TSTP Solution File: SWV488+2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SWV488+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 13:20:53 EDT 2022
% Result : Theorem 2.00s 2.20s
% Output : Refutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 15 ( 11 unt; 0 nHn; 13 RR)
% Number of literals : 29 ( 10 equ; 15 neg)
% Maximal clause size : 7 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( int_le_q(A,B)
| A != B ),
file('SWV488+2.p',unknown),
[] ).
cnf(12,axiom,
real_zero != real_one,
file('SWV488+2.p',unknown),
[] ).
cnf(15,axiom,
( ~ int_le_q(int_one,A)
| ~ int_le_q(A,n)
| ~ int_le_q(int_one,B)
| ~ int_le_q(B,n)
| ~ int_le_q(int_one,C)
| ~ int_le_q(C,B)
| a(C,C) = real_one ),
file('SWV488+2.p',unknown),
[] ).
cnf(16,plain,
( ~ int_le_q(int_one,A)
| ~ int_le_q(A,n)
| ~ int_le_q(int_one,B)
| ~ int_le_q(B,A)
| a(B,B) = real_one ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(copy,[status(thm)],[15])])]),
[iquote('copy,15,factor_simp,factor_simp')] ).
cnf(30,plain,
( ~ int_le_q(int_one,A)
| ~ int_le_q(A,n)
| ~ int_le_q(A,A)
| a(A,A) = real_one ),
inference(factor,[status(thm)],[16]),
[iquote('factor,16.1.3')] ).
cnf(65,axiom,
A = A,
file('SWV488+2.p',unknown),
[] ).
cnf(71,axiom,
int_le_q(int_one,dollar_c2),
file('SWV488+2.p',unknown),
[] ).
cnf(73,axiom,
int_le_q(dollar_c1,n),
file('SWV488+2.p',unknown),
[] ).
cnf(75,axiom,
dollar_c2 = dollar_c1,
file('SWV488+2.p',unknown),
[] ).
cnf(76,axiom,
a(dollar_c2,dollar_c1) = real_zero,
file('SWV488+2.p',unknown),
[] ).
cnf(78,plain,
a(dollar_c1,dollar_c1) = real_zero,
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[76]),75]),
[iquote('copy,76,demod,75')] ).
cnf(80,plain,
int_le_q(int_one,dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[71]),75]),
[iquote('back_demod,71,demod,75')] ).
cnf(81,plain,
int_le_q(A,A),
inference(hyper,[status(thm)],[65,3]),
[iquote('hyper,65,3')] ).
cnf(110,plain,
real_zero = real_one,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[81,30,80,73]),78]),
[iquote('hyper,81,30,80,73,demod,78')] ).
cnf(112,plain,
$false,
inference(binary,[status(thm)],[110,12]),
[iquote('binary,110.1,12.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV488+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 06:20:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.00/2.20 ----- Otter 3.3f, August 2004 -----
% 2.00/2.20 The process was started by sandbox on n026.cluster.edu,
% 2.00/2.20 Wed Jul 27 06:20:24 2022
% 2.00/2.20 The command was "./otter". The process ID is 32514.
% 2.00/2.20
% 2.00/2.20 set(prolog_style_variables).
% 2.00/2.20 set(auto).
% 2.00/2.20 dependent: set(auto1).
% 2.00/2.20 dependent: set(process_input).
% 2.00/2.20 dependent: clear(print_kept).
% 2.00/2.20 dependent: clear(print_new_demod).
% 2.00/2.20 dependent: clear(print_back_demod).
% 2.00/2.20 dependent: clear(print_back_sub).
% 2.00/2.20 dependent: set(control_memory).
% 2.00/2.20 dependent: assign(max_mem, 12000).
% 2.00/2.20 dependent: assign(pick_given_ratio, 4).
% 2.00/2.20 dependent: assign(stats_level, 1).
% 2.00/2.20 dependent: assign(max_seconds, 10800).
% 2.00/2.20 clear(print_given).
% 2.00/2.20
% 2.00/2.20 formula_list(usable).
