TSTP Solution File: ALG074+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ALG074+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 12:46:01 EDT 2022
% Result : Theorem 1.90s 2.09s
% Output : Refutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 13
% Syntax : Number of clauses : 28 ( 21 unt; 1 nHn; 27 RR)
% Number of literals : 42 ( 20 equ; 16 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 : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ sorti1(A)
| ~ sorti1(B)
| sorti1(op1(A,B)) ),
file('ALG074+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ sorti2(A)
| ~ sorti2(B)
| sorti2(op2(A,B)) ),
file('ALG074+1.p',unknown),
[] ).
cnf(3,axiom,
op1(dollar_c1,dollar_c2) != op1(dollar_c2,dollar_c1),
file('ALG074+1.p',unknown),
[] ).
cnf(4,plain,
op1(dollar_c2,dollar_c1) != op1(dollar_c1,dollar_c2),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[3])]),
[iquote('copy,3,flip.1')] ).
cnf(5,axiom,
op1(op1(dollar_c2,dollar_c1),dollar_c2) != dollar_c1,
file('ALG074+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ sorti2(A)
| ~ sorti2(B)
| op2(B,A) = op2(A,B)
| op2(op2(A,B),B) != A
| op2(op2(A,B),A) = B ),
file('ALG074+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ sorti1(A)
| sorti2(h(A)) ),
file('ALG074+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ sorti1(A)
| ~ sorti1(B)
| h(op1(A,B)) = op2(h(A),h(B)) ),
file('ALG074+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ sorti2(A)
| ~ sorti2(B)
| j(op2(A,B)) = op1(j(A),j(B)) ),
file('ALG074+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ sorti1(A)
| j(h(A)) = A ),
file('ALG074+1.p',unknown),
[] ).
cnf(17,axiom,
A = A,
file('ALG074+1.p',unknown),
[] ).
cnf(18,axiom,
sorti1(dollar_c2),
file('ALG074+1.p',unknown),
[] ).
cnf(19,axiom,
sorti1(dollar_c1),
file('ALG074+1.p',unknown),
[] ).
cnf(20,axiom,
op1(op1(dollar_c2,dollar_c1),dollar_c1) = dollar_c2,
file('ALG074+1.p',unknown),
[] ).
cnf(26,plain,
j(h(dollar_c2)) = dollar_c2,
inference(hyper,[status(thm)],[18,12]),
[iquote('hyper,18,12')] ).
cnf(27,plain,
sorti2(h(dollar_c2)),
inference(hyper,[status(thm)],[18,7]),
[iquote('hyper,18,7')] ).
cnf(32,plain,
j(h(dollar_c1)) = dollar_c1,
inference(hyper,[status(thm)],[19,12]),
[iquote('hyper,19,12')] ).
cnf(34,plain,
h(op1(dollar_c2,dollar_c1)) = op2(h(dollar_c2),h(dollar_c1)),
inference(hyper,[status(thm)],[19,9,18]),
[iquote('hyper,19,9,18')] ).
cnf(37,plain,
sorti2(h(dollar_c1)),
inference(hyper,[status(thm)],[19,7]),
[iquote('hyper,19,7')] ).
cnf(38,plain,
sorti1(op1(dollar_c2,dollar_c1)),
inference(hyper,[status(thm)],[19,1,18]),
[iquote('hyper,19,1,18')] ).
cnf(47,plain,
j(op2(h(dollar_c2),h(dollar_c1))) = op1(dollar_c2,dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[37,10,27]),26,32]),
[iquote('hyper,37,10,27,demod,26,32')] ).
cnf(48,plain,
j(op2(h(dollar_c1),h(dollar_c2))) = op1(dollar_c1,dollar_c2),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[37,10,27]),32,26]),
[iquote('hyper,37,10,27,demod,32,26')] ).
cnf(50,plain,
sorti2(op2(h(dollar_c2),h(dollar_c1))),
inference(hyper,[status(thm)],[37,2,27]),
[iquote('hyper,37,2,27')] ).
cnf(53,plain,
op2(op2(h(dollar_c2),h(dollar_c1)),h(dollar_c1)) = h(dollar_c2),
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[20,9]),34]),38,19])]),
[iquote('para_from,20.1.1,9.3.1.1,demod,34,unit_del,38,19,flip.1')] ).
cnf(198,plain,
j(op2(op2(h(dollar_c2),h(dollar_c1)),h(dollar_c2))) = op1(op1(dollar_c2,dollar_c1),dollar_c2),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[50,10,27]),47,26]),
[iquote('hyper,50,10,27,demod,47,26')] ).
cnf(2486,plain,
op2(op2(h(dollar_c2),h(dollar_c1)),h(dollar_c2)) = h(dollar_c1),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[48,6]),47,53]),4,27,37,17]),
[iquote('para_into,48.1.1.1,6.3.1,demod,47,53,unit_del,4,27,37,17')] ).
cnf(2597,plain,
op1(op1(dollar_c2,dollar_c1),dollar_c2) = dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[198]),2486,32])]),
[iquote('back_demod,198,demod,2486,32,flip.1')] ).
cnf(2599,plain,
$false,
inference(binary,[status(thm)],[2597,5]),
[iquote('binary,2597.1,5.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG074+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n022.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 03:57:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.90/2.09 ----- Otter 3.3f, August 2004 -----
% 1.90/2.09 The process was started by sandbox2 on n022.cluster.edu,
% 1.90/2.09 Wed Jul 27 03:57:50 2022
% 1.90/2.09 The command was "./otter". The process ID is 18518.
