%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : PUZ039-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 02:02:24 PM UTC 2026
% Result : Unsatisfiable 145.40s 21.46s
% Output : CNFRefutation 145.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 32
% Syntax : Number of clauses : 127 ( 127 unt; 0 nHn; 67 RR)
% Number of literals : 127 ( 126 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 2 con; 0-12 aty)
% Number of variables : 731 ( 35 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(swap_blanks,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X11,X12),e2(X13,X14)),true,state(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X13,X14),e2(X11,X12)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',swap_blanks) ).
cnf(initial_state,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',initial_state) ).
cnf(ifeq_axiom,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(v4_down,axiom,
ifeq(state(X1,X2,X3,X4,v4(X5,X6),X7,X8,X9,X10,X11,e1(s(s(X5)),X6),X12),true,state(X1,X2,X3,X4,v4(s(X5),X6),X7,X8,X9,X10,X11,e1(X5,X6),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v4_down) ).
cnf(v2_down,axiom,
ifeq(state(X1,X2,v2(X3,X4),X5,X6,X7,X8,X9,X10,X11,e1(s(s(X3)),X4),X12),true,state(X1,X2,v2(s(X3),X4),X5,X6,X7,X8,X9,X10,X11,e1(X3,X4),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v2_down) ).
cnf(v3_down,axiom,
ifeq(state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(s(s(X4)),X5),X12),true,state(X1,X2,X3,v3(s(X4),X5),X6,X7,X8,X9,X10,X11,e1(X4,X5),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v3_down) ).
cnf(v1_down,axiom,
ifeq(state(X1,v1(X2,X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(s(s(X2)),X3),X12),true,state(X1,v1(s(X2),X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(X2,X3),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1_down) ).
cnf(v2_up,axiom,
ifeq(state(X1,X2,v2(s(X3),X4),X5,X6,X7,X8,X9,X10,X11,e1(X3,X4),X12),true,state(X1,X2,v2(X3,X4),X5,X6,X7,X8,X9,X10,X11,e1(s(s(X3)),X4),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v2_up) ).
cnf(h_right,axiom,
ifeq(state(X1,X2,X3,X4,X5,h(X6,X7),X8,X9,X10,X11,e1(X6,s(s(X7))),X12),true,state(X1,X2,X3,X4,X5,h(X6,s(X7)),X8,X9,X10,X11,e1(X6,X7),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_right) ).
cnf(s1_up,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,s1(s(X7),X8),X9,X10,X11,e1(X7,X8),X12),true,state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(s(X7),X8),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_up) ).
cnf(s3_up,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,s3(s(X9),X10),X11,e1(X9,X10),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(s(X9),X10),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_up) ).
cnf(v1_up,axiom,
ifeq(state(X1,v1(s(X2),X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(X2,X3),X12),true,state(X1,v1(X2,X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(s(s(X2)),X3),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1_up) ).
cnf(s1_left,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,s1(X7,s(X8)),X9,X10,X11,e1(X7,X8),X12),true,state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(X7,s(X8)),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_left) ).
cnf(v3_right,axiom,
ifeq(state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(X4,s(X5)),e2(s(X4),s(X5))),true,state(X1,X2,X3,v3(X4,s(X5)),X6,X7,X8,X9,X10,X11,e1(X4,X5),e2(s(X4),X5)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v3_right) ).
cnf(s1_down,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(s(X7),X8),X12),true,state(X1,X2,X3,X4,X5,X6,s1(s(X7),X8),X9,X10,X11,e1(X7,X8),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_down) ).
cnf(s3_left,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,s(X10)),X11,e1(X9,X10),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(X9,s(X10)),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_left) ).
cnf(s3_down,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(s(X9),X10),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,s3(s(X9),X10),X11,e1(X9,X10),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_down) ).
cnf(h_left,axiom,
ifeq(state(X1,X2,X3,X4,X5,h(X6,s(X7)),X8,X9,X10,X11,e1(X6,X7),X12),true,state(X1,X2,X3,X4,X5,h(X6,X7),X8,X9,X10,X11,e1(X6,s(s(X7))),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_left) ).