% 2.00/2.20 all A (A=A).
% 2.00/2.20 all I J (int_le_q(I,J)<->int_less(I,J)|I=J).
% 2.00/2.20 all I J K (int_less(I,J)&int_less(J,K)->int_less(I,K)).
% 2.00/2.20 all I J (int_less(I,J)->I!=J).
% 2.00/2.20 all I J (int_less(I,J)|int_le_q(J,I)).
% 2.00/2.20 int_less(int_zero,int_one).
% 2.00/2.20 all I J (plus(I,J)=plus(J,I)).
% 2.00/2.20 all I (plus(I,int_zero)=I).
% 2.00/2.20 all I1 J1 I2 J2 (int_less(I1,J1)&int_le_q(I2,J2)->int_le_q(plus(I1,I2),plus(J1,J2))).
% 2.00/2.20 all I J (int_less(I,J)<-> (exists K (plus(I,K)=J&int_less(int_zero,K)))).
% 2.00/2.20 all I (int_less(int_zero,I)<->int_le_q(int_one,I)).
% 2.00/2.20 real_zero!=real_one.
% 2.00/2.20 all I J (int_le_q(int_one,I)&int_le_q(I,n)&int_le_q(int_one,J)&int_le_q(J,n)-> (all C (int_less(int_zero,C)&I=plus(J,C)-> (all K (int_le_q(int_one,K)&int_le_q(K,J)->a(plus(K,C),K)=lu(plus(K,C),K)))))& (all K (int_le_q(int_one,K)&int_le_q(K,J)->a(K,K)=real_one))& (all C (int_less(int_zero,C)&J=plus(I,C)-> (all K (int_le_q(int_one,K)&int_le_q(K,I)->a(K,plus(K,C))=real_zero))))).
% 2.00/2.20 -(all I J (int_le_q(int_one,I)&int_le_q(I,J)&int_le_q(J,n)-> (I=J->a(I,J)!=real_zero))).
% 2.00/2.20 end_of_list.
% 2.00/2.20
% 2.00/2.20 -------> usable clausifies to:
% 2.00/2.20
% 2.00/2.20 list(usable).
% 2.00/2.20 0 [] A=A.
% 2.00/2.20 0 [] -int_le_q(I,J)|int_less(I,J)|I=J.
% 2.00/2.20 0 [] int_le_q(I,J)| -int_less(I,J).
% 2.00/2.20 0 [] int_le_q(I,J)|I!=J.
% 2.00/2.20 0 [] -int_less(I,J)| -int_less(J,K)|int_less(I,K).
% 2.00/2.20 0 [] -int_less(I,J)|I!=J.
% 2.00/2.20 0 [] int_less(I,J)|int_le_q(J,I).
% 2.00/2.20 0 [] int_less(int_zero,int_one).
% 2.00/2.20 0 [] plus(I,J)=plus(J,I).
% 2.00/2.20 0 [] plus(I,int_zero)=I.
% 2.00/2.20 0 [] -int_less(I1,J1)| -int_le_q(I2,J2)|int_le_q(plus(I1,I2),plus(J1,J2)).
% 2.00/2.20 0 [] -int_less(I,J)|plus(I,$f1(I,J))=J.
% 2.00/2.20 0 [] -int_less(I,J)|int_less(int_zero,$f1(I,J)).
% 2.00/2.20 0 [] int_less(I,J)|plus(I,K)!=J| -int_less(int_zero,K).
% 2.00/2.20 0 [] -int_less(int_zero,I)|int_le_q(int_one,I).
% 2.00/2.20 0 [] int_less(int_zero,I)| -int_le_q(int_one,I).
% 2.00/2.20 0 [] real_zero!=real_one.
% 2.00/2.20 0 [] -int_le_q(int_one,I)| -int_le_q(I,n)| -int_le_q(int_one,J)| -int_le_q(J,n)| -int_less(int_zero,C)|I!=plus(J,C)| -int_le_q(int_one,K)| -int_le_q(K,J)|a(plus(K,C),K)=lu(plus(K,C),K).
