TSTP Solution File: CAT004-4 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : CAT004-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %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 : 300s
% DateTime : Wed Jul 27 12:47:45 EDT 2022
% Result : Unsatisfiable 2.91s 3.12s
% Output : Refutation 2.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of clauses : 19 ( 10 unt; 0 nHn; 15 RR)
% Number of literals : 36 ( 23 equ; 20 neg)
% Maximal clause size : 5 ( 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 : 29 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ e_quivalent(A,B)
| A = B ),
file('CAT004-4.p',unknown),
[] ).
cnf(3,axiom,
( ~ there_exists(A)
| A != B
| e_quivalent(A,B) ),
file('CAT004-4.p',unknown),
[] ).
cnf(9,axiom,
( compose(A,a) != B
| compose(C,a) != B
| A = C ),
file('CAT004-4.p',unknown),
[] ).
cnf(10,axiom,
( compose(A,b) != B
| compose(C,b) != B
| A = C ),
file('CAT004-4.p',unknown),
[] ).
cnf(11,axiom,
h != g,
file('CAT004-4.p',unknown),
[] ).
cnf(12,axiom,
A = A,
file('CAT004-4.p',unknown),
[] ).
cnf(13,axiom,
compose(A,compose(B,C)) = compose(compose(A,B),C),
file('CAT004-4.p',unknown),
[] ).
cnf(15,plain,
compose(compose(A,B),C) = compose(A,compose(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.1')] ).
cnf(17,axiom,
compose(A,domain(A)) = A,
file('CAT004-4.p',unknown),
[] ).
cnf(21,axiom,
there_exists(h),
file('CAT004-4.p',unknown),
[] ).
cnf(23,axiom,
compose(h,compose(a,b)) = compose(g,compose(a,b)),
file('CAT004-4.p',unknown),
[] ).
cnf(24,plain,
e_quivalent(h,h),
inference(hyper,[status(thm)],[21,3,12]),
[iquote('hyper,21,3,12')] ).
cnf(29,plain,
( e_quivalent(A,h)
| compose(h,a) != B
| compose(A,a) != B ),
inference(para_into,[status(thm),theory(equality)],[24,9]),
[iquote('para_into,24.1.1,9.3.1')] ).
cnf(96,plain,
( A = B
| ~ e_quivalent(B,A) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[17,2]),17]),
[iquote('para_into,16.1.1,2.2.1,demod,17')] ).
cnf(423,plain,
( A != g
| ~ e_quivalent(A,h) ),
inference(para_from,[status(thm),theory(equality)],[96,11]),
[iquote('para_from,96.1.1,11.1.1')] ).
cnf(482,plain,
( e_quivalent(A,h)
| B != C
| compose(A,a) != C
| compose(g,compose(a,b)) != D
| compose(B,b) != D ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[29,10]),15,23]),
[iquote('para_into,29.2.1,10.3.1,demod,15,23')] ).
cnf(1109,plain,
( A != g
| ~ e_quivalent(A,B)
| ~ e_quivalent(h,B) ),
inference(para_into,[status(thm),theory(equality)],[423,2]),
[iquote('para_into,423.2.2,2.2.1')] ).
cnf(3300,plain,
e_quivalent(g,h),
inference(hyper,[status(thm)],[482,12,12,12,15]),
[iquote('hyper,482,12,12,12,14')] ).
cnf(3302,plain,
$false,
inference(hyper,[status(thm)],[3300,1109,12,24]),
[iquote('hyper,3300,1109,12,24')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : CAT004-4 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n019.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 02:05:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.91/3.12 ----- Otter 3.3f, August 2004 -----
% 2.91/3.12 The process was started by sandbox2 on n019.cluster.edu,
% 2.91/3.12 Wed Jul 27 02:05:22 2022
% 2.91/3.12 The command was "./otter". The process ID is 2846.
% 2.91/3.12
% 2.91/3.12 set(prolog_style_variables).
% 2.91/3.12 set(auto).
% 2.91/3.12 dependent: set(auto1).
% 2.91/3.12 dependent: set(process_input).
% 2.91/3.12 dependent: clear(print_kept).
% 2.91/3.12 dependent: clear(print_new_demod).
% 2.91/3.12 dependent: clear(print_back_demod).
% 2.91/3.12 dependent: clear(print_back_sub).
% 2.91/3.12 dependent: set(control_memory).
