TSTP Solution File: ALG030-10 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ALG030-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 12:45:56 EDT 2022
% Result : Unsatisfiable 1.81s 1.98s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 15 RR)
% Number of literals : 27 ( 26 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-4 aty)
% Number of variables : 19 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
op1(sK2_ax3_U,sK1_ax3_V) != op1(sK1_ax3_V,sK2_ax3_U),
file('ALG030-10.p',unknown),
[] ).
cnf(4,axiom,
ife_q2(A,A,B,C) = B,
file('ALG030-10.p',unknown),
[] ).
cnf(6,axiom,
ife_q(A,A,B,C) = B,
file('ALG030-10.p',unknown),
[] ).
cnf(7,axiom,
ife_q(sorti1(A),true,ife_q(sorti1(B),true,sorti1(op1(B,A)),true),true) = true,
file('ALG030-10.p',unknown),
[] ).
cnf(11,axiom,
sorti1(sK1_ax3_V) = true,
file('ALG030-10.p',unknown),
[] ).
cnf(13,axiom,
sorti1(sK2_ax3_U) = true,
file('ALG030-10.p',unknown),
[] ).
cnf(15,axiom,
ife_q2(sorti2(A),true,ife_q2(sorti2(B),true,op2(B,A),op2(A,B)),op2(A,B)) = op2(A,B),
file('ALG030-10.p',unknown),
[] ).
cnf(17,axiom,
ife_q(sorti1(A),true,sorti2(h(A)),true) = true,
file('ALG030-10.p',unknown),
[] ).
cnf(19,axiom,
ife_q2(sorti1(A),true,ife_q2(sorti1(B),true,op2(h(B),h(A)),h(op1(B,A))),h(op1(B,A))) = h(op1(B,A)),
file('ALG030-10.p',unknown),
[] ).
cnf(21,axiom,
ife_q2(sorti1(A),true,j(h(A)),A) = A,
file('ALG030-10.p',unknown),
[] ).
cnf(29,plain,
ife_q(sorti1(A),true,sorti1(op1(A,sK2_ax3_U)),true) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,13]),6]),
[iquote('para_into,7.1.1.1,13.1.1,demod,6')] ).
cnf(31,plain,
ife_q(sorti1(A),true,sorti1(op1(A,sK1_ax3_V)),true) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,11]),6]),
[iquote('para_into,7.1.1.1,11.1.1,demod,6')] ).
cnf(37,plain,
sorti2(h(sK2_ax3_U)) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[17,13]),6]),
[iquote('para_into,17.1.1.1,13.1.1,demod,6')] ).
cnf(39,plain,
sorti2(h(sK1_ax3_V)) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[17,11]),6]),
[iquote('para_into,17.1.1.1,11.1.1,demod,6')] ).
cnf(53,plain,
ife_q2(sorti2(A),true,op2(A,h(sK1_ax3_V)),op2(h(sK1_ax3_V),A)) = op2(h(sK1_ax3_V),A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,39]),4]),
[iquote('para_into,15.1.1.1,39.1.1,demod,4')] ).
cnf(63,plain,
sorti1(op1(sK1_ax3_V,sK2_ax3_U)) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[29,11]),6]),
[iquote('para_into,29.1.1.1,11.1.1,demod,6')] ).
cnf(79,plain,
j(h(op1(sK1_ax3_V,sK2_ax3_U))) = op1(sK1_ax3_V,sK2_ax3_U),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[63,21]),4]),
[iquote('para_from,63.1.1,21.1.1.1,demod,4')] ).
cnf(97,plain,
ife_q2(sorti1(A),true,op2(h(A),h(sK2_ax3_U)),h(op1(A,sK2_ax3_U))) = h(op1(A,sK2_ax3_U)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,13]),4]),
[iquote('para_into,19.1.1.1,13.1.1,demod,4')] ).
cnf(99,plain,
ife_q2(sorti1(A),true,op2(h(A),h(sK1_ax3_V)),h(op1(A,sK1_ax3_V))) = h(op1(A,sK1_ax3_V)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,11]),4]),
[iquote('para_into,19.1.1.1,11.1.1,demod,4')] ).
cnf(209,plain,
sorti1(op1(sK2_ax3_U,sK1_ax3_V)) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[31,13]),6]),
[iquote('para_into,31.1.1.1,13.1.1,demod,6')] ).
cnf(221,plain,
j(h(op1(sK2_ax3_U,sK1_ax3_V))) = op1(sK2_ax3_U,sK1_ax3_V),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[209,21]),4]),
[iquote('para_from,209.1.1,21.1.1.1,demod,4')] ).