cnf(s2_up,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,s2(s(X8),X9),X10,X11,e1(X8,X9),X12),true,state(X1,X2,X3,X4,X5,X6,X7,s2(X8,X9),X10,X11,e1(s(X8),X9),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_up) ).
cnf(s4_up,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(s(X10),X11),e1(X10,X11),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,X11),e1(s(X10),X11),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_up) ).
cnf(s2_right,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,s2(X8,X9),X10,X11,e1(X8,s(X9)),X12),true,state(X1,X2,X3,X4,X5,X6,X7,s2(X8,s(X9)),X10,X11,e1(X8,X9),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_right) ).
cnf(s1_right,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(X7,s(X8)),X12),true,state(X1,X2,X3,X4,X5,X6,s1(X7,s(X8)),X9,X10,X11,e1(X7,X8),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_right) ).
cnf(h_down,axiom,
ifeq(state(X1,X2,X3,X4,X5,h(X6,X7),X8,X9,X10,X11,e1(s(X6),X7),e2(s(X6),s(X7))),true,state(X1,X2,X3,X4,X5,h(s(X6),X7),X8,X9,X10,X11,e1(X6,X7),e2(X6,s(X7))),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_down) ).
cnf(s4_left,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,s(X11)),e1(X10,X11),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,X11),e1(X10,s(X11)),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_left) ).
cnf(s2_left,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,s2(X8,s(X9)),X10,X11,e1(X8,X9),X12),true,state(X1,X2,X3,X4,X5,X6,X7,s2(X8,X9),X10,X11,e1(X8,s(X9)),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_left) ).
cnf(v3_up,axiom,
ifeq(state(X1,X2,X3,v3(s(X4),X5),X6,X7,X8,X9,X10,X11,e1(X4,X5),X12),true,state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(s(s(X4)),X5),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v3_up) ).
cnf(s3_right,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(X9,s(X10)),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,s(X10)),X11,e1(X9,X10),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_right) ).
cnf(v4_up,axiom,
ifeq(state(X1,X2,X3,X4,v4(s(X5),X6),X7,X8,X9,X10,X11,e1(X5,X6),X12),true,state(X1,X2,X3,X4,v4(X5,X6),X7,X8,X9,X10,X11,e1(s(s(X5)),X6),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v4_up) ).
cnf(s4_down,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,X11),e1(s(X10),X11),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(s(X10),X11),e1(X10,X11),X12),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_down) ).
cnf(v3_left,axiom,
ifeq(state(X1,X2,X3,v3(X4,s(X5)),X6,X7,X8,X9,X10,X11,e1(X4,X5),e2(s(X4),X5)),true,state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(X4,s(X5)),e2(s(X4),s(X5))),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v3_left) ).
cnf(goal_state,negated_conjecture,
state(X1,X2,X3,X4,v4(s(s(o)),s(s(o))),X5,X6,X7,X8,X9,X10,X11) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_state) ).
cnf(v4_left,axiom,
ifeq(state(X1,X2,X3,X4,v4(X5,s(X6)),X7,X8,X9,X10,X11,e1(X5,X6),e2(s(X5),X6)),true,state(X1,X2,X3,X4,v4(X5,X6),X7,X8,X9,X10,X11,e1(X5,s(X6)),e2(s(X5),s(X6))),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v4_left) ).
cnf(c_0_32,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X11,X12),e2(X13,X14)),true,state(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X13,X14),e2(X11,X12)),true) = true,
swap_blanks ).
cnf(c_0_33,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,
initial_state ).
cnf(c_0_34,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_35,axiom,
ifeq(state(X1,X2,X3,X4,v4(X5,X6),X7,X8,X9,X10,X11,e1(s(s(X5)),X6),X12),true,state(X1,X2,X3,X4,v4(s(X5),X6),X7,X8,X9,X10,X11,e1(X5,X6),X12),true) = true,
v4_down ).
