%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PLA011-2 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 : Sun Sep 27 08:20:22 AM UTC 2026
% Result : Unsatisfiable 47.97s 6.59s
% Output : CNFRefutation 47.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 21
% Syntax : Number of formulae : 72 ( 30 unt; 0 def)
% Number of atoms : 156 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 182 ( 98 ~; 84 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 92 ( 8 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(and_definition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ holds(VAR_1,VAR_2)
| ~ holds(VAR_0,VAR_2)
| holds(and(VAR_0,VAR_1),VAR_2) ),
file('theBenchmark.p',and_definition) ).
cnf(c_1,plain,
( ~ holds(B,C)
| ~ holds(A,C)
| holds(and(A,B),C) ),
inference(clausify,[status(thm)],[and_definition]) ).
fof(pickup_1,axiom,
! [VAR_0,VAR_1] :
( ~ differ(VAR_0,table)
| ~ holds(clear(VAR_0),VAR_1)
| ~ holds(empty,VAR_1)
| holds(holding(VAR_0),do(pickup(VAR_0),VAR_1)) ),
file('theBenchmark.p',pickup_1) ).
cnf(c_2,plain,
( ~ differ(A,table)
| ~ holds(clear(A),B)
| ~ holds(empty,B)
| holds(holding(A),do(pickup(A),B)) ),
inference(clausify,[status(thm)],[pickup_1]) ).
fof(pickup_2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ holds(empty,VAR_2)
| ~ holds(clear(VAR_1),VAR_2)
| ~ holds(on(VAR_1,VAR_0),VAR_2)
| holds(clear(VAR_0),do(pickup(VAR_1),VAR_2)) ),
file('theBenchmark.p',pickup_2) ).
cnf(c_3,plain,
( ~ holds(empty,C)
| ~ holds(clear(B),C)
| ~ holds(on(B,A),C)
| holds(clear(A),do(pickup(B),C)) ),
inference(clausify,[status(thm)],[pickup_2]) ).
fof(pickup_3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ differ(VAR_0,VAR_2)
| ~ holds(on(VAR_0,VAR_1),VAR_3)
| holds(on(VAR_0,VAR_1),do(pickup(VAR_2),VAR_3)) ),
file('theBenchmark.p',pickup_3) ).
cnf(c_4,plain,
( ~ differ(A,C)
| ~ holds(on(A,B),D)
| holds(on(A,B),do(pickup(C),D)) ),
inference(clausify,[status(thm)],[pickup_3]) ).
fof(pickup_4,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ differ(VAR_0,VAR_1)
| ~ holds(clear(VAR_0),VAR_2)
| holds(clear(VAR_0),do(pickup(VAR_1),VAR_2)) ),
file('theBenchmark.p',pickup_4) ).
cnf(c_5,plain,
( ~ differ(A,B)
| ~ holds(clear(A),C)
| holds(clear(A),do(pickup(B),C)) ),
inference(clausify,[status(thm)],[pickup_4]) ).
fof(putdown_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ holds(clear(VAR_1),VAR_2)
| ~ holds(holding(VAR_0),VAR_2)
| holds(empty,do(putdown(VAR_0,VAR_1),VAR_2)) ),
file('theBenchmark.p',putdown_1) ).
cnf(c_6,plain,
( ~ holds(clear(B),C)
| ~ holds(holding(A),C)
| holds(empty,do(putdown(A,B),C)) ),
inference(clausify,[status(thm)],[putdown_1]) ).
fof(putdown_2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ holds(clear(VAR_1),VAR_2)
| ~ holds(holding(VAR_0),VAR_2)
| holds(on(VAR_0,VAR_1),do(putdown(VAR_0,VAR_1),VAR_2)) ),
file('theBenchmark.p',putdown_2) ).
cnf(c_7,plain,
( ~ holds(clear(B),C)
| ~ holds(holding(A),C)
| holds(on(A,B),do(putdown(A,B),C)) ),
inference(clausify,[status(thm)],[putdown_2]) ).
