%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ040-1 : TPTP v9.3.1. Bugfixed v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /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 : Sun Sep 27 08:23:12 AM UTC 2026
% Result : Unsatisfiable 2.41s 0.69s
% Output : CNFRefutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 48 ( 24 unt; 0 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 54 ( 30 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-12 aty)
% Number of functors : 14 ( 14 usr; 1 con; 0-2 aty)
% Number of variables : 343 ( 44 sgn 155 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_left,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,VAR_11] :
( state(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,s1(VAR_6,VAR_7),VAR_8,VAR_9,VAR_10,e1(VAR_6,s(VAR_7)),VAR_11)
| ~ state(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,s1(VAR_6,s(VAR_7)),VAR_8,VAR_9,VAR_10,e1(VAR_6,VAR_7),VAR_11) ),
file('theBenchmark.p',s1_left) ).
cnf(c_2,plain,
( state(A,B,C,D,E,F,s1(V6,V7),V8,V9,V10,e1(V6,s(V7)),V11)
| ~ state(A,B,C,D,E,F,s1(V6,s(V7)),V8,V9,V10,e1(V6,V7),V11) ),
inference(clausify,[status(thm)],[s1_left]) ).
fof(s1_down,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,VAR_11] :
( state(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,s1(s(VAR_6),VAR_7),VAR_8,VAR_9,VAR_10,e1(VAR_6,VAR_7),VAR_11)
| ~ state(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,s1(VAR_6,VAR_7),VAR_8,VAR_9,VAR_10,e1(s(VAR_6),VAR_7),VAR_11) ),
file('theBenchmark.p',s1_down) ).
cnf(c_3,plain,
( state(A,B,C,D,E,F,s1(s(V6),V7),V8,V9,V10,e1(V6,V7),V11)
| ~ state(A,B,C,D,E,F,s1(V6,V7),V8,V9,V10,e1(s(V6),V7),V11) ),
inference(clausify,[status(thm)],[s1_down]) ).
fof(s1_up,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,VAR_11] :
( state(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,s1(VAR_6,VAR_7),VAR_8,VAR_9,VAR_10,e1(s(VAR_6),VAR_7),VAR_11)
| ~ state(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,s1(s(VAR_6),VAR_7),VAR_8,VAR_9,VAR_10,e1(VAR_6,VAR_7),VAR_11) ),
file('theBenchmark.p',s1_up) ).
cnf(c_4,plain,
( state(A,B,C,D,E,F,s1(V6,V7),V8,V9,V10,e1(s(V6),V7),V11)
| ~ state(A,B,C,D,E,F,s1(s(V6),V7),V8,V9,V10,e1(V6,V7),V11) ),
inference(clausify,[status(thm)],[s1_up]) ).
fof(s3_up,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,VAR_11] :
( state(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,s3(VAR_8,VAR_9),VAR_10,e1(s(VAR_8),VAR_9),VAR_11)
| ~ state(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,s3(s(VAR_8),VAR_9),VAR_10,e1(VAR_8,VAR_9),VAR_11) ),
file('theBenchmark.p',s3_up) ).
cnf(c_12,plain,
( state(A,B,C,D,E,F,V6,V7,s3(V8,V9),V10,e1(s(V8),V9),V11)
| ~ state(A,B,C,D,E,F,V6,V7,s3(s(V8),V9),V10,e1(V8,V9),V11) ),
inference(clausify,[status(thm)],[s3_up]) ).
fof(v1_down,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,VAR_11] :
( state(VAR_0,v1(s(VAR_1),VAR_2),VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,e1(VAR_1,VAR_2),VAR_11)
| ~ state(VAR_0,v1(VAR_1,VAR_2),VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,e1(s(s(VAR_1)),VAR_2),VAR_11) ),
file('theBenchmark.p',v1_down) ).
cnf(c_19,plain,
( state(A,v1(s(B),C),D,E,F,V6,V7,V8,V9,V10,e1(B,C),V11)
| ~ state(A,v1(B,C),D,E,F,V6,V7,V8,V9,V10,e1(s(s(B)),C),V11) ),
inference(clausify,[status(thm)],[v1_down]) ).
fof(v1_up,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,VAR_11] :
( state(VAR_0,v1(VAR_1,VAR_2),VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,e1(s(s(VAR_1)),VAR_2),VAR_11)
| ~ state(VAR_0,v1(s(VAR_1),VAR_2),VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,e1(VAR_1,VAR_2),VAR_11) ),
file('theBenchmark.p',v1_up) ).