cnf(838,plain,
op2(h(sK2_ax3_U),h(sK1_ax3_V)) = op2(h(sK1_ax3_V),h(sK2_ax3_U)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[53,37]),4]),
[iquote('para_into,53.1.1.1,37.1.1,demod,4')] ).
cnf(926,plain,
h(op1(sK1_ax3_V,sK2_ax3_U)) = op2(h(sK1_ax3_V),h(sK2_ax3_U)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[97,11]),4])]),
[iquote('para_into,97.1.1.1,11.1.1,demod,4,flip.1')] ).
cnf(930,plain,
j(op2(h(sK1_ax3_V),h(sK2_ax3_U))) = op1(sK1_ax3_V,sK2_ax3_U),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[79]),926]),
[iquote('back_demod,79,demod,926')] ).
cnf(932,plain,
h(op1(sK2_ax3_U,sK1_ax3_V)) = op2(h(sK1_ax3_V),h(sK2_ax3_U)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[99,13]),838,4])]),
[iquote('para_into,99.1.1.1,13.1.1,demod,838,4,flip.1')] ).
cnf(935,plain,
op1(sK2_ax3_U,sK1_ax3_V) = op1(sK1_ax3_V,sK2_ax3_U),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[221]),932,930])]),
[iquote('back_demod,221,demod,932,930,flip.1')] ).
cnf(937,plain,
$false,
inference(binary,[status(thm)],[935,1]),
[iquote('binary,935.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG030-10 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 03:56:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.75/1.95 ----- Otter 3.3f, August 2004 -----
% 1.75/1.95 The process was started by sandbox2 on n008.cluster.edu,
% 1.75/1.95 Wed Jul 27 03:56:53 2022
% 1.75/1.95 The command was "./otter". The process ID is 9407.
% 1.75/1.95
% 1.75/1.95 set(prolog_style_variables).
% 1.75/1.95 set(auto).
% 1.75/1.95 dependent: set(auto1).
% 1.75/1.95 dependent: set(process_input).
% 1.75/1.95 dependent: clear(print_kept).
% 1.75/1.95 dependent: clear(print_new_demod).
% 1.75/1.95 dependent: clear(print_back_demod).
% 1.75/1.95 dependent: clear(print_back_sub).
% 1.75/1.95 dependent: set(control_memory).
% 1.75/1.95 dependent: assign(max_mem, 12000).
% 1.75/1.95 dependent: assign(pick_given_ratio, 4).
% 1.75/1.95 dependent: assign(stats_level, 1).
% 1.75/1.95 dependent: assign(max_seconds, 10800).
% 1.75/1.95 clear(print_given).
% 1.75/1.95
% 1.75/1.95 list(usable).
% 1.75/1.95 0 [] A=A.
% 1.75/1.95 0 [] ife_q2(A,A,B,C)=B.
% 1.75/1.95 0 [] ife_q(A,A,B,C)=B.
% 1.75/1.95 0 [] ife_q(sorti1(V),true,ife_q(sorti1(U),true,sorti1(op1(U,V)),true),true)=true.
% 1.75/1.95 0 [] ife_q(sorti2(V),true,ife_q(sorti2(U),true,sorti2(op2(U,V)),true),true)=true.
% 1.75/1.95 0 [] op1(sK2_ax3_U,sK1_ax3_V)!=op1(sK1_ax3_V,sK2_ax3_U).
% 1.75/1.95 0 [] sorti1(sK1_ax3_V)=true.
% 1.75/1.95 0 [] sorti1(sK2_ax3_U)=true.
% 1.75/1.95 0 [] ife_q2(sorti2(V),true,ife_q2(sorti2(U),true,op2(U,V),op2(V,U)),op2(V,U))=op2(V,U).
% 1.75/1.95 0 [] ife_q(sorti1(U),true,sorti2(h(U)),true)=true.
% 1.75/1.95 0 [] ife_q2(sorti1(X),true,ife_q2(sorti1(W),true,op2(h(W),h(X)),h(op1(W,X))),h(op1(W,X)))=h(op1(W,X)).
% 1.75/1.95 0 [] ife_q2(sorti1(X2),true,j(h(X2)),X2)=X2.
% 1.75/1.95 0 [] ife_q(sorti2(V),true,sorti1(j(V)),true)=true.
% 1.75/1.95 0 [] ife_q2(sorti2(Z),true,ife_q2(sorti2(Y),true,op1(j(Y),j(Z)),j(op2(Y,Z))),j(op2(Y,Z)))=j(op2(Y,Z)).
