%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : COL002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 1.83s 2.07s
% Output : Refutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 16 ( 16 unt; 0 nHn; 6 RR)
% Number of literals : 16 ( 15 equ; 5 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
A != apply(fixed_pt,A),
file('COL002-1.p',unknown),
[] ).
cnf(2,plain,
apply(fixed_pt,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('COL002-1.p',unknown),
[] ).
cnf(5,axiom,
apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)),
file('COL002-1.p',unknown),
[] ).
cnf(7,axiom,
apply(apply(apply(c,A),B),C) = apply(apply(A,C),B),
file('COL002-1.p',unknown),
[] ).
cnf(8,axiom,
apply(i,A) = A,
file('COL002-1.p',unknown),
[] ).
cnf(10,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(11,plain,
apply(apply(A,B),C) = apply(apply(apply(c,A),C),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(13,plain,
apply(A,B) = apply(apply(apply(c,i),B),A),
inference(para_into,[status(thm),theory(equality)],[11,8]),
[iquote('para_into,11.1.1.1,8.1.1')] ).
cnf(53,plain,
apply(apply(apply(c,i),A),fixed_pt) != A,
inference(para_from,[status(thm),theory(equality)],[13,2]),
[iquote('para_from,13.1.1,2.1.1')] ).
cnf(69,plain,
apply(apply(apply(apply(apply(c,i),i),c),A),fixed_pt) != A,
inference(para_into,[status(thm),theory(equality)],[53,13]),
[iquote('para_into,53.1.1.1.1,13.1.1')] ).
cnf(89,plain,
apply(A,apply(B,A)) = apply(apply(apply(s,i),B),A),
inference(para_into,[status(thm),theory(equality)],[10,8]),
[iquote('para_into,10.1.1.1,8.1.1')] ).
cnf(244,plain,
apply(apply(apply(c,apply(apply(apply(c,i),i),c)),fixed_pt),A) != A,
inference(para_into,[status(thm),theory(equality)],[69,11]),
[iquote('para_into,69.1.1,11.1.1')] ).
cnf(361,plain,
apply(A,A) = apply(apply(apply(s,i),i),A),
inference(para_into,[status(thm),theory(equality)],[89,8]),
[iquote('para_into,89.1.1.2,8.1.1')] ).
cnf(441,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)],[361,5]),
[iquote('para_into,361.1.1,5.1.1')] ).
cnf(442,plain,
$false,
inference(binary,[status(thm)],[441,244]),
[iquote('binary,441.1,244.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : COL002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.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 02:46:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.83/2.07 ----- Otter 3.3f, August 2004 -----
% 1.83/2.07 The process was started by sandbox on n023.cluster.edu,
% 1.83/2.07 Wed Jul 27 02:46:48 2022
% 1.83/2.07 The command was "./otter". The process ID is 1212.
% 1.83/2.07
% 1.83/2.07 set(prolog_style_variables).
% 1.83/2.07 set(auto).
% 1.83/2.07 dependent: set(auto1).
% 1.83/2.07 dependent: set(process_input).
% 1.83/2.07 dependent: clear(print_kept).
% 1.83/2.07 dependent: clear(print_new_demod).
% 1.83/2.07 dependent: clear(print_back_demod).
% 1.83/2.07 dependent: clear(print_back_sub).
% 1.83/2.07 dependent: set(control_memory).
% 1.83/2.07 dependent: assign(max_mem, 12000).
% 1.83/2.07 dependent: assign(pick_given_ratio, 4).
% 1.83/2.07 dependent: assign(stats_level, 1).
% 1.83/2.07 dependent: assign(max_seconds, 10800).
% 1.83/2.07 clear(print_given).
% 1.83/2.07
% 1.83/2.07 list(usable).
% 1.83/2.07 0 [] A=A.
% 1.83/2.07 0 [] apply(apply(apply(s,X),Y),Z)=apply(apply(X,Z),apply(Y,Z)).
% 1.83/2.07 0 [] apply(apply(apply(b,X),Y),Z)=apply(X,apply(Y,Z)).
% 1.83/2.07 0 [] apply(apply(apply(c,X),Y),Z)=apply(apply(X,Z),Y).
% 1.83/2.07 0 [] apply(i,X)=X.
% 1.83/2.07 0 [] Y!=apply(fixed_pt,Y).
% 1.83/2.07 end_of_list.
% 1.83/2.07
% 1.83/2.07 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.83/2.07
% 1.83/2.07 All clauses are units, and equality is present; the
% 1.83/2.07 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.83/2.07
% 1.83/2.07 dependent: set(knuth_bendix).
