TSTP Solution File: CAT010-10 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : CAT010-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.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 12:47:47 EDT 2022
% Result : Unsatisfiable 1.70s 1.90s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 9 RR)
% Number of literals : 22 ( 21 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 : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 25 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
codomain(compose(a,b)) != codomain(a),
file('CAT010-10.p',unknown),
[] ).
cnf(6,axiom,
ife_q2(A,A,B,C) = B,
file('CAT010-10.p',unknown),
[] ).
cnf(8,axiom,
ife_q(A,A,B,C) = B,
file('CAT010-10.p',unknown),
[] ).
cnf(15,axiom,
ife_q(there_exists(domain(A)),true,there_exists(A),true) = true,
file('CAT010-10.p',unknown),
[] ).
cnf(19,axiom,
ife_q(there_exists(compose(A,B)),true,there_exists(domain(A)),true) = true,
file('CAT010-10.p',unknown),
[] ).
cnf(21,axiom,
ife_q2(there_exists(compose(A,B)),true,domain(A),codomain(B)) = codomain(B),
file('CAT010-10.p',unknown),
[] ).
cnf(25,axiom,
compose(A,compose(B,C)) = compose(compose(A,B),C),
file('CAT010-10.p',unknown),
[] ).
cnf(26,plain,
compose(compose(A,B),C) = compose(A,compose(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[25])]),
[iquote('copy,25,flip.1')] ).
cnf(28,axiom,
compose(A,domain(A)) = A,
file('CAT010-10.p',unknown),
[] ).
cnf(31,axiom,
compose(codomain(A),A) = A,
file('CAT010-10.p',unknown),
[] ).
cnf(32,axiom,
there_exists(compose(a,b)) = true,
file('CAT010-10.p',unknown),
[] ).
cnf(42,plain,
compose(codomain(A),compose(A,B)) = compose(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[26,31])]),
[iquote('para_into,26.1.1.1,30.1.1,flip.1')] ).
cnf(50,plain,
compose(codomain(codomain(A)),A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[42,31]),31]),
[iquote('para_into,42.1.1.2,30.1.1,demod,31')] ).
cnf(62,plain,
there_exists(domain(a)) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,32]),8]),
[iquote('para_into,19.1.1.1,32.1.1,demod,8')] ).
cnf(66,plain,
there_exists(a) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[62,15]),8]),
[iquote('para_from,62.1.1,15.1.1.1,demod,8')] ).
cnf(86,plain,
ife_q2(there_exists(A),true,domain(codomain(codomain(A))),codomain(A)) = codomain(A),
inference(para_into,[status(thm),theory(equality)],[21,50]),
[iquote('para_into,21.1.1.1.1,50.1.1')] ).
cnf(88,plain,
ife_q2(there_exists(compose(A,B)),true,domain(codomain(A)),codomain(compose(A,B))) = codomain(compose(A,B)),
inference(para_into,[status(thm),theory(equality)],[21,42]),
[iquote('para_into,21.1.1.1.1,42.1.1')] ).
cnf(488,plain,
domain(codomain(codomain(a))) = codomain(a),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[86,66]),6]),
[iquote('para_into,86.1.1.1,66.1.1,demod,6')] ).
cnf(491,plain,
codomain(codomain(a)) = codomain(a),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[488,28]),31])]),
[iquote('para_from,488.1.1,28.1.1.2,demod,31,flip.1')] ).
cnf(493,plain,
domain(codomain(a)) = codomain(a),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[488]),491]),
[iquote('back_demod,488,demod,491')] ).
cnf(498,plain,
codomain(compose(a,b)) = codomain(a),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[88,32]),493,6])]),
[iquote('para_into,88.1.1.1,32.1.1,demod,493,6,flip.1')] ).
cnf(500,plain,
$false,
inference(binary,[status(thm)],[498,1]),
[iquote('binary,498.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : CAT010-10 : TPTP v8.1.0. Released v7.3.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.32 % Computer : n028.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.32 % CPULimit : 300
% 0.19/0.32 % WCLimit : 300
% 0.19/0.32 % DateTime : Wed Jul 27 02:11:03 EDT 2022
% 0.19/0.33 % CPUTime :
% 1.70/1.89 ----- Otter 3.3f, August 2004 -----
% 1.70/1.89 The process was started by sandbox on n028.cluster.edu,
% 1.70/1.89 Wed Jul 27 02:11:03 2022
% 1.70/1.89 The command was "./otter". The process ID is 21996.
