%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ALG040+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n029.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 12:45:57 EDT 2022
% Result : Theorem 1.75s 1.93s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 16 ( 9 unt; 0 nHn; 16 RR)
% Number of literals : 24 ( 8 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ sorti1(A)
| op1(A,A) = dollar_c1 ),
file('ALG040+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ sorti2(A)
| sorti2(dollar_f1(A)) ),
file('ALG040+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ sorti2(A)
| op2(dollar_f1(A),dollar_f1(A)) != A ),
file('ALG040+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ sorti1(A)
| sorti2(h(A)) ),
file('ALG040+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ sorti2(A)
| sorti1(j(A)) ),
file('ALG040+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ sorti1(A)
| ~ sorti1(B)
| h(op1(A,B)) = op2(h(A),h(B)) ),
file('ALG040+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ sorti2(A)
| h(j(A)) = A ),
file('ALG040+1.p',unknown),
[] ).
cnf(13,axiom,
sorti1(dollar_c1),
file('ALG040+1.p',unknown),
[] ).
cnf(18,plain,
sorti2(h(dollar_c1)),
inference(hyper,[status(thm)],[13,6]),
[iquote('hyper,13,6')] ).
cnf(23,plain,
sorti2(dollar_f1(h(dollar_c1))),
inference(hyper,[status(thm)],[18,4]),
[iquote('hyper,18,4')] ).
cnf(25,plain,
h(j(dollar_f1(h(dollar_c1)))) = dollar_f1(h(dollar_c1)),
inference(hyper,[status(thm)],[23,10]),
[iquote('hyper,23,10')] ).
cnf(32,plain,
sorti1(j(dollar_f1(h(dollar_c1)))),
inference(hyper,[status(thm)],[23,7]),
[iquote('hyper,23,7')] ).
cnf(37,plain,
h(op1(j(dollar_f1(h(dollar_c1))),j(dollar_f1(h(dollar_c1))))) = op2(dollar_f1(h(dollar_c1)),dollar_f1(h(dollar_c1))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[32,8,32]),25,25]),
[iquote('hyper,32,8,32,demod,25,25')] ).
cnf(44,plain,
op1(j(dollar_f1(h(dollar_c1))),j(dollar_f1(h(dollar_c1)))) = dollar_c1,
inference(hyper,[status(thm)],[32,3]),
[iquote('hyper,32,3')] ).
cnf(47,plain,
op2(dollar_f1(h(dollar_c1)),dollar_f1(h(dollar_c1))) = h(dollar_c1),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[37]),44])]),
[iquote('back_demod,37,demod,44,flip.1')] ).
cnf(1377,plain,
$false,
inference(hyper,[status(thm)],[47,5,18]),
[iquote('hyper,47,5,18')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG040+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n029.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 03:46:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.75/1.93 ----- Otter 3.3f, August 2004 -----
% 1.75/1.93 The process was started by sandbox on n029.cluster.edu,
% 1.75/1.93 Wed Jul 27 03:46:44 2022
% 1.75/1.93 The command was "./otter". The process ID is 11157.
% 1.75/1.93
% 1.75/1.93 set(prolog_style_variables).
% 1.75/1.93 set(auto).
% 1.75/1.93 dependent: set(auto1).
% 1.75/1.93 dependent: set(process_input).
% 1.75/1.93 dependent: clear(print_kept).
% 1.75/1.93 dependent: clear(print_new_demod).
% 1.75/1.93 dependent: clear(print_back_demod).
% 1.75/1.93 dependent: clear(print_back_sub).
% 1.75/1.93 dependent: set(control_memory).
% 1.75/1.93 dependent: assign(max_mem, 12000).
% 1.75/1.93 dependent: assign(pick_given_ratio, 4).
% 1.75/1.93 dependent: assign(stats_level, 1).
% 1.75/1.93 dependent: assign(max_seconds, 10800).
% 1.75/1.93 clear(print_given).
% 1.75/1.93
% 1.75/1.93 formula_list(usable).
