TSTP Solution File: KLE078+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE078+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n005.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 13:00:41 EDT 2022
% Result : Theorem 3.01s 3.22s
% Output : Refutation 3.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of clauses : 35 ( 30 unt; 0 nHn; 7 RR)
% Number of literals : 40 ( 32 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ le_q(A,B)
| addition(A,B) = B ),
file('KLE078+1.p',unknown),
[] ).
cnf(2,axiom,
( le_q(A,B)
| addition(A,B) != B ),
file('KLE078+1.p',unknown),
[] ).
cnf(3,axiom,
domain(antidomain(dollar_c1)) != antidomain(dollar_c1),
file('KLE078+1.p',unknown),
[] ).
cnf(5,axiom,
addition(A,B) = addition(B,A),
file('KLE078+1.p',unknown),
[] ).
cnf(10,axiom,
addition(A,zero) = A,
file('KLE078+1.p',unknown),
[] ).
cnf(17,axiom,
multiplication(A,one) = A,
file('KLE078+1.p',unknown),
[] ).
cnf(19,axiom,
multiplication(one,A) = A,
file('KLE078+1.p',unknown),
[] ).
cnf(20,axiom,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('KLE078+1.p',unknown),
[] ).
cnf(22,axiom,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE078+1.p',unknown),
[] ).
cnf(27,axiom,
multiplication(zero,A) = zero,
file('KLE078+1.p',unknown),
[] ).
cnf(28,axiom,
addition(A,multiplication(domain(A),A)) = multiplication(domain(A),A),
file('KLE078+1.p',unknown),
[] ).
cnf(30,axiom,
domain(multiplication(A,B)) = domain(multiplication(A,domain(B))),
file('KLE078+1.p',unknown),
[] ).
cnf(31,plain,
domain(multiplication(A,domain(B))) = domain(multiplication(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[30])]),
[iquote('copy,30,flip.1')] ).
cnf(33,axiom,
addition(domain(A),one) = one,
file('KLE078+1.p',unknown),
[] ).
cnf(36,axiom,
domain(zero) = zero,
file('KLE078+1.p',unknown),
[] ).
cnf(39,axiom,
addition(domain(A),antidomain(A)) = one,
file('KLE078+1.p',unknown),
[] ).
cnf(42,axiom,
multiplication(domain(A),antidomain(A)) = zero,
file('KLE078+1.p',unknown),
[] ).
cnf(49,plain,
addition(zero,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,10])]),
[iquote('para_into,5.1.1,9.1.1,flip.1')] ).
cnf(51,plain,
( le_q(A,B)
| addition(B,A) != B ),
inference(para_from,[status(thm),theory(equality)],[5,2]),
[iquote('para_from,5.1.1,2.2.1')] ).
cnf(64,plain,
addition(one,domain(A)) = one,
inference(para_into,[status(thm),theory(equality)],[33,5]),
[iquote('para_into,33.1.1,5.1.1')] ).
cnf(92,plain,
( addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,C)
| ~ le_q(B,C) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[20,1])]),
[iquote('para_into,20.1.1.2,1.2.1,flip.1')] ).
cnf(109,plain,
addition(A,multiplication(domain(B),A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[22,64]),19,19])]),
[iquote('para_into,22.1.1.1,64.1.1,demod,19,19,flip.1')] ).
cnf(116,plain,
multiplication(domain(A),A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[28]),109])]),
[iquote('back_demod,28,demod,109,flip.1')] ).
cnf(130,plain,
addition(antidomain(A),domain(A)) = one,
inference(para_into,[status(thm),theory(equality)],[39,5]),
[iquote('para_into,39.1.1,5.1.1')] ).
cnf(134,plain,
addition(multiplication(A,domain(B)),multiplication(A,antidomain(B))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[39,20]),17])]),
[iquote('para_from,39.1.1,20.1.1.2,demod,17,flip.1')] ).
cnf(149,plain,
multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))) = multiplication(A,domain(B)),
inference(para_from,[status(thm),theory(equality)],[31,116]),
[iquote('para_from,31.1.1,115.1.1.1')] ).
cnf(235,plain,
addition(multiplication(A,antidomain(B)),multiplication(A,domain(B))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[130,20]),17])]),
[iquote('para_from,130.1.1,20.1.1.2,demod,17,flip.1')] ).
cnf(633,plain,
le_q(multiplication(domain(A),B),B),
inference(hyper,[status(thm)],[109,51]),
[iquote('hyper,108,51')] ).
cnf(1615,plain,
( multiplication(domain(A),B) = zero
| ~ le_q(B,antidomain(A)) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[92,42]),10,42]),
[iquote('para_into,92.1.1.2,41.1.1,demod,10,42')] ).
