%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ056-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 : Sun Sep 27 08:23:14 AM UTC 2026
% Result : Unsatisfiable 6.20s 1.24s
% Output : CNFRefutation 6.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 54 unt; 0 def)
% Number of atoms : 72 ( 37 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 19 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 105 ( 5 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(initial_state,axiom,
state(nextto(on(small,on(medium,on(large,pin(n1)))),nextto(pin(n2),pin(n3)))),
file('theBenchmark.p',initial_state) ).
cnf(c_1,plain,
state(nextto(on(small,on(medium,on(large,pin(n1)))),nextto(pin(n2),pin(n3)))),
inference(clausify,[status(thm)],[initial_state]) ).
fof(final_state,axiom,
~ state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))),
file('theBenchmark.p',final_state) ).
cnf(c_2,plain,
~ state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))),
inference(clausify,[status(thm)],[final_state]) ).
fof(nextto_commutative,axiom,
! [VAR_0,VAR_1] : nextto(VAR_0,VAR_1) = nextto(VAR_1,VAR_0),
file('theBenchmark.p',nextto_commutative) ).
cnf(c_3,plain,
nextto(A,B) = nextto(B,A),
inference(clausify,[status(thm)],[nextto_commutative]) ).
fof(nextto_associative,axiom,
! [VAR_0,VAR_1,VAR_2] : nextto(VAR_0,nextto(VAR_1,VAR_2)) = nextto(nextto(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',nextto_associative) ).
cnf(c_4,plain,
nextto(A,nextto(B,C)) = nextto(nextto(A,B),C),
inference(clausify,[status(thm)],[nextto_associative]) ).
cnf(c_5,plain,
nextto(nextto(A,B),C) = nextto(A,nextto(B,C)),
inference(copy,[status(thm)],[c_4]) ).
fof(a_move,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ fits(VAR_0,VAR_1)
| ~ fits(VAR_0,VAR_2)
| nextto(on(VAR_0,VAR_1),VAR_2) = nextto(VAR_1,on(VAR_0,VAR_2)) ),
file('theBenchmark.p',a_move) ).
cnf(c_6,plain,
( ~ fits(A,B)
| ~ fits(A,C)
| nextto(on(A,B),C) = nextto(B,on(A,C)) ),
inference(clausify,[status(thm)],[a_move]) ).
fof(fits_1,axiom,
! [VAR_0] : fits(small,pin(VAR_0)),
file('theBenchmark.p',fits_1) ).
cnf(c_7,plain,
fits(small,pin(A)),
inference(clausify,[status(thm)],[fits_1]) ).
fof(fits_2,axiom,
! [VAR_0] : fits(medium,pin(VAR_0)),
file('theBenchmark.p',fits_2) ).
cnf(c_8,plain,
fits(medium,pin(A)),
inference(clausify,[status(thm)],[fits_2]) ).
fof(fits_3,axiom,
! [VAR_0] : fits(large,pin(VAR_0)),
file('theBenchmark.p',fits_3) ).
cnf(c_9,plain,
fits(large,pin(A)),
inference(clausify,[status(thm)],[fits_3]) ).
fof(fits_4,axiom,
! [VAR_0] : fits(small,on(medium,VAR_0)),
file('theBenchmark.p',fits_4) ).
cnf(c_10,plain,
fits(small,on(medium,A)),
inference(clausify,[status(thm)],[fits_4]) ).
fof(fits_5,axiom,
! [VAR_0] : fits(medium,on(large,VAR_0)),
file('theBenchmark.p',fits_5) ).
cnf(c_11,plain,
fits(medium,on(large,A)),
inference(clausify,[status(thm)],[fits_5]) ).
cnf(c_3223,plain,
nextto(nextto(A,B),C) = nextto(B,nextto(A,C)),
inference(paramod,[status(thm)],[c_3,c_5]) ).
cnf(c_14,plain,
nextto(A,nextto(B,C)) = nextto(B,nextto(A,C)),
inference(paramod,[status(thm)],[c_5,c_3223]) ).
cnf(c_3224,plain,
( ~ fits(small,A)
| nextto(on(small,A),pin(B)) = nextto(A,on(small,pin(B))) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_15,plain,
nextto(on(small,pin(A)),pin(B)) = nextto(pin(A),on(small,pin(B))),
inference(resolve,[status(thm)],[c_3224,c_7]) ).
