TSTP Solution File: PLA009-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : PLA009-2 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 17:32:18 EDT 2022
% Result : Unsatisfiable 0.20s 0.58s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 24
% Syntax : Number of clauses : 48 ( 20 unt; 0 nHn; 48 RR)
% Number of literals : 156 ( 0 equ; 129 neg)
% Maximal clause size : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ holds(and__dfg(clear(d),on(a,b)),u),
file('PLA009-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ holds(u,v)
| ~ holds(w,v)
| holds(and__dfg(w,u),v) ),
file('PLA009-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ differ(u,table)
| ~ holds(empty,v)
| ~ holds(clear(u),v)
| holds(holding(u),do(pickup(u),v)) ),
file('PLA009-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ holds(empty,u)
| ~ holds(clear(v),u)
| ~ holds(on(v,w),u)
| holds(clear(w),do(pickup(v),u)) ),
file('PLA009-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ differ(u,v)
| ~ holds(clear(u),w)
| holds(clear(u),do(pickup(v),w)) ),
file('PLA009-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ holds(clear(u),v)
| ~ holds(holding(w),v)
| holds(empty,do(putdown(w,u),v)) ),
file('PLA009-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ holds(clear(u),v)
| ~ holds(holding(w),v)
| holds(on(w,u),do(putdown(w,u),v)) ),
file('PLA009-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ differ(u,v)
| ~ holds(clear(u),w)
| holds(clear(u),do(putdown(x,v),w)) ),
file('PLA009-2.p',unknown),
[] ).
cnf(12,axiom,
( ~ differ(u,v)
| differ(v,u) ),
file('PLA009-2.p',unknown),
[] ).
cnf(13,axiom,
differ(a,b),
file('PLA009-2.p',unknown),
[] ).
cnf(14,axiom,
differ(a,c),
file('PLA009-2.p',unknown),
[] ).
cnf(15,axiom,
differ(a,d),
file('PLA009-2.p',unknown),
[] ).
cnf(16,axiom,
differ(a,table),
file('PLA009-2.p',unknown),
[] ).
cnf(17,axiom,
differ(b,c),
file('PLA009-2.p',unknown),
[] ).
cnf(18,axiom,
differ(b,d),
file('PLA009-2.p',unknown),
[] ).
cnf(19,axiom,
differ(b,table),
file('PLA009-2.p',unknown),
[] ).
cnf(21,axiom,
differ(c,table),
file('PLA009-2.p',unknown),
[] ).
cnf(22,axiom,
differ(d,table),
file('PLA009-2.p',unknown),
[] ).
cnf(25,axiom,
holds(on(c,d),s0),
file('PLA009-2.p',unknown),
[] ).
cnf(27,axiom,
holds(clear(a),s0),
file('PLA009-2.p',unknown),
[] ).
cnf(28,axiom,
holds(clear(b),s0),
file('PLA009-2.p',unknown),
[] ).
cnf(29,axiom,
holds(clear(c),s0),
file('PLA009-2.p',unknown),
[] ).
cnf(30,axiom,
holds(empty,s0),
file('PLA009-2.p',unknown),
[] ).
cnf(31,axiom,
holds(clear(table),u),
file('PLA009-2.p',unknown),
[] ).
cnf(32,plain,
( ~ holds(clear(d),u)
| ~ holds(on(a,b),u) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.2,1.0')] ).
cnf(38,plain,
differ(d,b),
inference(res,[status(thm),theory(equality)],[18,12]),
[iquote('0:Res:18.0,12.0')] ).
cnf(39,plain,
differ(d,a),
inference(res,[status(thm),theory(equality)],[15,12]),
[iquote('0:Res:15.0,12.0')] ).
cnf(42,plain,
differ(b,a),
inference(res,[status(thm),theory(equality)],[13,12]),
[iquote('0:Res:13.0,12.0')] ).
cnf(61,plain,
( ~ holds(clear(b),u)
| ~ holds(holding(a),u)
| ~ holds(clear(d),do(putdown(a,b),u)) ),
inference(res,[status(thm),theory(equality)],[8,32]),
[iquote('0:Res:8.2,32.1')] ).
