TSTP Solution File: SET971+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET971+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n024.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 : 300s
% DateTime : Wed Jul 27 13:14:36 EDT 2022
% Result : Theorem 1.77s 1.98s
% Output : Refutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 15 ( 14 unt; 0 nHn; 11 RR)
% Number of literals : 16 ( 12 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
set_intersection2(cartesian_product2(dollar_c6,dollar_c3),cartesian_product2(dollar_c5,dollar_c4)) != cartesian_product2(dollar_c6,dollar_c4),
file('SET971+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ subset(A,B)
| set_intersection2(A,B) = A ),
file('SET971+1.p',unknown),
[] ).
cnf(4,axiom,
A = A,
file('SET971+1.p',unknown),
[] ).
cnf(5,axiom,
set_intersection2(A,B) = set_intersection2(B,A),
file('SET971+1.p',unknown),
[] ).
cnf(10,axiom,
cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
file('SET971+1.p',unknown),
[] ).
cnf(12,plain,
set_intersection2(cartesian_product2(A,B),cartesian_product2(C,D)) = cartesian_product2(set_intersection2(A,C),set_intersection2(B,D)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])]),
[iquote('copy,10,flip.1')] ).
cnf(13,axiom,
subset(dollar_c6,dollar_c5),
file('SET971+1.p',unknown),
[] ).
cnf(14,axiom,
subset(dollar_c4,dollar_c3),
file('SET971+1.p',unknown),
[] ).
cnf(15,plain,
cartesian_product2(set_intersection2(dollar_c6,dollar_c5),set_intersection2(dollar_c3,dollar_c4)) != cartesian_product2(dollar_c6,dollar_c4),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),12]),
[iquote('back_demod,2,demod,12')] ).
cnf(17,plain,
set_intersection2(dollar_c6,dollar_c5) = dollar_c6,
inference(hyper,[status(thm)],[13,3]),
[iquote('hyper,13,3')] ).
cnf(18,plain,
cartesian_product2(dollar_c6,set_intersection2(dollar_c3,dollar_c4)) != cartesian_product2(dollar_c6,dollar_c4),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[15]),17]),
[iquote('back_demod,15,demod,17')] ).
cnf(19,plain,
set_intersection2(dollar_c4,dollar_c3) = dollar_c4,
inference(hyper,[status(thm)],[14,3]),
[iquote('hyper,14,3')] ).
cnf(25,plain,
set_intersection2(dollar_c3,dollar_c4) = dollar_c4,
inference(para_into,[status(thm),theory(equality)],[19,5]),
[iquote('para_into,19.1.1,5.1.1')] ).
cnf(26,plain,
cartesian_product2(dollar_c6,dollar_c4) != cartesian_product2(dollar_c6,dollar_c4),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[18]),25]),
[iquote('back_demod,18,demod,25')] ).
cnf(27,plain,
$false,
inference(binary,[status(thm)],[26,4]),
[iquote('binary,26.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET971+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 10:39:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.77/1.98 ----- Otter 3.3f, August 2004 -----
% 1.77/1.98 The process was started by sandbox2 on n024.cluster.edu,
% 1.77/1.98 Wed Jul 27 10:39:10 2022
% 1.77/1.98 The command was "./otter". The process ID is 24725.
% 1.77/1.98
% 1.77/1.98 set(prolog_style_variables).
% 1.77/1.98 set(auto).
% 1.77/1.98 dependent: set(auto1).
% 1.77/1.98 dependent: set(process_input).
% 1.77/1.98 dependent: clear(print_kept).
% 1.77/1.98 dependent: clear(print_new_demod).
% 1.77/1.98 dependent: clear(print_back_demod).
% 1.77/1.98 dependent: clear(print_back_sub).
% 1.77/1.98 dependent: set(control_memory).
% 1.77/1.98 dependent: assign(max_mem, 12000).
% 1.77/1.98 dependent: assign(pick_given_ratio, 4).
% 1.77/1.98 dependent: assign(stats_level, 1).
% 1.77/1.98 dependent: assign(max_seconds, 10800).
% 1.77/1.98 clear(print_given).
% 1.77/1.98
% 1.77/1.98 formula_list(usable).
% 1.77/1.98 all A (A=A).
% 1.77/1.98 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.77/1.98 all A B (set_intersection2(A,A)=A).
% 1.77/1.98 exists A empty(A).
% 1.77/1.98 exists A (-empty(A)).
% 1.77/1.98 all A B subset(A,A).
% 1.77/1.98 all A B C D (cartesian_product2(set_intersection2(A,B),set_intersection2(C,D))=set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D))).
% 1.77/1.98 -(all A B C D (subset(A,B)&subset(C,D)->set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C))=cartesian_product2(A,C))).
% 1.77/1.98 all A B (subset(A,B)->set_intersection2(A,B)=A).
% 1.77/1.98 end_of_list.
% 1.77/1.98
% 1.77/1.98 -------> usable clausifies to:
% 1.77/1.98
% 1.77/1.98 list(usable).
% 1.77/1.98 0 [] A=A.
% 1.77/1.98 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.77/1.98 0 [] set_intersection2(A,A)=A.
% 1.77/1.98 0 [] empty($c1).
% 1.77/1.98 0 [] -empty($c2).
% 1.77/1.98 0 [] subset(A,A).
% 1.77/1.98 0 [] cartesian_product2(set_intersection2(A,B),set_intersection2(C,D))=set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)).