fof(putdown_3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ holds(clear(VAR_1),VAR_2)
| ~ holds(holding(VAR_0),VAR_2)
| holds(clear(VAR_0),do(putdown(VAR_0,VAR_1),VAR_2)) ),
file('theBenchmark.p',putdown_3) ).
cnf(c_8,plain,
( ~ holds(clear(B),C)
| ~ holds(holding(A),C)
| holds(clear(A),do(putdown(A,B),C)) ),
inference(clausify,[status(thm)],[putdown_3]) ).
fof(putdown_4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ holds(on(VAR_0,VAR_1),VAR_4)
| holds(on(VAR_0,VAR_1),do(putdown(VAR_2,VAR_3),VAR_4)) ),
file('theBenchmark.p',putdown_4) ).
cnf(c_9,plain,
( ~ holds(on(A,B),E)
| holds(on(A,B),do(putdown(C,D),E)) ),
inference(clausify,[status(thm)],[putdown_4]) ).
fof(putdown_5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ differ(VAR_0,VAR_2)
| ~ holds(clear(VAR_0),VAR_3)
| holds(clear(VAR_0),do(putdown(VAR_1,VAR_2),VAR_3)) ),
file('theBenchmark.p',putdown_5) ).
cnf(c_10,plain,
( ~ differ(A,C)
| ~ holds(clear(A),D)
| holds(clear(A),do(putdown(B,C),D)) ),
inference(clausify,[status(thm)],[putdown_5]) ).
fof(symmetry_of_differ,axiom,
! [VAR_0,VAR_1] :
( ~ differ(VAR_1,VAR_0)
| differ(VAR_0,VAR_1) ),
file('theBenchmark.p',symmetry_of_differ) ).
cnf(c_11,plain,
( ~ differ(B,A)
| differ(A,B) ),
inference(clausify,[status(thm)],[symmetry_of_differ]) ).
fof(differ_b_c,axiom,
differ(b,c),
file('theBenchmark.p',differ_b_c) ).
cnf(c_16,plain,
differ(b,c),
inference(clausify,[status(thm)],[differ_b_c]) ).
fof(differ_b_d,axiom,
differ(b,d),
file('theBenchmark.p',differ_b_d) ).
cnf(c_17,plain,
differ(b,d),
inference(clausify,[status(thm)],[differ_b_d]) ).
fof(differ_c_d,axiom,
differ(c,d),
file('theBenchmark.p',differ_c_d) ).
cnf(c_19,plain,
differ(c,d),
inference(clausify,[status(thm)],[differ_c_d]) ).
fof(differ_c_table,axiom,
differ(c,table),
file('theBenchmark.p',differ_c_table) ).
cnf(c_20,plain,
differ(c,table),
inference(clausify,[status(thm)],[differ_c_table]) ).
fof(differ_d_table,axiom,
differ(d,table),
file('theBenchmark.p',differ_d_table) ).
cnf(c_21,plain,
differ(d,table),
inference(clausify,[status(thm)],[differ_d_table]) ).
fof(initial_state3,axiom,
holds(on(c,d),s0),
file('theBenchmark.p',initial_state3) ).
cnf(c_24,plain,
holds(on(c,d),s0),
inference(clausify,[status(thm)],[initial_state3]) ).
fof(initial_state6,axiom,
holds(clear(b),s0),
file('theBenchmark.p',initial_state6) ).
cnf(c_27,plain,
holds(clear(b),s0),
inference(clausify,[status(thm)],[initial_state6]) ).
fof(initial_state7,axiom,
holds(clear(c),s0),
file('theBenchmark.p',initial_state7) ).
cnf(c_28,plain,
holds(clear(c),s0),
inference(clausify,[status(thm)],[initial_state7]) ).
fof(initial_state8,axiom,
holds(empty,s0),
file('theBenchmark.p',initial_state8) ).
cnf(c_29,plain,
holds(empty,s0),
inference(clausify,[status(thm)],[initial_state8]) ).
fof(prove_DCB,axiom,
! [VAR_0] : ~ holds(and(on(c,b),on(d,c)),VAR_0),
file('theBenchmark.p',prove_DCB) ).