cnf(c_0_36,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)))),s(s(s(o)))),e2(s(s(s(s(o)))),o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_37,axiom,
ifeq(state(X1,X2,v2(X3,X4),X5,X6,X7,X8,X9,X10,X11,e1(s(s(X3)),X4),X12),true,state(X1,X2,v2(s(X3),X4),X5,X6,X7,X8,X9,X10,X11,e1(X3,X4),X12),true) = true,
v2_down ).
cnf(c_0_38,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(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(o)),s(s(s(o)))),e2(s(s(s(s(o)))),o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_34]) ).
cnf(c_0_39,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(o)),o),v4(s(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(o,s(s(s(o)))),e2(s(s(s(s(o)))),o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_34]) ).
cnf(c_0_40,axiom,
ifeq(state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(s(s(X4)),X5),X12),true,state(X1,X2,X3,v3(s(X4),X5),X6,X7,X8,X9,X10,X11,e1(X4,X5),X12),true) = true,
v3_down ).
cnf(c_0_41,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(o)),o),v4(s(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(o,s(s(s(o))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_39]),c_0_34]) ).
cnf(c_0_42,axiom,
ifeq(state(X1,v1(X2,X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(s(s(X2)),X3),X12),true,state(X1,v1(s(X2),X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(X2,X3),X12),true) = true,
v1_down ).
cnf(c_0_43,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),o),v4(s(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(o)),o),e2(o,s(s(s(o))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_34]) ).
cnf(c_0_44,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),o),v4(s(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(o,o),e2(o,s(s(s(o))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_34]) ).
cnf(c_0_45,axiom,
ifeq(state(X1,X2,v2(s(X3),X4),X5,X6,X7,X8,X9,X10,X11,e1(X3,X4),X12),true,state(X1,X2,v2(X3,X4),X5,X6,X7,X8,X9,X10,X11,e1(s(s(X3)),X4),X12),true) = true,
v2_up ).
cnf(c_0_46,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),o),v4(s(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(o,s(s(s(o)))),e2(o,o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_44]),c_0_34]) ).
cnf(c_0_47,axiom,
ifeq(state(X1,X2,X3,X4,X5,h(X6,X7),X8,X9,X10,X11,e1(X6,s(s(X7))),X12),true,state(X1,X2,X3,X4,X5,h(X6,s(X7)),X8,X9,X10,X11,e1(X6,X7),X12),true) = true,
h_right ).
cnf(c_0_48,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(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(o)),s(s(s(o)))),e2(o,o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_34]) ).
cnf(c_0_49,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,s1(s(X7),X8),X9,X10,X11,e1(X7,X8),X12),true,state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(s(X7),X8),X12),true) = true,
s1_up ).
cnf(c_0_50,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(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(o)),s(o)),e2(o,o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_34]) ).
cnf(c_0_51,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,s3(s(X9),X10),X11,e1(X9,X10),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(s(X9),X10),X12),true) = true,
s3_up ).
cnf(c_0_52,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(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(o))),s(o)),e2(o,o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_34]) ).
cnf(c_0_53,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),s(o)),e2(o,o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_34]) ).
cnf(c_0_54,axiom,
ifeq(state(X1,v1(s(X2),X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(X2,X3),X12),true,state(X1,v1(X2,X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(s(s(X2)),X3),X12),true) = true,
v1_up ).
cnf(c_0_55,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(o,o),e2(s(s(s(s(o)))),s(o))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_53]),c_0_34]) ).
cnf(c_0_56,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,s1(X7,s(X8)),X9,X10,X11,e1(X7,X8),X12),true,state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(X7,s(X8)),X12),true) = true,
s1_left ).
cnf(c_0_57,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(s(s(s(s(o)))),s(o))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_34]) ).
cnf(c_0_58,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(o)),e2(s(s(s(s(o)))),s(o))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_34]) ).
cnf(c_0_59,axiom,
ifeq(state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(X4,s(X5)),e2(s(X4),s(X5))),true,state(X1,X2,X3,v3(X4,s(X5)),X6,X7,X8,X9,X10,X11,e1(X4,X5),e2(s(X4),X5)),true) = true,
v3_right ).
cnf(c_0_60,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(o))),s(o)),e2(s(s(s(s(o)))),s(o))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_58]),c_0_34]) ).