cnf(63,plain,
( ~ differ(d,b)
| ~ holds(clear(d),u)
| ~ holds(clear(b),u)
| ~ holds(holding(a),u) ),
inference(res,[status(thm),theory(equality)],[11,61]),
[iquote('0:Res:11.2,61.2')] ).
cnf(64,plain,
( ~ holds(clear(d),u)
| ~ holds(clear(b),u)
| ~ holds(holding(a),u) ),
inference(mrr,[status(thm)],[63,38]),
[iquote('0:MRR:63.0,38.0')] ).
cnf(65,plain,
( ~ differ(d,u)
| ~ holds(clear(d),v)
| ~ holds(clear(b),do(pickup(u),v))
| ~ holds(holding(a),do(pickup(u),v)) ),
inference(res,[status(thm),theory(equality)],[6,64]),
[iquote('0:Res:6.2,64.0')] ).
cnf(80,plain,
( ~ differ(b,u)
| ~ holds(clear(b),v)
| ~ differ(d,u)
| ~ holds(clear(d),v)
| ~ holds(holding(a),do(pickup(u),v)) ),
inference(res,[status(thm),theory(equality)],[6,65]),
[iquote('0:Res:6.2,65.2')] ).
cnf(82,plain,
( ~ differ(a,table)
| ~ holds(empty,u)
| ~ holds(clear(a),u)
| ~ differ(b,a)
| ~ holds(clear(b),u)
| ~ differ(d,a)
| ~ holds(clear(d),u) ),
inference(res,[status(thm),theory(equality)],[3,80]),
[iquote('0:Res:3.3,80.4')] ).
cnf(83,plain,
( ~ holds(empty,u)
| ~ holds(clear(a),u)
| ~ holds(clear(b),u)
| ~ holds(clear(d),u) ),
inference(mrr,[status(thm)],[82,16,42,39]),
[iquote('0:MRR:82.0,82.3,82.5,16.0,42.0,39.0')] ).
cnf(89,plain,
( ~ differ(d,u)
| ~ holds(clear(d),v)
| ~ holds(empty,do(putdown(w,u),v))
| ~ holds(clear(a),do(putdown(w,u),v))
| ~ holds(clear(b),do(putdown(w,u),v)) ),
inference(res,[status(thm),theory(equality)],[11,83]),
[iquote('0:Res:11.2,83.3')] ).
cnf(252,plain,
( ~ differ(a,u)
| ~ holds(clear(a),v)
| ~ differ(d,u)
| ~ holds(clear(d),v)
| ~ holds(empty,do(putdown(w,u),v))
| ~ holds(clear(b),do(putdown(w,u),v)) ),
inference(res,[status(thm),theory(equality)],[11,89]),
[iquote('0:Res:11.2,89.3')] ).
cnf(340,plain,
( ~ differ(b,u)
| ~ holds(clear(b),v)
| ~ differ(a,u)
| ~ holds(clear(a),v)
| ~ differ(d,u)
| ~ holds(clear(d),v)
| ~ holds(empty,do(putdown(w,u),v)) ),
inference(res,[status(thm),theory(equality)],[11,252]),
[iquote('0:Res:11.2,252.5')] ).
cnf(500,plain,
( ~ holds(clear(u),v)
| ~ holds(holding(w),v)
| ~ differ(b,u)
| ~ holds(clear(b),v)
| ~ differ(a,u)
| ~ holds(clear(a),v)
| ~ differ(d,u)
| ~ holds(clear(d),v) ),
inference(res,[status(thm),theory(equality)],[7,340]),
[iquote('0:Res:7.2,340.6')] ).
cnf(552,plain,
( ~ holds(holding(u),v)
| ~ differ(b,table)
| ~ holds(clear(b),v)
| ~ differ(a,table)
| ~ holds(clear(a),v)
| ~ differ(d,table)
| ~ holds(clear(d),v) ),
inference(res,[status(thm),theory(equality)],[31,500]),
[iquote('0:Res:31.0,500.0')] ).
cnf(557,plain,
( ~ holds(holding(u),v)
| ~ holds(clear(b),v)
| ~ holds(clear(a),v)
| ~ holds(clear(d),v) ),
inference(mrr,[status(thm)],[552,19,16,22]),
[iquote('0:MRR:552.1,552.3,552.5,19.0,16.0,22.0')] ).