cnf(c_31,plain,
~ holds(and(on(c,b),on(d,c)),A),
inference(clausify,[status(thm)],[prove_DCB]) ).
cnf(c_37,plain,
differ(d,b),
inference(resolve,[status(thm)],[c_11,c_17]) ).
cnf(c_13244,plain,
( ~ differ(b,A)
| holds(clear(b),do(pickup(A),s0)) ),
inference(resolve,[status(thm)],[c_5,c_27]) ).
cnf(c_94,plain,
holds(clear(b),do(pickup(c),s0)),
inference(resolve,[status(thm)],[c_13244,c_16]) ).
cnf(c_13245,plain,
( ~ holds(empty,s0)
| ~ holds(clear(c),s0)
| holds(clear(d),do(pickup(c),s0)) ),
inference(resolve,[status(thm)],[c_3,c_24]) ).
cnf(c_13246,plain,
( ~ holds(empty,s0)
| holds(clear(d),do(pickup(c),s0)) ),
inference(resolve,[status(thm)],[c_13245,c_28]) ).
cnf(c_123,plain,
holds(clear(d),do(pickup(c),s0)),
inference(resolve,[status(thm)],[c_13246,c_29]) ).
cnf(c_13247,plain,
( ~ differ(A,table)
| ~ holds(clear(A),s0)
| holds(holding(A),do(pickup(A),s0)) ),
inference(resolve,[status(thm)],[c_2,c_29]) ).
cnf(c_13248,plain,
( ~ differ(c,table)
| holds(holding(c),do(pickup(c),s0)) ),
inference(resolve,[status(thm)],[c_13247,c_28]) ).
cnf(c_124,plain,
holds(holding(c),do(pickup(c),s0)),
inference(resolve,[status(thm)],[c_13248,c_20]) ).
cnf(c_159,plain,
( ~ holds(on(d,c),A)
| ~ holds(on(c,b),A) ),
inference(resolve,[status(thm)],[c_31,c_1]) ).
cnf(c_166,plain,
( ~ holds(on(c,b),C)
| ~ holds(on(d,c),do(putdown(A,B),C)) ),
inference(resolve,[status(thm)],[c_159,c_9]) ).
cnf(c_172,plain,
( ~ holds(clear(c),A)
| ~ holds(holding(d),A)
| ~ holds(on(c,b),A) ),
inference(resolve,[status(thm)],[c_166,c_7]) ).
cnf(c_178,plain,
( ~ differ(c,A)
| ~ holds(on(c,b),B)
| ~ holds(clear(c),do(pickup(A),B))
| ~ holds(holding(d),do(pickup(A),B)) ),
inference(resolve,[status(thm)],[c_172,c_4]) ).
cnf(c_13249,plain,
( ~ differ(d,B)
| holds(clear(d),do(putdown(A,B),do(pickup(c),s0))) ),
inference(resolve,[status(thm)],[c_10,c_123]) ).
cnf(c_1154,plain,
holds(clear(d),do(putdown(A,b),do(pickup(c),s0))),
inference(resolve,[status(thm)],[c_13249,c_37]) ).
cnf(c_13250,plain,
( ~ holds(clear(A),do(pickup(c),s0))
| holds(clear(c),do(putdown(c,A),do(pickup(c),s0))) ),
inference(resolve,[status(thm)],[c_8,c_124]) ).
cnf(c_1171,plain,
holds(clear(c),do(putdown(c,b),do(pickup(c),s0))),
inference(resolve,[status(thm)],[c_13250,c_94]) ).
cnf(c_13251,plain,
( ~ holds(clear(A),do(pickup(c),s0))
| holds(on(c,A),do(putdown(c,A),do(pickup(c),s0))) ),
inference(resolve,[status(thm)],[c_7,c_124]) ).
cnf(c_1175,plain,
holds(on(c,b),do(putdown(c,b),do(pickup(c),s0))),
inference(resolve,[status(thm)],[c_13251,c_94]) ).
