%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PLA018-1 : 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 : n003.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 08:20:24 AM UTC 2026
% Result : Unsatisfiable 40.43s 12.25s
% Output : CNFRefutation 40.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 26
% Syntax : Number of formulae : 99 ( 43 unt; 0 def)
% Number of atoms : 234 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 299 ( 164 ~; 135 |; 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 : 118 ( 11 sgn 37 !; 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_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_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_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(clear_table,axiom,
! [VAR_0] : holds(clear(table),VAR_0),
file('theBenchmark.p',clear_table) ).
cnf(c_30,plain,
holds(clear(table),A),
inference(clausify,[status(thm)],[clear_table]) ).
fof(prove_AB_DC,axiom,
! [VAR_0] : ~ holds(and(on(a,b),on(d,c)),VAR_0),
file('theBenchmark.p',prove_AB_DC) ).
cnf(c_31,plain,
~ holds(and(on(a,b),on(d,c)),A),
inference(clausify,[status(thm)],[prove_AB_DC]) ).
cnf(c_33,plain,
differ(b,a),
inference(resolve,[status(thm)],[c_11,c_12]) ).
cnf(c_34,plain,
differ(c,a),
inference(resolve,[status(thm)],[c_11,c_13]) ).
cnf(c_37,plain,
differ(c,b),
inference(resolve,[status(thm)],[c_11,c_16]) ).
cnf(c_16668,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_16669,plain,
( ~ differ(a,table)
| holds(holding(a),do(pickup(a),s0)) ),
inference(resolve,[status(thm)],[c_16668,c_26]) ).
cnf(c_127,plain,
holds(holding(a),do(pickup(a),s0)),
inference(resolve,[status(thm)],[c_16669,c_15]) ).
cnf(c_160,plain,
( ~ holds(on(d,c),A)
| ~ holds(on(a,b),A) ),
inference(resolve,[status(thm)],[c_31,c_1]) ).
cnf(c_16670,plain,
( ~ differ(b,A)
| holds(clear(b),do(pickup(A),s0)) ),
inference(resolve,[status(thm)],[c_5,c_27]) ).
cnf(c_162,plain,
holds(clear(b),do(pickup(a),s0)),
inference(resolve,[status(thm)],[c_16670,c_33]) ).
cnf(c_164,plain,
( ~ holds(on(a,b),C)
| ~ holds(on(d,c),do(putdown(A,B),C)) ),
inference(resolve,[status(thm)],[c_160,c_9]) ).
cnf(c_170,plain,
( ~ holds(clear(c),A)
| ~ holds(holding(d),A)
| ~ holds(on(a,b),A) ),
inference(resolve,[status(thm)],[c_164,c_7]) ).
cnf(c_176,plain,
( ~ differ(a,A)
| ~ holds(on(a,b),B)
| ~ holds(clear(c),do(pickup(A),B))
| ~ holds(holding(d),do(pickup(A),B)) ),
inference(resolve,[status(thm)],[c_170,c_4]) ).
cnf(c_16671,plain,
( ~ differ(c,A)
| holds(clear(c),do(pickup(A),s0)) ),
inference(resolve,[status(thm)],[c_5,c_28]) ).
cnf(c_184,plain,
holds(clear(c),do(pickup(a),s0)),
inference(resolve,[status(thm)],[c_16671,c_34]) ).
cnf(c_16672,plain,
( ~ differ(c,A)
| holds(on(c,d),do(pickup(A),s0)) ),
inference(resolve,[status(thm)],[c_4,c_24]) ).
cnf(c_185,plain,
holds(on(c,d),do(pickup(a),s0)),
inference(resolve,[status(thm)],[c_16672,c_34]) ).
cnf(c_16673,plain,
( ~ holds(clear(A),do(pickup(a),s0))
| holds(on(a,A),do(putdown(a,A),do(pickup(a),s0))) ),
inference(resolve,[status(thm)],[c_7,c_127]) ).
cnf(c_2377,plain,
holds(on(a,b),do(putdown(a,b),do(pickup(a),s0))),
inference(resolve,[status(thm)],[c_16673,c_162]) ).
cnf(c_16674,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_127]) ).
cnf(c_2378,plain,
holds(empty,do(putdown(a,b),do(pickup(a),s0))),
inference(resolve,[status(thm)],[c_16674,c_162]) ).
cnf(c_16675,plain,
( ~ differ(c,B)
| holds(clear(c),do(putdown(A,B),do(pickup(a),s0))) ),
inference(resolve,[status(thm)],[c_10,c_184]) ).
