TSTP Solution File: PLA008-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : PLA008-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 27
% Syntax : Number of clauses : 79 ( 22 unt; 0 nHn; 79 RR)
% Number of literals : 278 ( 0 equ; 246 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ holds(and__dfg(on(b,d),on(a,c)),u),
file('PLA008-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ holds(u,v)
| ~ holds(w,v)
| holds(and__dfg(w,u),v) ),
file('PLA008-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ differ(u,table)
| ~ holds(empty,v)
| ~ holds(clear(u),v)
| holds(holding(u),do(pickup(u),v)) ),
file('PLA008-1.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('PLA008-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ differ(u,v)
| ~ holds(on(u,w),x)
| holds(on(u,w),do(pickup(v),x)) ),
file('PLA008-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ differ(u,v)
| ~ holds(clear(u),w)
| holds(clear(u),do(pickup(v),w)) ),
file('PLA008-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ holds(clear(u),v)
| ~ holds(holding(w),v)
| holds(empty,do(putdown(w,u),v)) ),
file('PLA008-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ holds(clear(u),v)
| ~ holds(holding(w),v)
| holds(on(w,u),do(putdown(w,u),v)) ),
file('PLA008-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ holds(clear(u),v)
| ~ holds(holding(w),v)
| holds(clear(w),do(putdown(w,u),v)) ),
file('PLA008-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ holds(on(u,v),w)
| holds(on(u,v),do(putdown(x,y),w)) ),
file('PLA008-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ differ(u,v)
| ~ holds(clear(u),w)
| holds(clear(u),do(putdown(x,v),w)) ),
file('PLA008-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ differ(u,v)
| differ(v,u) ),
file('PLA008-1.p',unknown),
[] ).
cnf(13,axiom,
differ(a,b),
file('PLA008-1.p',unknown),
[] ).
cnf(14,axiom,
differ(a,c),
file('PLA008-1.p',unknown),
[] ).
cnf(15,axiom,
differ(a,d),
file('PLA008-1.p',unknown),
[] ).
cnf(16,axiom,
differ(a,table),
file('PLA008-1.p',unknown),
[] ).
cnf(17,axiom,
differ(b,c),
file('PLA008-1.p',unknown),
[] ).
cnf(18,axiom,
differ(b,d),
file('PLA008-1.p',unknown),
[] ).
cnf(19,axiom,
differ(b,table),
file('PLA008-1.p',unknown),
[] ).
cnf(20,axiom,
differ(c,d),
file('PLA008-1.p',unknown),
[] ).
cnf(21,axiom,
differ(c,table),
file('PLA008-1.p',unknown),
[] ).
cnf(25,axiom,
holds(on(c,d),s0),
file('PLA008-1.p',unknown),
[] ).
cnf(27,axiom,
holds(clear(a),s0),
file('PLA008-1.p',unknown),
[] ).
cnf(28,axiom,
holds(clear(b),s0),
file('PLA008-1.p',unknown),
[] ).
cnf(29,axiom,
holds(clear(c),s0),
file('PLA008-1.p',unknown),
[] ).
cnf(30,axiom,
holds(empty,s0),
file('PLA008-1.p',unknown),
[] ).
cnf(31,axiom,
holds(clear(table),u),
file('PLA008-1.p',unknown),
[] ).
cnf(32,plain,
( ~ holds(on(a,c),u)
| ~ holds(on(b,d),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(40,plain,
differ(c,b),
inference(res,[status(thm),theory(equality)],[17,12]),
[iquote('0:Res:17.0,12.0')] ).
cnf(41,plain,
differ(c,a),
inference(res,[status(thm),theory(equality)],[14,12]),
[iquote('0:Res:14.0,12.0')] ).
cnf(42,plain,
differ(b,a),
inference(res,[status(thm),theory(equality)],[13,12]),
[iquote('0:Res:13.0,12.0')] ).
cnf(54,plain,
( ~ holds(on(b,d),u)
| ~ holds(on(a,c),do(putdown(v,w),u)) ),
inference(res,[status(thm),theory(equality)],[10,32]),
[iquote('0:Res:10.1,32.1')] ).
cnf(59,plain,
( ~ holds(clear(c),u)
| ~ holds(holding(a),u)
| ~ holds(on(b,d),u) ),
inference(res,[status(thm),theory(equality)],[8,54]),
[iquote('0:Res:8.2,54.1')] ).