% 1.70/1.89
% 1.70/1.89 set(prolog_style_variables).
% 1.70/1.89 set(auto).
% 1.70/1.89 dependent: set(auto1).
% 1.70/1.89 dependent: set(process_input).
% 1.70/1.89 dependent: clear(print_kept).
% 1.70/1.89 dependent: clear(print_new_demod).
% 1.70/1.89 dependent: clear(print_back_demod).
% 1.70/1.89 dependent: clear(print_back_sub).
% 1.70/1.89 dependent: set(control_memory).
% 1.70/1.89 dependent: assign(max_mem, 12000).
% 1.70/1.89 dependent: assign(pick_given_ratio, 4).
% 1.70/1.89 dependent: assign(stats_level, 1).
% 1.70/1.89 dependent: assign(max_seconds, 10800).
% 1.70/1.89 clear(print_given).
% 1.70/1.89
% 1.70/1.89 list(usable).
% 1.70/1.89 0 [] A=A.
% 1.70/1.89 0 [] ife_q3(A,A,B,C)=B.
% 1.70/1.89 0 [] ife_q2(A,A,B,C)=B.
% 1.70/1.89 0 [] ife_q(A,A,B,C)=B.
% 1.70/1.89 0 [] ife_q(e_quivalent(X,Y),true,there_exists(X),true)=true.
% 1.70/1.89 0 [] ife_q2(e_quivalent(X,Y),true,X,Y)=Y.
% 1.70/1.89 0 [] ife_q(there_exists(Y),true,e_quivalent(Y,Y),true)=true.
% 1.70/1.89 0 [] ife_q(there_exists(domain(X)),true,there_exists(X),true)=true.
% 1.70/1.89 0 [] ife_q(there_exists(codomain(X)),true,there_exists(X),true)=true.
% 1.70/1.89 0 [] ife_q(there_exists(compose(X,Y)),true,there_exists(domain(X)),true)=true.
% 1.70/1.89 0 [] ife_q2(there_exists(compose(X,Y)),true,domain(X),codomain(Y))=codomain(Y).
% 1.70/1.89 0 [] ife_q(there_exists(domain(X)),true,ife_q3(domain(X),codomain(Y),there_exists(compose(X,Y)),true),true)=true.
% 1.70/1.89 0 [] compose(X,compose(Y,Z))=compose(compose(X,Y),Z).
% 1.70/1.89 0 [] compose(X,domain(X))=X.
% 1.70/1.89 0 [] compose(codomain(X),X)=X.
% 1.70/1.89 0 [] there_exists(compose(a,b))=true.
% 1.70/1.89 0 [] codomain(compose(a,b))!=codomain(a).
% 1.70/1.89 end_of_list.
% 1.70/1.89
% 1.70/1.89 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.70/1.89
% 1.70/1.89 All clauses are units, and equality is present; the
% 1.70/1.89 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.70/1.89
% 1.70/1.89 dependent: set(knuth_bendix).
% 1.70/1.89 dependent: set(anl_eq).
% 1.70/1.89 dependent: set(para_from).
% 1.70/1.89 dependent: set(para_into).
% 1.70/1.89 dependent: clear(para_from_right).
% 1.70/1.89 dependent: clear(para_into_right).
% 1.70/1.89 dependent: set(para_from_vars).
% 1.70/1.89 dependent: set(eq_units_both_ways).
% 1.70/1.89 dependent: set(dynamic_demod_all).
% 1.70/1.89 dependent: set(dynamic_demod).
