%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PLA014-1 : 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 : n010.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 08:20:23 AM UTC 2026
% Result : Unsatisfiable 112.39s 15.72s
% Output : CNFRefutation 112.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 70 ( 31 unt; 0 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 156 ( 85 ~; 71 |; 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 : 86 ( 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_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_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(differ_b_table,axiom,
differ(b,table),
file('theBenchmark.p',differ_b_table) ).
cnf(c_18,plain,
differ(b,table),
inference(clausify,[status(thm)],[differ_b_table]) ).
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_ABC,axiom,
! [VAR_0] : ~ holds(and(on(a,b),on(b,c)),VAR_0),
file('theBenchmark.p',prove_ABC) ).
cnf(c_31,plain,
~ holds(and(on(a,b),on(b,c)),A),
inference(clausify,[status(thm)],[prove_ABC]) ).
cnf(c_32,plain,
differ(b,a),
inference(resolve,[status(thm)],[c_12,c_11]) ).
cnf(c_49,plain,
differ(c,b),
inference(resolve,[status(thm)],[c_16,c_11]) ).
cnf(c_19014,plain,
( ~ differ(a,A)
| holds(clear(a),do(pickup(A),s0)) ),
inference(resolve,[status(thm)],[c_5,c_26]) ).
cnf(c_135,plain,
holds(clear(a),do(pickup(b),s0)),
inference(resolve,[status(thm)],[c_19014,c_12]) ).
cnf(c_19015,plain,
( ~ differ(b,table)
| ~ holds(empty,s0)
| holds(holding(b),do(pickup(b),s0)) ),
inference(resolve,[status(thm)],[c_27,c_2]) ).
cnf(c_19016,plain,
( ~ differ(b,table)
| holds(holding(b),do(pickup(b),s0)) ),
inference(resolve,[status(thm)],[c_29,c_19015]) ).
cnf(c_151,plain,
holds(holding(b),do(pickup(b),s0)),
inference(resolve,[status(thm)],[c_18,c_19016]) ).
cnf(c_240,plain,
( ~ holds(on(b,c),A)
| ~ holds(on(a,b),A) ),
inference(resolve,[status(thm)],[c_31,c_1]) ).
cnf(c_244,plain,
( ~ holds(on(b,c),C)
| ~ holds(on(a,b),do(putdown(A,B),C)) ),
inference(resolve,[status(thm)],[c_240,c_9]) ).
cnf(c_19017,plain,
( ~ differ(c,A)
| holds(clear(c),do(pickup(A),s0)) ),
inference(resolve,[status(thm)],[c_5,c_28]) ).
cnf(c_281,plain,
holds(clear(c),do(pickup(b),s0)),
inference(resolve,[status(thm)],[c_19017,c_49]) ).
cnf(c_287,plain,
( ~ holds(clear(b),A)
| ~ holds(holding(a),A)
| ~ holds(on(b,c),A) ),
inference(resolve,[status(thm)],[c_244,c_7]) ).
cnf(c_294,plain,
( ~ differ(b,A)
| ~ holds(on(b,c),B)
| ~ holds(clear(b),do(pickup(A),B))
| ~ holds(holding(a),do(pickup(A),B)) ),
inference(resolve,[status(thm)],[c_287,c_4]) ).
cnf(c_19018,plain,
( ~ differ(a,B)
| holds(clear(a),do(putdown(A,B),do(pickup(b),s0))) ),
inference(resolve,[status(thm)],[c_10,c_135]) ).
cnf(c_717,plain,
holds(clear(a),do(putdown(A,c),do(pickup(b),s0))),
inference(resolve,[status(thm)],[c_19018,c_13]) ).
cnf(c_19019,plain,
( ~ holds(clear(A),do(pickup(b),s0))
| holds(clear(b),do(putdown(b,A),do(pickup(b),s0))) ),
inference(resolve,[status(thm)],[c_8,c_151]) ).
cnf(c_2588,plain,
holds(clear(b),do(putdown(b,c),do(pickup(b),s0))),
inference(resolve,[status(thm)],[c_19019,c_281]) ).
cnf(c_19020,plain,
( ~ holds(clear(A),do(pickup(b),s0))
| holds(on(b,A),do(putdown(b,A),do(pickup(b),s0))) ),
inference(resolve,[status(thm)],[c_7,c_151]) ).
