TSTP Solution File: KLE056+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE056+1 : TPTP v8.1.0. Released v4.0.0.
% 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 13:00:38 EDT 2022
% Result : Theorem 1.65s 1.86s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 5 RR)
% Number of literals : 14 ( 13 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 13 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
dollar_c1 != zero,
file('KLE056+1.p',unknown),
[] ).
cnf(4,plain,
zero != dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[3])]),
[iquote('copy,3,flip.1')] ).
cnf(6,axiom,
addition(A,B) = addition(B,A),
file('KLE056+1.p',unknown),
[] ).
cnf(20,axiom,
multiplication(one,A) = A,
file('KLE056+1.p',unknown),
[] ).
cnf(23,axiom,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE056+1.p',unknown),
[] ).
cnf(28,axiom,
multiplication(zero,A) = zero,
file('KLE056+1.p',unknown),
[] ).
cnf(29,axiom,
addition(A,multiplication(domain(A),A)) = multiplication(domain(A),A),
file('KLE056+1.p',unknown),
[] ).
cnf(34,axiom,
addition(domain(A),one) = one,
file('KLE056+1.p',unknown),
[] ).
cnf(40,axiom,
domain(dollar_c1) = zero,
file('KLE056+1.p',unknown),
[] ).
cnf(63,plain,
addition(one,domain(A)) = one,
inference(para_into,[status(thm),theory(equality)],[34,6]),
[iquote('para_into,34.1.1,6.1.1')] ).
cnf(99,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)],[23,63]),20,20])]),
[iquote('para_into,23.1.1.1,63.1.1,demod,20,20,flip.1')] ).
cnf(105,plain,
multiplication(domain(A),A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[29]),99])]),
[iquote('back_demod,29,demod,99,flip.1')] ).
cnf(111,plain,
zero = dollar_c1,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[105,40]),28]),
[iquote('para_into,105.1.1.1,40.1.1,demod,28')] ).
cnf(113,plain,
$false,
inference(binary,[status(thm)],[111,4]),
[iquote('binary,111.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE056+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Jul 27 06:35:23 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.65/1.86 ----- Otter 3.3f, August 2004 -----
% 1.65/1.86 The process was started by sandbox2 on n008.cluster.edu,
% 1.65/1.86 Wed Jul 27 06:35:23 2022
% 1.65/1.86 The command was "./otter". The process ID is 19889.
% 1.65/1.86
% 1.65/1.86 set(prolog_style_variables).
% 1.65/1.86 set(auto).
% 1.65/1.86 dependent: set(auto1).
% 1.65/1.86 dependent: set(process_input).
% 1.65/1.86 dependent: clear(print_kept).
% 1.65/1.86 dependent: clear(print_new_demod).
% 1.65/1.86 dependent: clear(print_back_demod).
% 1.65/1.86 dependent: clear(print_back_sub).
% 1.65/1.86 dependent: set(control_memory).
% 1.65/1.86 dependent: assign(max_mem, 12000).
% 1.65/1.86 dependent: assign(pick_given_ratio, 4).
% 1.65/1.86 dependent: assign(stats_level, 1).
% 1.65/1.86 dependent: assign(max_seconds, 10800).
% 1.65/1.86 clear(print_given).
% 1.65/1.86
% 1.65/1.86 formula_list(usable).
% 1.65/1.86 all A (A=A).
% 1.65/1.86 all A B (addition(A,B)=addition(B,A)).
% 1.65/1.86 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.65/1.86 all A (addition(A,zero)=A).
% 1.65/1.86 all A (addition(A,A)=A).
% 1.65/1.86 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.65/1.86 all A (multiplication(A,one)=A).
% 1.65/1.86 all A (multiplication(one,A)=A).
% 1.65/1.86 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.65/1.86 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.65/1.86 all A (multiplication(A,zero)=zero).
% 1.65/1.86 all A (multiplication(zero,A)=zero).
% 1.65/1.86 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.65/1.86 all X0 (addition(X0,multiplication(domain(X0),X0))=multiplication(domain(X0),X0)).
% 1.65/1.86 all X0 X1 (domain(multiplication(X0,X1))=domain(multiplication(X0,domain(X1)))).
% 1.65/1.86 all X0 (addition(domain(X0),one)=one).
% 1.65/1.86 domain(zero)=zero.
% 1.65/1.86 all X0 X1 (domain(addition(X0,X1))=addition(domain(X0),domain(X1))).
% 1.65/1.86 -(all X0 (domain(X0)=zero->X0=zero)).
% 1.65/1.86 end_of_list.
% 1.65/1.86
% 1.65/1.86 -------> usable clausifies to:
% 1.65/1.86
% 1.65/1.86 list(usable).
% 1.65/1.86 0 [] A=A.