cnf(c_2393,plain,
holds(clear(c),do(putdown(A,b),do(pickup(a),s0))),
inference(resolve,[status(thm)],[c_16675,c_37]) ).
cnf(c_7911,plain,
holds(on(c,d),do(putdown(A,B),do(pickup(a),s0))),
inference(resolve,[status(thm)],[c_9,c_185]) ).
cnf(c_16676,plain,
( ~ differ(d,table)
| ~ holds(clear(d),A)
| ~ holds(empty,A)
| ~ differ(a,d)
| ~ holds(on(a,b),A)
| ~ holds(clear(c),do(pickup(d),A)) ),
inference(resolve,[status(thm)],[c_176,c_2]) ).
cnf(c_16677,plain,
( ~ differ(d,table)
| ~ holds(clear(d),A)
| ~ holds(empty,A)
| ~ holds(on(a,b),A)
| ~ holds(clear(c),do(pickup(d),A)) ),
inference(resolve,[status(thm)],[c_14,c_16676]) ).
cnf(c_8037,plain,
( ~ holds(clear(d),A)
| ~ holds(empty,A)
| ~ holds(on(a,b),A)
| ~ holds(clear(c),do(pickup(d),A)) ),
inference(resolve,[status(thm)],[c_21,c_16677]) ).
cnf(c_16678,plain,
( ~ differ(c,d)
| ~ holds(clear(c),A)
| ~ holds(clear(d),A)
| ~ holds(empty,A)
| ~ holds(on(a,b),A) ),
inference(resolve,[status(thm)],[c_8037,c_5]) ).
cnf(c_8349,plain,
( ~ holds(clear(c),A)
| ~ holds(clear(d),A)
| ~ holds(empty,A)
| ~ holds(on(a,b),A) ),
inference(resolve,[status(thm)],[c_19,c_16678]) ).
cnf(c_8359,plain,
( ~ holds(on(a,b),C)
| ~ holds(clear(c),do(putdown(A,B),C))
| ~ holds(clear(d),do(putdown(A,B),C))
| ~ holds(empty,do(putdown(A,B),C)) ),
inference(resolve,[status(thm)],[c_8349,c_9]) ).
cnf(c_15770,plain,
( ~ differ(d,B)
| ~ holds(clear(d),C)
| ~ holds(on(a,b),C)
| ~ holds(clear(c),do(putdown(A,B),C))
| ~ holds(empty,do(putdown(A,B),C)) ),
inference(resolve,[status(thm)],[c_8359,c_10]) ).
cnf(c_15800,plain,
( ~ holds(clear(d),B)
| ~ holds(on(a,b),B)
| ~ holds(clear(c),do(putdown(A,table),B))
| ~ holds(empty,do(putdown(A,table),B)) ),
inference(resolve,[status(thm)],[c_15770,c_21]) ).
cnf(c_16679,plain,
( ~ holds(clear(table),A)
| ~ holds(holding(c),A)
| ~ holds(clear(d),A)
| ~ holds(on(a,b),A)
| ~ holds(empty,do(putdown(c,table),A)) ),
inference(resolve,[status(thm)],[c_15800,c_8]) ).
cnf(c_16093,plain,
( ~ holds(holding(c),A)
| ~ holds(clear(d),A)
| ~ holds(on(a,b),A)
| ~ holds(empty,do(putdown(c,table),A)) ),
inference(resolve,[status(thm)],[c_30,c_16679]) ).
cnf(c_16680,plain,
( ~ holds(clear(table),A)
| ~ holds(holding(c),A)
| ~ holds(holding(c),A)
| ~ holds(clear(d),A)
| ~ holds(on(a,b),A) ),
inference(resolve,[status(thm)],[c_16093,c_6]) ).
cnf(c_16681,plain,
( ~ holds(clear(table),A)
| ~ holds(holding(c),A)
| ~ holds(clear(d),A)
| ~ holds(on(a,b),A) ),
inference(copy,[status(thm)],[c_16680]) ).
cnf(c_16147,plain,
( ~ holds(holding(c),A)
| ~ holds(clear(d),A)
| ~ holds(on(a,b),A) ),
inference(resolve,[status(thm)],[c_30,c_16681]) ).
cnf(c_16162,plain,
( ~ differ(a,A)
| ~ holds(on(a,b),B)
| ~ holds(holding(c),do(pickup(A),B))
| ~ holds(clear(d),do(pickup(A),B)) ),
inference(resolve,[status(thm)],[c_16147,c_4]) ).