cnf(c_0_61,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(s(X7),X8),X12),true,state(X1,X2,X3,X4,X5,X6,s1(s(X7),X8),X9,X10,X11,e1(X7,X8),X12),true) = true,
s1_down ).
cnf(c_0_62,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(o))),o),e2(s(s(s(s(o)))),o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_34]) ).
cnf(c_0_63,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,s(X10)),X11,e1(X9,X10),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(X9,s(X10)),X12),true) = true,
s3_left ).
cnf(c_0_64,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(o))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(s(s(s(s(o)))),o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_34]) ).
cnf(c_0_65,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(o))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(o)),e2(s(s(s(s(o)))),o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_34]) ).
cnf(c_0_66,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(o))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(o)),s(o))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_65]),c_0_34]) ).
cnf(c_0_67,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(s(X9),X10),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,s3(s(X9),X10),X11,e1(X9,X10),X12),true) = true,
s3_down ).
cnf(c_0_68,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(o))),o),e2(s(s(o)),s(o))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_66]),c_0_34]) ).
cnf(c_0_69,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(s(s(o)),s(o))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_34]) ).
cnf(c_0_70,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(o,o),e2(s(s(o)),s(o))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_69]),c_0_34]) ).
cnf(c_0_71,axiom,
ifeq(state(X1,X2,X3,X4,X5,h(X6,s(X7)),X8,X9,X10,X11,e1(X6,X7),X12),true,state(X1,X2,X3,X4,X5,h(X6,X7),X8,X9,X10,X11,e1(X6,s(s(X7))),X12),true) = true,
h_left ).
cnf(c_0_72,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(o)),e2(o,o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_70]),c_0_34]) ).
cnf(c_0_73,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(s(s(o)))),e2(o,o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_34]) ).
cnf(c_0_74,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(o,s(s(s(o)))),e2(o,o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_73]),c_0_34]) ).
cnf(c_0_75,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(o,o),e2(o,s(s(s(o))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_74]),c_0_34]) ).
cnf(c_0_76,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(o,s(s(s(o))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_75]),c_0_34]) ).
cnf(c_0_77,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,s2(s(X8),X9),X10,X11,e1(X8,X9),X12),true,state(X1,X2,X3,X4,X5,X6,X7,s2(X8,X9),X10,X11,e1(s(X8),X9),X12),true) = true,
s2_up ).
cnf(c_0_78,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(s(o))),e2(o,s(s(s(o))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_76]),c_0_34]) ).
cnf(c_0_79,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(s(X10),X11),e1(X10,X11),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,X11),e1(s(X10),X11),X12),true) = true,
s4_up ).
cnf(c_0_80,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),o),s2(s(s(o)),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(o))),s(s(o))),e2(o,s(s(s(o))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_34]) ).
cnf(c_0_81,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),o),s2(s(s(o)),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(o))),s(s(o))),e1(s(s(s(s(o)))),s(s(o))),e2(o,s(s(s(o))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_34]) ).
cnf(c_0_82,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),o),s2(s(s(o)),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(o))),s(s(o))),e1(o,s(s(s(o)))),e2(s(s(s(s(o)))),s(s(o)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_81]),c_0_34]) ).
cnf(c_0_83,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,s2(X8,X9),X10,X11,e1(X8,s(X9)),X12),true,state(X1,X2,X3,X4,X5,X6,X7,s2(X8,s(X9)),X10,X11,e1(X8,X9),X12),true) = true,
s2_right ).
cnf(c_0_84,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),o),s2(s(s(o)),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(o))),s(s(o))),e1(s(s(o)),s(s(s(o)))),e2(s(s(s(s(o)))),s(s(o)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_82]),c_0_34]) ).
cnf(c_0_85,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),o),s2(s(s(o)),s(s(s(o)))),s3(s(s(s(o))),o),s4(s(s(s(o))),s(s(o))),e1(s(s(o)),s(s(o))),e2(s(s(s(s(o)))),s(s(o)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_34]) ).
