%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PLA009-2 : 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 : n019.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 10.55s 6.73s
% Output : CNFRefutation 10.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 20
% Syntax : Number of formulae : 67 ( 32 unt; 0 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 138 ( 74 ~; 64 |; 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 : 82 ( 8 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_table,axiom,
differ(a,table),
file('theBenchmark.p',differ_a_table) ).
cnf(c_15,plain,
differ(a,table),
inference(clausify,[status(thm)],[differ_a_table]) ).
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(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_D_AB,axiom,
! [VAR_0] : ~ holds(and(clear(d),on(a,b)),VAR_0),
file('theBenchmark.p',prove_D_AB) ).
cnf(c_31,plain,
~ holds(and(clear(d),on(a,b)),A),
inference(clausify,[status(thm)],[prove_D_AB]) ).
cnf(c_33,plain,
differ(b,a),
inference(resolve,[status(thm)],[c_12,c_11]) ).
cnf(c_37,plain,
differ(c,a),
inference(resolve,[status(thm)],[c_13,c_11]) ).
cnf(c_40,plain,
( ~ holds(on(a,A),B)
| holds(on(a,A),do(pickup(c),B)) ),
inference(resolve,[status(thm)],[c_13,c_4]) ).
cnf(c_50,plain,
differ(c,b),
inference(resolve,[status(thm)],[c_16,c_11]) ).
cnf(c_13181,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_13182,plain,
( ~ differ(a,table)
| holds(holding(a),do(pickup(a),s0)) ),
inference(resolve,[status(thm)],[c_13181,c_26]) ).
cnf(c_189,plain,
holds(holding(a),do(pickup(a),s0)),
inference(resolve,[status(thm)],[c_13182,c_15]) ).
cnf(c_228,plain,
( ~ holds(on(a,b),A)
| ~ holds(clear(d),A) ),
inference(resolve,[status(thm)],[c_31,c_1]) ).
cnf(c_13183,plain,
( ~ differ(b,A)
| holds(clear(b),do(pickup(A),s0)) ),
inference(resolve,[status(thm)],[c_5,c_27]) ).
cnf(c_233,plain,
holds(clear(b),do(pickup(a),s0)),
inference(resolve,[status(thm)],[c_13183,c_33]) ).
cnf(c_13184,plain,
( ~ differ(c,A)
| holds(clear(c),do(pickup(A),s0)) ),
inference(resolve,[status(thm)],[c_5,c_28]) ).
cnf(c_259,plain,
holds(clear(c),do(pickup(a),s0)),
inference(resolve,[status(thm)],[c_13184,c_37]) ).
cnf(c_13185,plain,
( ~ differ(c,A)
| holds(on(c,d),do(pickup(A),s0)) ),
inference(resolve,[status(thm)],[c_4,c_24]) ).
cnf(c_260,plain,
holds(on(c,d),do(pickup(a),s0)),
inference(resolve,[status(thm)],[c_13185,c_37]) ).
cnf(c_334,plain,
( ~ holds(clear(d),do(pickup(c),A))
| ~ holds(on(a,b),A) ),
inference(resolve,[status(thm)],[c_40,c_228]) ).
cnf(c_345,plain,
( ~ holds(empty,A)
| ~ holds(clear(c),A)
| ~ holds(on(c,d),A)
| ~ holds(on(a,b),A) ),
inference(resolve,[status(thm)],[c_334,c_3]) ).
cnf(c_350,plain,
( ~ holds(clear(b),A)
| ~ holds(holding(a),A)
| ~ holds(empty,do(putdown(a,b),A))
| ~ holds(clear(c),do(putdown(a,b),A))
| ~ holds(on(c,d),do(putdown(a,b),A)) ),
inference(resolve,[status(thm)],[c_345,c_7]) ).
cnf(c_13186,plain,
( ~ holds(clear(A),do(pickup(a),s0))
| holds(empty,do(putdown(a,A),do(pickup(a),s0))) ),
inference(resolve,[status(thm)],[c_6,c_189]) ).
cnf(c_2632,plain,
holds(empty,do(putdown(a,b),do(pickup(a),s0))),
inference(resolve,[status(thm)],[c_13186,c_233]) ).
cnf(c_13187,plain,
( ~ differ(c,B)
| holds(clear(c),do(putdown(A,B),do(pickup(a),s0))) ),
inference(resolve,[status(thm)],[c_10,c_259]) ).
cnf(c_2652,plain,
holds(clear(c),do(putdown(A,b),do(pickup(a),s0))),
inference(resolve,[status(thm)],[c_13187,c_50]) ).
cnf(c_8345,plain,
holds(on(c,d),do(putdown(A,B),do(pickup(a),s0))),
inference(resolve,[status(thm)],[c_260,c_9]) ).
cnf(c_13188,plain,
( ~ holds(clear(b),do(pickup(a),s0))
| ~ holds(empty,do(putdown(a,b),do(pickup(a),s0)))
| ~ holds(clear(c),do(putdown(a,b),do(pickup(a),s0)))
| ~ holds(on(c,d),do(putdown(a,b),do(pickup(a),s0))) ),
inference(resolve,[status(thm)],[c_350,c_189]) ).
cnf(c_13189,plain,
( ~ holds(clear(b),do(pickup(a),s0))
| ~ holds(empty,do(putdown(a,b),do(pickup(a),s0)))
| ~ holds(clear(c),do(putdown(a,b),do(pickup(a),s0))) ),
inference(resolve,[status(thm)],[c_8345,c_13188]) ).
cnf(c_13190,plain,
( ~ holds(clear(b),do(pickup(a),s0))
| ~ holds(empty,do(putdown(a,b),do(pickup(a),s0))) ),
inference(resolve,[status(thm)],[c_2652,c_13189]) ).
cnf(c_13191,plain,
~ holds(clear(b),do(pickup(a),s0)),
inference(resolve,[status(thm)],[c_2632,c_13190]) ).
cnf(c_13180,plain,
$false,
inference(resolve,[status(thm)],[c_233,c_13191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PLA009-2 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n019.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Sat Sep 26 04:43:40 UTC 2026
% 0.10/5.36 % CPUTime :
% 0.10/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.37 % Process 425670 was started by sandbox2 on n019,
% 0.10/5.37 % Sat Sep 26 04:43:40 2026
% 0.10/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.37
% 0.10/5.37 % From the command line: assign(max_seconds, 300).
% 10.55/6.73
% 10.55/6.73 % given #500 (W,wt=25): 2665 holds(and(clear(c),holding(a)),do(pickup(a),s0)). [ur(1,b,259,a,c,189,a)].
% 10.55/6.73
% 10.55/6.73 % SZS status Unsatisfiable for theBenchmark
% 10.55/6.73
% 10.55/6.73 % Proof 1 at 0.94 (+ 0.38) seconds.
% 10.55/6.73 % Length of proof is 36.
% 10.55/6.73 % Level of proof is 5.
% 10.55/6.73 % Maximum clause weight is 47.000.
% 10.55/6.73 % Given clauses 658.
% 10.55/6.73
% 10.55/6.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------