cnf(c_16682,plain,
( ~ differ(c,table)
| ~ holds(clear(c),A)
| ~ holds(empty,A)
| ~ differ(a,c)
| ~ holds(on(a,b),A)
| ~ holds(clear(d),do(pickup(c),A)) ),
inference(resolve,[status(thm)],[c_16162,c_2]) ).
cnf(c_16683,plain,
( ~ differ(c,table)
| ~ holds(clear(c),A)
| ~ holds(empty,A)
| ~ holds(on(a,b),A)
| ~ holds(clear(d),do(pickup(c),A)) ),
inference(resolve,[status(thm)],[c_13,c_16682]) ).
cnf(c_16291,plain,
( ~ holds(clear(c),A)
| ~ holds(empty,A)
| ~ holds(on(a,b),A)
| ~ holds(clear(d),do(pickup(c),A)) ),
inference(resolve,[status(thm)],[c_20,c_16683]) ).
cnf(c_16684,plain,
( ~ holds(empty,A)
| ~ holds(clear(c),A)
| ~ holds(on(c,d),A)
| ~ holds(clear(c),A)
| ~ holds(empty,A)
| ~ holds(on(a,b),A) ),
inference(resolve,[status(thm)],[c_16291,c_3]) ).
cnf(c_16685,plain,
( ~ holds(empty,A)
| ~ holds(on(c,d),A)
| ~ holds(clear(c),A)
| ~ holds(empty,A)
| ~ holds(on(a,b),A) ),
inference(copy,[status(thm)],[c_16684]) ).
cnf(c_16301,plain,
( ~ holds(on(c,d),A)
| ~ holds(clear(c),A)
| ~ holds(empty,A)
| ~ holds(on(a,b),A) ),
inference(copy,[status(thm)],[c_16685]) ).
cnf(c_16686,plain,
( ~ holds(on(c,d),do(putdown(a,b),do(pickup(a),s0)))
| ~ holds(clear(c),do(putdown(a,b),do(pickup(a),s0)))
| ~ holds(on(a,b),do(putdown(a,b),do(pickup(a),s0))) ),
inference(resolve,[status(thm)],[c_2378,c_16301]) ).
cnf(c_16687,plain,
( ~ holds(on(c,d),do(putdown(a,b),do(pickup(a),s0)))
| ~ holds(clear(c),do(putdown(a,b),do(pickup(a),s0))) ),
inference(resolve,[status(thm)],[c_2377,c_16686]) ).
cnf(c_16688,plain,
~ holds(on(c,d),do(putdown(a,b),do(pickup(a),s0))),
inference(resolve,[status(thm)],[c_2393,c_16687]) ).
cnf(c_16667,plain,
$false,
inference(resolve,[status(thm)],[c_7911,c_16688]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : PLA018-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.45 % Computer : n003.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.45 % CPULimit : 300
% 0.18/5.45 % WCLimit : 300
% 0.18/5.45 % DateTime : Sat Sep 26 04:46:14 UTC 2026
% 0.18/5.46 % CPUTime :
% 0.18/5.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.46 % Process 2053128 was started by sandbox2 on n003,
% 0.18/5.46 % Sat Sep 26 04:46:14 2026
% 0.18/5.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/5.47
% 0.18/5.47 % From the command line: assign(max_seconds, 300).
% 40.43/12.25
% 40.43/12.25 % given #500 (T,wt=26): 1129 holds(and(holding(b),on(a,table)),do(pickup(b),s0)). [ur(1,b,126,a,c,47,a)].
% 40.43/12.25
% 40.43/12.25 % given #1000 (W,wt=27): 8090 holds(and(on(a,table),on(c,d)),do(pickup(b),s0)). [ur(1,b,47,a,c,189,a)].
% 40.43/12.25
% 40.43/12.25 % given #1500 (F,wt=43): 7838 -holds(holding(a),do(putdown(A,table),do(putdown(B,a),s0))) | -holds(on(d,c),do(putdown(B,a),s0)). [resolve(161,a,5481,c)].
% 40.43/12.25
% 40.43/12.25 % SZS status Unsatisfiable for theBenchmark
% 40.43/12.25
% 40.43/12.25 % Proof 1 at 4.16 (+ 2.59) seconds.
% 40.43/12.25 % Length of proof is 52.
% 40.43/12.25 % Level of proof is 15.
% 40.43/12.25 % Maximum clause weight is 43.000.
% 40.43/12.25 % Given clauses 1824.
% 40.43/12.25
% 40.43/12.25 % SZS output start CNFRefutation for theBenchmark
% See solution above
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