% 2.00/2.20 0 [] -int_le_q(int_one,I)| -int_le_q(I,n)| -int_le_q(int_one,J)| -int_le_q(J,n)| -int_le_q(int_one,X1)| -int_le_q(X1,J)|a(X1,X1)=real_one.
% 2.00/2.20 0 [] -int_le_q(int_one,I)| -int_le_q(I,n)| -int_le_q(int_one,J)| -int_le_q(J,n)| -int_less(int_zero,X2)|J!=plus(I,X2)| -int_le_q(int_one,X3)| -int_le_q(X3,I)|a(X3,plus(X3,X2))=real_zero.
% 2.00/2.20 0 [] int_le_q(int_one,$c2).
% 2.00/2.20 0 [] int_le_q($c2,$c1).
% 2.00/2.20 0 [] int_le_q($c1,n).
% 2.00/2.20 0 [] $c2=$c1.
% 2.00/2.20 0 [] a($c2,$c1)=real_zero.
% 2.00/2.20 end_of_list.
% 2.00/2.20
% 2.00/2.20 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=9.
% 2.00/2.20
% 2.00/2.20 This ia a non-Horn set with equality. The strategy will be
% 2.00/2.20 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.00/2.20 deletion, with positive clauses in sos and nonpositive
% 2.00/2.20 clauses in usable.
% 2.00/2.20
% 2.00/2.20 dependent: set(knuth_bendix).
% 2.00/2.20 dependent: set(anl_eq).
% 2.00/2.20 dependent: set(para_from).
% 2.00/2.20 dependent: set(para_into).
% 2.00/2.20 dependent: clear(para_from_right).
% 2.00/2.20 dependent: clear(para_into_right).
% 2.00/2.20 dependent: set(para_from_vars).
% 2.00/2.20 dependent: set(eq_units_both_ways).
% 2.00/2.20 dependent: set(dynamic_demod_all).
% 2.00/2.20 dependent: set(dynamic_demod).
% 2.00/2.20 dependent: set(order_eq).
% 2.00/2.20 dependent: set(back_demod).
% 2.00/2.20 dependent: set(lrpo).
% 2.00/2.20 dependent: set(hyper_res).
% 2.00/2.20 dependent: set(unit_deletion).
% 2.00/2.20 dependent: set(factor).
% 2.00/2.20
% 2.00/2.20 ------------> process usable:
% 2.00/2.20 ** KEPT (pick-wt=9): 1 [] -int_le_q(A,B)|int_less(A,B)|A=B.
% 2.00/2.20 ** KEPT (pick-wt=6): 2 [] int_le_q(A,B)| -int_less(A,B).
% 2.00/2.20 ** KEPT (pick-wt=6): 3 [] int_le_q(A,B)|A!=B.
% 2.00/2.20 ** KEPT (pick-wt=9): 4 [] -int_less(A,B)| -int_less(B,C)|int_less(A,C).
% 2.00/2.20 ** KEPT (pick-wt=6): 5 [] -int_less(A,B)|A!=B.
% 2.00/2.20 ** KEPT (pick-wt=13): 6 [] -int_less(A,B)| -int_le_q(C,D)|int_le_q(plus(A,C),plus(B,D)).
% 2.00/2.20 ** KEPT (pick-wt=10): 7 [] -int_less(A,B)|plus(A,$f1(A,B))=B.
% 2.00/2.20 ** KEPT (pick-wt=8): 8 [] -int_less(A,B)|int_less(int_zero,$f1(A,B)).
% 2.00/2.20 ** KEPT (pick-wt=11): 9 [] int_less(A,B)|plus(A,C)!=B| -int_less(int_zero,C).
% 2.00/2.20 ** KEPT (pick-wt=6): 10 [] -int_less(int_zero,A)|int_le_q(int_one,A).
% 2.00/2.20 ** KEPT (pick-wt=6): 11 [] int_less(int_zero,A)| -int_le_q(int_one,A).