% 1.75/1.93 all A (A=A).
% 1.75/1.93 all U (sorti1(U)-> (all V (sorti1(V)->sorti1(op1(U,V))))).
% 1.75/1.93 all U (sorti2(U)-> (all V (sorti2(V)->sorti2(op2(U,V))))).
% 1.75/1.93 exists U (sorti1(U)& (all V (sorti1(V)->op1(V,V)=U))).
% 1.75/1.93 -(exists U (sorti2(U)& (all V (sorti2(V)->op2(V,V)=U)))).
% 1.75/1.93 -((all U (sorti1(U)->sorti2(h(U))))& (all V (sorti2(V)->sorti1(j(V))))-> -((all W (sorti1(W)-> (all X (sorti1(X)->h(op1(W,X))=op2(h(W),h(X))))))& (all Y (sorti2(Y)-> (all Z (sorti2(Z)->j(op2(Y,Z))=op1(j(Y),j(Z))))))& (all X1 (sorti2(X1)->h(j(X1))=X1))& (all X2 (sorti1(X2)->j(h(X2))=X2)))).
% 1.75/1.93 end_of_list.
% 1.75/1.93
% 1.75/1.93 -------> usable clausifies to:
% 1.75/1.93
% 1.75/1.93 list(usable).
% 1.75/1.93 0 [] A=A.
% 1.75/1.93 0 [] -sorti1(U)| -sorti1(V)|sorti1(op1(U,V)).
% 1.75/1.93 0 [] -sorti2(U)| -sorti2(V)|sorti2(op2(U,V)).
% 1.75/1.93 0 [] sorti1($c1).
% 1.75/1.93 0 [] -sorti1(V)|op1(V,V)=$c1.
% 1.75/1.93 0 [] -sorti2(U)|sorti2($f1(U)).
% 1.75/1.93 0 [] -sorti2(U)|op2($f1(U),$f1(U))!=U.
% 1.75/1.93 0 [] -sorti1(U)|sorti2(h(U)).
% 1.75/1.93 0 [] -sorti2(V)|sorti1(j(V)).
% 1.75/1.93 0 [] -sorti1(W)| -sorti1(X)|h(op1(W,X))=op2(h(W),h(X)).
% 1.75/1.93 0 [] -sorti2(Y)| -sorti2(Z)|j(op2(Y,Z))=op1(j(Y),j(Z)).
% 1.75/1.93 0 [] -sorti2(X1)|h(j(X1))=X1.
% 1.75/1.93 0 [] -sorti1(X2)|j(h(X2))=X2.
% 1.75/1.93 end_of_list.
% 1.75/1.93
% 1.75/1.93 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.75/1.93
% 1.75/1.93 This is a Horn set with equality. The strategy will be
% 1.75/1.93 Knuth-Bendix and hyper_res, with positive clauses in
% 1.75/1.93 sos and nonpositive clauses in usable.
% 1.75/1.93
% 1.75/1.93 dependent: set(knuth_bendix).
% 1.75/1.93 dependent: set(anl_eq).
% 1.75/1.93 dependent: set(para_from).
% 1.75/1.93 dependent: set(para_into).
% 1.75/1.93 dependent: clear(para_from_right).
% 1.75/1.93 dependent: clear(para_into_right).
% 1.75/1.93 dependent: set(para_from_vars).
% 1.75/1.93 dependent: set(eq_units_both_ways).
% 1.75/1.93 dependent: set(dynamic_demod_all).
% 1.75/1.93 dependent: set(dynamic_demod).
% 1.75/1.93 dependent: set(order_eq).
% 1.75/1.93 dependent: set(back_demod).
% 1.75/1.93 dependent: set(lrpo).
% 1.75/1.93 dependent: set(hyper_res).
% 1.75/1.93 dependent: clear(order_hyper).
% 1.75/1.93
% 1.75/1.93 ------------> process usable:
% 1.75/1.93 ** KEPT (pick-wt=8): 1 [] -sorti1(A)| -sorti1(B)|sorti1(op1(A,B)).