% 2.91/3.12 dependent: assign(max_mem, 12000).
% 2.91/3.12 dependent: assign(pick_given_ratio, 4).
% 2.91/3.12 dependent: assign(stats_level, 1).
% 2.91/3.12 dependent: assign(max_seconds, 10800).
% 2.91/3.12 clear(print_given).
% 2.91/3.12
% 2.91/3.12 list(usable).
% 2.91/3.12 0 [] A=A.
% 2.91/3.12 0 [] -e_quivalent(X,Y)|there_exists(X).
% 2.91/3.12 0 [] -e_quivalent(X,Y)|X=Y.
% 2.91/3.12 0 [] -there_exists(X)|X!=Y|e_quivalent(X,Y).
% 2.91/3.12 0 [] -there_exists(domain(X))|there_exists(X).
% 2.91/3.12 0 [] -there_exists(codomain(X))|there_exists(X).
% 2.91/3.12 0 [] -there_exists(compose(X,Y))|there_exists(domain(X)).
% 2.91/3.12 0 [] -there_exists(compose(X,Y))|domain(X)=codomain(Y).
% 2.91/3.12 0 [] -there_exists(domain(X))|domain(X)!=codomain(Y)|there_exists(compose(X,Y)).
% 2.91/3.12 0 [] compose(X,compose(Y,Z))=compose(compose(X,Y),Z).
% 2.91/3.12 0 [] compose(X,domain(X))=X.
% 2.91/3.12 0 [] compose(codomain(X),X)=X.
% 2.91/3.12 0 [] there_exists(compose(a,b)).
% 2.91/3.12 0 [] compose(X,a)!=Y|compose(Z,a)!=Y|X=Z.
% 2.91/3.12 0 [] compose(X,b)!=Y|compose(Z,b)!=Y|X=Z.
% 2.91/3.12 0 [] there_exists(h).
% 2.91/3.12 0 [] compose(h,compose(a,b))=compose(g,compose(a,b)).
% 2.91/3.12 0 [] h!=g.
% 2.91/3.12 end_of_list.
% 2.91/3.12
% 2.91/3.12 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 2.91/3.12
% 2.91/3.12 This is a Horn set with equality. The strategy will be
% 2.91/3.12 Knuth-Bendix and hyper_res, with positive clauses in
% 2.91/3.12 sos and nonpositive clauses in usable.
% 2.91/3.12
% 2.91/3.12 dependent: set(knuth_bendix).
% 2.91/3.12 dependent: set(anl_eq).
% 2.91/3.12 dependent: set(para_from).
% 2.91/3.12 dependent: set(para_into).
% 2.91/3.12 dependent: clear(para_from_right).
% 2.91/3.12 dependent: clear(para_into_right).
% 2.91/3.12 dependent: set(para_from_vars).
% 2.91/3.12 dependent: set(eq_units_both_ways).
% 2.91/3.12 dependent: set(dynamic_demod_all).
% 2.91/3.12 dependent: set(dynamic_demod).
% 2.91/3.12 dependent: set(order_eq).
% 2.91/3.12 dependent: set(back_demod).
% 2.91/3.12 dependent: set(lrpo).
% 2.91/3.12 dependent: set(hyper_res).
% 2.91/3.12 dependent: clear(order_hyper).
% 2.91/3.12
% 2.91/3.12 ------------> process usable:
% 2.91/3.12 ** KEPT (pick-wt=5): 1 [] -e_quivalent(A,B)|there_exists(A).
% 2.91/3.12 ** KEPT (pick-wt=6): 2 [] -e_quivalent(A,B)|A=B.
% 2.91/3.12 ** KEPT (pick-wt=8): 3 [] -there_exists(A)|A!=B|e_quivalent(A,B).
% 2.91/3.12 ** KEPT (pick-wt=5): 4 [] -there_exists(domain(A))|there_exists(A).
% 2.91/3.12 ** KEPT (pick-wt=5): 5 [] -there_exists(codomain(A))|there_exists(A).
% 2.91/3.12 ** KEPT (pick-wt=7): 6 [] -there_exists(compose(A,B))|there_exists(domain(A)).
% 2.91/3.12 ** KEPT (pick-wt=9): 7 [] -there_exists(compose(A,B))|domain(A)=codomain(B).
