TSTP Solution File: ALG073+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ALG073+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 12:46:00 EDT 2022
% Result : Theorem 1.83s 2.00s
% Output : Refutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of clauses : 25 ( 20 unt; 0 nHn; 24 RR)
% Number of literals : 35 ( 18 equ; 11 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 9 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ sorti1(A)
| ~ sorti1(B)
| sorti1(op1(A,B)) ),
file('ALG073+1.p',unknown),
[] ).
cnf(3,axiom,
op1(dollar_c2,dollar_c1) != dollar_c2,
file('ALG073+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ sorti2(A)
| ~ sorti2(B)
| op2(A,A) != B
| op2(B,B) != A
| op2(A,B) = A ),
file('ALG073+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ sorti1(A)
| sorti2(h(A)) ),
file('ALG073+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ sorti1(A)
| ~ sorti1(B)
| h(op1(A,B)) = op2(h(A),h(B)) ),
file('ALG073+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ sorti1(A)
| j(h(A)) = A ),
file('ALG073+1.p',unknown),
[] ).
cnf(11,axiom,
A = A,
file('ALG073+1.p',unknown),
[] ).
cnf(12,axiom,
sorti1(dollar_c2),
file('ALG073+1.p',unknown),
[] ).
cnf(13,axiom,
sorti1(dollar_c1),
file('ALG073+1.p',unknown),
[] ).
cnf(15,axiom,
op1(dollar_c2,dollar_c2) = dollar_c1,
file('ALG073+1.p',unknown),
[] ).
cnf(17,axiom,
op1(dollar_c1,dollar_c1) = dollar_c2,
file('ALG073+1.p',unknown),
[] ).
cnf(18,plain,
j(h(dollar_c2)) = dollar_c2,
inference(hyper,[status(thm)],[12,10]),
[iquote('hyper,12,10')] ).
cnf(20,plain,
op2(h(dollar_c2),h(dollar_c2)) = h(dollar_c1),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[12,7,12]),15])]),
[iquote('hyper,12,7,12,demod,15,flip.1')] ).
cnf(22,plain,
sorti2(h(dollar_c2)),
inference(hyper,[status(thm)],[12,5]),
[iquote('hyper,12,5')] ).
cnf(26,plain,
h(dollar_c2) = op2(h(dollar_c1),h(dollar_c1)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[13,7,13]),17]),
[iquote('hyper,13,7,13,demod,17')] ).
cnf(28,plain,
h(op1(dollar_c2,dollar_c1)) = op2(op2(h(dollar_c1),h(dollar_c1)),h(dollar_c1)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[13,7,12]),26]),
[iquote('hyper,13,7,12,demod,26')] ).
cnf(31,plain,
sorti2(h(dollar_c1)),
inference(hyper,[status(thm)],[13,5]),
[iquote('hyper,13,5')] ).
cnf(32,plain,
sorti1(op1(dollar_c2,dollar_c1)),
inference(hyper,[status(thm)],[13,1,12]),
[iquote('hyper,13,1,12')] ).
cnf(34,plain,
sorti2(op2(h(dollar_c1),h(dollar_c1))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[22]),26]),
[iquote('back_demod,22,demod,26')] ).
cnf(35,plain,
op2(op2(h(dollar_c1),h(dollar_c1)),op2(h(dollar_c1),h(dollar_c1))) = h(dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[20]),26,26]),
[iquote('back_demod,20,demod,26,26')] ).
cnf(38,plain,
j(op2(h(dollar_c1),h(dollar_c1))) = dollar_c2,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[18]),26]),
[iquote('back_demod,18,demod,26')] ).
cnf(39,plain,
j(op2(op2(h(dollar_c1),h(dollar_c1)),h(dollar_c1))) = op1(dollar_c2,dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[32,10]),28]),
[iquote('hyper,32,10,demod,28')] ).
cnf(745,plain,
op2(op2(h(dollar_c1),h(dollar_c1)),h(dollar_c1)) = op2(h(dollar_c1),h(dollar_c1)),
inference(hyper,[status(thm)],[35,4,34,31,11]),
[iquote('hyper,35,4,34,31,11')] ).
cnf(1190,plain,
op1(dollar_c2,dollar_c1) = dollar_c2,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[39]),745,38])]),
[iquote('back_demod,39,demod,745,38,flip.1')] ).
cnf(1192,plain,
$false,
inference(binary,[status(thm)],[1190,3]),
[iquote('binary,1190.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ALG073+1 : TPTP v8.1.0. Released v2.7.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Jul 27 03:41:39 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.83/2.00 ----- Otter 3.3f, August 2004 -----
% 1.83/2.00 The process was started by sandbox on n014.cluster.edu,
% 1.83/2.00 Wed Jul 27 03:41:39 2022
% 1.83/2.00 The command was "./otter". The process ID is 31930.