% 1.75/1.93 ** KEPT (pick-wt=8): 2 [] -sorti2(A)| -sorti2(B)|sorti2(op2(A,B)).
% 1.75/1.93 ** KEPT (pick-wt=7): 3 [] -sorti1(A)|op1(A,A)=$c1.
% 1.75/1.93 ** KEPT (pick-wt=5): 4 [] -sorti2(A)|sorti2($f1(A)).
% 1.75/1.93 ** KEPT (pick-wt=9): 5 [] -sorti2(A)|op2($f1(A),$f1(A))!=A.
% 1.75/1.93 ** KEPT (pick-wt=5): 6 [] -sorti1(A)|sorti2(h(A)).
% 1.75/1.93 ** KEPT (pick-wt=5): 7 [] -sorti2(A)|sorti1(j(A)).
% 1.75/1.93 ** KEPT (pick-wt=14): 8 [] -sorti1(A)| -sorti1(B)|h(op1(A,B))=op2(h(A),h(B)).
% 1.75/1.93 ** KEPT (pick-wt=14): 9 [] -sorti2(A)| -sorti2(B)|j(op2(A,B))=op1(j(A),j(B)).
% 1.75/1.93 ** KEPT (pick-wt=7): 10 [] -sorti2(A)|h(j(A))=A.
% 1.75/1.93 ** KEPT (pick-wt=7): 11 [] -sorti1(A)|j(h(A))=A.
% 1.75/1.93
% 1.75/1.93 ------------> process sos:
% 1.75/1.93 ** KEPT (pick-wt=3): 12 [] A=A.
% 1.75/1.93 ** KEPT (pick-wt=2): 13 [] sorti1($c1).
% 1.75/1.93 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] A=A.
% 1.75/1.93
% 1.75/1.93 ======= end of input processing =======
% 1.75/1.93
% 1.75/1.93 =========== start of search ===========
% 1.75/1.93
% 1.75/1.93
% 1.75/1.93 Resetting weight limit to 11.
% 1.75/1.93
% 1.75/1.93
% 1.75/1.93 Resetting weight limit to 11.
% 1.75/1.93
% 1.75/1.93 sos_size=827
% 1.75/1.93
% 1.75/1.93 -------- PROOF --------
% 1.75/1.93
% 1.75/1.93 -----> EMPTY CLAUSE at 0.02 sec ----> 1377 [hyper,47,5,18] $F.
% 1.75/1.93
% 1.75/1.93 Length of proof is 7. Level of proof is 5.
% 1.75/1.93
% 1.75/1.93 ---------------- PROOF ----------------
% 1.75/1.93 % SZS status Theorem
% 1.75/1.93 % SZS output start Refutation
% See solution above
% 1.75/1.93 ------------ end of proof -------------
% 1.75/1.93
% 1.75/1.93
% 1.75/1.93 Search stopped by max_proofs option.
% 1.75/1.93
% 1.75/1.93
% 1.75/1.93 Search stopped by max_proofs option.
% 1.75/1.93
% 1.75/1.93 ============ end of search ============
% 1.75/1.93
% 1.75/1.93 -------------- statistics -------------
% 1.75/1.93 clauses given 46
% 1.75/1.93 clauses generated 1462
% 1.75/1.93 clauses kept 918
% 1.75/1.93 clauses forward subsumed 185
% 1.75/1.93 clauses back subsumed 0
% 1.75/1.93 Kbytes malloced 4882
% 1.75/1.93
% 1.75/1.93 ----------- times (seconds) -----------
% 1.75/1.93 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.75/1.93 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.93 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.75/1.93
% 1.75/1.93 That finishes the proof of the theorem.
% 1.75/1.93
% 1.75/1.93 Process 11157 finished Wed Jul 27 03:46:45 2022
% 1.75/1.93 Otter interrupted
% 1.75/1.93 PROOF FOUND
%------------------------------------------------------------------------------