cnf(558,plain,
( ~ differ(u,table)
| ~ holds(empty,v)
| ~ holds(clear(u),v)
| ~ holds(clear(b),do(pickup(u),v))
| ~ holds(clear(a),do(pickup(u),v))
| ~ holds(clear(d),do(pickup(u),v)) ),
inference(res,[status(thm),theory(equality)],[3,557]),
[iquote('0:Res:3.3,557.0')] ).
cnf(560,plain,
( ~ holds(empty,u)
| ~ holds(clear(v),u)
| ~ holds(on(v,d),u)
| ~ differ(v,table)
| ~ holds(empty,u)
| ~ holds(clear(v),u)
| ~ holds(clear(b),do(pickup(v),u))
| ~ holds(clear(a),do(pickup(v),u)) ),
inference(res,[status(thm),theory(equality)],[4,558]),
[iquote('0:Res:4.3,558.5')] ).
cnf(561,plain,
( ~ holds(on(u,d),v)
| ~ differ(u,table)
| ~ holds(empty,v)
| ~ holds(clear(u),v)
| ~ holds(clear(b),do(pickup(u),v))
| ~ holds(clear(a),do(pickup(u),v)) ),
inference(obv,[status(thm),theory(equality)],[560]),
[iquote('0:Obv:560.1')] ).
cnf(562,plain,
( ~ differ(a,u)
| ~ holds(clear(a),v)
| ~ holds(on(u,d),v)
| ~ differ(u,table)
| ~ holds(empty,v)
| ~ holds(clear(u),v)
| ~ holds(clear(b),do(pickup(u),v)) ),
inference(res,[status(thm),theory(equality)],[6,561]),
[iquote('0:Res:6.2,561.5')] ).
cnf(585,plain,
( ~ differ(b,u)
| ~ holds(clear(b),v)
| ~ differ(a,u)
| ~ holds(clear(a),v)
| ~ holds(on(u,d),v)
| ~ differ(u,table)
| ~ holds(empty,v)
| ~ holds(clear(u),v) ),
inference(res,[status(thm),theory(equality)],[6,562]),
[iquote('0:Res:6.2,562.6')] ).
cnf(602,plain,
( ~ differ(b,c)
| ~ holds(clear(b),s0)
| ~ differ(a,c)
| ~ holds(clear(a),s0)
| ~ differ(c,table)
| ~ holds(empty,s0)
| ~ holds(clear(c),s0) ),
inference(res,[status(thm),theory(equality)],[25,585]),
[iquote('0:Res:25.0,585.4')] ).
cnf(606,plain,
$false,
inference(mrr,[status(thm)],[602,17,28,14,27,21,30,29]),
[iquote('0:MRR:602.0,602.1,602.2,602.3,602.4,602.5,602.6,17.0,28.0,14.0,27.0,21.0,30.0,29.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PLA009-2 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue May 31 22:49:06 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.58
% 0.20/0.58 SPASS V 3.9
% 0.20/0.58 SPASS beiseite: Proof found.
% 0.20/0.58 % SZS status Theorem
% 0.20/0.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.58 SPASS derived 462 clauses, backtracked 0 clauses, performed 0 splits and kept 385 clauses.
% 0.20/0.58 SPASS allocated 63819 KBytes.
% 0.20/0.58 SPASS spent 0:00:00.22 on the problem.
% 0.20/0.58 0:00:00.03 for the input.
% 0.20/0.58 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.58 0:00:00.02 for inferences.
% 0.20/0.58 0:00:00.00 for the backtracking.
% 0.20/0.58 0:00:00.14 for the reduction.
% 0.20/0.58
% 0.20/0.58
% 0.20/0.58 Here is a proof with depth 16, length 48 :
% 0.20/0.58 % SZS output start Refutation
% See solution above
% 0.20/0.58 Formulae used in the proof : prove_D_AB and_definition pickup_1 pickup_2 pickup_4 putdown_1 putdown_2 putdown_5 symmetry_of_differ differ_a_b differ_a_c differ_a_d differ_a_table differ_b_c differ_b_d differ_b_table differ_c_table differ_d_table initial_state3 initial_state5 initial_state6 initial_state7 initial_state8 clear_table
% 0.20/0.58
%------------------------------------------------------------------------------