% 1.83/2.00
% 1.83/2.00 set(prolog_style_variables).
% 1.83/2.00 set(auto).
% 1.83/2.00 dependent: set(auto1).
% 1.83/2.00 dependent: set(process_input).
% 1.83/2.00 dependent: clear(print_kept).
% 1.83/2.00 dependent: clear(print_new_demod).
% 1.83/2.00 dependent: clear(print_back_demod).
% 1.83/2.00 dependent: clear(print_back_sub).
% 1.83/2.00 dependent: set(control_memory).
% 1.83/2.00 dependent: assign(max_mem, 12000).
% 1.83/2.00 dependent: assign(pick_given_ratio, 4).
% 1.83/2.00 dependent: assign(stats_level, 1).
% 1.83/2.00 dependent: assign(max_seconds, 10800).
% 1.83/2.00 clear(print_given).
% 1.83/2.00
% 1.83/2.00 formula_list(usable).
% 1.83/2.00 all A (A=A).
% 1.83/2.00 all U (sorti1(U)-> (all V (sorti1(V)->sorti1(op1(U,V))))).
% 1.83/2.00 all U (sorti2(U)-> (all V (sorti2(V)->sorti2(op2(U,V))))).
% 1.83/2.00 exists U (sorti1(U)& (exists V (sorti1(V)&op1(U,U)=V&op1(V,V)=U&op1(U,V)!=U))).
% 1.83/2.00 -(exists U (sorti2(U)& (exists V (sorti2(V)&op2(U,U)=V&op2(V,V)=U&op2(U,V)!=U)))).
% 1.83/2.00 -((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)))).
% 1.83/2.00 end_of_list.
% 1.83/2.00
% 1.83/2.00 -------> usable clausifies to:
% 1.83/2.00
% 1.83/2.00 list(usable).
% 1.83/2.00 0 [] A=A.
% 1.83/2.00 0 [] -sorti1(U)| -sorti1(V)|sorti1(op1(U,V)).
% 1.83/2.00 0 [] -sorti2(U)| -sorti2(V)|sorti2(op2(U,V)).
% 1.83/2.00 0 [] sorti1($c2).
% 1.83/2.00 0 [] sorti1($c1).
% 1.83/2.00 0 [] op1($c2,$c2)=$c1.
% 1.83/2.00 0 [] op1($c1,$c1)=$c2.
% 1.83/2.00 0 [] op1($c2,$c1)!=$c2.
% 1.83/2.00 0 [] -sorti2(U)| -sorti2(V)|op2(U,U)!=V|op2(V,V)!=U|op2(U,V)=U.
% 1.83/2.00 0 [] -sorti1(U)|sorti2(h(U)).
% 1.83/2.00 0 [] -sorti2(V)|sorti1(j(V)).
% 1.83/2.00 0 [] -sorti1(W)| -sorti1(X)|h(op1(W,X))=op2(h(W),h(X)).
% 1.83/2.00 0 [] -sorti2(Y)| -sorti2(Z)|j(op2(Y,Z))=op1(j(Y),j(Z)).
% 1.83/2.00 0 [] -sorti2(X1)|h(j(X1))=X1.
% 1.83/2.00 0 [] -sorti1(X2)|j(h(X2))=X2.
% 1.83/2.00 end_of_list.
% 1.83/2.00
% 1.83/2.00 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=5.
% 1.83/2.00
% 1.83/2.00 This is a Horn set with equality. The strategy will be
% 1.83/2.00 Knuth-Bendix and hyper_res, with positive clauses in
% 1.83/2.00 sos and nonpositive clauses in usable.
% 1.83/2.00
% 1.83/2.00 dependent: set(knuth_bendix).
% 1.83/2.00 dependent: set(anl_eq).
% 1.83/2.00 dependent: set(para_from).
% 1.83/2.00 dependent: set(para_into).
% 1.83/2.00 dependent: clear(para_from_right).
% 1.83/2.00 dependent: clear(para_into_right).
% 1.83/2.00 dependent: set(para_from_vars).
% 1.83/2.00 dependent: set(eq_units_both_ways).
% 1.83/2.00 dependent: set(dynamic_demod_all).
% 1.83/2.00 dependent: set(dynamic_demod).
% 1.83/2.00 dependent: set(order_eq).
% 1.83/2.00 dependent: set(back_demod).
% 1.83/2.00 dependent: set(lrpo).