% 1.65/1.86 0 [] addition(A,B)=addition(B,A).
% 1.65/1.86 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.65/1.86 0 [] addition(A,zero)=A.
% 1.65/1.86 0 [] addition(A,A)=A.
% 1.65/1.86 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.65/1.86 0 [] multiplication(A,one)=A.
% 1.65/1.86 0 [] multiplication(one,A)=A.
% 1.65/1.86 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.65/1.86 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.65/1.86 0 [] multiplication(A,zero)=zero.
% 1.65/1.86 0 [] multiplication(zero,A)=zero.
% 1.65/1.86 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.65/1.86 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.65/1.86 0 [] addition(X0,multiplication(domain(X0),X0))=multiplication(domain(X0),X0).
% 1.65/1.86 0 [] domain(multiplication(X0,X1))=domain(multiplication(X0,domain(X1))).
% 1.65/1.86 0 [] addition(domain(X0),one)=one.
% 1.65/1.86 0 [] domain(zero)=zero.
% 1.65/1.86 0 [] domain(addition(X0,X1))=addition(domain(X0),domain(X1)).
% 1.65/1.86 0 [] domain($c1)=zero.
% 1.65/1.86 0 [] $c1!=zero.
% 1.65/1.86 end_of_list.
% 1.65/1.86
% 1.65/1.86 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.65/1.86
% 1.65/1.86 This is a Horn set with equality. The strategy will be
% 1.65/1.86 Knuth-Bendix and hyper_res, with positive clauses in
% 1.65/1.86 sos and nonpositive clauses in usable.
% 1.65/1.86
% 1.65/1.86 dependent: set(knuth_bendix).
% 1.65/1.86 dependent: set(anl_eq).
% 1.65/1.86 dependent: set(para_from).
% 1.65/1.86 dependent: set(para_into).
% 1.65/1.86 dependent: clear(para_from_right).
% 1.65/1.86 dependent: clear(para_into_right).
% 1.65/1.86 dependent: set(para_from_vars).
% 1.65/1.86 dependent: set(eq_units_both_ways).
% 1.65/1.86 dependent: set(dynamic_demod_all).
% 1.65/1.86 dependent: set(dynamic_demod).
% 1.65/1.86 dependent: set(order_eq).
% 1.65/1.86 dependent: set(back_demod).
% 1.65/1.86 dependent: set(lrpo).
% 1.65/1.86 dependent: set(hyper_res).
% 1.65/1.86 dependent: clear(order_hyper).
% 1.65/1.86
% 1.65/1.86 ------------> process usable:
% 1.65/1.86 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.65/1.86 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.65/1.86 ** KEPT (pick-wt=3): 4 [copy,3,flip.1] zero!=$c1.
% 1.65/1.86
% 1.65/1.86 ------------> process sos:
% 1.65/1.86 ** KEPT (pick-wt=3): 5 [] A=A.
% 1.65/1.86 ** KEPT (pick-wt=7): 6 [] addition(A,B)=addition(B,A).
% 1.65/1.86 ** KEPT (pick-wt=11): 8 [copy,7,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.65/1.86 ---> New Demodulator: 9 [new_demod,8] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.65/1.86 ** KEPT (pick-wt=5): 10 [] addition(A,zero)=A.
% 1.65/1.86 ---> New Demodulator: 11 [new_demod,10] addition(A,zero)=A.
% 1.65/1.86 ** KEPT (pick-wt=5): 12 [] addition(A,A)=A.
% 1.65/1.86 ---> New Demodulator: 13 [new_demod,12] addition(A,A)=A.
% 1.65/1.86 ** KEPT (pick-wt=11): 15 [copy,14,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.65/1.86 ---> New Demodulator: 16 [new_demod,15] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.65/1.86 ** KEPT (pick-wt=5): 17 [] multiplication(A,one)=A.
% 1.65/1.86 ---> New Demodulator: 18 [new_demod,17] multiplication(A,one)=A.
% 1.65/1.86 ** KEPT (pick-wt=5): 19 [] multiplication(one,A)=A.
% 1.65/1.86 ---> New Demodulator: 20 [new_demod,19] multiplication(one,A)=A.
% 1.65/1.86 ** KEPT (pick-wt=13): 21 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.65/1.86 ---> New Demodulator: 22 [new_demod,21] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.65/1.86 ** KEPT (pick-wt=13): 23 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.65/1.86 ---> New Demodulator: 24 [new_demod,23] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.65/1.86 ** KEPT (pick-wt=5): 25 [] multiplication(A,zero)=zero.
% 1.65/1.86 ---> New Demodulator: 26 [new_demod,25] multiplication(A,zero)=zero.
% 1.65/1.86 ** KEPT (pick-wt=5): 27 [] multiplication(zero,A)=zero.