cnf(c_3225,plain,
( ~ fits(large,A)
| nextto(on(large,A),pin(B)) = nextto(A,on(large,pin(B))) ),
inference(resolve,[status(thm)],[c_6,c_9]) ).
cnf(c_17,plain,
nextto(on(large,pin(A)),pin(B)) = nextto(pin(A),on(large,pin(B))),
inference(resolve,[status(thm)],[c_3225,c_9]) ).
cnf(c_3226,plain,
( ~ fits(small,A)
| nextto(on(small,A),pin(B)) = nextto(A,on(small,pin(B))) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_3227,plain,
nextto(on(small,on(medium,A)),pin(B)) = nextto(on(medium,A),on(small,pin(B))),
inference(resolve,[status(thm)],[c_3226,c_10]) ).
cnf(c_19,plain,
nextto(on(medium,A),on(small,pin(B))) = nextto(on(small,on(medium,A)),pin(B)),
inference(copy,[status(thm)],[c_3227]) ).
cnf(c_3228,plain,
( ~ fits(small,A)
| nextto(on(small,A),on(medium,B)) = nextto(A,on(small,on(medium,B))) ),
inference(resolve,[status(thm)],[c_6,c_10]) ).
cnf(c_20,plain,
nextto(on(small,pin(A)),on(medium,B)) = nextto(pin(A),on(small,on(medium,B))),
inference(resolve,[status(thm)],[c_3228,c_7]) ).
cnf(c_3229,plain,
( ~ fits(medium,A)
| nextto(on(medium,A),pin(B)) = nextto(A,on(medium,pin(B))) ),
inference(resolve,[status(thm)],[c_6,c_8]) ).
cnf(c_3230,plain,
nextto(on(medium,on(large,A)),pin(B)) = nextto(on(large,A),on(medium,pin(B))),
inference(resolve,[status(thm)],[c_3229,c_11]) ).
cnf(c_22,plain,
nextto(on(large,A),on(medium,pin(B))) = nextto(on(medium,on(large,A)),pin(B)),
inference(copy,[status(thm)],[c_3230]) ).
cnf(c_3231,plain,
( ~ fits(medium,A)
| nextto(on(medium,A),on(large,B)) = nextto(A,on(medium,on(large,B))) ),
inference(resolve,[status(thm)],[c_6,c_11]) ).
cnf(c_23,plain,
nextto(on(medium,pin(A)),on(large,B)) = nextto(pin(A),on(medium,on(large,B))),
inference(resolve,[status(thm)],[c_3231,c_8]) ).
cnf(c_3232,plain,
nextto(nextto(pin(A),on(small,pin(B))),C) = nextto(on(small,pin(A)),nextto(pin(B),C)),
inference(paramod,[status(thm)],[c_15,c_5]) ).
cnf(c_3233,plain,
nextto(pin(A),nextto(on(small,pin(B)),C)) = nextto(on(small,pin(A)),nextto(pin(B),C)),
inference(paramod,[status(thm)],[c_5,c_3232]) ).
cnf(c_31,plain,
nextto(on(small,pin(A)),nextto(pin(B),C)) = nextto(pin(A),nextto(on(small,pin(B)),C)),
inference(copy,[status(thm)],[c_3233]) ).
cnf(c_3234,plain,
nextto(A,nextto(on(large,pin(B)),pin(C))) = nextto(pin(B),nextto(A,on(large,pin(C)))),
inference(paramod,[status(thm)],[c_17,c_14]) ).
cnf(c_46,plain,
nextto(pin(A),nextto(B,on(large,pin(C)))) = nextto(B,nextto(on(large,pin(A)),pin(C))),
inference(copy,[status(thm)],[c_3234]) ).
cnf(c_3235,plain,
nextto(nextto(on(small,on(medium,A)),pin(B)),C) = nextto(on(medium,A),nextto(on(small,pin(B)),C)),
inference(paramod,[status(thm)],[c_19,c_5]) ).
cnf(c_3236,plain,
nextto(on(small,on(medium,A)),nextto(pin(B),C)) = nextto(on(medium,A),nextto(on(small,pin(B)),C)),
inference(paramod,[status(thm)],[c_5,c_3235]) ).
cnf(c_70,plain,
nextto(on(medium,A),nextto(on(small,pin(B)),C)) = nextto(on(small,on(medium,A)),nextto(pin(B),C)),
inference(copy,[status(thm)],[c_3236]) ).