cnf(c_20,plain,
( state(A,v1(B,C),D,E,F,V6,V7,V8,V9,V10,e1(s(s(B)),C),V11)
| ~ state(A,v1(s(B),C),D,E,F,V6,V7,V8,V9,V10,e1(B,C),V11) ),
inference(clausify,[status(thm)],[v1_up]) ).
fof(v3_right,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10] :
( state(VAR_0,VAR_1,VAR_2,v3(VAR_3,s(VAR_4)),VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,e1(VAR_3,VAR_4),e2(s(VAR_3),VAR_4))
| ~ state(VAR_0,VAR_1,VAR_2,v3(VAR_3,VAR_4),VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,e1(VAR_3,s(VAR_4)),e2(s(VAR_3),s(VAR_4))) ),
file('theBenchmark.p',v3_right) ).
cnf(c_25,plain,
( state(A,B,C,v3(D,s(E)),F,V6,V7,V8,V9,V10,e1(D,E),e2(s(D),E))
| ~ state(A,B,C,v3(D,E),F,V6,V7,V8,V9,V10,e1(D,s(E)),e2(s(D),s(E))) ),
inference(clausify,[status(thm)],[v3_right]) ).
fof(v3_down,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,VAR_11] :
( state(VAR_0,VAR_1,VAR_2,v3(s(VAR_3),VAR_4),VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,e1(VAR_3,VAR_4),VAR_11)
| ~ state(VAR_0,VAR_1,VAR_2,v3(VAR_3,VAR_4),VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,e1(s(s(VAR_3)),VAR_4),VAR_11) ),
file('theBenchmark.p',v3_down) ).
cnf(c_27,plain,
( state(A,B,C,v3(s(D),E),F,V6,V7,V8,V9,V10,e1(D,E),V11)
| ~ state(A,B,C,v3(D,E),F,V6,V7,V8,V9,V10,e1(s(s(D)),E),V11) ),
inference(clausify,[status(thm)],[v3_down]) ).
fof(v4_down,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,VAR_11] :
( state(VAR_0,VAR_1,VAR_2,VAR_3,v4(s(VAR_4),VAR_5),VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,e1(VAR_4,VAR_5),VAR_11)
| ~ state(VAR_0,VAR_1,VAR_2,VAR_3,v4(VAR_4,VAR_5),VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,e1(s(s(VAR_4)),VAR_5),VAR_11) ),
file('theBenchmark.p',v4_down) ).
cnf(c_31,plain,
( state(A,B,C,D,v4(s(E),F),V6,V7,V8,V9,V10,e1(E,F),V11)
| ~ state(A,B,C,D,v4(E,F),V6,V7,V8,V9,V10,e1(s(s(E)),F),V11) ),
inference(clausify,[status(thm)],[v4_down]) ).
fof(h_right,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,VAR_11] :
( state(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,h(VAR_5,s(VAR_6)),VAR_7,VAR_8,VAR_9,VAR_10,e1(VAR_5,VAR_6),VAR_11)
| ~ state(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,h(VAR_5,VAR_6),VAR_7,VAR_8,VAR_9,VAR_10,e1(VAR_5,s(s(VAR_6))),VAR_11) ),
file('theBenchmark.p',h_right) ).
cnf(c_33,plain,
( state(A,B,C,D,E,h(F,s(V6)),V7,V8,V9,V10,e1(F,V6),V11)
| ~ state(A,B,C,D,E,h(F,V6),V7,V8,V9,V10,e1(F,s(s(V6))),V11) ),
inference(clausify,[status(thm)],[h_right]) ).
fof(b_left,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10] :
( state(bb(VAR_0,VAR_1),VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,e1(VAR_0,s(s(VAR_1))),e2(s(VAR_0),s(s(VAR_1))))
| ~ state(bb(VAR_0,s(VAR_1)),VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,e1(VAR_0,VAR_1),e2(s(VAR_0),VAR_1)) ),
file('theBenchmark.p',b_left) ).
cnf(c_38,plain,
( state(bb(A,B),C,D,E,F,V6,V7,V8,V9,V10,e1(A,s(s(B))),e2(s(A),s(s(B))))
| ~ state(bb(A,s(B)),C,D,E,F,V6,V7,V8,V9,V10,e1(A,B),e2(s(A),B)) ),
inference(clausify,[status(thm)],[b_left]) ).
fof(swap_blanks,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,VAR_11,VAR_12,VAR_13] :
( state(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,e1(VAR_12,VAR_13),e2(VAR_10,VAR_11))
| ~ state(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,e1(VAR_10,VAR_11),e2(VAR_12,VAR_13)) ),
file('theBenchmark.p',swap_blanks) ).
