TSTP Solution File: CAT003-3 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : CAT003-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n005.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 12:47:45 EDT 2022
% Result : Unsatisfiable 20.06s 20.23s
% Output : Refutation 20.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 20 ( 13 unt; 0 nHn; 15 RR)
% Number of literals : 31 ( 20 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 23 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ e_quivalent(A,B)
| A = B ),
file('CAT003-3.p',unknown),
[] ).
cnf(3,axiom,
( ~ there_exists(A)
| A != B
| e_quivalent(A,B) ),
file('CAT003-3.p',unknown),
[] ).
cnf(13,axiom,
( compose(A,compose(a,b)) != B
| compose(C,compose(a,b)) != B
| A = C ),
file('CAT003-3.p',unknown),
[] ).
cnf(14,axiom,
g != h,
file('CAT003-3.p',unknown),
[] ).
cnf(15,plain,
h != g,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[14])]),
[iquote('copy,14,flip.1')] ).
cnf(18,axiom,
A = A,
file('CAT003-3.p',unknown),
[] ).
cnf(19,axiom,
compose(A,compose(B,C)) = compose(compose(A,B),C),
file('CAT003-3.p',unknown),
[] ).
cnf(21,plain,
compose(compose(A,B),C) = compose(A,compose(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[19])]),
[iquote('copy,19,flip.1')] ).
cnf(23,axiom,
compose(A,domain(A)) = A,
file('CAT003-3.p',unknown),
[] ).
cnf(30,axiom,
there_exists(h),
file('CAT003-3.p',unknown),
[] ).
cnf(31,axiom,
compose(h,a) = compose(g,a),
file('CAT003-3.p',unknown),
[] ).
cnf(33,plain,
e_quivalent(h,h),
inference(hyper,[status(thm)],[30,3,18]),
[iquote('hyper,30,3,18')] ).
cnf(39,plain,
( e_quivalent(h,A)
| compose(h,compose(a,b)) != B
| compose(A,compose(a,b)) != B ),
inference(para_into,[status(thm),theory(equality)],[33,13]),
[iquote('para_into,33.1.2,13.3.1')] ).
cnf(98,plain,
( A = B
| ~ e_quivalent(B,A) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[23,2]),23]),
[iquote('para_into,22.1.1,2.2.1,demod,23')] ).
cnf(513,plain,
compose(h,compose(a,A)) = compose(g,compose(a,A)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[31,21]),21])]),
[iquote('para_from,31.1.1,20.1.1.1,demod,21,flip.1')] ).
cnf(521,plain,
( e_quivalent(h,A)
| compose(g,compose(a,b)) != B
| compose(A,compose(a,b)) != B ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[39]),513]),
[iquote('back_demod,39,demod,513')] ).
cnf(528,plain,
( e_quivalent(h,g)
| compose(g,compose(a,b)) != A ),
inference(factor,[status(thm)],[521]),
[iquote('factor,521.2.3')] ).
cnf(2122,plain,
e_quivalent(h,g),
inference(hyper,[status(thm)],[528,18]),
[iquote('hyper,528,18')] ).
cnf(2130,plain,
h = g,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2122,98])]),
[iquote('hyper,2122,98,flip.1')] ).
cnf(2132,plain,
$false,
inference(binary,[status(thm)],[2130,15]),
[iquote('binary,2130.1,15.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT003-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n005.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 : 300
% 0.14/0.34 % DateTime : Wed Jul 27 01:54:05 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.69/1.83 ----- Otter 3.3f, August 2004 -----
% 1.69/1.83 The process was started by sandbox on n005.cluster.edu,
% 1.69/1.83 Wed Jul 27 01:54:05 2022
% 1.69/1.83 The command was "./otter". The process ID is 22744.
% 1.69/1.83
% 1.69/1.83 set(prolog_style_variables).
% 1.69/1.83 set(auto).
% 1.69/1.83 dependent: set(auto1).
% 1.69/1.83 dependent: set(process_input).
% 1.69/1.83 dependent: clear(print_kept).
% 1.69/1.83 dependent: clear(print_new_demod).
% 1.69/1.83 dependent: clear(print_back_demod).
% 1.69/1.83 dependent: clear(print_back_sub).
% 1.69/1.83 dependent: set(control_memory).
% 1.69/1.83 dependent: assign(max_mem, 12000).
% 1.69/1.83 dependent: assign(pick_given_ratio, 4).
% 1.69/1.83 dependent: assign(stats_level, 1).
% 1.69/1.83 dependent: assign(max_seconds, 10800).
% 1.69/1.83 clear(print_given).
% 1.69/1.83
% 1.69/1.83 list(usable).
% 1.69/1.83 0 [] A=A.
% 1.69/1.83 0 [] -e_quivalent(X,Y)|there_exists(X).
% 1.69/1.83 0 [] -e_quivalent(X,Y)|X=Y.