cnf(2290,plain,
multiplication(domain(A),domain(antidomain(A))) = zero,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[149,42]),36,27])]),
[iquote('para_into,149.1.1.1.1,41.1.1,demod,36,27,flip.1')] ).
cnf(2296,plain,
multiplication(domain(A),antidomain(antidomain(A))) = domain(A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[2290,134]),49]),
[iquote('para_from,2290.1.1,134.1.1.1,demod,49')] ).
cnf(2456,plain,
le_q(domain(A),antidomain(antidomain(A))),
inference(para_from,[status(thm),theory(equality)],[2296,633]),
[iquote('para_from,2296.1.1,633.1.1')] ).
cnf(2612,plain,
multiplication(domain(antidomain(A)),domain(A)) = zero,
inference(hyper,[status(thm)],[1615,2456]),
[iquote('hyper,1615,2456')] ).
cnf(2616,plain,
domain(antidomain(A)) = antidomain(A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[2612,235]),116,10])]),
[iquote('para_from,2612.1.1,235.1.1.2,demod,116,10,flip.1')] ).
cnf(2618,plain,
$false,
inference(binary,[status(thm)],[2616,3]),
[iquote('binary,2616.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KLE078+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n005.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 06:29:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.80/1.99 ----- Otter 3.3f, August 2004 -----
% 1.80/1.99 The process was started by sandbox2 on n005.cluster.edu,
% 1.80/1.99 Wed Jul 27 06:29:35 2022
% 1.80/1.99 The command was "./otter". The process ID is 5699.
% 1.80/1.99
% 1.80/1.99 set(prolog_style_variables).
% 1.80/1.99 set(auto).
% 1.80/1.99 dependent: set(auto1).
% 1.80/1.99 dependent: set(process_input).
% 1.80/1.99 dependent: clear(print_kept).
% 1.80/1.99 dependent: clear(print_new_demod).
% 1.80/1.99 dependent: clear(print_back_demod).
% 1.80/1.99 dependent: clear(print_back_sub).
% 1.80/1.99 dependent: set(control_memory).
% 1.80/1.99 dependent: assign(max_mem, 12000).
% 1.80/1.99 dependent: assign(pick_given_ratio, 4).
% 1.80/1.99 dependent: assign(stats_level, 1).
% 1.80/1.99 dependent: assign(max_seconds, 10800).
% 1.80/1.99 clear(print_given).
% 1.80/1.99
% 1.80/1.99 formula_list(usable).
% 1.80/1.99 all A (A=A).
% 1.80/1.99 all A B (addition(A,B)=addition(B,A)).
% 1.80/1.99 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.80/1.99 all A (addition(A,zero)=A).
% 1.80/1.99 all A (addition(A,A)=A).
% 1.80/1.99 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.80/1.99 all A (multiplication(A,one)=A).
% 1.80/1.99 all A (multiplication(one,A)=A).
% 1.80/1.99 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.80/1.99 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.80/1.99 all A (multiplication(A,zero)=zero).
% 1.80/1.99 all A (multiplication(zero,A)=zero).
% 1.80/1.99 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.80/1.99 all X0 (addition(X0,multiplication(domain(X0),X0))=multiplication(domain(X0),X0)).
% 1.80/1.99 all X0 X1 (domain(multiplication(X0,X1))=domain(multiplication(X0,domain(X1)))).
% 1.80/1.99 all X0 (addition(domain(X0),one)=one).
% 1.80/1.99 domain(zero)=zero.
% 1.80/1.99 all X0 X1 (domain(addition(X0,X1))=addition(domain(X0),domain(X1))).
% 1.80/1.99 -(all X0 ((all X1 (addition(domain(X1),antidomain(X1))=one&multiplication(domain(X1),antidomain(X1))=zero))->domain(antidomain(X0))=antidomain(X0))).
% 1.80/1.99 end_of_list.
% 1.80/1.99
% 1.80/1.99 -------> usable clausifies to:
% 1.80/1.99
% 1.80/1.99 list(usable).
% 1.80/1.99 0 [] A=A.
% 1.80/1.99 0 [] addition(A,B)=addition(B,A).
% 1.80/1.99 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.80/1.99 0 [] addition(A,zero)=A.
% 1.80/1.99 0 [] addition(A,A)=A.
% 1.80/1.99 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.80/1.99 0 [] multiplication(A,one)=A.
% 1.80/1.99 0 [] multiplication(one,A)=A.
% 1.80/1.99 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.80/1.99 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.80/1.99 0 [] multiplication(A,zero)=zero.
% 1.80/1.99 0 [] multiplication(zero,A)=zero.
% 1.80/1.99 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.80/1.99 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.80/1.99 0 [] addition(X0,multiplication(domain(X0),X0))=multiplication(domain(X0),X0).
% 1.80/1.99 0 [] domain(multiplication(X0,X1))=domain(multiplication(X0,domain(X1))).