% 1.83/2.00 dependent: set(hyper_res).
% 1.83/2.00 dependent: clear(order_hyper).
% 1.83/2.00
% 1.83/2.00 ------------> process usable:
% 1.83/2.00 ** KEPT (pick-wt=8): 1 [] -sorti1(A)| -sorti1(B)|sorti1(op1(A,B)).
% 1.83/2.00 ** KEPT (pick-wt=8): 2 [] -sorti2(A)| -sorti2(B)|sorti2(op2(A,B)).
% 1.83/2.00 ** KEPT (pick-wt=5): 3 [] op1($c2,$c1)!=$c2.
% 1.83/2.00 ** KEPT (pick-wt=19): 4 [] -sorti2(A)| -sorti2(B)|op2(A,A)!=B|op2(B,B)!=A|op2(A,B)=A.
% 1.83/2.00 ** KEPT (pick-wt=5): 5 [] -sorti1(A)|sorti2(h(A)).
% 1.83/2.00 ** KEPT (pick-wt=5): 6 [] -sorti2(A)|sorti1(j(A)).
% 1.83/2.00 ** KEPT (pick-wt=14): 7 [] -sorti1(A)| -sorti1(B)|h(op1(A,B))=op2(h(A),h(B)).
% 1.83/2.00 ** KEPT (pick-wt=14): 8 [] -sorti2(A)| -sorti2(B)|j(op2(A,B))=op1(j(A),j(B)).
% 1.83/2.00 ** KEPT (pick-wt=7): 9 [] -sorti2(A)|h(j(A))=A.
% 1.83/2.00 ** KEPT (pick-wt=7): 10 [] -sorti1(A)|j(h(A))=A.
% 1.83/2.00
% 1.83/2.00 ------------> process sos:
% 1.83/2.00 ** KEPT (pick-wt=3): 11 [] A=A.
% 1.83/2.00 ** KEPT (pick-wt=2): 12 [] sorti1($c2).
% 1.83/2.00 ** KEPT (pick-wt=2): 13 [] sorti1($c1).
% 1.83/2.00 ** KEPT (pick-wt=5): 14 [] op1($c2,$c2)=$c1.
% 1.83/2.00 ---> New Demodulator: 15 [new_demod,14] op1($c2,$c2)=$c1.
% 1.83/2.00 ** KEPT (pick-wt=5): 16 [] op1($c1,$c1)=$c2.
% 1.83/2.00 ---> New Demodulator: 17 [new_demod,16] op1($c1,$c1)=$c2.
% 1.83/2.00 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] A=A.
% 1.83/2.00 >>>> Starting back demodulation with 15.
% 1.83/2.00 >>>> Starting back demodulation with 17.
% 1.83/2.00
% 1.83/2.00 ======= end of input processing =======
% 1.83/2.00
% 1.83/2.00 =========== start of search ===========
% 1.83/2.00
% 1.83/2.00 -------- PROOF --------
% 1.83/2.00
% 1.83/2.00 ----> UNIT CONFLICT at 0.03 sec ----> 1192 [binary,1190.1,3.1] $F.
% 1.83/2.00
% 1.83/2.00 Length of proof is 13. Level of proof is 4.
% 1.83/2.00
% 1.83/2.00 ---------------- PROOF ----------------
% 1.83/2.00 % SZS status Theorem
% 1.83/2.00 % SZS output start Refutation
% See solution above
% 1.83/2.00 ------------ end of proof -------------
% 1.83/2.00
% 1.83/2.00
% 1.83/2.00 Search stopped by max_proofs option.
% 1.83/2.00
% 1.83/2.00
% 1.83/2.00 Search stopped by max_proofs option.
% 1.83/2.00
% 1.83/2.00 ============ end of search ============
% 1.83/2.00
% 1.83/2.00 -------------- statistics -------------
% 1.83/2.00 clauses given 26
% 1.83/2.00 clauses generated 566
% 1.83/2.00 clauses kept 722
% 1.83/2.00 clauses forward subsumed 110
% 1.83/2.00 clauses back subsumed 0
% 1.83/2.00 Kbytes malloced 1953
% 1.83/2.00
% 1.83/2.00 ----------- times (seconds) -----------
% 1.83/2.00 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.83/2.00 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.83/2.00 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.83/2.00
% 1.83/2.00 That finishes the proof of the theorem.
% 1.83/2.00
% 1.83/2.00 Process 31930 finished Wed Jul 27 03:41:41 2022
% 1.83/2.00 Otter interrupted
% 1.83/2.01 PROOF FOUND
%------------------------------------------------------------------------------