TSTP Solution File: COL001-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : COL001-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 12:47:56 EDT 2022
% Result : Unsatisfiable 1.71s 1.91s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 10 ( 10 unt; 0 nHn; 3 RR)
% Number of literals : 10 ( 9 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
A != apply(combinator,A),
file('COL001-2.p',unknown),
[] ).
cnf(2,plain,
apply(combinator,A) != A,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(4,axiom,
apply(apply(apply(s,A),B),C) = apply(apply(A,C),apply(B,C)),
file('COL001-2.p',unknown),
[] ).
cnf(7,axiom,
apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)),
file('COL001-2.p',unknown),
[] ).
cnf(9,axiom,
apply(i,A) = A,
file('COL001-2.p',unknown),
[] ).
cnf(14,plain,
apply(apply(A,B),apply(C,B)) = apply(apply(apply(s,A),C),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,flip.1')] ).
cnf(19,plain,
apply(A,apply(B,A)) = apply(apply(apply(s,i),B),A),
inference(para_into,[status(thm),theory(equality)],[14,9]),
[iquote('para_into,14.1.1.1,9.1.1')] ).
cnf(75,plain,
apply(A,A) = apply(apply(apply(s,i),i),A),
inference(para_into,[status(thm),theory(equality)],[19,9]),
[iquote('para_into,19.1.1.2,9.1.1')] ).
cnf(151,plain,
apply(A,apply(B,apply(apply(b,A),B))) = apply(apply(apply(s,i),i),apply(apply(b,A),B)),
inference(para_into,[status(thm),theory(equality)],[75,7]),
[iquote('para_into,75.1.1,7.1.1')] ).
cnf(152,plain,
$false,
inference(binary,[status(thm)],[151,2]),
[iquote('binary,151.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : COL001-2 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n009.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 02:21:21 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.71/1.91 ----- Otter 3.3f, August 2004 -----
% 1.71/1.91 The process was started by sandbox on n009.cluster.edu,
% 1.71/1.91 Wed Jul 27 02:21:21 2022
% 1.71/1.91 The command was "./otter". The process ID is 24777.
% 1.71/1.91
% 1.71/1.91 set(prolog_style_variables).
% 1.71/1.91 set(auto).
% 1.71/1.91 dependent: set(auto1).
% 1.71/1.91 dependent: set(process_input).
% 1.71/1.91 dependent: clear(print_kept).
% 1.71/1.91 dependent: clear(print_new_demod).
% 1.71/1.91 dependent: clear(print_back_demod).
% 1.71/1.91 dependent: clear(print_back_sub).
% 1.71/1.91 dependent: set(control_memory).
% 1.71/1.91 dependent: assign(max_mem, 12000).
% 1.71/1.91 dependent: assign(pick_given_ratio, 4).
% 1.71/1.91 dependent: assign(stats_level, 1).
% 1.71/1.91 dependent: assign(max_seconds, 10800).
% 1.71/1.91 clear(print_given).
% 1.71/1.91
% 1.71/1.91 list(usable).
% 1.71/1.91 0 [] A=A.
% 1.71/1.91 0 [] apply(apply(apply(s,X),Y),Z)=apply(apply(X,Z),apply(Y,Z)).
% 1.71/1.91 0 [] apply(apply(k,X),Y)=X.
% 1.71/1.91 0 [] apply(apply(apply(b,X),Y),Z)=apply(X,apply(Y,Z)).
% 1.71/1.91 0 [] apply(i,X)=X.
% 1.71/1.91 0 [] apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i))=apply(x,apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i))).
% 1.71/1.91 0 [] Y!=apply(combinator,Y).
% 1.71/1.91 end_of_list.
% 1.71/1.91
% 1.71/1.91 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.71/1.91
% 1.71/1.91 All clauses are units, and equality is present; the
% 1.71/1.91 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.71/1.91
% 1.71/1.91 dependent: set(knuth_bendix).
% 1.71/1.91 dependent: set(anl_eq).
% 1.71/1.91 dependent: set(para_from).
% 1.71/1.91 dependent: set(para_into).
% 1.71/1.91 dependent: clear(para_from_right).
% 1.71/1.91 dependent: clear(para_into_right).
% 1.71/1.91 dependent: set(para_from_vars).
% 1.71/1.91 dependent: set(eq_units_both_ways).
% 1.71/1.91 dependent: set(dynamic_demod_all).
% 1.71/1.91 dependent: set(dynamic_demod).
