%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PLA005-2 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 08:20:21 AM UTC 2026
% Result : Unsatisfiable 58.39s 7.83s
% Output : CNFRefutation 58.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 24
% Syntax : Number of formulae : 81 ( 40 unt; 0 def)
% Number of atoms : 162 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 176 ( 95 ~; 81 |; 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 : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 89 ( 10 sgn 33 !; 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_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_a_b,axiom,
differ(a,b),
file('theBenchmark.p',differ_a_b) ).
cnf(c_12,plain,
differ(a,b),
inference(clausify,[status(thm)],[differ_a_b]) ).
fof(differ_a_c,axiom,
differ(a,c),
file('theBenchmark.p',differ_a_c) ).
cnf(c_13,plain,
differ(a,c),
inference(clausify,[status(thm)],[differ_a_c]) ).
fof(differ_a_d,axiom,
differ(a,d),
file('theBenchmark.p',differ_a_d) ).
cnf(c_14,plain,
differ(a,d),
inference(clausify,[status(thm)],[differ_a_d]) ).
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_state5,axiom,
holds(clear(a),s0),
file('theBenchmark.p',initial_state5) ).
cnf(c_26,plain,
holds(clear(a),s0),
inference(clausify,[status(thm)],[initial_state5]) ).
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_DB_AC,axiom,
! [VAR_0] : ~ holds(and(on(d,b),on(c,a)),VAR_0),
file('theBenchmark.p',prove_DB_AC) ).
cnf(c_31,plain,
~ holds(and(on(d,b),on(c,a)),A),
inference(clausify,[status(thm)],[prove_DB_AC]) ).
cnf(c_33,plain,
differ(b,a),
inference(resolve,[status(thm)],[c_11,c_12]) ).
cnf(c_35,plain,
differ(d,a),
inference(resolve,[status(thm)],[c_11,c_14]) ).
cnf(c_15971,plain,
( ~ differ(a,A)
| holds(clear(a),do(pickup(A),s0)) ),
inference(resolve,[status(thm)],[c_5,c_26]) ).
cnf(c_79,plain,
holds(clear(a),do(pickup(c),s0)),
inference(resolve,[status(thm)],[c_15971,c_13]) ).
cnf(c_15972,plain,
( ~ differ(b,A)
| holds(clear(b),do(pickup(A),s0)) ),
inference(resolve,[status(thm)],[c_5,c_27]) ).
cnf(c_95,plain,
holds(clear(b),do(pickup(c),s0)),
inference(resolve,[status(thm)],[c_15972,c_16]) ).
cnf(c_15973,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_15974,plain,
( ~ holds(empty,s0)
| holds(clear(d),do(pickup(c),s0)) ),
inference(resolve,[status(thm)],[c_15973,c_28]) ).
cnf(c_124,plain,
holds(clear(d),do(pickup(c),s0)),
inference(resolve,[status(thm)],[c_15974,c_29]) ).
cnf(c_15975,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_15976,plain,
( ~ differ(c,table)
| holds(holding(c),do(pickup(c),s0)) ),
inference(resolve,[status(thm)],[c_15975,c_28]) ).
cnf(c_125,plain,
holds(holding(c),do(pickup(c),s0)),
inference(resolve,[status(thm)],[c_15976,c_20]) ).
cnf(c_160,plain,
( ~ holds(on(c,a),A)
| ~ holds(on(d,b),A) ),
inference(resolve,[status(thm)],[c_31,c_1]) ).
cnf(c_167,plain,
( ~ holds(on(c,a),C)
| ~ holds(on(d,b),do(putdown(A,B),C)) ),
inference(resolve,[status(thm)],[c_160,c_9]) ).
cnf(c_192,plain,
( ~ holds(clear(b),A)
| ~ holds(holding(d),A)
| ~ holds(on(c,a),A) ),
inference(resolve,[status(thm)],[c_167,c_7]) ).
cnf(c_198,plain,
( ~ differ(c,A)
| ~ holds(on(c,a),B)
| ~ holds(clear(b),do(pickup(A),B))
| ~ holds(holding(d),do(pickup(A),B)) ),
inference(resolve,[status(thm)],[c_192,c_4]) ).
cnf(c_15977,plain,
( ~ differ(b,B)
| holds(clear(b),do(putdown(A,B),do(pickup(c),s0))) ),
inference(resolve,[status(thm)],[c_10,c_95]) ).
cnf(c_636,plain,
holds(clear(b),do(putdown(A,a),do(pickup(c),s0))),
inference(resolve,[status(thm)],[c_15977,c_33]) ).