cnf(c_13252,plain,
( ~ holds(clear(A),do(pickup(c),s0))
| holds(empty,do(putdown(c,A),do(pickup(c),s0))) ),
inference(resolve,[status(thm)],[c_6,c_124]) ).
cnf(c_1179,plain,
holds(empty,do(putdown(c,b),do(pickup(c),s0))),
inference(resolve,[status(thm)],[c_13252,c_94]) ).
cnf(c_13253,plain,
( ~ differ(d,table)
| ~ holds(clear(d),A)
| ~ holds(empty,A)
| ~ differ(c,d)
| ~ holds(on(c,b),A)
| ~ holds(clear(c),do(pickup(d),A)) ),
inference(resolve,[status(thm)],[c_178,c_2]) ).
cnf(c_13254,plain,
( ~ differ(d,table)
| ~ holds(clear(d),A)
| ~ holds(empty,A)
| ~ holds(on(c,b),A)
| ~ holds(clear(c),do(pickup(d),A)) ),
inference(resolve,[status(thm)],[c_19,c_13253]) ).
cnf(c_9485,plain,
( ~ holds(clear(d),A)
| ~ holds(empty,A)
| ~ holds(on(c,b),A)
| ~ holds(clear(c),do(pickup(d),A)) ),
inference(resolve,[status(thm)],[c_21,c_13254]) ).
cnf(c_13255,plain,
( ~ differ(c,d)
| ~ holds(clear(c),A)
| ~ holds(clear(d),A)
| ~ holds(empty,A)
| ~ holds(on(c,b),A) ),
inference(resolve,[status(thm)],[c_9485,c_5]) ).
cnf(c_9504,plain,
( ~ holds(clear(c),A)
| ~ holds(clear(d),A)
| ~ holds(empty,A)
| ~ holds(on(c,b),A) ),
inference(resolve,[status(thm)],[c_19,c_13255]) ).
cnf(c_13256,plain,
( ~ holds(clear(c),do(putdown(c,b),do(pickup(c),s0)))
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),s0)))
| ~ holds(on(c,b),do(putdown(c,b),do(pickup(c),s0))) ),
inference(resolve,[status(thm)],[c_1179,c_9504]) ).
cnf(c_13257,plain,
( ~ holds(clear(c),do(putdown(c,b),do(pickup(c),s0)))
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),s0))) ),
inference(resolve,[status(thm)],[c_1175,c_13256]) ).
cnf(c_13258,plain,
~ holds(clear(c),do(putdown(c,b),do(pickup(c),s0))),
inference(resolve,[status(thm)],[c_1154,c_13257]) ).
cnf(c_13243,plain,
$false,
inference(resolve,[status(thm)],[c_1171,c_13258]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : PLA011-2 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n001.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 04:49:58 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 933400 was started by sandbox2 on n001,
% 0.19/0.45 % Sat Sep 26 04:49:58 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 47.97/6.59
% 47.97/6.59 % given #500 (A,wt=31): 252 holds(and(and(clear(b),empty),and(clear(b),empty)),s0). [ur(1,b,129,a,c,129,a)].
% 47.97/6.59
% 47.97/6.59 % given #1000 (T,wt=27): 4629 holds(and(on(d,table),clear(b)),do(putdown(A,c),s0)). [ur(1,b,63,a,c,91,a)].
% 47.97/6.59
% 47.97/6.59 % given #1500 (F,wt=40): 10114 -holds(holding(c),do(putdown(d,c),do(putdown(A,d),s0))) | -holds(holding(d),do(putdown(A,d),s0)). [resolve(196,d,107,a),unit_del(b,4416)].
% 47.97/6.59
% 47.97/6.59 % SZS status Unsatisfiable for theBenchmark
% 47.97/6.59
% 47.97/6.59 % Proof 1 at 3.40 (+ 2.68) seconds.
% 47.97/6.59 % Length of proof is 36.
% 47.97/6.59 % Level of proof is 7.
% 47.97/6.59 % Maximum clause weight is 37.000.
% 47.97/6.59 % Given clauses 1601.
% 47.97/6.59
% 47.97/6.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------