cnf(c_77,plain,
~ state(nextto(pin(n1),nextto(on(small,pin(n2)),on(medium,on(large,pin(n3)))))),
inference(paramod,[status(thm)],[c_20,c_2]) ).
cnf(c_3237,plain,
nextto(nextto(pin(A),on(small,on(medium,B))),C) = nextto(on(small,pin(A)),nextto(on(medium,B),C)),
inference(paramod,[status(thm)],[c_20,c_5]) ).
cnf(c_3238,plain,
nextto(pin(A),nextto(on(small,on(medium,B)),C)) = nextto(on(small,pin(A)),nextto(on(medium,B),C)),
inference(paramod,[status(thm)],[c_5,c_3237]) ).
cnf(c_78,plain,
nextto(on(small,pin(A)),nextto(on(medium,B),C)) = nextto(pin(A),nextto(on(small,on(medium,B)),C)),
inference(copy,[status(thm)],[c_3238]) ).
cnf(c_3239,plain,
nextto(nextto(on(medium,on(large,A)),pin(B)),C) = nextto(on(large,A),nextto(on(medium,pin(B)),C)),
inference(paramod,[status(thm)],[c_22,c_5]) ).
cnf(c_3240,plain,
nextto(on(medium,on(large,A)),nextto(pin(B),C)) = nextto(on(large,A),nextto(on(medium,pin(B)),C)),
inference(paramod,[status(thm)],[c_5,c_3239]) ).
cnf(c_84,plain,
nextto(on(large,A),nextto(on(medium,pin(B)),C)) = nextto(on(medium,on(large,A)),nextto(pin(B),C)),
inference(copy,[status(thm)],[c_3240]) ).
cnf(c_166,plain,
~ state(nextto(on(small,pin(n1)),nextto(pin(n2),on(medium,on(large,pin(n3)))))),
inference(paramod,[status(thm)],[c_31,c_77]) ).
cnf(c_207,plain,
~ state(nextto(on(small,pin(n1)),nextto(on(medium,pin(n2)),on(large,pin(n3))))),
inference(paramod,[status(thm)],[c_23,c_166]) ).
cnf(c_1004,plain,
state(nextto(on(medium,on(large,pin(n1))),nextto(on(small,pin(n2)),pin(n3)))),
inference(paramod,[status(thm)],[c_70,c_1]) ).
cnf(c_1095,plain,
state(nextto(on(medium,on(large,pin(n1))),nextto(pin(n2),on(small,pin(n3))))),
inference(paramod,[status(thm)],[c_15,c_1004]) ).
cnf(c_1838,plain,
~ state(nextto(pin(n1),nextto(on(small,on(medium,pin(n2))),on(large,pin(n3))))),
inference(paramod,[status(thm)],[c_78,c_207]) ).
cnf(c_3241,plain,
~ state(nextto(on(small,on(medium,pin(n2))),nextto(on(large,pin(n1)),pin(n3)))),
inference(paramod,[status(thm)],[c_46,c_1838]) ).
cnf(c_1922,plain,
~ state(nextto(on(large,pin(n1)),nextto(on(small,on(medium,pin(n2))),pin(n3)))),
inference(paramod,[status(thm)],[c_14,c_3241]) ).
cnf(c_1924,plain,
~ state(nextto(on(large,pin(n1)),nextto(on(medium,pin(n2)),on(small,pin(n3))))),
inference(paramod,[status(thm)],[c_19,c_1922]) ).
cnf(c_3221,plain,
state(nextto(on(large,pin(n1)),nextto(on(medium,pin(n2)),on(small,pin(n3))))),
inference(paramod,[status(thm)],[c_84,c_1095]) ).
cnf(c_3222,plain,
$false,
inference(resolve,[status(thm)],[c_3221,c_1924]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ056-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n007.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 05:07:09 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.39 % Process 2846783 was started by sandbox2 on n007,
% 0.12/0.39 % Sat Sep 26 05:07:09 2026
% 0.12/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.39
% 0.12/0.39 % From the command line: assign(max_seconds, 300).
% 6.20/1.24
% 6.20/1.24 % SZS status Unsatisfiable for theBenchmark
% 6.20/1.24
% 6.20/1.24 % Proof 1 at 0.71 (+ 0.12) seconds.
% 6.20/1.24 % Length of proof is 33.
% 6.20/1.24 % Level of proof is 8.
% 6.20/1.24 % Maximum clause weight is 21.000.
% 6.20/1.24 % Given clauses 136.
% 6.20/1.24
% 6.20/1.24 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------