cnf(61,plain,
( ~ differ(b,u)
| ~ holds(on(b,d),v)
| ~ holds(clear(c),do(pickup(u),v))
| ~ holds(holding(a),do(pickup(u),v)) ),
inference(res,[status(thm),theory(equality)],[5,59]),
[iquote('0:Res:5.2,59.2')] ).
cnf(67,plain,
( ~ differ(a,table)
| ~ holds(empty,u)
| ~ holds(clear(a),u)
| ~ differ(b,a)
| ~ holds(on(b,d),u)
| ~ holds(clear(c),do(pickup(a),u)) ),
inference(res,[status(thm),theory(equality)],[3,61]),
[iquote('0:Res:3.3,61.3')] ).
cnf(68,plain,
( ~ holds(empty,u)
| ~ holds(clear(a),u)
| ~ holds(on(b,d),u)
| ~ holds(clear(c),do(pickup(a),u)) ),
inference(mrr,[status(thm)],[67,16,42]),
[iquote('0:MRR:67.0,67.3,16.0,42.0')] ).
cnf(69,plain,
( ~ differ(c,a)
| ~ holds(clear(c),u)
| ~ holds(empty,u)
| ~ holds(clear(a),u)
| ~ holds(on(b,d),u) ),
inference(res,[status(thm),theory(equality)],[6,68]),
[iquote('0:Res:6.2,68.3')] ).
cnf(71,plain,
( ~ holds(clear(c),u)
| ~ holds(empty,u)
| ~ holds(clear(a),u)
| ~ holds(on(b,d),u) ),
inference(mrr,[status(thm)],[69,41]),
[iquote('0:MRR:69.0,41.0')] ).
cnf(73,plain,
( ~ holds(on(b,d),u)
| ~ holds(clear(c),do(putdown(v,w),u))
| ~ holds(empty,do(putdown(v,w),u))
| ~ holds(clear(a),do(putdown(v,w),u)) ),
inference(res,[status(thm),theory(equality)],[10,71]),
[iquote('0:Res:10.1,71.3')] ).
cnf(99,plain,
( ~ differ(a,u)
| ~ holds(clear(a),v)
| ~ holds(on(b,d),v)
| ~ holds(clear(c),do(putdown(w,u),v))
| ~ holds(empty,do(putdown(w,u),v)) ),
inference(res,[status(thm),theory(equality)],[11,73]),
[iquote('0:Res:11.2,73.3')] ).
cnf(108,plain,
( ~ holds(clear(u),v)
| ~ holds(holding(c),v)
| ~ differ(a,u)
| ~ holds(clear(a),v)
| ~ holds(on(b,d),v)
| ~ holds(empty,do(putdown(c,u),v)) ),
inference(res,[status(thm),theory(equality)],[9,99]),
[iquote('0:Res:9.2,99.3')] ).
cnf(109,plain,
( ~ holds(clear(u),v)
| ~ holds(holding(c),v)
| ~ differ(a,u)
| ~ holds(clear(a),v)
| ~ holds(on(b,d),v) ),
inference(mrr,[status(thm)],[108,7]),
[iquote('0:MRR:108.5,7.2')] ).
cnf(111,plain,
( ~ differ(b,u)
| ~ holds(on(b,d),v)
| ~ holds(clear(w),do(pickup(u),v))
| ~ holds(holding(c),do(pickup(u),v))
| ~ differ(a,w)
| ~ holds(clear(a),do(pickup(u),v)) ),
inference(res,[status(thm),theory(equality)],[5,109]),
[iquote('0:Res:5.2,109.4')] ).
cnf(316,plain,
( ~ differ(b,u)
| ~ holds(on(b,d),v)
| ~ holds(holding(c),do(pickup(u),v))
| ~ differ(a,table)
| ~ holds(clear(a),do(pickup(u),v)) ),
inference(res,[status(thm),theory(equality)],[31,111]),
[iquote('0:Res:31.0,111.2')] ).
cnf(319,plain,
( ~ differ(b,u)
| ~ holds(on(b,d),v)
| ~ holds(holding(c),do(pickup(u),v))
| ~ holds(clear(a),do(pickup(u),v)) ),
inference(mrr,[status(thm)],[316,16]),
[iquote('0:MRR:316.3,16.0')] ).