% 1.90/2.09
% 1.90/2.09 set(prolog_style_variables).
% 1.90/2.09 set(auto).
% 1.90/2.09 dependent: set(auto1).
% 1.90/2.09 dependent: set(process_input).
% 1.90/2.09 dependent: clear(print_kept).
% 1.90/2.09 dependent: clear(print_new_demod).
% 1.90/2.09 dependent: clear(print_back_demod).
% 1.90/2.09 dependent: clear(print_back_sub).
% 1.90/2.09 dependent: set(control_memory).
% 1.90/2.09 dependent: assign(max_mem, 12000).
% 1.90/2.09 dependent: assign(pick_given_ratio, 4).
% 1.90/2.09 dependent: assign(stats_level, 1).
% 1.90/2.09 dependent: assign(max_seconds, 10800).
% 1.90/2.09 clear(print_given).
% 1.90/2.09
% 1.90/2.09 formula_list(usable).
% 1.90/2.09 all A (A=A).
% 1.90/2.09 all U (sorti1(U)-> (all V (sorti1(V)->sorti1(op1(U,V))))).
% 1.90/2.09 all U (sorti2(U)-> (all V (sorti2(V)->sorti2(op2(U,V))))).
% 1.90/2.09 exists U (sorti1(U)& (exists V (sorti1(V)&op1(V,U)!=op1(U,V)&op1(op1(U,V),V)=U&op1(op1(U,V),U)!=V))).
% 1.90/2.09 -(exists U (sorti2(U)& (exists V (sorti2(V)&op2(V,U)!=op2(U,V)&op2(op2(U,V),V)=U&op2(op2(U,V),U)!=V)))).
% 1.90/2.09 -((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)))).
% 1.90/2.09 end_of_list.
% 1.90/2.09
% 1.90/2.09 -------> usable clausifies to:
% 1.90/2.09
% 1.90/2.09 list(usable).
% 1.90/2.09 0 [] A=A.
% 1.90/2.09 0 [] -sorti1(U)| -sorti1(V)|sorti1(op1(U,V)).
% 1.90/2.09 0 [] -sorti2(U)| -sorti2(V)|sorti2(op2(U,V)).
% 1.90/2.09 0 [] sorti1($c2).
% 1.90/2.09 0 [] sorti1($c1).
% 1.90/2.09 0 [] op1($c1,$c2)!=op1($c2,$c1).
% 1.90/2.09 0 [] op1(op1($c2,$c1),$c1)=$c2.
% 1.90/2.09 0 [] op1(op1($c2,$c1),$c2)!=$c1.
% 1.90/2.09 0 [] -sorti2(U)| -sorti2(V)|op2(V,U)=op2(U,V)|op2(op2(U,V),V)!=U|op2(op2(U,V),U)=V.
% 1.90/2.09 0 [] -sorti1(U)|sorti2(h(U)).
% 1.90/2.09 0 [] -sorti2(V)|sorti1(j(V)).
% 1.90/2.09 0 [] -sorti1(W)| -sorti1(X)|h(op1(W,X))=op2(h(W),h(X)).
% 1.90/2.09 0 [] -sorti2(Y)| -sorti2(Z)|j(op2(Y,Z))=op1(j(Y),j(Z)).
% 1.90/2.09 0 [] -sorti2(X1)|h(j(X1))=X1.
% 1.90/2.09 0 [] -sorti1(X2)|j(h(X2))=X2.
% 1.90/2.09 end_of_list.
% 1.90/2.09
% 1.90/2.09 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.90/2.09
% 1.90/2.09 This ia a non-Horn set with equality. The strategy will be
% 1.90/2.09 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.90/2.09 deletion, with positive clauses in sos and nonpositive
% 1.90/2.09 clauses in usable.
% 1.90/2.09
% 1.90/2.09 dependent: set(knuth_bendix).
% 1.90/2.09 dependent: set(anl_eq).
% 1.90/2.09 dependent: set(para_from).
% 1.90/2.09 dependent: set(para_into).
% 1.90/2.09 dependent: clear(para_from_right).
% 1.90/2.09 dependent: clear(para_into_right).
% 1.90/2.09 dependent: set(para_from_vars).
% 1.90/2.09 dependent: set(eq_units_both_ways).
% 1.90/2.09 dependent: set(dynamic_demod_all).