% 1.80/1.99 0 [] addition(domain(X0),one)=one.
% 1.80/1.99 0 [] domain(zero)=zero.
% 1.80/1.99 0 [] domain(addition(X0,X1))=addition(domain(X0),domain(X1)).
% 1.80/1.99 0 [] addition(domain(X1),antidomain(X1))=one.
% 1.80/1.99 0 [] multiplication(domain(X1),antidomain(X1))=zero.
% 1.80/1.99 0 [] domain(antidomain($c1))!=antidomain($c1).
% 1.80/1.99 end_of_list.
% 1.80/1.99
% 1.80/1.99 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.80/1.99
% 1.80/1.99 This is a Horn set with equality. The strategy will be
% 1.80/1.99 Knuth-Bendix and hyper_res, with positive clauses in
% 1.80/1.99 sos and nonpositive clauses in usable.
% 1.80/1.99
% 1.80/1.99 dependent: set(knuth_bendix).
% 1.80/1.99 dependent: set(anl_eq).
% 1.80/1.99 dependent: set(para_from).
% 1.80/1.99 dependent: set(para_into).
% 1.80/1.99 dependent: clear(para_from_right).
% 1.80/1.99 dependent: clear(para_into_right).
% 1.80/1.99 dependent: set(para_from_vars).
% 1.80/1.99 dependent: set(eq_units_both_ways).
% 1.80/1.99 dependent: set(dynamic_demod_all).
% 1.80/1.99 dependent: set(dynamic_demod).
% 1.80/1.99 dependent: set(order_eq).
% 1.80/1.99 dependent: set(back_demod).
% 1.80/1.99 dependent: set(lrpo).
% 1.80/1.99 dependent: set(hyper_res).
% 1.80/1.99 dependent: clear(order_hyper).
% 1.80/1.99
% 1.80/1.99 ------------> process usable:
% 1.80/1.99 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.80/1.99 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.80/1.99 ** KEPT (pick-wt=6): 3 [] domain(antidomain($c1))!=antidomain($c1).
% 1.80/1.99
% 1.80/1.99 ------------> process sos:
% 1.80/1.99 ** KEPT (pick-wt=3): 4 [] A=A.
% 1.80/1.99 ** KEPT (pick-wt=7): 5 [] addition(A,B)=addition(B,A).
% 1.80/1.99 ** KEPT (pick-wt=11): 7 [copy,6,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.80/1.99 ---> New Demodulator: 8 [new_demod,7] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.80/1.99 ** KEPT (pick-wt=5): 9 [] addition(A,zero)=A.
% 1.80/1.99 ---> New Demodulator: 10 [new_demod,9] addition(A,zero)=A.
% 3.01/3.22 ** KEPT (pick-wt=5): 11 [] addition(A,A)=A.
% 3.01/3.22 ---> New Demodulator: 12 [new_demod,11] addition(A,A)=A.
% 3.01/3.22 ** KEPT (pick-wt=11): 14 [copy,13,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 3.01/3.22 ---> New Demodulator: 15 [new_demod,14] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 3.01/3.22 ** KEPT (pick-wt=5): 16 [] multiplication(A,one)=A.
% 3.01/3.22 ---> New Demodulator: 17 [new_demod,16] multiplication(A,one)=A.
% 3.01/3.22 ** KEPT (pick-wt=5): 18 [] multiplication(one,A)=A.
% 3.01/3.22 ---> New Demodulator: 19 [new_demod,18] multiplication(one,A)=A.
% 3.01/3.22 ** KEPT (pick-wt=13): 20 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 3.01/3.22 ---> New Demodulator: 21 [new_demod,20] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 3.01/3.22 ** KEPT (pick-wt=13): 22 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 3.01/3.22 ---> New Demodulator: 23 [new_demod,22] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 3.01/3.22 ** KEPT (pick-wt=5): 24 [] multiplication(A,zero)=zero.
% 3.01/3.22 ---> New Demodulator: 25 [new_demod,24] multiplication(A,zero)=zero.
% 3.01/3.22 ** KEPT (pick-wt=5): 26 [] multiplication(zero,A)=zero.
% 3.01/3.22 ---> New Demodulator: 27 [new_demod,26] multiplication(zero,A)=zero.
% 3.01/3.22 ** KEPT (pick-wt=11): 28 [] addition(A,multiplication(domain(A),A))=multiplication(domain(A),A).
% 3.01/3.22 ---> New Demodulator: 29 [new_demod,28] addition(A,multiplication(domain(A),A))=multiplication(domain(A),A).
% 3.01/3.22 ** KEPT (pick-wt=10): 31 [copy,30,flip.1] domain(multiplication(A,domain(B)))=domain(multiplication(A,B)).
% 3.01/3.22 ---> New Demodulator: 32 [new_demod,31] domain(multiplication(A,domain(B)))=domain(multiplication(A,B)).
