%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ042-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 195.61s 26.65s
% Output : CNFRefutation 195.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 12 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 29 ( 17 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 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 : 192 ( 35 sgn 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(s2_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,VAR_6,s2(s(VAR_7),VAR_8),VAR_9,VAR_10,e1(VAR_7,VAR_8),VAR_11)
| ~ state(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,s2(VAR_7,VAR_8),VAR_9,VAR_10,e1(s(VAR_7),VAR_8),VAR_11) ),
file('theBenchmark.p',s2_down) ).
cnf(c_7,plain,
( state(A,B,C,D,E,F,V6,s2(s(V7),V8),V9,V10,e1(V7,V8),V11)
| ~ state(A,B,C,D,E,F,V6,s2(V7,V8),V9,V10,e1(s(V7),V8),V11) ),
inference(clausify,[status(thm)],[s2_down]) ).
fof(s3_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,VAR_6,VAR_7,s3(VAR_8,VAR_9),VAR_10,e1(VAR_8,s(VAR_9)),VAR_11)
| ~ state(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,s3(VAR_8,s(VAR_9)),VAR_10,e1(VAR_8,VAR_9),VAR_11) ),
file('theBenchmark.p',s3_left) ).
cnf(c_10,plain,
( state(A,B,C,D,E,F,V6,V7,s3(V8,V9),V10,e1(V8,s(V9)),V11)
| ~ state(A,B,C,D,E,F,V6,V7,s3(V8,s(V9)),V10,e1(V8,V9),V11) ),
inference(clausify,[status(thm)],[s3_left]) ).
fof(s4_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,VAR_5,VAR_6,VAR_7,VAR_8,s4(VAR_9,s(VAR_10)),e1(VAR_9,VAR_10),VAR_11)
| ~ state(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,s4(VAR_9,VAR_10),e1(VAR_9,s(VAR_10)),VAR_11) ),
file('theBenchmark.p',s4_right) ).
cnf(c_13,plain,
( state(A,B,C,D,E,F,V6,V7,V8,s4(V9,s(V10)),e1(V9,V10),V11)
| ~ state(A,B,C,D,E,F,V6,V7,V8,s4(V9,V10),e1(V9,s(V10)),V11) ),
inference(clausify,[status(thm)],[s4_right]) ).
fof(h_down,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,VAR_3,VAR_4,h(s(VAR_5),VAR_6),VAR_7,VAR_8,VAR_9,VAR_10,e1(VAR_5,VAR_6),e2(VAR_5,s(VAR_6)))
| ~ 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(s(VAR_5),VAR_6),e2(s(VAR_5),s(VAR_6))) ),
file('theBenchmark.p',h_down) ).
cnf(c_35,plain,
( state(A,B,C,D,E,h(s(F),V6),V7,V8,V9,V10,e1(F,V6),e2(F,s(V6)))
| ~ state(A,B,C,D,E,h(F,V6),V7,V8,V9,V10,e1(s(F),V6),e2(s(F),s(V6))) ),
inference(clausify,[status(thm)],[h_down]) ).
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(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,h(s(s(s(o))),s(o)),VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10),
file('theBenchmark.p',goal_state) ).
cnf(c_43,plain,
~ state(A,B,C,D,E,h(s(s(s(o))),s(o)),F,V6,V7,V8,V9,V10),
inference(clausify,[status(thm)],[goal_state]) ).
cnf(c_44,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)))),s(s(s(o)))),e2(s(s(s(s(o)))),o)),
inference(resolve,[status(thm)],[c_41,c_42]) ).
cnf(c_48,plain,
~ state(A,B,C,D,E,h(s(s(o)),s(o)),F,V6,V7,V8,e1(s(s(s(o))),s(o)),e2(s(s(s(o))),s(s(o)))),
inference(resolve,[status(thm)],[c_43,c_35]) ).
cnf(c_52,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(s(o)))),e1(s(s(s(s(o)))),s(s(o))),e2(s(s(s(s(o)))),o)),
inference(resolve,[status(thm)],[c_13,c_44]) ).
cnf(c_240,plain,
~ state(A,B,C,D,E,h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),F,V6,V7,e1(s(s(s(s(o)))),s(o)),e2(s(s(s(o))),s(s(o)))),
inference(resolve,[status(thm)],[c_48,c_3]) ).
cnf(c_377,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(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(s(o))),s(s(o))),e2(s(s(s(s(o)))),o)),
inference(resolve,[status(thm)],[c_7,c_52]) ).
cnf(c_6110,plain,
~ state(A,B,C,D,E,h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),F,s3(s(s(s(s(o)))),s(o)),V6,e1(s(s(s(s(o)))),o),e2(s(s(s(o))),s(s(o)))),
inference(resolve,[status(thm)],[c_240,c_10]) ).
cnf(c_8751,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(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(s(s(o)))),o),e2(s(s(s(o))),s(s(o)))),
inference(resolve,[status(thm)],[c_41,c_377]) ).
cnf(c_8750,plain,
$false,
inference(resolve,[status(thm)],[c_6110,c_8751]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ042-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n018.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 05:10:06 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 3783356 was started by sandbox2 on n018,
% 0.07/0.35 % Sat Sep 26 05:10:06 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 195.61/26.65
% 195.61/26.65 % given #500 (A,wt=52): 209 -state(A,B,C,D,E,h(s(s(s(s(o)))),s(o)),F,s2(s(s(s(o))),s(o)),V6,V7,e1(s(s(s(s(o)))),s(o)),e2(s(s(s(o))),s(s(o)))). [resolve(47,a,7,b)].
% 195.61/26.65
% 195.61/26.65 % SZS status Unsatisfiable for theBenchmark
% 195.61/26.65
% 195.61/26.65 % Proof 1 at 1.48 (+ 0.43) seconds.
% 195.61/26.65 % Length of proof is 15.
% 195.61/26.65 % Level of proof is 4.
% 195.61/26.65 % Maximum clause weight is 94.000.
% 195.61/26.65 % Given clauses 896.
% 195.61/26.65
% 195.61/26.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------