% 1.83/2.07 dependent: set(anl_eq).
% 1.83/2.07 dependent: set(para_from).
% 1.83/2.07 dependent: set(para_into).
% 1.83/2.07 dependent: clear(para_from_right).
% 1.83/2.07 dependent: clear(para_into_right).
% 1.83/2.07 dependent: set(para_from_vars).
% 1.83/2.07 dependent: set(eq_units_both_ways).
% 1.83/2.07 dependent: set(dynamic_demod_all).
% 1.83/2.07 dependent: set(dynamic_demod).
% 1.83/2.07 dependent: set(order_eq).
% 1.83/2.07 dependent: set(back_demod).
% 1.83/2.07 dependent: set(lrpo).
% 1.83/2.07
% 1.83/2.07 ------------> process usable:
% 1.83/2.07 ** KEPT (pick-wt=5): 2 [copy,1,flip.1] apply(fixed_pt,A)!=A.
% 1.83/2.07
% 1.83/2.07 ------------> process sos:
% 1.83/2.07 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.83/2.07 ** KEPT (pick-wt=15): 4 [] apply(apply(apply(s,A),B),C)=apply(apply(A,C),apply(B,C)).
% 1.83/2.07 ** KEPT (pick-wt=13): 5 [] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.83/2.07 ---> New Demodulator: 6 [new_demod,5] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.83/2.07 ** KEPT (pick-wt=13): 7 [] apply(apply(apply(c,A),B),C)=apply(apply(A,C),B).
% 1.83/2.07 ** KEPT (pick-wt=5): 8 [] apply(i,A)=A.
% 1.83/2.07 ---> New Demodulator: 9 [new_demod,8] apply(i,A)=A.
% 1.83/2.07 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.83/2.07 ** KEPT (pick-wt=15): 10 [copy,4,flip.1] apply(apply(A,B),apply(C,B))=apply(apply(apply(s,A),C),B).
% 1.83/2.07 >>>> Starting back demodulation with 6.
% 1.83/2.07 ** KEPT (pick-wt=13): 11 [copy,7,flip.1] apply(apply(A,B),C)=apply(apply(apply(c,A),C),B).
% 1.83/2.07 >>>> Starting back demodulation with 9.
% 1.83/2.07 Following clause subsumed by 4 during input processing: 0 [copy,10,flip.1] apply(apply(apply(s,A),B),C)=apply(apply(A,C),apply(B,C)).
% 1.83/2.07 Following clause subsumed by 7 during input processing: 0 [copy,11,flip.1] apply(apply(apply(c,A),B),C)=apply(apply(A,C),B).
% 1.83/2.07
% 1.83/2.07 ======= end of input processing =======
% 1.83/2.07
% 1.83/2.07 =========== start of search ===========
% 1.83/2.07
% 1.83/2.07 -------- PROOF --------
% 1.83/2.07
% 1.83/2.07 ----> UNIT CONFLICT at 0.02 sec ----> 442 [binary,441.1,244.1] $F.
% 1.83/2.07
% 1.83/2.07 Length of proof is 10. Level of proof is 5.
% 1.83/2.07
% 1.83/2.07 ---------------- PROOF ----------------
% 1.83/2.07 % SZS status Unsatisfiable
% 1.83/2.07 % SZS output start Refutation
% See solution above
% 1.83/2.07 ------------ end of proof -------------
% 1.83/2.07
% 1.83/2.07
% 1.83/2.07 Search stopped by max_proofs option.
% 1.83/2.07
% 1.83/2.07
% 1.83/2.07 Search stopped by max_proofs option.
% 1.83/2.07
% 1.83/2.07 ============ end of search ============
% 1.83/2.07
% 1.83/2.07 -------------- statistics -------------
% 1.83/2.07 clauses given 23
% 1.83/2.07 clauses generated 404
% 1.83/2.07 clauses kept 368
% 1.83/2.07 clauses forward subsumed 321
% 1.83/2.07 clauses back subsumed 0
% 1.83/2.07 Kbytes malloced 1953
% 1.83/2.07
% 1.83/2.07 ----------- times (seconds) -----------
% 1.83/2.07 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.83/2.07 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.83/2.07 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.83/2.07
% 1.83/2.07 That finishes the proof of the theorem.
% 1.83/2.07
% 1.83/2.07 Process 1212 finished Wed Jul 27 02:46:50 2022
% 1.83/2.07 Otter interrupted
% 1.83/2.07 PROOF FOUND
%------------------------------------------------------------------------------