o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,o),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),sF2_fnc),e1(s(s(sF2_fnc)),s(sF2_fnc)),e2(sF2_fnc,sF2_fnc)),true) = true,
inference(paramodulation,[status(thm)],[f3082,f86]) ).
fof(f3541,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(s(sF2_fnc),o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,o),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),sF2_fnc),e1(s(s(sF2_fnc)),s(sF2_fnc)),e2(sF2_fnc,sF2_fnc)) = true,
inference(forward_demodulation,[status(thm)],[f45,f3537]) ).
fof(f4178,plain,
ifeq(true,true,state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(s(sF2_fnc),o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,o),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),s(sF2_fnc)),e1(s(s(sF2_fnc)),sF2_fnc),e2(sF2_fnc,sF2_fnc)),true) = true,
inference(paramodulation,[status(thm)],[f3541,f58]) ).
fof(f4182,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(s(sF2_fnc),o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,o),s1(s(sF2_fnc),sF3_fnc),s2(s(sF2_fnc),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),s(sF2_fnc)),e1(s(s(sF2_fnc)),sF2_fnc),e2(sF2_fnc,sF2_fnc)) = true,
inference(forward_demodulation,[status(thm)],[f45,f4178]) ).
fof(f5480,plain,
ifeq(true,true,state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(s(sF2_fnc),o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,o),s1(s(sF2_fnc),sF3_fnc),s2(s(s(sF2_fnc)),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),s(sF2_fnc)),e1(s(sF2_fnc),sF2_fnc),e2(sF2_fnc,sF2_fnc)),true) = true,
inference(paramodulation,[status(thm)],[f4182,f52]) ).
fof(f5487,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(s(sF2_fnc),o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,o),s1(s(sF2_fnc),sF3_fnc),s2(s(s(sF2_fnc)),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),s(sF2_fnc)),e1(s(sF2_fnc),sF2_fnc),e2(sF2_fnc,sF2_fnc)) = true,
inference(forward_demodulation,[status(thm)],[f45,f5480]) ).
fof(f7855,plain,
ifeq(true,true,state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(s(sF2_fnc),o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,o),s1(s(sF2_fnc),sF3_fnc),s2(s(s(sF2_fnc)),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),s(sF2_fnc)),e1(sF2_fnc,sF2_fnc),e2(s(sF2_fnc),sF2_fnc)),true) = true,
inference(paramodulation,[status(thm)],[f5487,f86]) ).
fof(f7859,plain,
state(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(s(sF2_fnc),o),v4(sF2_fnc,s(sF2_fnc)),h(sF2_fnc,o),s1(s(sF2_fnc),sF3_fnc),s2(s(s(sF2_fnc)),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),s(sF2_fnc)),e1(sF2_fnc,sF2_fnc),e2(s(sF2_fnc),sF2_fnc)) = true,
inference(forward_demodulation,[status(thm)],[f45,f7855]) ).
fof(f12084,plain,
ifeq(true,true,sF0_fnc(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(s(sF2_fnc),o),h(sF2_fnc,o),s1(s(sF2_fnc),sF3_fnc),s2(s(s(sF2_fnc)),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),s(sF2_fnc)),e1(sF2_fnc,s(sF2_fnc)),e2(s(sF2_fnc),s(sF2_fnc))),true) = true,
inference(paramodulation,[status(thm)],[f7859,f166]) ).
fof(f12092,plain,
sF0_fnc(bb(o,sF3_fnc),v1(o,o),v2(o,s(sF2_fnc)),v3(s(sF2_fnc),o),h(sF2_fnc,o),s1(s(sF2_fnc),sF3_fnc),s2(s(s(sF2_fnc)),sF2_fnc),s3(s(s(sF2_fnc)),sF3_fnc),s4(s(s(sF2_fnc)),s(sF2_fnc)),e1(sF2_fnc,s(sF2_fnc)),e2(s(sF2_fnc),s(sF2_fnc))) = true,
inference(forward_demodulation,[status(thm)],[f45,f12084]) ).
fof(f12093,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f12092,f94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ039-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.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 03:51:59 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 7.89/1.44 % Refutation found
% 7.89/1.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 7.89/1.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.10/1.53 % Elapsed time: 1.144817 seconds
% 1.10/1.53 % CPU time: 8.706821 seconds
% 1.10/1.53 % Total memory used: 191.857 MB
% 1.10/1.53 % Net memory used: 190.402 MB
%------------------------------------------------------------------------------