cnf(c_15978,plain,
( ~ differ(d,B)
| holds(clear(d),do(putdown(A,B),do(pickup(c),s0))) ),
inference(resolve,[status(thm)],[c_10,c_124]) ).
cnf(c_1069,plain,
holds(clear(d),do(putdown(A,a),do(pickup(c),s0))),
inference(resolve,[status(thm)],[c_15978,c_35]) ).
cnf(c_15979,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_125]) ).
cnf(c_1103,plain,
holds(on(c,a),do(putdown(c,a),do(pickup(c),s0))),
inference(resolve,[status(thm)],[c_15979,c_79]) ).
cnf(c_15980,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_125]) ).
cnf(c_1107,plain,
holds(empty,do(putdown(c,a),do(pickup(c),s0))),
inference(resolve,[status(thm)],[c_15980,c_79]) ).
cnf(c_15981,plain,
( ~ differ(d,table)
| ~ holds(clear(d),A)
| ~ holds(empty,A)
| ~ differ(c,d)
| ~ holds(on(c,a),A)
| ~ holds(clear(b),do(pickup(d),A)) ),
inference(resolve,[status(thm)],[c_198,c_2]) ).
cnf(c_15982,plain,
( ~ differ(d,table)
| ~ holds(clear(d),A)
| ~ holds(empty,A)
| ~ holds(on(c,a),A)
| ~ holds(clear(b),do(pickup(d),A)) ),
inference(resolve,[status(thm)],[c_19,c_15981]) ).
cnf(c_10030,plain,
( ~ holds(clear(d),A)
| ~ holds(empty,A)
| ~ holds(on(c,a),A)
| ~ holds(clear(b),do(pickup(d),A)) ),
inference(resolve,[status(thm)],[c_21,c_15982]) ).
cnf(c_15983,plain,
( ~ differ(b,d)
| ~ holds(clear(b),A)
| ~ holds(clear(d),A)
| ~ holds(empty,A)
| ~ holds(on(c,a),A) ),
inference(resolve,[status(thm)],[c_10030,c_5]) ).
cnf(c_10042,plain,
( ~ holds(clear(b),A)
| ~ holds(clear(d),A)
| ~ holds(empty,A)
| ~ holds(on(c,a),A) ),
inference(resolve,[status(thm)],[c_17,c_15983]) ).
cnf(c_15984,plain,
( ~ holds(clear(b),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(clear(d),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(on(c,a),do(putdown(c,a),do(pickup(c),s0))) ),
inference(resolve,[status(thm)],[c_1107,c_10042]) ).
cnf(c_15985,plain,
( ~ holds(clear(b),do(putdown(c,a),do(pickup(c),s0)))
| ~ holds(clear(d),do(putdown(c,a),do(pickup(c),s0))) ),
inference(resolve,[status(thm)],[c_1103,c_15984]) ).
cnf(c_15986,plain,
~ holds(clear(b),do(putdown(c,a),do(pickup(c),s0))),
inference(resolve,[status(thm)],[c_1069,c_15985]) ).
cnf(c_15970,plain,
$false,
inference(resolve,[status(thm)],[c_636,c_15986]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PLA005-2 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 04:45:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.14/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.37 % Process 3158700 was started by sandbox on n015,
% 0.14/0.37 % Sat Sep 26 04:45:58 2026
% 0.14/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 58.39/7.83
% 58.39/7.83 % given #500 (T,wt=26): 1130 holds(and(holding(b),on(a,table)),do(pickup(b),s0)). [ur(1,b,126,a,c,47,a)].
% 58.39/7.83
% 58.39/7.83 % given #1000 (W,wt=27): 8086 holds(and(on(a,table),on(c,d)),do(pickup(b),s0)). [ur(1,b,47,a,c,189,a)].
% 58.39/7.83
% 58.39/7.83 % given #1500 (F,wt=38): 15758 -holds(holding(d),do(putdown(A,c),do(putdown(c,a),s0))) | -holds(holding(c),s0). [resolve(7853,b,7,a),unit_del(c,26)].
% 58.39/7.83
% 58.39/7.83 % SZS status Unsatisfiable for theBenchmark
% 58.39/7.83
% 58.39/7.83 % Proof 1 at 4.44 (+ 2.75) seconds.
% 58.39/7.83 % Length of proof is 41.
% 58.39/7.83 % Level of proof is 7.
% 58.39/7.83 % Maximum clause weight is 37.000.
% 58.39/7.83 % Given clauses 1571.
% 58.39/7.83
% 58.39/7.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------