% 1.69/1.83 0 [] -there_exists(X)|X!=Y|e_quivalent(X,Y).
% 1.69/1.83 0 [] -there_exists(domain(X))|there_exists(X).
% 1.69/1.83 0 [] -there_exists(codomain(X))|there_exists(X).
% 1.69/1.83 0 [] -there_exists(compose(X,Y))|there_exists(domain(X)).
% 1.69/1.83 0 [] -there_exists(compose(X,Y))|domain(X)=codomain(Y).
% 1.69/1.83 0 [] -there_exists(domain(X))|domain(X)!=codomain(Y)|there_exists(compose(X,Y)).
% 1.69/1.83 0 [] compose(X,compose(Y,Z))=compose(compose(X,Y),Z).
% 1.69/1.83 0 [] compose(X,domain(X))=X.
% 1.69/1.83 0 [] compose(codomain(X),X)=X.
% 1.69/1.83 0 [] -e_quivalent(X,Y)|there_exists(Y).
% 1.69/1.83 0 [] -there_exists(X)| -there_exists(Y)|X!=Y|e_quivalent(X,Y).
% 1.69/1.83 0 [] -there_exists(compose(X,Y))|there_exists(codomain(X)).
% 1.69/1.83 0 [] there_exists(f1(X,Y))|X=Y.
% 1.69/1.83 0 [] X=f1(X,Y)|Y=f1(X,Y)|X=Y.
% 1.69/1.83 0 [] X!=f1(X,Y)|Y!=f1(X,Y)|X=Y.
% 1.69/1.83 0 [] there_exists(compose(a,b)).
% 1.69/1.83 0 [] compose(X,compose(a,b))!=Y|compose(Z,compose(a,b))!=Y|X=Z.
% 1.69/1.83 0 [] there_exists(h).
% 1.69/1.83 0 [] compose(h,a)=compose(g,a).
% 1.69/1.83 0 [] g!=h.
% 1.69/1.83 end_of_list.
% 1.69/1.83
% 1.69/1.83 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.69/1.83
% 1.69/1.83 This ia a non-Horn set with equality. The strategy will be
% 1.69/1.83 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.69/1.83 deletion, with positive clauses in sos and nonpositive
% 1.69/1.83 clauses in usable.
% 1.69/1.83
% 1.69/1.83 dependent: set(knuth_bendix).
% 1.69/1.83 dependent: set(anl_eq).
% 1.69/1.83 dependent: set(para_from).
% 1.69/1.83 dependent: set(para_into).
% 1.69/1.83 dependent: clear(para_from_right).
% 1.69/1.83 dependent: clear(para_into_right).
% 1.69/1.83 dependent: set(para_from_vars).
% 1.69/1.83 dependent: set(eq_units_both_ways).
% 1.69/1.83 dependent: set(dynamic_demod_all).
% 1.69/1.83 dependent: set(dynamic_demod).
% 1.69/1.83 dependent: set(order_eq).
% 1.69/1.83 dependent: set(back_demod).
% 1.69/1.83 dependent: set(lrpo).
% 1.69/1.83 dependent: set(hyper_res).
% 1.69/1.83 dependent: set(unit_deletion).
% 1.69/1.83 dependent: set(factor).
% 1.69/1.83
% 1.69/1.83 ------------> process usable:
% 1.69/1.83 ** KEPT (pick-wt=5): 1 [] -e_quivalent(A,B)|there_exists(A).
% 1.69/1.83 ** KEPT (pick-wt=6): 2 [] -e_quivalent(A,B)|A=B.
% 1.69/1.83 ** KEPT (pick-wt=8): 3 [] -there_exists(A)|A!=B|e_quivalent(A,B).
% 1.69/1.83 ** KEPT (pick-wt=5): 4 [] -there_exists(domain(A))|there_exists(A).
% 1.69/1.83 ** KEPT (pick-wt=5): 5 [] -there_exists(codomain(A))|there_exists(A).
% 1.69/1.83 ** KEPT (pick-wt=7): 6 [] -there_exists(compose(A,B))|there_exists(domain(A)).
% 1.69/1.83 ** KEPT (pick-wt=9): 7 [] -there_exists(compose(A,B))|domain(A)=codomain(B).
% 1.69/1.83 ** KEPT (pick-wt=12): 8 [] -there_exists(domain(A))|domain(A)!=codomain(B)|there_exists(compose(A,B)).
% 1.69/1.83 ** KEPT (pick-wt=5): 9 [] -e_quivalent(A,B)|there_exists(B).
% 1.69/1.83 Following clause subsumed by 3 during input processing: 0 [] -there_exists(A)| -there_exists(B)|A!=B|e_quivalent(A,B).
% 1.69/1.83 ** KEPT (pick-wt=7): 10 [] -there_exists(compose(A,B))|there_exists(codomain(A)).