cnf(c_41,plain,
( state(A,B,C,D,E,F,V6,V7,V8,V9,e1(V12,V13),e2(V10,V11))
| ~ state(A,B,C,D,E,F,V6,V7,V8,V9,e1(V10,V11),e2(V12,V13)) ),
inference(clausify,[status(thm)],[swap_blanks]) ).
fof(initial_state,axiom,
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))))),
file('theBenchmark.p',initial_state) ).
cnf(c_42,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))))),
inference(clausify,[status(thm)],[initial_state]) ).
fof(goal_state,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10] : ~ state(bb(o,o),VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10),
file('theBenchmark.p',goal_state) ).
cnf(c_43,plain,
~ state(bb(o,o),A,B,C,D,E,F,V6,V7,V8,V9,V10),
inference(clausify,[status(thm)],[goal_state]) ).
cnf(c_45,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(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(o)),o),e2(s(s(s(s(o)))),s(s(s(o))))),
inference(resolve,[status(thm)],[c_27,c_42]) ).
cnf(c_48,plain,
~ state(bb(o,s(o)),A,B,C,D,E,F,V6,V7,V8,e1(o,o),e2(s(o),o)),
inference(resolve,[status(thm)],[c_43,c_38]) ).
cnf(c_66,plain,
~ state(bb(o,s(o)),A,B,C,D,E,F,V6,V7,V8,e1(s(o),o),e2(o,o)),
inference(resolve,[status(thm)],[c_48,c_41]) ).
cnf(c_105,plain,
~ state(bb(o,s(o)),v1(s(o),o),A,B,C,D,E,F,V6,V7,e1(s(s(s(o))),o),e2(o,o)),
inference(resolve,[status(thm)],[c_66,c_19]) ).
cnf(c_120,plain,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(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(o,o),e2(s(s(s(s(o)))),s(s(s(o))))),
inference(resolve,[status(thm)],[c_19,c_45]) ).
cnf(c_121,plain,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(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(o,o)),
inference(resolve,[status(thm)],[c_41,c_120]) ).
cnf(c_122,plain,
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)),
inference(resolve,[status(thm)],[c_31,c_121]) ).
cnf(c_125,plain,
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)),
inference(resolve,[status(thm)],[c_33,c_122]) ).
cnf(c_159,plain,
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)),
inference(resolve,[status(thm)],[c_4,c_125]) ).
cnf(c_163,plain,
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)),
inference(resolve,[status(thm)],[c_12,c_159]) ).
cnf(c_186,plain,
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))),
inference(resolve,[status(thm)],[c_41,c_163]) ).
cnf(c_239,plain,
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))),
inference(resolve,[status(thm)],[c_20,c_186]) ).
cnf(c_742,plain,
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))),
inference(resolve,[status(thm)],[c_2,c_239]) ).
cnf(c_1186,plain,
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))),
inference(resolve,[status(thm)],[c_12,c_742]) ).
cnf(c_1749,plain,
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)),
inference(resolve,[status(thm)],[c_25,c_1186]) ).
cnf(c_1752,plain,
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)),
inference(resolve,[status(thm)],[c_3,c_1749]) ).
cnf(c_1768,plain,
~ state(bb(o,s(o)),v1(s(o),o),A,B,C,D,s1(s(s(s(o))),o),E,F,V6,e1(s(s(s(s(o)))),o),e2(o,o)),
inference(resolve,[status(thm)],[c_105,c_3]) ).
cnf(c_1807,plain,
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(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(o,o),e2(s(s(s(s(o)))),o)),
inference(resolve,[status(thm)],[c_19,c_1752]) ).
cnf(c_1809,plain,
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(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(s(o)))),o),e2(o,o)),
inference(resolve,[status(thm)],[c_41,c_1807]) ).
cnf(c_1810,plain,
$false,
inference(resolve,[status(thm)],[c_1809,c_1768]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ040-1 : TPTP v9.3.1. Bugfixed v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n005.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 05:07:02 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 1260250 was started by sandbox on n005,
% 0.07/0.35 % Sat Sep 26 05:07:02 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.35
% 0.13/0.35 % From the command line: assign(max_seconds, 300).
% 2.41/0.69
% 2.41/0.69 % SZS status Unsatisfiable for theBenchmark
% 2.41/0.69
% 2.41/0.69 % Proof 1 at 0.26 (+ 0.06) seconds.
% 2.41/0.69 % Length of proof is 34.
% 2.41/0.69 % Level of proof is 16.
% 2.41/0.69 % Maximum clause weight is 82.000.
% 2.41/0.69 % Given clauses 266.
% 2.41/0.69
% 2.41/0.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------