% 1.65/1.86 ---> New Demodulator: 28 [new_demod,27] multiplication(zero,A)=zero.
% 1.65/1.86 ** KEPT (pick-wt=11): 29 [] addition(A,multiplication(domain(A),A))=multiplication(domain(A),A).
% 1.65/1.86 ---> New Demodulator: 30 [new_demod,29] addition(A,multiplication(domain(A),A))=multiplication(domain(A),A).
% 1.65/1.86 ** KEPT (pick-wt=10): 32 [copy,31,flip.1] domain(multiplication(A,domain(B)))=domain(multiplication(A,B)).
% 1.65/1.86 ---> New Demodulator: 33 [new_demod,32] domain(multiplication(A,domain(B)))=domain(multiplication(A,B)).
% 1.65/1.86 ** KEPT (pick-wt=6): 34 [] addition(domain(A),one)=one.
% 1.65/1.86 ---> New Demodulator: 35 [new_demod,34] addition(domain(A),one)=one.
% 1.65/1.86 ** KEPT (pick-wt=4): 36 [] domain(zero)=zero.
% 1.65/1.86 ---> New Demodulator: 37 [new_demod,36] domain(zero)=zero.
% 1.65/1.86 ** KEPT (pick-wt=10): 38 [] domain(addition(A,B))=addition(domain(A),domain(B)).
% 1.65/1.86 ---> New Demodulator: 39 [new_demod,38] domain(addition(A,B))=addition(domain(A),domain(B)).
% 1.65/1.86 ** KEPT (pick-wt=4): 40 [] domain($c1)=zero.
% 1.65/1.86 ---> New Demodulator: 41 [new_demod,40] domain($c1)=zero.
% 1.65/1.86 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] A=A.
% 1.65/1.86 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] addition(A,B)=addition(B,A).
% 1.65/1.86 >>>> Starting back demodulation with 9.
% 1.65/1.86 >>>> Starting back demodulation with 11.
% 1.65/1.86 >>>> Starting back demodulation with 13.
% 1.65/1.86 >>>> Starting back demodulation with 16.
% 1.65/1.86 >>>> Starting back demodulation with 18.
% 1.65/1.86 >>>> Starting back demodulation with 20.
% 1.65/1.86 >>>> Starting back demodulation with 22.
% 1.65/1.86 >>>> Starting back demodulation with 24.
% 1.65/1.86 >>>> Starting back demodulation with 26.
% 1.65/1.86 >>>> Starting back demodulation with 28.
% 1.65/1.86 >>>> Starting back demodulation with 30.
% 1.65/1.86 >>>> Starting back demodulation with 33.
% 1.65/1.86 >>>> Starting back demodulation with 35.
% 1.65/1.86 >>>> Starting back demodulation with 37.
% 1.65/1.86 >>>> Starting back demodulation with 39.
% 1.65/1.86 >>>> Starting back demodulation with 41.
% 1.65/1.86
% 1.65/1.86 ======= end of input processing =======
% 1.65/1.86
% 1.65/1.86 =========== start of search ===========
% 1.65/1.86
% 1.65/1.86 -------- PROOF --------
% 1.65/1.86
% 1.65/1.86 ----> UNIT CONFLICT at 0.00 sec ----> 113 [binary,111.1,4.1] $F.
% 1.65/1.86
% 1.65/1.86 Length of proof is 5. Level of proof is 4.
% 1.65/1.86
% 1.65/1.86 ---------------- PROOF ----------------
% 1.65/1.86 % SZS status Theorem
% 1.65/1.86 % SZS output start Refutation
% See solution above
% 1.65/1.86 ------------ end of proof -------------
% 1.65/1.86
% 1.65/1.86
% 1.65/1.86 Search stopped by max_proofs option.
% 1.65/1.86
% 1.65/1.86
% 1.65/1.86 Search stopped by max_proofs option.
% 1.65/1.86
% 1.65/1.86 ============ end of search ============
% 1.65/1.86
% 1.65/1.86 -------------- statistics -------------
% 1.65/1.86 clauses given 28
% 1.65/1.86 clauses generated 232
% 1.65/1.86 clauses kept 80
% 1.65/1.86 clauses forward subsumed 181
% 1.65/1.86 clauses back subsumed 3
% 1.65/1.86 Kbytes malloced 976
% 1.65/1.86
% 1.65/1.86 ----------- times (seconds) -----------
% 1.65/1.86 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.86 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.86 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.65/1.86
% 1.65/1.86 That finishes the proof of the theorem.
% 1.65/1.86
% 1.65/1.86 Process 19889 finished Wed Jul 27 06:35:25 2022
% 1.65/1.86 Otter interrupted
% 1.65/1.86 PROOF FOUND
%------------------------------------------------------------------------------