TSTP Solution File: COL030-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : COL030-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n016.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 12:48:01 EDT 2022
% Result : Unsatisfiable 1.70s 1.91s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of clauses : 8 ( 8 unt; 0 nHn; 4 RR)
% Number of literals : 8 ( 7 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
apply(A,f(A)) != apply(f(A),apply(A,f(A))),
file('COL030-1.p',unknown),
[] ).
cnf(2,plain,
apply(f(A),apply(A,f(A))) != apply(A,f(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('COL030-1.p',unknown),
[] ).
cnf(5,axiom,
apply(apply(l,A),B) = apply(A,apply(B,B)),
file('COL030-1.p',unknown),
[] ).
cnf(6,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(24,plain,
apply(f(apply(apply(s,A),B)),apply(apply(A,f(apply(apply(s,A),B))),apply(B,f(apply(apply(s,A),B))))) != apply(apply(apply(s,A),B),f(apply(apply(s,A),B))),
inference(para_from,[status(thm),theory(equality)],[4,2]),
[iquote('para_from,4.1.1,2.1.1.2')] ).
cnf(36,plain,
apply(A,apply(apply(B,A),apply(B,A))) = apply(apply(apply(s,l),B),A),
inference(para_into,[status(thm),theory(equality)],[6,5]),
[iquote('para_into,6.1.1,5.1.1')] ).
cnf(37,plain,
$false,
inference(binary,[status(thm)],[36,24]),
[iquote('binary,36.1,24.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COL030-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 02:44:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.70/1.91 ----- Otter 3.3f, August 2004 -----
% 1.70/1.91 The process was started by sandbox2 on n016.cluster.edu,
% 1.70/1.91 Wed Jul 27 02:44:37 2022
% 1.70/1.91 The command was "./otter". The process ID is 30189.
% 1.70/1.91
% 1.70/1.91 set(prolog_style_variables).
% 1.70/1.91 set(auto).
% 1.70/1.91 dependent: set(auto1).
% 1.70/1.91 dependent: set(process_input).
% 1.70/1.91 dependent: clear(print_kept).
% 1.70/1.91 dependent: clear(print_new_demod).
% 1.70/1.91 dependent: clear(print_back_demod).
% 1.70/1.91 dependent: clear(print_back_sub).
% 1.70/1.91 dependent: set(control_memory).
% 1.70/1.91 dependent: assign(max_mem, 12000).
% 1.70/1.91 dependent: assign(pick_given_ratio, 4).
% 1.70/1.91 dependent: assign(stats_level, 1).
% 1.70/1.91 dependent: assign(max_seconds, 10800).
% 1.70/1.91 clear(print_given).
% 1.70/1.91
% 1.70/1.91 list(usable).
% 1.70/1.91 0 [] A=A.
% 1.70/1.91 0 [] apply(apply(apply(s,X),Y),Z)=apply(apply(X,Z),apply(Y,Z)).
% 1.70/1.91 0 [] apply(apply(l,X),Y)=apply(X,apply(Y,Y)).
% 1.70/1.91 0 [] apply(Y,f(Y))!=apply(f(Y),apply(Y,f(Y))).
% 1.70/1.91 end_of_list.
% 1.70/1.91
% 1.70/1.91 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.70/1.91
% 1.70/1.91 All clauses are units, and equality is present; the
% 1.70/1.91 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.70/1.91
% 1.70/1.91 dependent: set(knuth_bendix).
% 1.70/1.91 dependent: set(anl_eq).
% 1.70/1.91 dependent: set(para_from).
% 1.70/1.91 dependent: set(para_into).
% 1.70/1.91 dependent: clear(para_from_right).
% 1.70/1.91 dependent: clear(para_into_right).
% 1.70/1.91 dependent: set(para_from_vars).
% 1.70/1.91 dependent: set(eq_units_both_ways).
% 1.70/1.91 dependent: set(dynamic_demod_all).
% 1.70/1.91 dependent: set(dynamic_demod).
% 1.70/1.91 dependent: set(order_eq).
% 1.70/1.91 dependent: set(back_demod).
% 1.70/1.91 dependent: set(lrpo).
% 1.70/1.91
% 1.70/1.91 ------------> process usable:
% 1.70/1.91 ** KEPT (pick-wt=12): 2 [copy,1,flip.1] apply(f(A),apply(A,f(A)))!=apply(A,f(A)).
% 1.70/1.91
% 1.70/1.91 ------------> process sos:
% 1.70/1.91 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.70/1.91 ** KEPT (pick-wt=15): 4 [] apply(apply(apply(s,A),B),C)=apply(apply(A,C),apply(B,C)).
% 1.70/1.91 ** KEPT (pick-wt=11): 5 [] apply(apply(l,A),B)=apply(A,apply(B,B)).
% 1.70/1.91 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.70/1.91 ** KEPT (pick-wt=15): 6 [copy,4,flip.1] apply(apply(A,B),apply(C,B))=apply(apply(apply(s,A),C),B).
% 1.70/1.91 ** KEPT (pick-wt=11): 7 [copy,5,flip.1] apply(A,apply(B,B))=apply(apply(l,A),B).
% 1.70/1.91 Following clause subsumed by 4 during input processing: 0 [copy,6,flip.1] apply(apply(apply(s,A),B),C)=apply(apply(A,C),apply(B,C)).
% 1.70/1.91 Following clause subsumed by 5 during input processing: 0 [copy,7,flip.1] apply(apply(l,A),B)=apply(A,apply(B,B)).
% 1.70/1.91
% 1.70/1.91 ======= end of input processing =======
% 1.70/1.91
% 1.70/1.91 =========== start of search ===========
% 1.70/1.91
% 1.70/1.91 -------- PROOF --------
% 1.70/1.91
% 1.70/1.91 ----> UNIT CONFLICT at 0.00 sec ----> 37 [binary,36.1,24.1] $F.
% 1.70/1.91
% 1.70/1.91 Length of proof is 4. Level of proof is 2.
% 1.70/1.91
% 1.70/1.91 ---------------- PROOF ----------------
% 1.70/1.91 % SZS status Unsatisfiable
% 1.70/1.91 % SZS output start Refutation
% See solution above
% 1.70/1.91 ------------ end of proof -------------
% 1.70/1.91
% 1.70/1.91
% 1.70/1.91 Search stopped by max_proofs option.
% 1.70/1.91
% 1.70/1.91
% 1.70/1.91 Search stopped by max_proofs option.
% 1.70/1.91
% 1.70/1.91 ============ end of search ============
% 1.70/1.91
% 1.70/1.91 -------------- statistics -------------
% 1.70/1.91 clauses given 5
% 1.70/1.91 clauses generated 30
% 1.70/1.91 clauses kept 34
% 1.70/1.91 clauses forward subsumed 21
% 1.70/1.91 clauses back subsumed 0
% 1.70/1.91 Kbytes malloced 976
% 1.70/1.91
% 1.70/1.91 ----------- times (seconds) -----------
% 1.70/1.91 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.70/1.91 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.70/1.91 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.70/1.91
% 1.70/1.91 That finishes the proof of the theorem.
% 1.70/1.91
% 1.70/1.91 Process 30189 finished Wed Jul 27 02:44:38 2022
% 1.70/1.91 Otter interrupted
% 1.70/1.91 PROOF FOUND
%------------------------------------------------------------------------------