cnf(c_0_86,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),o),s2(s(s(o)),s(s(s(o)))),s3(s(s(s(o))),o),s4(s(s(o)),s(s(o))),e1(s(s(s(o))),s(s(o))),e2(s(s(s(s(o)))),s(s(o)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_85]),c_0_34]) ).
cnf(c_0_87,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),o),s2(s(s(o)),s(s(s(o)))),s3(s(s(s(o))),o),s4(s(s(o)),s(s(o))),e1(s(s(s(o))),s(o)),e2(s(s(s(s(o)))),s(o))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_86]),c_0_34]) ).
cnf(c_0_88,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(X7,s(X8)),X12),true,state(X1,X2,X3,X4,X5,X6,s1(X7,s(X8)),X9,X10,X11,e1(X7,X8),X12),true) = true,
s1_right ).
cnf(c_0_89,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),o),s2(s(s(o)),s(s(s(o)))),s3(s(s(s(o))),o),s4(s(s(o)),s(s(o))),e1(s(s(s(s(o)))),s(o)),e2(s(s(s(o))),s(o))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_87]),c_0_34]) ).
cnf(c_0_90,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(s(o)))),s3(s(s(s(o))),o),s4(s(s(o)),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(o))),s(o))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_34]) ).
cnf(c_0_91,axiom,
ifeq(state(X1,X2,X3,X4,X5,h(X6,X7),X8,X9,X10,X11,e1(s(X6),X7),e2(s(X6),s(X7))),true,state(X1,X2,X3,X4,X5,h(s(X6),X7),X8,X9,X10,X11,e1(X6,X7),e2(X6,s(X7))),true) = true,
h_down ).
cnf(c_0_92,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(s(o)))),s3(s(s(s(s(o)))),o),s4(s(s(o)),s(s(o))),e1(s(s(s(o))),o),e2(s(s(s(o))),s(o))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_90]),c_0_34]) ).
cnf(c_0_93,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(s(o)))),s3(s(s(s(s(o)))),o),s4(s(s(o)),s(s(o))),e1(s(s(o)),o),e2(s(s(o)),s(o))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_34]) ).
cnf(c_0_94,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(s(o)))),s3(s(s(s(s(o)))),o),s4(s(s(o)),s(s(o))),e1(o,o),e2(s(s(o)),s(o))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_93]),c_0_34]) ).
cnf(c_0_95,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,s(X11)),e1(X10,X11),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,X11),e1(X10,s(X11)),X12),true) = true,
s4_left ).
cnf(c_0_96,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(s(o)))),s3(s(s(s(s(o)))),o),s4(s(s(o)),s(s(o))),e1(s(s(o)),s(o)),e2(o,o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_94]),c_0_34]) ).
cnf(c_0_97,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,s2(X8,s(X9)),X10,X11,e1(X8,X9),X12),true,state(X1,X2,X3,X4,X5,X6,X7,s2(X8,X9),X10,X11,e1(X8,s(X9)),X12),true) = true,
s2_left ).
cnf(c_0_98,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(s(o)))),s3(s(s(s(s(o)))),o),s4(s(s(o)),s(o)),e1(s(s(o)),s(s(o))),e2(o,o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_34]) ).
cnf(c_0_99,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(o))),s3(s(s(s(s(o)))),o),s4(s(s(o)),s(o)),e1(s(s(o)),s(s(s(o)))),e2(o,o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_34]) ).
cnf(c_0_100,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(o))),s3(s(s(s(s(o)))),o),s4(s(s(o)),s(o)),e1(o,s(s(s(o)))),e2(o,o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_99]),c_0_34]) ).
cnf(c_0_101,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(o))),s3(s(s(s(s(o)))),o),s4(s(s(o)),s(o)),e1(o,o),e2(o,s(s(s(o))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_100]),c_0_34]) ).
cnf(c_0_102,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(o))),s3(s(s(s(s(o)))),o),s4(s(s(o)),s(o)),e1(s(s(o)),o),e2(o,s(s(s(o))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_101]),c_0_34]) ).
cnf(c_0_103,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(o))),s3(s(s(s(s(o)))),o),s4(s(s(o)),o),e1(s(s(o)),s(o)),e2(o,s(s(s(o))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_102]),c_0_34]) ).
