%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ALG069-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 : Unsatisfiable 1.95s 2.12s
% Output : Refutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 11 RR)
% Number of literals : 20 ( 19 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-4 aty)
% Number of variables : 15 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
tuple(op2(A,A),sorti2(A)) != tuple(sK1_ax4_U,true),
file('ALG069-10.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('ALG069-10.p',unknown),
[] ).
cnf(4,axiom,
ife_q2(A,A,B,C) = B,
file('ALG069-10.p',unknown),
[] ).
cnf(6,axiom,
ife_q(A,A,B,C) = B,
file('ALG069-10.p',unknown),
[] ).
cnf(11,axiom,
ife_q(sorti1(A),true,sorti1(sK2_ax3_V(A)),true) = true,
file('ALG069-10.p',unknown),
[] ).
cnf(13,axiom,
ife_q2(sorti1(A),true,op1(sK2_ax3_V(A),sK2_ax3_V(A)),A) = A,
file('ALG069-10.p',unknown),
[] ).
cnf(15,axiom,
sorti2(sK1_ax4_U) = true,
file('ALG069-10.p',unknown),
[] ).
cnf(17,axiom,
ife_q(sorti1(A),true,sorti2(h(A)),true) = true,
file('ALG069-10.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('ALG069-10.p',unknown),
[] ).
cnf(23,axiom,
ife_q(sorti2(A),true,sorti1(j(A)),true) = true,
file('ALG069-10.p',unknown),
[] ).
cnf(27,axiom,
ife_q2(sorti2(A),true,h(j(A)),A) = A,
file('ALG069-10.p',unknown),
[] ).
cnf(30,plain,
sorti1(j(sK1_ax4_U)) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[23,15]),6]),
[iquote('para_into,23.1.1.1,15.1.1,demod,6')] ).
cnf(43,plain,
sorti1(sK2_ax3_V(j(sK1_ax4_U))) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[30,11]),6]),
[iquote('para_from,30.1.1,11.1.1.1,demod,6')] ).
cnf(55,plain,
sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[43,17]),6]),
[iquote('para_from,42.1.1,17.1.1.1,demod,6')] ).
cnf(64,plain,
op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))) = j(sK1_ax4_U),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[13,30]),4]),
[iquote('para_into,13.1.1.1,30.1.1,demod,4')] ).
cnf(69,plain,
tuple(op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),true) != tuple(sK1_ax4_U,true),
inference(para_from,[status(thm),theory(equality)],[55,1]),
[iquote('para_from,55.1.1,1.1.1.2')] ).
cnf(137,plain,
h(j(sK1_ax4_U)) = sK1_ax4_U,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[27,15]),4]),
[iquote('para_into,27.1.1.1,15.1.1,demod,4')] ).
cnf(159,plain,
op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))) = sK1_ax4_U,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[64,19]),43,43,64,137,4,137,4,64,137]),
[iquote('para_from,63.1.1,19.1.1.4.1,demod,43,43,64,137,4,137,4,64,137')] ).
cnf(160,plain,
tuple(sK1_ax4_U,true) != tuple(sK1_ax4_U,true),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[69]),159]),
[iquote('back_demod,69,demod,159')] ).
cnf(161,plain,
$false,
inference(binary,[status(thm)],[160,2]),
[iquote('binary,160.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG069-10 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.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 04:03:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.95/2.12 ----- Otter 3.3f, August 2004 -----
% 1.95/2.12 The process was started by sandbox2 on n023.cluster.edu,
% 1.95/2.12 Wed Jul 27 04:03:33 2022
% 1.95/2.12 The command was "./otter". The process ID is 23182.
% 1.95/2.12
% 1.95/2.12 set(prolog_style_variables).
% 1.95/2.12 set(auto).
% 1.95/2.12 dependent: set(auto1).
% 1.95/2.12 dependent: set(process_input).
% 1.95/2.12 dependent: clear(print_kept).
% 1.95/2.12 dependent: clear(print_new_demod).
% 1.95/2.12 dependent: clear(print_back_demod).
% 1.95/2.12 dependent: clear(print_back_sub).
% 1.95/2.12 dependent: set(control_memory).
% 1.95/2.12 dependent: assign(max_mem, 12000).
% 1.95/2.12 dependent: assign(pick_given_ratio, 4).
% 1.95/2.12 dependent: assign(stats_level, 1).
% 1.95/2.12 dependent: assign(max_seconds, 10800).
% 1.95/2.12 clear(print_given).
% 1.95/2.12
% 1.95/2.12 list(usable).
% 1.95/2.12 0 [] A=A.
% 1.95/2.12 0 [] ife_q2(A,A,B,C)=B.