cnf(320,plain,
( ~ differ(c,table)
| ~ holds(empty,u)
| ~ holds(clear(c),u)
| ~ differ(b,c)
| ~ holds(on(b,d),u)
| ~ holds(clear(a),do(pickup(c),u)) ),
inference(res,[status(thm),theory(equality)],[3,319]),
[iquote('0:Res:3.3,319.2')] ).
cnf(321,plain,
( ~ holds(empty,u)
| ~ holds(clear(c),u)
| ~ holds(on(b,d),u)
| ~ holds(clear(a),do(pickup(c),u)) ),
inference(mrr,[status(thm)],[320,21,17]),
[iquote('0:MRR:320.0,320.3,21.0,17.0')] ).
cnf(323,plain,
( ~ holds(empty,u)
| ~ holds(clear(c),u)
| ~ holds(on(c,a),u)
| ~ holds(empty,u)
| ~ holds(clear(c),u)
| ~ holds(on(b,d),u) ),
inference(res,[status(thm),theory(equality)],[4,321]),
[iquote('0:Res:4.3,321.3')] ).
cnf(324,plain,
( ~ holds(on(c,a),u)
| ~ holds(empty,u)
| ~ holds(clear(c),u)
| ~ holds(on(b,d),u) ),
inference(obv,[status(thm),theory(equality)],[323]),
[iquote('0:Obv:323.1')] ).
cnf(327,plain,
( ~ holds(clear(d),u)
| ~ holds(holding(b),u)
| ~ holds(on(c,a),do(putdown(b,d),u))
| ~ holds(empty,do(putdown(b,d),u))
| ~ holds(clear(c),do(putdown(b,d),u)) ),
inference(res,[status(thm),theory(equality)],[8,324]),
[iquote('0:Res:8.2,324.3')] ).
cnf(328,plain,
( ~ holds(clear(d),u)
| ~ holds(holding(b),u)
| ~ holds(on(c,a),do(putdown(b,d),u))
| ~ holds(clear(c),do(putdown(b,d),u)) ),
inference(mrr,[status(thm)],[327,7]),
[iquote('0:MRR:327.3,7.2')] ).
cnf(329,plain,
( ~ holds(on(c,a),u)
| ~ holds(clear(d),u)
| ~ holds(holding(b),u)
| ~ holds(clear(c),do(putdown(b,d),u)) ),
inference(res,[status(thm),theory(equality)],[10,328]),
[iquote('0:Res:10.1,328.2')] ).
cnf(334,plain,
( ~ differ(c,d)
| ~ holds(clear(c),u)
| ~ holds(on(c,a),u)
| ~ holds(clear(d),u)
| ~ holds(holding(b),u) ),
inference(res,[status(thm),theory(equality)],[11,329]),
[iquote('0:Res:11.2,329.3')] ).
cnf(335,plain,
( ~ holds(clear(c),u)
| ~ holds(on(c,a),u)
| ~ holds(clear(d),u)
| ~ holds(holding(b),u) ),
inference(mrr,[status(thm)],[334,20]),
[iquote('0:MRR:334.0,20.0')] ).
cnf(337,plain,
( ~ differ(c,u)
| ~ holds(on(c,a),v)
| ~ holds(clear(c),do(pickup(u),v))
| ~ holds(clear(d),do(pickup(u),v))
| ~ holds(holding(b),do(pickup(u),v)) ),
inference(res,[status(thm),theory(equality)],[5,335]),
[iquote('0:Res:5.2,335.1')] ).
cnf(412,plain,
( ~ differ(b,table)
| ~ holds(empty,u)
| ~ holds(clear(b),u)
| ~ differ(c,b)
| ~ holds(on(c,a),u)
| ~ holds(clear(c),do(pickup(b),u))
| ~ holds(clear(d),do(pickup(b),u)) ),
inference(res,[status(thm),theory(equality)],[3,337]),
[iquote('0:Res:3.3,337.4')] ).
cnf(413,plain,
( ~ holds(empty,u)
| ~ holds(clear(b),u)
| ~ holds(on(c,a),u)
| ~ holds(clear(c),do(pickup(b),u))
| ~ holds(clear(d),do(pickup(b),u)) ),
inference(mrr,[status(thm)],[412,19,40]),
[iquote('0:MRR:412.0,412.3,19.0,40.0')] ).