cnf(c_0_104,axiom,
ifeq(state(X1,X2,X3,v3(s(X4),X5),X6,X7,X8,X9,X10,X11,e1(X4,X5),X12),true,state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(s(s(X4)),X5),X12),true) = true,
v3_up ).
cnf(c_0_105,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),o),s4(s(s(o)),o),e1(s(s(o)),s(s(o))),e2(o,s(s(s(o))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_103]),c_0_34]) ).
cnf(c_0_106,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),o),s4(s(s(o)),o),e1(s(s(s(s(o)))),s(s(o))),e2(o,s(s(s(o))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_34]) ).
cnf(c_0_107,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(X9,s(X10)),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,s(X10)),X11,e1(X9,X10),X12),true) = true,
s3_right ).
cnf(c_0_108,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(s(o))),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),o),s4(s(s(o)),o),e1(s(s(s(s(o)))),s(o)),e2(o,s(s(s(o))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_106]),c_0_34]) ).
cnf(c_0_109,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(s(o))),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),s(o)),s4(s(s(o)),o),e1(s(s(s(s(o)))),o),e2(o,s(s(s(o))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_34]) ).
cnf(c_0_110,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(s(o))),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),s(o)),s4(s(s(o)),o),e1(o,s(s(s(o)))),e2(s(s(s(s(o)))),o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_109]),c_0_34]) ).
cnf(c_0_111,axiom,
ifeq(state(X1,X2,X3,X4,v4(s(X5),X6),X7,X8,X9,X10,X11,e1(X5,X6),X12),true,state(X1,X2,X3,X4,v4(X5,X6),X7,X8,X9,X10,X11,e1(s(s(X5)),X6),X12),true) = true,
v4_up ).
cnf(c_0_112,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(s(o))),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),s(o)),s4(s(s(o)),o),e1(s(s(o)),s(s(s(o)))),e2(s(s(s(s(o)))),o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_110]),c_0_34]) ).
cnf(c_0_113,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(o)),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(s(o))),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),s(o)),s4(s(s(o)),o),e1(s(s(s(s(o)))),s(s(s(o)))),e2(s(s(s(s(o)))),o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_34]) ).
cnf(c_0_114,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(o)),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(s(s(o)))),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),s(o)),s4(s(s(o)),o),e1(s(s(s(s(o)))),s(s(o))),e2(s(s(s(s(o)))),o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_113]),c_0_34]) ).
cnf(c_0_115,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(o)),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(s(s(o)))),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),s(s(o))),s4(s(s(o)),o),e1(s(s(s(s(o)))),s(o)),e2(s(s(s(s(o)))),o)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_114]),c_0_34]) ).
cnf(c_0_116,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(o)),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(s(s(o)))),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),s(s(o))),s4(s(s(o)),o),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(o))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_115]),c_0_34]) ).
cnf(c_0_117,axiom,
ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,X11),e1(s(X10),X11),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(s(X10),X11),e1(X10,X11),X12),true) = true,
s4_down ).
cnf(c_0_118,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(o)),s(s(s(o)))),h(s(s(s(s(o)))),o),s1(s(s(s(s(o)))),s(s(s(o)))),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),s(s(o))),s4(s(s(o)),o),e1(s(s(s(o))),o),e2(s(s(s(o))),s(o))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_116]),c_0_34]) ).
cnf(c_0_119,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(o)),s(s(s(o)))),h(s(s(s(s(o)))),o),s1(s(s(s(s(o)))),s(s(s(o)))),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),s(s(o))),s4(s(s(s(o))),o),e1(s(s(o)),o),e2(s(s(s(o))),s(o))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_34]) ).
cnf(c_0_120,axiom,
ifeq(state(X1,X2,X3,v3(X4,s(X5)),X6,X7,X8,X9,X10,X11,e1(X4,X5),e2(s(X4),X5)),true,state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(X4,s(X5)),e2(s(X4),s(X5))),true) = true,
v3_left ).