% 1.70/1.89 dependent: set(order_eq).
% 1.70/1.89 dependent: set(back_demod).
% 1.70/1.89 dependent: set(lrpo).
% 1.70/1.89
% 1.70/1.89 ------------> process usable:
% 1.70/1.89 ** KEPT (pick-wt=7): 1 [] codomain(compose(a,b))!=codomain(a).
% 1.70/1.89
% 1.70/1.89 ------------> process sos:
% 1.70/1.89 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.70/1.89 ** KEPT (pick-wt=7): 3 [] ife_q3(A,A,B,C)=B.
% 1.70/1.89 ---> New Demodulator: 4 [new_demod,3] ife_q3(A,A,B,C)=B.
% 1.70/1.89 ** KEPT (pick-wt=7): 5 [] ife_q2(A,A,B,C)=B.
% 1.70/1.89 ---> New Demodulator: 6 [new_demod,5] ife_q2(A,A,B,C)=B.
% 1.70/1.89 ** KEPT (pick-wt=7): 7 [] ife_q(A,A,B,C)=B.
% 1.70/1.89 ---> New Demodulator: 8 [new_demod,7] ife_q(A,A,B,C)=B.
% 1.70/1.89 ** KEPT (pick-wt=10): 9 [] ife_q(e_quivalent(A,B),true,there_exists(A),true)=true.
% 1.70/1.89 ---> New Demodulator: 10 [new_demod,9] ife_q(e_quivalent(A,B),true,there_exists(A),true)=true.
% 1.70/1.89 ** KEPT (pick-wt=9): 11 [] ife_q2(e_quivalent(A,B),true,A,B)=B.
% 1.70/1.89 ---> New Demodulator: 12 [new_demod,11] ife_q2(e_quivalent(A,B),true,A,B)=B.
% 1.70/1.89 ** KEPT (pick-wt=10): 13 [] ife_q(there_exists(A),true,e_quivalent(A,A),true)=true.
% 1.70/1.89 ---> New Demodulator: 14 [new_demod,13] ife_q(there_exists(A),true,e_quivalent(A,A),true)=true.
% 1.70/1.89 ** KEPT (pick-wt=10): 15 [] ife_q(there_exists(domain(A)),true,there_exists(A),true)=true.
% 1.70/1.89 ---> New Demodulator: 16 [new_demod,15] ife_q(there_exists(domain(A)),true,there_exists(A),true)=true.
% 1.70/1.89 ** KEPT (pick-wt=10): 17 [] ife_q(there_exists(codomain(A)),true,there_exists(A),true)=true.
% 1.70/1.89 ---> New Demodulator: 18 [new_demod,17] ife_q(there_exists(codomain(A)),true,there_exists(A),true)=true.
% 1.70/1.89 ** KEPT (pick-wt=12): 19 [] ife_q(there_exists(compose(A,B)),true,there_exists(domain(A)),true)=true.
% 1.70/1.89 ---> New Demodulator: 20 [new_demod,19] ife_q(there_exists(compose(A,B)),true,there_exists(domain(A)),true)=true.
% 1.70/1.89 ** KEPT (pick-wt=13): 21 [] ife_q2(there_exists(compose(A,B)),true,domain(A),codomain(B))=codomain(B).
% 1.70/1.89 ---> New Demodulator: 22 [new_demod,21] ife_q2(there_exists(compose(A,B)),true,domain(A),codomain(B))=codomain(B).
% 1.70/1.89 ** KEPT (pick-wt=18): 23 [] ife_q(there_exists(domain(A)),true,ife_q3(domain(A),codomain(B),there_exists(compose(A,B)),true),true)=true.
% 1.70/1.89 ---> New Demodulator: 24 [new_demod,23] ife_q(there_exists(domain(A)),true,ife_q3(domain(A),codomain(B),there_exists(compose(A,B)),true),true)=true.