% 1.71/1.91 dependent: set(order_eq).
% 1.71/1.91 dependent: set(back_demod).
% 1.71/1.91 dependent: set(lrpo).
% 1.71/1.91
% 1.71/1.91 ------------> process usable:
% 1.71/1.91 ** KEPT (pick-wt=5): 2 [copy,1,flip.1] apply(combinator,A)!=A.
% 1.71/1.91
% 1.71/1.91 ------------> process sos:
% 1.71/1.91 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.71/1.91 ** KEPT (pick-wt=15): 4 [] apply(apply(apply(s,A),B),C)=apply(apply(A,C),apply(B,C)).
% 1.71/1.91 ** KEPT (pick-wt=7): 5 [] apply(apply(k,A),B)=A.
% 1.71/1.91 ---> New Demodulator: 6 [new_demod,5] apply(apply(k,A),B)=A.
% 1.71/1.91 ** KEPT (pick-wt=13): 7 [] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.71/1.91 ---> New Demodulator: 8 [new_demod,7] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.71/1.91 ** KEPT (pick-wt=5): 9 [] apply(i,A)=A.
% 1.71/1.91 ---> New Demodulator: 10 [new_demod,9] apply(i,A)=A.
% 1.71/1.91 ** KEPT (pick-wt=33): 12 [copy,11,flip.1] apply(x,apply(apply(apply(s,apply(b,A)),i),apply(apply(s,apply(b,A)),i)))=apply(apply(apply(s,apply(b,A)),i),apply(apply(s,apply(b,A)),i)).
% 1.71/1.91 ---> New Demodulator: 13 [new_demod,12] apply(x,apply(apply(apply(s,apply(b,A)),i),apply(apply(s,apply(b,A)),i)))=apply(apply(apply(s,apply(b,A)),i),apply(apply(s,apply(b,A)),i)).
% 1.71/1.91 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.71/1.91 ** KEPT (pick-wt=15): 14 [copy,4,flip.1] apply(apply(A,B),apply(C,B))=apply(apply(apply(s,A),C),B).
% 1.71/1.91 >>>> Starting back demodulation with 6.
% 1.71/1.91 >>>> Starting back demodulation with 8.
% 1.71/1.91 >>>> Starting back demodulation with 10.
% 1.71/1.91 >>>> Starting back demodulation with 13.
% 1.71/1.91 Following clause subsumed by 4 during input processing: 0 [copy,14,flip.1] apply(apply(apply(s,A),B),C)=apply(apply(A,C),apply(B,C)).
% 1.71/1.91
% 1.71/1.91 ======= end of input processing =======
% 1.71/1.91
% 1.71/1.91 =========== start of search ===========
% 1.71/1.91
% 1.71/1.91 -------- PROOF --------
% 1.71/1.91
% 1.71/1.91 ----> UNIT CONFLICT at 0.01 sec ----> 152 [binary,151.1,2.1] $F.
% 1.71/1.91
% 1.71/1.91 Length of proof is 5. Level of proof is 4.
% 1.71/1.91
% 1.71/1.91 ---------------- PROOF ----------------
% 1.71/1.91 % SZS status Unsatisfiable
% 1.71/1.91 % SZS output start Refutation
% See solution above
% 1.71/1.91 ------------ end of proof -------------
% 1.71/1.91
% 1.71/1.91
% 1.71/1.91 Search stopped by max_proofs option.
% 1.71/1.91
% 1.71/1.91
% 1.71/1.91 Search stopped by max_proofs option.
% 1.71/1.91
% 1.71/1.91 ============ end of search ============
% 1.71/1.91
% 1.71/1.91 -------------- statistics -------------
% 1.71/1.91 clauses given 12
% 1.71/1.91 clauses generated 115
% 1.71/1.91 clauses kept 112
% 1.71/1.91 clauses forward subsumed 81
% 1.71/1.91 clauses back subsumed 0
% 1.71/1.91 Kbytes malloced 1953
% 1.71/1.91
% 1.71/1.91 ----------- times (seconds) -----------
% 1.71/1.91 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.71/1.91 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.91 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.71/1.91
% 1.71/1.91 That finishes the proof of the theorem.
% 1.71/1.91
% 1.71/1.91 Process 24777 finished Wed Jul 27 02:21:22 2022
% 1.71/1.91 Otter interrupted
% 1.71/1.91 PROOF FOUND
%------------------------------------------------------------------------------