% 2.91/3.12 ** KEPT (pick-wt=12): 8 [] -there_exists(domain(A))|domain(A)!=codomain(B)|there_exists(compose(A,B)).
% 2.91/3.12 ** KEPT (pick-wt=13): 9 [] compose(A,a)!=B|compose(C,a)!=B|A=C.
% 2.91/3.12 ** KEPT (pick-wt=13): 10 [] compose(A,b)!=B|compose(C,b)!=B|A=C.
% 2.91/3.12 ** KEPT (pick-wt=3): 11 [] h!=g.
% 2.91/3.12
% 2.91/3.12 ------------> process sos:
% 2.91/3.12 ** KEPT (pick-wt=3): 12 [] A=A.
% 2.91/3.12 ** KEPT (pick-wt=11): 14 [copy,13,flip.1] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 2.91/3.12 ---> New Demodulator: 15 [new_demod,14] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 2.91/3.12 ** KEPT (pick-wt=6): 16 [] compose(A,domain(A))=A.
% 2.91/3.12 ---> New Demodulator: 17 [new_demod,16] compose(A,domain(A))=A.
% 2.91/3.12 ** KEPT (pick-wt=6): 18 [] compose(codomain(A),A)=A.
% 2.91/3.12 ---> New Demodulator: 19 [new_demod,18] compose(codomain(A),A)=A.
% 2.91/3.12 ** KEPT (pick-wt=4): 20 [] there_exists(compose(a,b)).
% 2.91/3.12 ** KEPT (pick-wt=2): 21 [] there_exists(h).
% 2.91/3.12 ** KEPT (pick-wt=11): 22 [] compose(h,compose(a,b))=compose(g,compose(a,b)).
% 2.91/3.12 ---> New Demodulator: 23 [new_demod,22] compose(h,compose(a,b))=compose(g,compose(a,b)).
% 2.91/3.12 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] A=A.
% 2.91/3.12 >>>> Starting back demodulation with 15.
% 2.91/3.12 >>>> Starting back demodulation with 17.
% 2.91/3.12 >>>> Starting back demodulation with 19.
% 2.91/3.12 >>>> Starting back demodulation with 23.
% 2.91/3.12
% 2.91/3.12 ======= end of input processing =======
% 2.91/3.12
% 2.91/3.12 =========== start of search ===========
% 2.91/3.12
% 2.91/3.12
% 2.91/3.12 Resetting weight limit to 8.
% 2.91/3.12
% 2.91/3.12
% 2.91/3.12 Resetting weight limit to 8.
% 2.91/3.12
% 2.91/3.12 sos_size=2349
% 2.91/3.12
% 2.91/3.12 -------- PROOF --------
% 2.91/3.12
% 2.91/3.12 -----> EMPTY CLAUSE at 1.20 sec ----> 3302 [hyper,3300,1109,12,24] $F.
% 2.91/3.12
% 2.91/3.12 Length of proof is 8. Level of proof is 4.
% 2.91/3.12
% 2.91/3.12 ---------------- PROOF ----------------
% 2.91/3.12 % SZS status Unsatisfiable
% 2.91/3.12 % SZS output start Refutation
% See solution above
% 2.91/3.12 ------------ end of proof -------------
% 2.91/3.12
% 2.91/3.12
% 2.91/3.12 Search stopped by max_proofs option.
% 2.91/3.12
% 2.91/3.12
% 2.91/3.12 Search stopped by max_proofs option.
% 2.91/3.12
% 2.91/3.12 ============ end of search ============
% 2.91/3.12
% 2.91/3.12 -------------- statistics -------------
% 2.91/3.12 clauses given 1227
% 2.91/3.12 clauses generated 137241
% 2.91/3.12 clauses kept 3215
% 2.91/3.12 clauses forward subsumed 10169
% 2.91/3.12 clauses back subsumed 25
% 2.91/3.12 Kbytes malloced 5859
% 2.91/3.12
% 2.91/3.12 ----------- times (seconds) -----------
% 2.91/3.12 user CPU time 1.20 (0 hr, 0 min, 1 sec)
% 2.91/3.12 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.91/3.12 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.91/3.12
% 2.91/3.12 That finishes the proof of the theorem.
% 2.91/3.12
% 2.91/3.12 Process 2846 finished Wed Jul 27 02:05:24 2022
% 2.91/3.12 Otter interrupted
% 2.91/3.12 PROOF FOUND
%------------------------------------------------------------------------------