% 1.70/1.90 ** KEPT (pick-wt=11): 26 [copy,25,flip.1] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 1.70/1.90 ---> New Demodulator: 27 [new_demod,26] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 1.70/1.90 ** KEPT (pick-wt=6): 28 [] compose(A,domain(A))=A.
% 1.70/1.90 ---> New Demodulator: 29 [new_demod,28] compose(A,domain(A))=A.
% 1.70/1.90 ** KEPT (pick-wt=6): 30 [] compose(codomain(A),A)=A.
% 1.70/1.90 ---> New Demodulator: 31 [new_demod,30] compose(codomain(A),A)=A.
% 1.70/1.90 ** KEPT (pick-wt=6): 32 [] there_exists(compose(a,b))=true.
% 1.70/1.90 ---> New Demodulator: 33 [new_demod,32] there_exists(compose(a,b))=true.
% 1.70/1.90 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.70/1.90 >>>> Starting back demodulation with 4.
% 1.70/1.90 >>>> Starting back demodulation with 6.
% 1.70/1.90 >>>> Starting back demodulation with 8.
% 1.70/1.90 >>>> Starting back demodulation with 10.
% 1.70/1.90 >>>> Starting back demodulation with 12.
% 1.70/1.90 >>>> Starting back demodulation with 14.
% 1.70/1.90 >>>> Starting back demodulation with 16.
% 1.70/1.90 >>>> Starting back demodulation with 18.
% 1.70/1.90 >>>> Starting back demodulation with 20.
% 1.70/1.90 >>>> Starting back demodulation with 22.
% 1.70/1.90 >>>> Starting back demodulation with 24.
% 1.70/1.90 >>>> Starting back demodulation with 27.
% 1.70/1.90 >>>> Starting back demodulation with 29.
% 1.70/1.90 >>>> Starting back demodulation with 31.
% 1.70/1.90 >>>> Starting back demodulation with 33.
% 1.70/1.90
% 1.70/1.90 ======= end of input processing =======
% 1.70/1.90
% 1.70/1.90 =========== start of search ===========
% 1.70/1.90
% 1.70/1.90
% 1.70/1.90 Resetting weight limit to 9.
% 1.70/1.90
% 1.70/1.90
% 1.70/1.90 Resetting weight limit to 9.
% 1.70/1.90
% 1.70/1.90 sos_size=144
% 1.70/1.90
% 1.70/1.90 -------- PROOF --------
% 1.70/1.90
% 1.70/1.90 ----> UNIT CONFLICT at 0.01 sec ----> 500 [binary,498.1,1.1] $F.
% 1.70/1.90
% 1.70/1.90 Length of proof is 11. Level of proof is 8.
% 1.70/1.90
% 1.70/1.90 ---------------- PROOF ----------------
% 1.70/1.90 % SZS status Unsatisfiable
% 1.70/1.90 % SZS output start Refutation
% See solution above
% 1.70/1.90 ------------ end of proof -------------
% 1.70/1.90
% 1.70/1.90
% 1.70/1.90 Search stopped by max_proofs option.
% 1.70/1.90
% 1.70/1.90
% 1.70/1.90 Search stopped by max_proofs option.
% 1.70/1.90
% 1.70/1.90 ============ end of search ============
% 1.70/1.90
% 1.70/1.90 -------------- statistics -------------
% 1.70/1.90 clauses given 86
% 1.70/1.90 clauses generated 882
% 1.70/1.90 clauses kept 250
% 1.70/1.90 clauses forward subsumed 568
% 1.70/1.90 clauses back subsumed 0
% 1.70/1.90 Kbytes malloced 4882
% 1.70/1.90
% 1.70/1.90 ----------- times (seconds) -----------
% 1.70/1.90 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.70/1.90 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.70/1.90 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.70/1.90
% 1.70/1.90 That finishes the proof of the theorem.
% 1.70/1.90
% 1.70/1.90 Process 21996 finished Wed Jul 27 02:11:05 2022
% 1.70/1.90 Otter interrupted
% 1.70/1.90 PROOF FOUND
%------------------------------------------------------------------------------