% 1.75/1.95 0 [] ife_q2(sorti2(X1),true,h(j(X1)),X1)=X1.
% 1.75/1.95 end_of_list.
% 1.75/1.95
% 1.75/1.95 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.75/1.95
% 1.75/1.95 All clauses are units, and equality is present; the
% 1.75/1.95 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.75/1.95
% 1.75/1.95 dependent: set(knuth_bendix).
% 1.75/1.95 dependent: set(anl_eq).
% 1.75/1.95 dependent: set(para_from).
% 1.75/1.95 dependent: set(para_into).
% 1.75/1.95 dependent: clear(para_from_right).
% 1.75/1.95 dependent: clear(para_into_right).
% 1.75/1.95 dependent: set(para_from_vars).
% 1.75/1.95 dependent: set(eq_units_both_ways).
% 1.75/1.95 dependent: set(dynamic_demod_all).
% 1.75/1.95 dependent: set(dynamic_demod).
% 1.75/1.95 dependent: set(order_eq).
% 1.75/1.95 dependent: set(back_demod).
% 1.75/1.95 dependent: set(lrpo).
% 1.75/1.95
% 1.75/1.95 ------------> process usable:
% 1.75/1.95 ** KEPT (pick-wt=7): 1 [] op1(sK2_ax3_U,sK1_ax3_V)!=op1(sK1_ax3_V,sK2_ax3_U).
% 1.75/1.95
% 1.75/1.95 ------------> process sos:
% 1.75/1.95 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.75/1.95 ** KEPT (pick-wt=7): 3 [] ife_q2(A,A,B,C)=B.
% 1.75/1.95 ---> New Demodulator: 4 [new_demod,3] ife_q2(A,A,B,C)=B.
% 1.75/1.95 ** KEPT (pick-wt=7): 5 [] ife_q(A,A,B,C)=B.
% 1.75/1.95 ---> New Demodulator: 6 [new_demod,5] ife_q(A,A,B,C)=B.
% 1.75/1.95 ** KEPT (pick-wt=16): 7 [] ife_q(sorti1(A),true,ife_q(sorti1(B),true,sorti1(op1(B,A)),true),true)=true.
% 1.75/1.95 ---> New Demodulator: 8 [new_demod,7] ife_q(sorti1(A),true,ife_q(sorti1(B),true,sorti1(op1(B,A)),true),true)=true.
% 1.75/1.95 ** KEPT (pick-wt=16): 9 [] ife_q(sorti2(A),true,ife_q(sorti2(B),true,sorti2(op2(B,A)),true),true)=true.
% 1.75/1.95 ---> New Demodulator: 10 [new_demod,9] ife_q(sorti2(A),true,ife_q(sorti2(B),true,sorti2(op2(B,A)),true),true)=true.
% 1.75/1.95 ** KEPT (pick-wt=4): 11 [] sorti1(sK1_ax3_V)=true.
% 1.75/1.95 ---> New Demodulator: 12 [new_demod,11] sorti1(sK1_ax3_V)=true.
% 1.75/1.95 ** KEPT (pick-wt=4): 13 [] sorti1(sK2_ax3_U)=true.
% 1.75/1.95 ---> New Demodulator: 14 [new_demod,13] sorti1(sK2_ax3_U)=true.
% 1.75/1.95 ** KEPT (pick-wt=21): 15 [] ife_q2(sorti2(A),true,ife_q2(sorti2(B),true,op2(B,A),op2(A,B)),op2(A,B))=op2(A,B).
% 1.75/1.95 ---> New Demodulator: 16 [new_demod,15] ife_q2(sorti2(A),true,ife_q2(sorti2(B),true,op2(B,A),op2(A,B)),op2(A,B))=op2(A,B).
% 1.75/1.95 ** KEPT (pick-wt=10): 17 [] ife_q(sorti1(A),true,sorti2(h(A)),true)=true.
% 1.75/1.95 ---> New Demodulator: 18 [new_demod,17] ife_q(sorti1(A),true,sorti2(h(A)),true)=true.
% 1.75/1.95 ** KEPT (pick-wt=26): 19 [] ife_q2(sorti1(A),true,ife_q2(sorti1(B),true,op2(h(B),h(A)),h(op1(B,A))),h(op1(B,A)))=h(op1(B,A)).
% 1.75/1.95 ---> New Demodulator: 20 [new_demod,19] ife_q2(sorti1(A),true,ife_q2(sorti1(B),true,op2(h(B),h(A)),h(op1(B,A))),h(op1(B,A)))=h(op1(B,A)).