% 1.90/2.09 dependent: set(dynamic_demod).
% 1.90/2.09 dependent: set(order_eq).
% 1.90/2.09 dependent: set(back_demod).
% 1.90/2.09 dependent: set(lrpo).
% 1.90/2.09 dependent: set(hyper_res).
% 1.90/2.09 dependent: set(unit_deletion).
% 1.90/2.09 dependent: set(factor).
% 1.90/2.09
% 1.90/2.09 ------------> process usable:
% 1.90/2.09 ** KEPT (pick-wt=8): 1 [] -sorti1(A)| -sorti1(B)|sorti1(op1(A,B)).
% 1.90/2.09 ** KEPT (pick-wt=8): 2 [] -sorti2(A)| -sorti2(B)|sorti2(op2(A,B)).
% 1.90/2.09 ** KEPT (pick-wt=7): 4 [copy,3,flip.1] op1($c2,$c1)!=op1($c1,$c2).
% 1.90/2.09 ** KEPT (pick-wt=7): 5 [] op1(op1($c2,$c1),$c2)!=$c1.
% 1.90/2.09 ** KEPT (pick-wt=25): 6 [] -sorti2(A)| -sorti2(B)|op2(B,A)=op2(A,B)|op2(op2(A,B),B)!=A|op2(op2(A,B),A)=B.
% 1.90/2.09 ** KEPT (pick-wt=5): 7 [] -sorti1(A)|sorti2(h(A)).
% 1.90/2.09 ** KEPT (pick-wt=5): 8 [] -sorti2(A)|sorti1(j(A)).
% 1.90/2.09 ** KEPT (pick-wt=14): 9 [] -sorti1(A)| -sorti1(B)|h(op1(A,B))=op2(h(A),h(B)).
% 1.90/2.09 ** KEPT (pick-wt=14): 10 [] -sorti2(A)| -sorti2(B)|j(op2(A,B))=op1(j(A),j(B)).
% 1.90/2.09 ** KEPT (pick-wt=7): 11 [] -sorti2(A)|h(j(A))=A.
% 1.90/2.09 ** KEPT (pick-wt=7): 12 [] -sorti1(A)|j(h(A))=A.
% 1.90/2.09
% 1.90/2.09 ------------> process sos:
% 1.90/2.09 ** KEPT (pick-wt=3): 17 [] A=A.
% 1.90/2.09 ** KEPT (pick-wt=2): 18 [] sorti1($c2).
% 1.90/2.09 ** KEPT (pick-wt=2): 19 [] sorti1($c1).
% 1.90/2.09 ** KEPT (pick-wt=7): 20 [] op1(op1($c2,$c1),$c1)=$c2.
% 1.90/2.09 ---> New Demodulator: 21 [new_demod,20] op1(op1($c2,$c1),$c1)=$c2.
% 1.90/2.09 Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] A=A.
% 1.90/2.09 >>>> Starting back demodulation with 21.
% 1.90/2.09
% 1.90/2.09 ======= end of input processing =======
% 1.90/2.09
% 1.90/2.09 =========== start of search ===========
% 1.90/2.09
% 1.90/2.09 -------- PROOF --------
% 1.90/2.09
% 1.90/2.09 ----> UNIT CONFLICT at 0.09 sec ----> 2599 [binary,2597.1,5.1] $F.
% 1.90/2.09
% 1.90/2.09 Length of proof is 14. Level of proof is 4.
% 1.90/2.09
% 1.90/2.09 ---------------- PROOF ----------------
% 1.90/2.09 % SZS status Theorem
% 1.90/2.09 % SZS output start Refutation
% See solution above
% 1.90/2.09 ------------ end of proof -------------
% 1.90/2.09
% 1.90/2.09
% 1.90/2.09 Search stopped by max_proofs option.
% 1.90/2.09
% 1.90/2.09
% 1.90/2.09 Search stopped by max_proofs option.
% 1.90/2.09
% 1.90/2.09 ============ end of search ============
% 1.90/2.09
% 1.90/2.09 -------------- statistics -------------
% 1.90/2.09 clauses given 46
% 1.90/2.09 clauses generated 1925
% 1.90/2.09 clauses kept 1718
% 1.90/2.09 clauses forward subsumed 275
% 1.90/2.09 clauses back subsumed 0
% 1.90/2.09 Kbytes malloced 2929
% 1.90/2.09
% 1.90/2.09 ----------- times (seconds) -----------
% 1.90/2.09 user CPU time 0.09 (0 hr, 0 min, 0 sec)
% 1.90/2.09 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.90/2.09 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.90/2.09
% 1.90/2.09 That finishes the proof of the theorem.
% 1.90/2.09
% 1.90/2.09 Process 18518 finished Wed Jul 27 03:57:52 2022
% 1.90/2.09 Otter interrupted
% 1.90/2.09 PROOF FOUND
%------------------------------------------------------------------------------