cnf(c_0_121,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(o)),s(s(s(o)))),h(s(s(s(s(o)))),o),s1(s(s(s(s(o)))),s(s(s(o)))),s2(s(s(o)),o),s3(s(s(s(s(o)))),s(s(o))),s4(s(s(s(o))),o),e1(s(s(o)),s(o)),e2(s(s(s(o))),s(o))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_119]),c_0_34]) ).
cnf(c_0_122,negated_conjecture,
state(X1,X2,X3,X4,v4(s(s(o)),s(s(o))),X5,X6,X7,X8,X9,X10,X11) != true,
inference(fof_simplification,[status(thm)],[goal_state]) ).
cnf(c_0_123,axiom,
ifeq(state(X1,X2,X3,X4,v4(X5,s(X6)),X7,X8,X9,X10,X11,e1(X5,X6),e2(s(X5),X6)),true,state(X1,X2,X3,X4,v4(X5,X6),X7,X8,X9,X10,X11,e1(X5,s(X6)),e2(s(X5),s(X6))),true) = true,
v4_left ).
cnf(c_0_124,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),s(o)),v4(s(s(o)),s(s(s(o)))),h(s(s(s(s(o)))),o),s1(s(s(s(s(o)))),s(s(s(o)))),s2(s(s(o)),o),s3(s(s(s(s(o)))),s(s(o))),s4(s(s(s(o))),o),e1(s(s(o)),s(s(o))),e2(s(s(s(o))),s(s(o)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_34]) ).
cnf(c_0_125,negated_conjecture,
state(X1,X2,X3,X4,v4(s(s(o)),s(s(o))),X5,X6,X7,X8,X9,X10,X11) != true,
c_0_122 ).
cnf(c_0_126,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_34]),c_0_125]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ039-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.03/0.37 % CPULimit : 300
% 0.03/0.37 % WCLimit : 300
% 0.03/0.37 % DateTime : Mon Sep 21 03:46:21 UTC 2026
% 0.03/0.37 % CPUTime :
% 0.03/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.41 Running first-order theorem proving
% 0.03/0.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 145.40/21.46 % Version: 3.5.1
% 145.40/21.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 145.40/21.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 145.40/21.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 145.40/21.46 % Starting new_bool_3 with 300s (1) cores
% 145.40/21.46 % Starting new_bool_1 with 300s (1) cores
% 145.40/21.46 % Starting sh5l with 300s (1) cores
% 145.40/21.46 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2175538 completed with status 0
% 145.40/21.46 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 145.40/21.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 145.40/21.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 145.40/21.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 145.40/21.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 145.40/21.46 % No SInE strategy applied
% 145.40/21.46 % Search class: FUUPM-FFLF32-DFFFFFNN
% 145.40/21.46 % partial match(1): FUUPM-FFSF32-DFFFFFNN
% 145.40/21.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 145.40/21.46 % Starting SubtermCWHack with 136s (1) cores
% 145.40/21.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 145.40/21.46 % Starting G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with 136s (1) cores
% 145.40/21.46 % Starting new_bool_3 with 136s (1) cores
% 145.40/21.46 % Starting new_bool_1 with 136s (1) cores
% 145.40/21.46 % G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with pid 2175545 completed with status 0
% 145.40/21.46 % Result found by G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S
% 145.40/21.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 145.40/21.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 145.40/21.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 145.40/21.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 145.40/21.46 % No SInE strategy applied
% 145.40/21.46 % Search class: FUUPM-FFLF32-DFFFFFNN
% 145.40/21.46 % partial match(1): FUUPM-FFSF32-DFFFFFNN
% 145.40/21.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 145.40/21.46 % Starting SubtermCWHack with 136s (1) cores
% 145.40/21.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 145.40/21.46 % Starting G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with 136s (1) cores
% 145.40/21.46 % Preprocessing time : 0.001 s
% 145.40/21.46 % Presaturation interreduction done
% 145.40/21.46
% 145.40/21.46 % Proof found!