% 1.95/2.12 0 [] ife_q(A,A,B,C)=B.
% 1.95/2.12 0 [] ife_q(sorti1(V),true,ife_q(sorti1(U),true,sorti1(op1(U,V)),true),true)=true.
% 1.95/2.12 0 [] ife_q(sorti2(V),true,ife_q(sorti2(U),true,sorti2(op2(U,V)),true),true)=true.
% 1.95/2.12 0 [] ife_q(sorti1(U),true,sorti1(sK2_ax3_V(U)),true)=true.
% 1.95/2.12 0 [] ife_q2(sorti1(U),true,op1(sK2_ax3_V(U),sK2_ax3_V(U)),U)=U.
% 1.95/2.12 0 [] tuple(op2(V,V),sorti2(V))!=tuple(sK1_ax4_U,true).
% 1.95/2.12 0 [] sorti2(sK1_ax4_U)=true.
% 1.95/2.12 0 [] ife_q(sorti1(U),true,sorti2(h(U)),true)=true.
% 1.95/2.12 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)).
% 1.95/2.12 0 [] ife_q2(sorti1(X2),true,j(h(X2)),X2)=X2.
% 1.95/2.12 0 [] ife_q(sorti2(V),true,sorti1(j(V)),true)=true.
% 1.95/2.12 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)).
% 1.95/2.12 0 [] ife_q2(sorti2(X1),true,h(j(X1)),X1)=X1.
% 1.95/2.12 end_of_list.
% 1.95/2.12
% 1.95/2.12 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.95/2.12
% 1.95/2.12 All clauses are units, and equality is present; the
% 1.95/2.12 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.95/2.12
% 1.95/2.12 dependent: set(knuth_bendix).
% 1.95/2.12 dependent: set(anl_eq).
% 1.95/2.12 dependent: set(para_from).
% 1.95/2.12 dependent: set(para_into).
% 1.95/2.12 dependent: clear(para_from_right).
% 1.95/2.12 dependent: clear(para_into_right).
% 1.95/2.12 dependent: set(para_from_vars).
% 1.95/2.12 dependent: set(eq_units_both_ways).
% 1.95/2.12 dependent: set(dynamic_demod_all).
% 1.95/2.12 dependent: set(dynamic_demod).
% 1.95/2.12 dependent: set(order_eq).
% 1.95/2.12 dependent: set(back_demod).
% 1.95/2.12 dependent: set(lrpo).
% 1.95/2.12
% 1.95/2.12 ------------> process usable:
% 1.95/2.12 ** KEPT (pick-wt=10): 1 [] tuple(op2(A,A),sorti2(A))!=tuple(sK1_ax4_U,true).
% 1.95/2.12
% 1.95/2.12 ------------> process sos:
% 1.95/2.12 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.95/2.12 ** KEPT (pick-wt=7): 3 [] ife_q2(A,A,B,C)=B.
% 1.95/2.12 ---> New Demodulator: 4 [new_demod,3] ife_q2(A,A,B,C)=B.
% 1.95/2.12 ** KEPT (pick-wt=7): 5 [] ife_q(A,A,B,C)=B.
% 1.95/2.12 ---> New Demodulator: 6 [new_demod,5] ife_q(A,A,B,C)=B.
% 1.95/2.12 ** KEPT (pick-wt=16): 7 [] ife_q(sorti1(A),true,ife_q(sorti1(B),true,sorti1(op1(B,A)),true),true)=true.
% 1.95/2.12 ---> New Demodulator: 8 [new_demod,7] ife_q(sorti1(A),true,ife_q(sorti1(B),true,sorti1(op1(B,A)),true),true)=true.
% 1.95/2.12 ** KEPT (pick-wt=16): 9 [] ife_q(sorti2(A),true,ife_q(sorti2(B),true,sorti2(op2(B,A)),true),true)=true.
% 1.95/2.12 ---> New Demodulator: 10 [new_demod,9] ife_q(sorti2(A),true,ife_q(sorti2(B),true,sorti2(op2(B,A)),true),true)=true.
% 1.95/2.12 ** KEPT (pick-wt=10): 11 [] ife_q(sorti1(A),true,sorti1(sK2_ax3_V(A)),true)=true.
% 1.95/2.12 ---> New Demodulator: 12 [new_demod,11] ife_q(sorti1(A),true,sorti1(sK2_ax3_V(A)),true)=true.
% 1.95/2.12 ** KEPT (pick-wt=12): 13 [] ife_q2(sorti1(A),true,op1(sK2_ax3_V(A),sK2_ax3_V(A)),A)=A.