cnf(c_2589,plain,
holds(on(b,c),do(putdown(b,c),do(pickup(b),s0))),
inference(resolve,[status(thm)],[c_19020,c_281]) ).
cnf(c_19021,plain,
( ~ holds(clear(A),do(pickup(b),s0))
| holds(empty,do(putdown(b,A),do(pickup(b),s0))) ),
inference(resolve,[status(thm)],[c_6,c_151]) ).
cnf(c_2590,plain,
holds(empty,do(putdown(b,c),do(pickup(b),s0))),
inference(resolve,[status(thm)],[c_19021,c_281]) ).
cnf(c_7872,plain,
( ~ holds(on(b,c),A)
| ~ holds(clear(b),do(pickup(a),A))
| ~ holds(holding(a),do(pickup(a),A)) ),
inference(resolve,[status(thm)],[c_294,c_32]) ).
cnf(c_19022,plain,
( ~ differ(b,a)
| ~ holds(clear(b),A)
| ~ holds(on(b,c),A)
| ~ holds(holding(a),do(pickup(a),A)) ),
inference(resolve,[status(thm)],[c_7872,c_5]) ).
cnf(c_7883,plain,
( ~ holds(clear(b),A)
| ~ holds(on(b,c),A)
| ~ holds(holding(a),do(pickup(a),A)) ),
inference(resolve,[status(thm)],[c_32,c_19022]) ).
cnf(c_19023,plain,
( ~ differ(a,table)
| ~ holds(clear(a),A)
| ~ holds(empty,A)
| ~ holds(clear(b),A)
| ~ holds(on(b,c),A) ),
inference(resolve,[status(thm)],[c_7883,c_2]) ).
cnf(c_7916,plain,
( ~ holds(clear(a),A)
| ~ holds(empty,A)
| ~ holds(clear(b),A)
| ~ holds(on(b,c),A) ),
inference(resolve,[status(thm)],[c_15,c_19023]) ).
cnf(c_19024,plain,
( ~ holds(clear(a),do(putdown(b,c),do(pickup(b),s0)))
| ~ holds(clear(b),do(putdown(b,c),do(pickup(b),s0)))
| ~ holds(on(b,c),do(putdown(b,c),do(pickup(b),s0))) ),
inference(resolve,[status(thm)],[c_2590,c_7916]) ).
cnf(c_19025,plain,
( ~ holds(clear(a),do(putdown(b,c),do(pickup(b),s0)))
| ~ holds(clear(b),do(putdown(b,c),do(pickup(b),s0))) ),
inference(resolve,[status(thm)],[c_2589,c_19024]) ).
cnf(c_19026,plain,
~ holds(clear(a),do(putdown(b,c),do(pickup(b),s0))),
inference(resolve,[status(thm)],[c_2588,c_19025]) ).
cnf(c_19013,plain,
$false,
inference(resolve,[status(thm)],[c_717,c_19026]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PLA014-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n010.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 04:44:03 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 2503193 was started by sandbox2 on n010,
% 0.12/0.39 % Sat Sep 26 04:44:03 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).
% 112.39/15.72
% 112.39/15.72 % given #500 (W,wt=17): 10349 -holds(holding(a),s0) | -differ(b,b). [resolve(10347,b,145,a)].
% 112.39/15.72
% 112.39/15.72 % given #1000 (W,wt=27): 7274 holds(and(on(a,table),clear(table)),do(putdown(A,B),s0)). [ur(1,b,76,a,c,30,a)].
% 112.39/15.72
% 112.39/15.72 % given #1500 (W,wt=31): 2685 holds(and(on(b,table),A),do(pickup(table),s0)) | -holds(A,do(pickup(table),s0)). [resolve(89,a,1,b)].
% 112.39/15.72
% 112.39/15.72 % given #2000 (W,wt=32): 2112 holds(and(and(clear(b),clear(table)),clear(b)),s0). [ur(1,b,226,a,c,27,a)].
% 112.39/15.72
% 112.39/15.72 % SZS status Unsatisfiable for theBenchmark
% 112.39/15.72
% 112.39/15.72 % Proof 1 at 4.39 (+ 2.79) seconds.
% 112.39/15.72 % Length of proof is 37.
% 112.39/15.72 % Level of proof is 8.
% 112.39/15.72 % Maximum clause weight is 37.000.
% 112.39/15.72 % Given clauses 2077.
% 112.39/15.72
% 112.39/15.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------