% 1.75/1.95 ** KEPT (pick-wt=10): 21 [] ife_q2(sorti1(A),true,j(h(A)),A)=A.
% 1.75/1.95 ---> New Demodulator: 22 [new_demod,21] ife_q2(sorti1(A),true,j(h(A)),A)=A.
% 1.75/1.95 ** KEPT (pick-wt=10): 23 [] ife_q(sorti2(A),true,sorti1(j(A)),true)=true.
% 1.75/1.95 ---> New Demodulator: 24 [new_demod,23] ife_q(sorti2(A),true,sorti1(j(A)),true)=true.
% 1.75/1.95 ** KEPT (pick-wt=26): 25 [] ife_q2(sorti2(A),true,ife_q2(sorti2(B),true,op1(j(B),j(A)),j(op2(B,A))),j(op2(B,A)))=j(op2(B,A)).
% 1.81/1.98 ---> New Demodulator: 26 [new_demod,25] ife_q2(sorti2(A),true,ife_q2(sorti2(B),true,op1(j(B),j(A)),j(op2(B,A))),j(op2(B,A)))=j(op2(B,A)).
% 1.81/1.98 ** KEPT (pick-wt=10): 27 [] ife_q2(sorti2(A),true,h(j(A)),A)=A.
% 1.81/1.98 ---> New Demodulator: 28 [new_demod,27] ife_q2(sorti2(A),true,h(j(A)),A)=A.
% 1.81/1.98 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.81/1.98 >>>> Starting back demodulation with 4.
% 1.81/1.98 >>>> Starting back demodulation with 6.
% 1.81/1.98 >>>> Starting back demodulation with 8.
% 1.81/1.98 >>>> Starting back demodulation with 10.
% 1.81/1.98 >>>> Starting back demodulation with 12.
% 1.81/1.98 >>>> Starting back demodulation with 14.
% 1.81/1.98 >>>> Starting back demodulation with 16.
% 1.81/1.98 >>>> Starting back demodulation with 18.
% 1.81/1.98 >>>> Starting back demodulation with 20.
% 1.81/1.98 >>>> Starting back demodulation with 22.
% 1.81/1.98 >>>> Starting back demodulation with 24.
% 1.81/1.98 >>>> Starting back demodulation with 26.
% 1.81/1.98 >>>> Starting back demodulation with 28.
% 1.81/1.98
% 1.81/1.98 ======= end of input processing =======
% 1.81/1.98
% 1.81/1.98 =========== start of search ===========
% 1.81/1.98
% 1.81/1.98
% 1.81/1.98 Resetting weight limit to 10.
% 1.81/1.98
% 1.81/1.98
% 1.81/1.98 Resetting weight limit to 10.
% 1.81/1.98
% 1.81/1.98 sos_size=353
% 1.81/1.98
% 1.81/1.98 -------- PROOF --------
% 1.81/1.98
% 1.81/1.98 ----> UNIT CONFLICT at 0.04 sec ----> 937 [binary,935.1,1.1] $F.
% 1.81/1.98
% 1.81/1.98 Length of proof is 16. Level of proof is 5.
% 1.81/1.98
% 1.81/1.98 ---------------- PROOF ----------------
% 1.81/1.98 % SZS status Unsatisfiable
% 1.81/1.98 % SZS output start Refutation
% See solution above
% 1.81/1.98 ------------ end of proof -------------
% 1.81/1.98
% 1.81/1.98
% 1.81/1.98 Search stopped by max_proofs option.
% 1.81/1.98
% 1.81/1.98
% 1.81/1.98 Search stopped by max_proofs option.
% 1.81/1.98
% 1.81/1.98 ============ end of search ============
% 1.81/1.98
% 1.81/1.98 -------------- statistics -------------
% 1.81/1.98 clauses given 141
% 1.81/1.98 clauses generated 2354
% 1.81/1.98 clauses kept 469
% 1.81/1.98 clauses forward subsumed 633
% 1.81/1.98 clauses back subsumed 0
% 1.81/1.98 Kbytes malloced 4882
% 1.81/1.98
% 1.81/1.98 ----------- times (seconds) -----------
% 1.81/1.98 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.81/1.98 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.81/1.98 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.81/1.98
% 1.81/1.98 That finishes the proof of the theorem.
% 1.81/1.98
% 1.81/1.98 Process 9407 finished Wed Jul 27 03:56:55 2022
% 1.81/1.99 Otter interrupted
% 1.81/1.99 PROOF FOUND
%------------------------------------------------------------------------------