% 1.69/1.83 ** KEPT (pick-wt=13): 12 [copy,11,flip.1,flip.2] f1(A,B)!=A|f1(A,B)!=B|A=B.
% 1.69/1.83 ** KEPT (pick-wt=17): 13 [] compose(A,compose(a,b))!=B|compose(C,compose(a,b))!=B|A=C.
% 1.69/1.83 ** KEPT (pick-wt=3): 15 [copy,14,flip.1] h!=g.
% 1.69/1.83
% 1.69/1.83 ------------> process sos:
% 1.69/1.83 ** KEPT (pick-wt=3): 18 [] A=A.
% 1.69/1.83 ** KEPT (pick-wt=11): 20 [copy,19,flip.1] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 1.69/1.83 ---> New Demodulator: 21 [new_demod,20] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 1.69/1.83 ** KEPT (pick-wt=6): 22 [] compose(A,domain(A))=A.
% 1.69/1.83 ---> New Demodulator: 23 [new_demod,22] compose(A,domain(A))=A.
% 1.69/1.83 ** KEPT (pick-wt=6): 24 [] compose(codomain(A),A)=A.
% 1.69/1.83 ---> New Demodulator: 25 [new_demod,24] compose(codomain(A),A)=A.
% 1.69/1.83 ** KEPT (pick-wt=7): 26 [] there_exists(f1(A,B))|A=B.
% 1.69/1.83 ** KEPT (pick-wt=13): 28 [copy,27,flip.1,flip.2] f1(A,B)=A|f1(A,B)=B|A=B.
% 1.69/1.83 ** KEPT (pick-wt=4): 29 [] there_exists(compose(a,b)).
% 20.06/20.23 ** KEPT (pick-wt=2): 30 [] there_exists(h).
% 20.06/20.23 ** KEPT (pick-wt=7): 31 [] compose(h,a)=compose(g,a).
% 20.06/20.23 ---> New Demodulator: 32 [new_demod,31] compose(h,a)=compose(g,a).
% 20.06/20.23 Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] A=A.
% 20.06/20.23 18 back subsumes 17.
% 20.06/20.23 18 back subsumes 16.
% 20.06/20.23 >>>> Starting back demodulation with 21.
% 20.06/20.23 >>>> Starting back demodulation with 23.
% 20.06/20.23 >>>> Starting back demodulation with 25.
% 20.06/20.23 >>>> Starting back demodulation with 32.
% 20.06/20.23
% 20.06/20.23 ======= end of input processing =======
% 20.06/20.23
% 20.06/20.23 =========== start of search ===========
% 20.06/20.23
% 20.06/20.23
% 20.06/20.23 Resetting weight limit to 7.
% 20.06/20.23
% 20.06/20.23
% 20.06/20.23 Resetting weight limit to 7.
% 20.06/20.23
% 20.06/20.23 sos_size=1712
% 20.06/20.23
% 20.06/20.23 -- HEY sandbox, WE HAVE A PROOF!! --
% 20.06/20.23
% 20.06/20.23 ----> UNIT CONFLICT at 18.39 sec ----> 2132 [binary,2130.1,15.1] $F.
% 20.06/20.23
% 20.06/20.23 Length of proof is 10. Level of proof is 6.
% 20.06/20.23
% 20.06/20.23 ---------------- PROOF ----------------
% 20.06/20.23 % SZS status Unsatisfiable
% 20.06/20.23 % SZS output start Refutation
% See solution above
% 20.06/20.23 ------------ end of proof -------------
% 20.06/20.23
% 20.06/20.23
% 20.06/20.23 Search stopped by max_proofs option.
% 20.06/20.23
% 20.06/20.23
% 20.06/20.23 Search stopped by max_proofs option.
% 20.06/20.23
% 20.06/20.23 ============ end of search ============
% 20.06/20.23
% 20.06/20.23 -------------- statistics -------------
% 20.06/20.23 clauses given 899
% 20.06/20.23 clauses generated 498881
% 20.06/20.23 clauses kept 2096
% 20.06/20.23 clauses forward subsumed 6438
% 20.06/20.23 clauses back subsumed 46
% 20.06/20.23 Kbytes malloced 5859
% 20.06/20.23
% 20.06/20.23 ----------- times (seconds) -----------
% 20.06/20.23 user CPU time 18.39 (0 hr, 0 min, 18 sec)
% 20.06/20.23 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 20.06/20.23 wall-clock time 20 (0 hr, 0 min, 20 sec)
% 20.06/20.23
% 20.06/20.23 That finishes the proof of the theorem.
% 20.06/20.23
% 20.06/20.23 Process 22744 finished Wed Jul 27 01:54:25 2022
% 20.06/20.23 Otter interrupted
% 20.06/20.23 PROOF FOUND
%------------------------------------------------------------------------------