% 3.01/3.22 ** KEPT (pick-wt=6): 33 [] addition(domain(A),one)=one.
% 3.01/3.22 ---> New Demodulator: 34 [new_demod,33] addition(domain(A),one)=one.
% 3.01/3.22 ** KEPT (pick-wt=4): 35 [] domain(zero)=zero.
% 3.01/3.22 ---> New Demodulator: 36 [new_demod,35] domain(zero)=zero.
% 3.01/3.22 ** KEPT (pick-wt=10): 37 [] domain(addition(A,B))=addition(domain(A),domain(B)).
% 3.01/3.22 ---> New Demodulator: 38 [new_demod,37] domain(addition(A,B))=addition(domain(A),domain(B)).
% 3.01/3.22 ** KEPT (pick-wt=7): 39 [] addition(domain(A),antidomain(A))=one.
% 3.01/3.22 ---> New Demodulator: 40 [new_demod,39] addition(domain(A),antidomain(A))=one.
% 3.01/3.22 ** KEPT (pick-wt=7): 41 [] multiplication(domain(A),antidomain(A))=zero.
% 3.01/3.22 ---> New Demodulator: 42 [new_demod,41] multiplication(domain(A),antidomain(A))=zero.
% 3.01/3.22 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 3.01/3.22 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] addition(A,B)=addition(B,A).
% 3.01/3.22 >>>> Starting back demodulation with 8.
% 3.01/3.22 >>>> Starting back demodulation with 10.
% 3.01/3.22 >>>> Starting back demodulation with 12.
% 3.01/3.22 >>>> Starting back demodulation with 15.
% 3.01/3.22 >>>> Starting back demodulation with 17.
% 3.01/3.22 >>>> Starting back demodulation with 19.
% 3.01/3.22 >>>> Starting back demodulation with 21.
% 3.01/3.22 >>>> Starting back demodulation with 23.
% 3.01/3.22 >>>> Starting back demodulation with 25.
% 3.01/3.22 >>>> Starting back demodulation with 27.
% 3.01/3.22 >>>> Starting back demodulation with 29.
% 3.01/3.22 >>>> Starting back demodulation with 32.
% 3.01/3.22 >>>> Starting back demodulation with 34.
% 3.01/3.22 >>>> Starting back demodulation with 36.
% 3.01/3.22 >>>> Starting back demodulation with 38.
% 3.01/3.22 >>>> Starting back demodulation with 40.
% 3.01/3.22 >>>> Starting back demodulation with 42.
% 3.01/3.22
% 3.01/3.22 ======= end of input processing =======
% 3.01/3.22
% 3.01/3.22 =========== start of search ===========
% 3.01/3.22
% 3.01/3.22
% 3.01/3.22 Resetting weight limit to 9.
% 3.01/3.22
% 3.01/3.22
% 3.01/3.22 Resetting weight limit to 9.
% 3.01/3.22
% 3.01/3.22 sos_size=1670
% 3.01/3.22
% 3.01/3.22 -------- PROOF --------
% 3.01/3.22
% 3.01/3.22 ----> UNIT CONFLICT at 1.23 sec ----> 2618 [binary,2616.1,3.1] $F.
% 3.01/3.22
% 3.01/3.22 Length of proof is 18. Level of proof is 9.
% 3.01/3.22
% 3.01/3.22 ---------------- PROOF ----------------
% 3.01/3.22 % SZS status Theorem
% 3.01/3.22 % SZS output start Refutation
% See solution above
% 3.01/3.22 ------------ end of proof -------------
% 3.01/3.22
% 3.01/3.22
% 3.01/3.22 Search stopped by max_proofs option.
% 3.01/3.22
% 3.01/3.22
% 3.01/3.22 Search stopped by max_proofs option.
% 3.01/3.22
% 3.01/3.22 ============ end of search ============
% 3.01/3.22
% 3.01/3.22 -------------- statistics -------------
% 3.01/3.22 clauses given 793
% 3.01/3.22 clauses generated 239679
% 3.01/3.22 clauses kept 2382
% 3.01/3.22 clauses forward subsumed 46681
% 3.01/3.22 clauses back subsumed 265
% 3.01/3.22 Kbytes malloced 5859
% 3.01/3.22
% 3.01/3.22 ----------- times (seconds) -----------
% 3.01/3.22 user CPU time 1.23 (0 hr, 0 min, 1 sec)
% 3.01/3.22 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 3.01/3.22 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.01/3.22
% 3.01/3.22 That finishes the proof of the theorem.
% 3.01/3.22
% 3.01/3.22 Process 5699 finished Wed Jul 27 06:29:38 2022
% 3.01/3.22 Otter interrupted
% 3.01/3.22 PROOF FOUND
%------------------------------------------------------------------------------