%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : COL004-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.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 12:47:58 EDT 2022
% Result : Unsatisfiable 1.66s 1.86s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of clauses : 10 ( 10 unt; 0 nHn; 4 RR)
% Number of literals : 10 ( 9 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 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 : 16 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y)),
file('COL004-3.p',unknown),
[] ).
cnf(3,axiom,
apply(apply(apply(s,A),B),C) = apply(apply(A,C),apply(B,C)),
file('COL004-3.p',unknown),
[] ).
cnf(5,axiom,
apply(apply(k,A),B) = A,
file('COL004-3.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)],[3])]),
[iquote('copy,3,flip.1')] ).
cnf(7,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),y) != apply(y,apply(apply(x,x),y)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[3,1]),5]),
[iquote('para_from,3.1.1,1.1.1.1,demod,5')] ).
cnf(16,plain,
apply(apply(apply(s,k),A),B) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[6,5])]),
[iquote('para_into,6.1.1,4.1.1,flip.1')] ).
cnf(31,plain,
apply(A,apply(B,A)) = apply(apply(apply(s,apply(apply(s,k),C)),B),A),
inference(para_from,[status(thm),theory(equality)],[16,6]),
[iquote('para_from,15.1.1,6.1.1.1')] ).
cnf(33,plain,
apply(apply(apply(s,apply(apply(s,k),A)),B),C) = apply(C,apply(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[31])]),
[iquote('copy,31,flip.1')] ).
cnf(34,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(x,x)),y) != apply(y,apply(apply(x,x),y)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,3]),16,16]),
[iquote('para_into,7.1.1.1.2,3.1.1,demod,16,16')] ).
cnf(35,plain,
$false,
inference(binary,[status(thm)],[34,33]),
[iquote('binary,34.1,33.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL004-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n028.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 02:34:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.66/1.86 ----- Otter 3.3f, August 2004 -----
% 1.66/1.86 The process was started by sandbox on n028.cluster.edu,
% 1.66/1.86 Wed Jul 27 02:34:03 2022
% 1.66/1.86 The command was "./otter". The process ID is 17613.
% 1.66/1.86
% 1.66/1.86 set(prolog_style_variables).
% 1.66/1.86 set(auto).
% 1.66/1.86 dependent: set(auto1).
% 1.66/1.86 dependent: set(process_input).
% 1.66/1.86 dependent: clear(print_kept).
% 1.66/1.86 dependent: clear(print_new_demod).
% 1.66/1.86 dependent: clear(print_back_demod).
% 1.66/1.86 dependent: clear(print_back_sub).
% 1.66/1.86 dependent: set(control_memory).
% 1.66/1.86 dependent: assign(max_mem, 12000).
% 1.66/1.86 dependent: assign(pick_given_ratio, 4).
% 1.66/1.86 dependent: assign(stats_level, 1).
% 1.66/1.86 dependent: assign(max_seconds, 10800).
% 1.66/1.86 clear(print_given).
% 1.66/1.86
% 1.66/1.86 list(usable).
% 1.66/1.86 0 [] A=A.
% 1.66/1.86 0 [] apply(apply(apply(s,X),Y),Z)=apply(apply(X,Z),apply(Y,Z)).
% 1.66/1.86 0 [] apply(apply(k,X),Y)=X.
% 1.66/1.86 0 [] apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y)!=apply(y,apply(apply(x,x),y)).
% 1.66/1.86 end_of_list.
% 1.66/1.86
% 1.66/1.86 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.66/1.86
% 1.66/1.86 All clauses are units, and equality is present; the
% 1.66/1.86 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.66/1.86
% 1.66/1.86 dependent: set(knuth_bendix).
% 1.66/1.86 dependent: set(anl_eq).
% 1.66/1.86 dependent: set(para_from).
% 1.66/1.86 dependent: set(para_into).
% 1.66/1.86 dependent: clear(para_from_right).
% 1.66/1.86 dependent: clear(para_into_right).
% 1.66/1.86 dependent: set(para_from_vars).
% 1.66/1.86 dependent: set(eq_units_both_ways).
% 1.66/1.86 dependent: set(dynamic_demod_all).
% 1.66/1.86 dependent: set(dynamic_demod).
% 1.66/1.86 dependent: set(order_eq).
% 1.66/1.86 dependent: set(back_demod).
% 1.66/1.86 dependent: set(lrpo).
% 1.66/1.86
% 1.66/1.86 ------------> process usable:
% 1.66/1.86 ** KEPT (pick-wt=37): 1 [] apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y)!=apply(y,apply(apply(x,x),y)).
% 1.66/1.86
% 1.66/1.86 ------------> process sos:
% 1.66/1.86 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.66/1.86 ** KEPT (pick-wt=15): 3 [] apply(apply(apply(s,A),B),C)=apply(apply(A,C),apply(B,C)).
% 1.66/1.86 ** KEPT (pick-wt=7): 4 [] apply(apply(k,A),B)=A.
% 1.66/1.86 ---> New Demodulator: 5 [new_demod,4] apply(apply(k,A),B)=A.
% 1.66/1.86 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.66/1.86 ** KEPT (pick-wt=15): 6 [copy,3,flip.1] apply(apply(A,B),apply(C,B))=apply(apply(apply(s,A),C),B).
% 1.66/1.86 >>>> Starting back demodulation with 5.
% 1.66/1.86 Following clause subsumed by 3 during input processing: 0 [copy,6,flip.1] apply(apply(apply(s,A),B),C)=apply(apply(A,C),apply(B,C)).
% 1.66/1.86
% 1.66/1.86 ======= end of input processing =======
% 1.66/1.86
% 1.66/1.86 =========== start of search ===========
% 1.66/1.86
% 1.66/1.86 -------- PROOF --------
% 1.66/1.86
% 1.66/1.86 ----> UNIT CONFLICT at 0.00 sec ----> 35 [binary,34.1,33.1] $F.
% 1.66/1.86
% 1.66/1.86 Length of proof is 6. Level of proof is 4.
% 1.66/1.86
% 1.66/1.86 ---------------- PROOF ----------------
% 1.66/1.86 % SZS status Unsatisfiable
% 1.66/1.86 % SZS output start Refutation
% See solution above
% 1.66/1.86 ------------ end of proof -------------
% 1.66/1.86
% 1.66/1.86
% 1.66/1.86 Search stopped by max_proofs option.
% 1.66/1.86
% 1.66/1.86
% 1.66/1.86 Search stopped by max_proofs option.
% 1.66/1.86
% 1.66/1.86 ============ end of search ============
% 1.66/1.86
% 1.66/1.86 -------------- statistics -------------
% 1.66/1.86 clauses given 6
% 1.66/1.86 clauses generated 30
% 1.66/1.86 clauses kept 29
% 1.66/1.86 clauses forward subsumed 27
% 1.66/1.86 clauses back subsumed 0
% 1.66/1.86 Kbytes malloced 976
% 1.66/1.86
% 1.66/1.86 ----------- times (seconds) -----------
% 1.66/1.86 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.86 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.86 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.66/1.86
% 1.66/1.86 That finishes the proof of the theorem.
% 1.66/1.86
% 1.66/1.86 Process 17613 finished Wed Jul 27 02:34:05 2022
% 1.66/1.86 Otter interrupted
% 1.66/1.86 PROOF FOUND
%------------------------------------------------------------------------------