cnf(414,plain,
( ~ differ(d,b)
| ~ holds(clear(d),u)
| ~ holds(empty,u)
| ~ holds(clear(b),u)
| ~ holds(on(c,a),u)
| ~ holds(clear(c),do(pickup(b),u)) ),
inference(res,[status(thm),theory(equality)],[6,413]),
[iquote('0:Res:6.2,413.4')] ).
cnf(416,plain,
( ~ holds(clear(d),u)
| ~ holds(empty,u)
| ~ holds(clear(b),u)
| ~ holds(on(c,a),u)
| ~ holds(clear(c),do(pickup(b),u)) ),
inference(mrr,[status(thm)],[414,38]),
[iquote('0:MRR:414.0,38.0')] ).
cnf(418,plain,
( ~ differ(c,b)
| ~ holds(clear(c),u)
| ~ holds(clear(d),u)
| ~ holds(empty,u)
| ~ holds(clear(b),u)
| ~ holds(on(c,a),u) ),
inference(res,[status(thm),theory(equality)],[6,416]),
[iquote('0:Res:6.2,416.4')] ).
cnf(420,plain,
( ~ holds(clear(c),u)
| ~ holds(clear(d),u)
| ~ holds(empty,u)
| ~ holds(clear(b),u)
| ~ holds(on(c,a),u) ),
inference(mrr,[status(thm)],[418,40]),
[iquote('0:MRR:418.0,40.0')] ).
cnf(424,plain,
( ~ holds(clear(a),u)
| ~ holds(holding(c),u)
| ~ holds(clear(c),do(putdown(c,a),u))
| ~ holds(clear(d),do(putdown(c,a),u))
| ~ holds(empty,do(putdown(c,a),u))
| ~ holds(clear(b),do(putdown(c,a),u)) ),
inference(res,[status(thm),theory(equality)],[8,420]),
[iquote('0:Res:8.2,420.4')] ).
cnf(425,plain,
( ~ holds(clear(a),u)
| ~ holds(holding(c),u)
| ~ holds(clear(d),do(putdown(c,a),u))
| ~ holds(clear(b),do(putdown(c,a),u)) ),
inference(mrr,[status(thm)],[424,9,7]),
[iquote('0:MRR:424.2,424.4,9.2,7.2')] ).
cnf(431,plain,
( ~ differ(b,a)
| ~ holds(clear(b),u)
| ~ holds(clear(a),u)
| ~ holds(holding(c),u)
| ~ holds(clear(d),do(putdown(c,a),u)) ),
inference(res,[status(thm),theory(equality)],[11,425]),
[iquote('0:Res:11.2,425.3')] ).
cnf(432,plain,
( ~ holds(clear(b),u)
| ~ holds(clear(a),u)
| ~ holds(holding(c),u)
| ~ holds(clear(d),do(putdown(c,a),u)) ),
inference(mrr,[status(thm)],[431,42]),
[iquote('0:MRR:431.0,42.0')] ).
cnf(433,plain,
( ~ differ(d,a)
| ~ holds(clear(d),u)
| ~ holds(clear(b),u)
| ~ holds(clear(a),u)
| ~ holds(holding(c),u) ),
inference(res,[status(thm),theory(equality)],[11,432]),
[iquote('0:Res:11.2,432.3')] ).
cnf(434,plain,
( ~ holds(clear(d),u)
| ~ holds(clear(b),u)
| ~ holds(clear(a),u)
| ~ holds(holding(c),u) ),
inference(mrr,[status(thm)],[433,39]),
[iquote('0:MRR:433.0,39.0')] ).
cnf(435,plain,
( ~ differ(c,table)
| ~ holds(empty,u)
| ~ holds(clear(c),u)
| ~ holds(clear(d),do(pickup(c),u))
| ~ holds(clear(b),do(pickup(c),u))
| ~ holds(clear(a),do(pickup(c),u)) ),
inference(res,[status(thm),theory(equality)],[3,434]),
[iquote('0:Res:3.3,434.3')] ).
