%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PLA019-1 : 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 : n014.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 11.58s 6.96s
% Output : CNFRefutation 11.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of formulae : 59 ( 27 unt; 0 def)
% Number of atoms : 125 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 145 ( 79 ~; 66 |; 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 : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 67 ( 4 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_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_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_DC,axiom,
! [VAR_0] : ~ holds(on(d,c),VAR_0),
file('theBenchmark.p',prove_DC) ).
cnf(c_31,plain,
~ holds(on(d,c),A),
inference(clausify,[status(thm)],[prove_DC]) ).
cnf(c_38,plain,
differ(d,b),
inference(resolve,[status(thm)],[c_11,c_17]) ).
cnf(c_9144,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_9144,c_16]) ).
cnf(c_9145,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_9146,plain,
( ~ holds(empty,s0)
| holds(clear(d),do(pickup(c),s0)) ),
inference(resolve,[status(thm)],[c_9145,c_28]) ).
cnf(c_124,plain,
holds(clear(d),do(pickup(c),s0)),
inference(resolve,[status(thm)],[c_9146,c_29]) ).
cnf(c_9147,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_9148,plain,
( ~ differ(c,table)
| holds(holding(c),do(pickup(c),s0)) ),
inference(resolve,[status(thm)],[c_9147,c_28]) ).
cnf(c_125,plain,
holds(holding(c),do(pickup(c),s0)),
inference(resolve,[status(thm)],[c_9148,c_20]) ).
cnf(c_160,plain,
( ~ holds(clear(c),A)
| ~ holds(holding(d),A) ),
inference(resolve,[status(thm)],[c_31,c_7]) ).
cnf(c_9149,plain,
( ~ differ(d,table)
| ~ holds(clear(d),A)
| ~ holds(empty,A)
| ~ holds(clear(c),do(pickup(d),A)) ),
inference(resolve,[status(thm)],[c_160,c_2]) ).
cnf(c_165,plain,
( ~ holds(clear(d),A)
| ~ holds(empty,A)
| ~ holds(clear(c),do(pickup(d),A)) ),
inference(resolve,[status(thm)],[c_21,c_9149]) ).
cnf(c_9150,plain,
( ~ differ(c,d)
| ~ holds(clear(c),A)
| ~ holds(clear(d),A)
| ~ holds(empty,A) ),
inference(resolve,[status(thm)],[c_165,c_5]) ).
cnf(c_170,plain,
( ~ holds(clear(c),A)
| ~ holds(clear(d),A)
| ~ holds(empty,A) ),
inference(resolve,[status(thm)],[c_19,c_9150]) ).
cnf(c_186,plain,
( ~ holds(clear(B),C)
| ~ holds(holding(A),C)
| ~ holds(clear(c),do(putdown(A,B),C))
| ~ holds(clear(d),do(putdown(A,B),C)) ),
inference(resolve,[status(thm)],[c_170,c_6]) ).
cnf(c_9151,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_1086,plain,
holds(clear(d),do(putdown(A,b),do(pickup(c),s0))),
inference(resolve,[status(thm)],[c_9151,c_38]) ).
cnf(c_9152,plain,
( ~ holds(clear(A),B)
| ~ holds(holding(c),B)
| ~ holds(clear(A),B)
| ~ holds(holding(c),B)
| ~ holds(clear(d),do(putdown(c,A),B)) ),
inference(resolve,[status(thm)],[c_186,c_8]) ).
cnf(c_9153,plain,
( ~ holds(clear(A),B)
| ~ holds(clear(A),B)
| ~ holds(holding(c),B)
| ~ holds(clear(d),do(putdown(c,A),B)) ),
inference(copy,[status(thm)],[c_9152]) ).
cnf(c_9083,plain,
( ~ holds(clear(A),B)
| ~ holds(holding(c),B)
| ~ holds(clear(d),do(putdown(c,A),B)) ),
inference(copy,[status(thm)],[c_9153]) ).
cnf(c_9154,plain,
( ~ holds(holding(c),do(pickup(c),s0))
| ~ holds(clear(d),do(putdown(c,b),do(pickup(c),s0))) ),
inference(resolve,[status(thm)],[c_9083,c_95]) ).
cnf(c_9155,plain,
~ holds(holding(c),do(pickup(c),s0)),
inference(resolve,[status(thm)],[c_1086,c_9154]) ).
cnf(c_9143,plain,
$false,
inference(resolve,[status(thm)],[c_125,c_9155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : PLA019-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.44 % Computer : n014.cluster.edu
% 0.18/5.44 % Model : x86_64 x86_64
% 0.18/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.44 % Memory : 8046.5625MB
% 0.18/5.44 % OS : Linux 6.8.0-71-generic
% 0.18/5.44 % CPULimit : 300
% 0.18/5.44 % WCLimit : 300
% 0.18/5.44 % DateTime : Sat Sep 26 04:44:24 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.45 % Process 2162539 was started by sandbox2 on n014,
% 0.18/5.45 % Sat Sep 26 04:44:24 2026
% 0.18/5.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/5.46
% 0.18/5.46 % From the command line: assign(max_seconds, 300).
% 11.58/6.96
% 11.58/6.96 % SZS status Unsatisfiable for theBenchmark
% 11.58/6.96
% 11.58/6.96 % Proof 1 at 1.00 (+ 0.46) seconds.
% 11.58/6.96 % Length of proof is 29.
% 11.58/6.96 % Level of proof is 6.
% 11.58/6.96 % Maximum clause weight is 39.000.
% 11.58/6.96 % Given clauses 311.
% 11.58/6.96
% 11.58/6.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------