% 1.95/2.12 ---> New Demodulator: 14 [new_demod,13] ife_q2(sorti1(A),true,op1(sK2_ax3_V(A),sK2_ax3_V(A)),A)=A.
% 1.95/2.12 ** KEPT (pick-wt=4): 15 [] sorti2(sK1_ax4_U)=true.
% 1.95/2.12 ---> New Demodulator: 16 [new_demod,15] sorti2(sK1_ax4_U)=true.
% 1.95/2.12 ** KEPT (pick-wt=10): 17 [] ife_q(sorti1(A),true,sorti2(h(A)),true)=true.
% 1.95/2.12 ---> New Demodulator: 18 [new_demod,17] ife_q(sorti1(A),true,sorti2(h(A)),true)=true.
% 1.95/2.12 ** 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)).
% 1.95/2.12 ---> 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)).
% 1.95/2.12 ** KEPT (pick-wt=10): 21 [] ife_q2(sorti1(A),true,j(h(A)),A)=A.
% 1.95/2.12 ---> New Demodulator: 22 [new_demod,21] ife_q2(sorti1(A),true,j(h(A)),A)=A.
% 1.95/2.12 ** KEPT (pick-wt=10): 23 [] ife_q(sorti2(A),true,sorti1(j(A)),true)=true.
% 1.95/2.12 ---> New Demodulator: 24 [new_demod,23] ife_q(sorti2(A),true,sorti1(j(A)),true)=true.
% 1.95/2.12 ** 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)).
% 1.95/2.12 ---> 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)).
% 1.95/2.12 ** KEPT (pick-wt=10): 27 [] ife_q2(sorti2(A),true,h(j(A)),A)=A.
% 1.95/2.12 ---> New Demodulator: 28 [new_demod,27] ife_q2(sorti2(A),true,h(j(A)),A)=A.
% 1.95/2.12 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.95/2.12 >>>> Starting back demodulation with 4.
% 1.95/2.12 >>>> Starting back demodulation with 6.
% 1.95/2.12 >>>> Starting back demodulation with 8.
% 1.95/2.12 >>>> Starting back demodulation with 10.
% 1.95/2.12 >>>> Starting back demodulation with 12.
% 1.95/2.12 >>>> Starting back demodulation with 14.
% 1.95/2.12 >>>> Starting back demodulation with 16.
% 1.95/2.12 >>>> Starting back demodulation with 18.
% 1.95/2.12 >>>> Starting back demodulation with 20.
% 1.95/2.12 >>>> Starting back demodulation with 22.
% 1.95/2.12 >>>> Starting back demodulation with 24.
% 1.95/2.12 >>>> Starting back demodulation with 26.
% 1.95/2.12 >>>> Starting back demodulation with 28.
% 1.95/2.12
% 1.95/2.12 ======= end of input processing =======
% 1.95/2.12
% 1.95/2.12 =========== start of search ===========
% 1.95/2.12
% 1.95/2.12 -------- PROOF --------
% 1.95/2.12
% 1.95/2.12 ----> UNIT CONFLICT at 0.01 sec ----> 161 [binary,160.1,2.1] $F.
% 1.95/2.12
% 1.95/2.12 Length of proof is 8. Level of proof is 5.
% 1.95/2.12
% 1.95/2.12 ---------------- PROOF ----------------
% 1.95/2.12 % SZS status Unsatisfiable
% 1.95/2.12 % SZS output start Refutation
% See solution above
% 1.95/2.12 ------------ end of proof -------------
% 1.95/2.12
% 1.95/2.12
% 1.95/2.12 Search stopped by max_proofs option.
% 1.95/2.12
% 1.95/2.12
% 1.95/2.12 Search stopped by max_proofs option.
% 1.95/2.12
% 1.95/2.12 ============ end of search ============
% 1.95/2.12
% 1.95/2.12 -------------- statistics -------------
% 1.95/2.12 clauses given 28
% 1.95/2.12 clauses generated 151
% 1.95/2.12 clauses kept 84
% 1.95/2.12 clauses forward subsumed 91
% 1.95/2.12 clauses back subsumed 0
% 1.95/2.12 Kbytes malloced 2929
% 1.95/2.12
% 1.95/2.12 ----------- times (seconds) -----------
% 1.95/2.12 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.95/2.12 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.95/2.12 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.95/2.12
% 1.95/2.12 That finishes the proof of the theorem.
% 1.95/2.12
% 1.95/2.12 Process 23182 finished Wed Jul 27 04:03:35 2022
% 1.95/2.12 Otter interrupted
% 1.95/2.12 PROOF FOUND
%------------------------------------------------------------------------------