cnf(436,plain,
( ~ holds(empty,u)
| ~ holds(clear(c),u)
| ~ holds(clear(d),do(pickup(c),u))
| ~ holds(clear(b),do(pickup(c),u))
| ~ holds(clear(a),do(pickup(c),u)) ),
inference(mrr,[status(thm)],[435,21]),
[iquote('0:MRR:435.0,21.0')] ).
cnf(457,plain,
( ~ differ(b,c)
| ~ holds(clear(b),u)
| ~ holds(empty,u)
| ~ holds(clear(c),u)
| ~ holds(clear(d),do(pickup(c),u))
| ~ holds(clear(a),do(pickup(c),u)) ),
inference(res,[status(thm),theory(equality)],[6,436]),
[iquote('0:Res:6.2,436.3')] ).
cnf(459,plain,
( ~ holds(clear(b),u)
| ~ holds(empty,u)
| ~ holds(clear(c),u)
| ~ holds(clear(d),do(pickup(c),u))
| ~ holds(clear(a),do(pickup(c),u)) ),
inference(mrr,[status(thm)],[457,17]),
[iquote('0:MRR:457.0,17.0')] ).
cnf(463,plain,
( ~ holds(empty,u)
| ~ holds(clear(c),u)
| ~ holds(on(c,d),u)
| ~ holds(clear(b),u)
| ~ holds(empty,u)
| ~ holds(clear(c),u)
| ~ holds(clear(a),do(pickup(c),u)) ),
inference(res,[status(thm),theory(equality)],[4,459]),
[iquote('0:Res:4.3,459.3')] ).
cnf(465,plain,
( ~ holds(on(c,d),u)
| ~ holds(clear(b),u)
| ~ holds(empty,u)
| ~ holds(clear(c),u)
| ~ holds(clear(a),do(pickup(c),u)) ),
inference(obv,[status(thm),theory(equality)],[463]),
[iquote('0:Obv:463.1')] ).
cnf(469,plain,
( ~ differ(a,c)
| ~ holds(clear(a),u)
| ~ holds(on(c,d),u)
| ~ holds(clear(b),u)
| ~ holds(empty,u)
| ~ holds(clear(c),u) ),
inference(res,[status(thm),theory(equality)],[6,465]),
[iquote('0:Res:6.2,465.4')] ).
cnf(471,plain,
( ~ holds(clear(a),u)
| ~ holds(on(c,d),u)
| ~ holds(clear(b),u)
| ~ holds(empty,u)
| ~ holds(clear(c),u) ),
inference(mrr,[status(thm)],[469,14]),
[iquote('0:MRR:469.0,14.0')] ).
cnf(473,plain,
( ~ holds(clear(a),s0)
| ~ holds(clear(b),s0)
| ~ holds(empty,s0)
| ~ holds(clear(c),s0) ),
inference(res,[status(thm),theory(equality)],[25,471]),
[iquote('0:Res:25.0,471.1')] ).
cnf(477,plain,
$false,
inference(mrr,[status(thm)],[473,27,28,30,29]),
[iquote('0:MRR:473.0,473.1,473.2,473.3,27.0,28.0,30.0,29.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : PLA008-1 : TPTP v8.1.0. Released v1.1.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue May 31 23:44:40 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.50
% 0.20/0.50 SPASS V 3.9
% 0.20/0.50 SPASS beiseite: Proof found.
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.50 SPASS derived 327 clauses, backtracked 0 clauses, performed 0 splits and kept 294 clauses.
% 0.20/0.50 SPASS allocated 63664 KBytes.
% 0.20/0.50 SPASS spent 0:00:00.15 on the problem.
% 0.20/0.50 0:00:00.03 for the input.
% 0.20/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.50 0:00:00.01 for inferences.
% 0.20/0.50 0:00:00.00 for the backtracking.
% 0.20/0.50 0:00:00.08 for the reduction.
% 0.20/0.50
% 0.20/0.50
% 0.20/0.50 Here is a proof with depth 28, length 79 :
% 0.20/0.50 % SZS output start Refutation
% See solution above
% 0.20/0.50 Formulae used in the proof : prove_BD_AC and_definition pickup_1 pickup_2 pickup_3 pickup_4 putdown_1 putdown_2 putdown_3 putdown_4 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_d differ_c_table initial_state3 initial_state5 initial_state6 initial_state7 initial_state8 clear_table
% 0.20/0.50
%------------------------------------------------------------------------------