% 145.40/21.46 % SZS status Unsatisfiable
% 145.40/21.46 % SZS output start CNFRefutation
% See solution above
% 145.40/21.46 % Parsed axioms : 44
% 145.40/21.46 % Removed by relevancy pruning/SinE : 0
% 145.40/21.46 % Initial clauses : 44
% 145.40/21.46 % Removed in clause preprocessing : 0
% 145.40/21.46 % Initial clauses in saturation : 44
% 145.40/21.46 % Processed clauses : 13417
% 145.40/21.46 % ...of these trivial : 3213
% 145.40/21.46 % ...subsumed : 0
% 145.40/21.46 % ...remaining for further processing : 10204
% 145.40/21.46 % Other redundant clauses eliminated : 0
% 145.40/21.46 % Clauses deleted for lack of memory : 0
% 145.40/21.46 % Backward-subsumed : 0
% 145.40/21.46 % Backward-rewritten : 20
% 145.40/21.46 % Generated clauses : 54416
% 145.40/21.46 % ...of the previous two non-redundant : 28458
% 145.40/21.46 % ...aggressively subsumed : 0
% 145.40/21.46 % Contextual simplify-reflections : 0
% 145.40/21.46 % Paramodulations : 54416
% 145.40/21.46 % Factorizations : 0
% 145.40/21.46 % NegExts : 0
% 145.40/21.46 % Equation resolutions : 0
% 145.40/21.46 % Disequality decompositions : 0
% 145.40/21.46 % Total rewrite steps : 69973
% 145.40/21.46 % ...of those cached : 49341
% 145.40/21.46 % Propositional unsat checks : 2
% 145.40/21.46 % Propositional check models : 2
% 145.40/21.46 % Propositional check unsatisfiable : 0
% 145.40/21.46 % Propositional clauses : 0
% 145.40/21.46 % Propositional clauses after purity: 0
% 145.40/21.46 % Propositional unsat core size : 0
% 145.40/21.46 % Propositional preprocessing time : 0.000
% 145.40/21.46 % Propositional encoding time : 0.025
% 145.40/21.46 % Propositional solver time : 0.001
% 145.40/21.46 % Success case prop preproc time : 0.000
% 145.40/21.46 % Success case prop encoding time : 0.000
% 145.40/21.46 % Success case prop solver time : 0.000
% 145.40/21.46 % Current number of processed clauses : 10140
% 145.40/21.46 % Positive orientable unit clauses : 10139
% 145.40/21.46 % Positive unorientable unit clauses: 0
% 145.40/21.46 % Negative unit clauses : 1
% 145.40/21.46 % Non-unit-clauses : 0
% 145.40/21.46 % Current number of unprocessed clauses: 15129
% 145.40/21.46 % ...number of literals in the above : 15129
% 145.40/21.46 % Current number of archived formulas : 0
% 145.40/21.46 % Current number of archived clauses : 64
% 145.40/21.46 % Clause-clause subsumption calls (NU) : 0
% 145.40/21.46 % Rec. Clause-clause subsumption calls : 0
% 145.40/21.46 % Non-unit clause-clause subsumptions : 0
% 145.40/21.46 % Unit Clause-clause subsumption calls : 0
% 145.40/21.46 % Rewrite failures with RHS unbound : 0
% 145.40/21.46 % BW rewrite match attempts : 32199456
% 145.40/21.46 % BW rewrite match successes : 20
% 145.40/21.46 % Condensation attempts : 0
% 145.40/21.46 % Condensation successes : 0
% 145.40/21.46 % Termbank termtop insertions : 4645634
% 145.40/21.46 % Search garbage collected termcells : 2
% 145.40/21.46
% 145.40/21.46 % -------------------------------------------------
% 145.40/21.46 % User time : 20.596 s
% 145.40/21.46 % System time : 0.228 s
% 145.40/21.46 % Total time : 20.824 s
% 145.40/21.46 % Maximum resident set size: 3424 pages
% 145.40/21.46
% 145.40/21.46 % -------------------------------------------------
% 145.40/21.46 % User time : 102.025 s
% 145.40/21.46 % System time : 1.286 s
% 145.40/21.46 % Total time : 103.312 s
% 145.40/21.46 % Maximum resident set size: 4608 pages
% 145.40/21.46 % E exiting
%------------------------------------------------------------------------------