% 1.77/1.98 0 [] subset($c6,$c5).
% 1.77/1.98 0 [] subset($c4,$c3).
% 1.77/1.98 0 [] set_intersection2(cartesian_product2($c6,$c3),cartesian_product2($c5,$c4))!=cartesian_product2($c6,$c4).
% 1.77/1.98 0 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.77/1.98 end_of_list.
% 1.77/1.98
% 1.77/1.98 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.77/1.98
% 1.77/1.98 This is a Horn set with equality. The strategy will be
% 1.77/1.98 Knuth-Bendix and hyper_res, with positive clauses in
% 1.77/1.98 sos and nonpositive clauses in usable.
% 1.77/1.98
% 1.77/1.98 dependent: set(knuth_bendix).
% 1.77/1.98 dependent: set(anl_eq).
% 1.77/1.98 dependent: set(para_from).
% 1.77/1.98 dependent: set(para_into).
% 1.77/1.98 dependent: clear(para_from_right).
% 1.77/1.98 dependent: clear(para_into_right).
% 1.77/1.98 dependent: set(para_from_vars).
% 1.77/1.98 dependent: set(eq_units_both_ways).
% 1.77/1.98 dependent: set(dynamic_demod_all).
% 1.77/1.98 dependent: set(dynamic_demod).
% 1.77/1.98 dependent: set(order_eq).
% 1.77/1.98 dependent: set(back_demod).
% 1.77/1.98 dependent: set(lrpo).
% 1.77/1.98 dependent: set(hyper_res).
% 1.77/1.98 dependent: clear(order_hyper).
% 1.77/1.98
% 1.77/1.98 ------------> process usable:
% 1.77/1.98 ** KEPT (pick-wt=2): 1 [] -empty($c2).
% 1.77/1.98 ** KEPT (pick-wt=11): 2 [] set_intersection2(cartesian_product2($c6,$c3),cartesian_product2($c5,$c4))!=cartesian_product2($c6,$c4).
% 1.77/1.98 ** KEPT (pick-wt=8): 3 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.77/1.98
% 1.77/1.98 ------------> process sos:
% 1.77/1.98 ** KEPT (pick-wt=3): 4 [] A=A.
% 1.77/1.98 ** KEPT (pick-wt=7): 5 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.77/1.98 ** KEPT (pick-wt=5): 6 [] set_intersection2(A,A)=A.
% 1.77/1.98 ---> New Demodulator: 7 [new_demod,6] set_intersection2(A,A)=A.
% 1.77/1.98 ** KEPT (pick-wt=2): 8 [] empty($c1).
% 1.77/1.98 ** KEPT (pick-wt=3): 9 [] subset(A,A).
% 1.77/1.98 ** KEPT (pick-wt=15): 11 [copy,10,flip.1] set_intersection2(cartesian_product2(A,B),cartesian_product2(C,D))=cartesian_product2(set_intersection2(A,C),set_intersection2(B,D)).
% 1.77/1.98 ---> New Demodulator: 12 [new_demod,11] set_intersection2(cartesian_product2(A,B),cartesian_product2(C,D))=cartesian_product2(set_intersection2(A,C),set_intersection2(B,D)).
% 1.77/1.98 ** KEPT (pick-wt=3): 13 [] subset($c6,$c5).
% 1.77/1.98 ** KEPT (pick-wt=3): 14 [] subset($c4,$c3).
% 1.77/1.98 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 1.77/1.98 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 1.77/1.98 >>>> Starting back demodulation with 7.
% 1.77/1.98 >>>> Starting back demodulation with 12.
% 1.77/1.98 >> back demodulating 2 with 12.
% 1.77/1.98
% 1.77/1.98 ======= end of input processing =======
% 1.77/1.98
% 1.77/1.98 =========== start of search ===========
% 1.77/1.98
% 1.77/1.98 -------- PROOF --------
% 1.77/1.98
% 1.77/1.98 ----> UNIT CONFLICT at 0.00 sec ----> 27 [binary,26.1,4.1] $F.
% 1.77/1.98
% 1.77/1.98 Length of proof is 7. Level of proof is 4.
% 1.77/1.98
% 1.77/1.98 ---------------- PROOF ----------------
% 1.77/1.98 % SZS status Theorem
% 1.77/1.98 % SZS output start Refutation
% See solution above
% 1.77/1.98 ------------ end of proof -------------
% 1.77/1.98
% 1.77/1.98
% 1.77/1.98 Search stopped by max_proofs option.
% 1.77/1.98
% 1.77/1.98
% 1.77/1.98 Search stopped by max_proofs option.
% 1.77/1.98
% 1.77/1.98 ============ end of search ============
% 1.77/1.98
% 1.77/1.98 -------------- statistics -------------
% 1.77/1.98 clauses given 9
% 1.77/1.98 clauses generated 22
% 1.77/1.98 clauses kept 19
% 1.77/1.98 clauses forward subsumed 19
% 1.77/1.98 clauses back subsumed 0
% 1.77/1.98 Kbytes malloced 976
% 1.77/1.98
% 1.77/1.98 ----------- times (seconds) -----------
% 1.77/1.98 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.77/1.98 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.77/1.98 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.77/1.98
% 1.77/1.98 That finishes the proof of the theorem.
% 1.77/1.98
% 1.77/1.98 Process 24725 finished Wed Jul 27 10:39:11 2022
% 1.77/1.98 Otter interrupted
% 1.77/1.98 PROOF FOUND
%------------------------------------------------------------------------------