% 2.00/2.20 ** KEPT (pick-wt=3): 12 [] real_zero!=real_one.
% 2.00/2.20 ** KEPT (pick-wt=37): 14 [copy,13,flip.9] -int_le_q(int_one,A)| -int_le_q(A,n)| -int_le_q(int_one,B)| -int_le_q(B,n)| -int_less(int_zero,C)|A!=plus(B,C)| -int_le_q(int_one,D)| -int_le_q(D,B)|lu(plus(D,C),D)=a(plus(D,C),D).
% 2.00/2.20 ** KEPT (pick-wt=17): 16 [copy,15,factor_simp,factor_simp] -int_le_q(int_one,A)| -int_le_q(A,n)| -int_le_q(int_one,B)| -int_le_q(B,A)|a(B,B)=real_one.
% 2.00/2.20 ** KEPT (pick-wt=33): 17 [] -int_le_q(int_one,A)| -int_le_q(A,n)| -int_le_q(int_one,B)| -int_le_q(B,n)| -int_less(int_zero,C)|B!=plus(A,C)| -int_le_q(int_one,D)| -int_le_q(D,A)|a(D,plus(D,C))=real_zero.
% 2.00/2.20
% 2.00/2.20 ------------> process sos:
% 2.00/2.20 ** KEPT (pick-wt=3): 65 [] A=A.
% 2.00/2.20 ** KEPT (pick-wt=6): 66 [] int_less(A,B)|int_le_q(B,A).
% 2.00/2.20 ** KEPT (pick-wt=3): 67 [] int_less(int_zero,int_one).
% 2.00/2.20 ** KEPT (pick-wt=7): 68 [] plus(A,B)=plus(B,A).
% 2.00/2.20 ** KEPT (pick-wt=5): 69 [] plus(A,int_zero)=A.
% 2.00/2.20 ---> New Demodulator: 70 [new_demod,69] plus(A,int_zero)=A.
% 2.00/2.20 ** KEPT (pick-wt=3): 71 [] int_le_q(int_one,$c2).
% 2.00/2.20 ** KEPT (pick-wt=3): 72 [] int_le_q($c2,$c1).
% 2.00/2.20 ** KEPT (pick-wt=3): 73 [] int_le_q($c1,n).
% 2.00/2.20 ** KEPT (pick-wt=3): 74 [] $c2=$c1.
% 2.00/2.20 ---> New Demodulator: 75 [new_demod,74] $c2=$c1.
% 2.00/2.20 ** KEPT (pick-wt=5): 77 [copy,76,demod,75] a($c1,$c1)=real_zero.
% 2.00/2.20 ---> New Demodulator: 78 [new_demod,77] a($c1,$c1)=real_zero.
% 2.00/2.20 Following clause subsumed by 65 during input processing: 0 [copy,65,flip.1] A=A.
% 2.00/2.20 Following clause subsumed by 68 during input processing: 0 [copy,68,flip.1] plus(A,B)=plus(B,A).
% 2.00/2.20 >>>> Starting back demodulation with 70.
% 2.00/2.20 >>>> Starting back demodulation with 75.
% 2.00/2.20 >> back demodulating 72 with 75.
% 2.00/2.20 >> back demodulating 71 with 75.
% 2.00/2.20 >>>> Starting back demodulation with 78.
% 2.00/2.20
% 2.00/2.20 ======= end of input processing =======
% 2.00/2.20
% 2.00/2.20 =========== start of search ===========
% 2.00/2.20
% 2.00/2.20 -------- PROOF --------
% 2.00/2.20
% 2.00/2.20 ----> UNIT CONFLICT at 0.01 sec ----> 112 [binary,110.1,12.1] $F.
% 2.00/2.20
% 2.00/2.20 Length of proof is 6. Level of proof is 3.
% 2.00/2.20
% 2.00/2.20 ---------------- PROOF ----------------
% 2.00/2.20 % SZS status Theorem
% 2.00/2.20 % SZS output start Refutation
% See solution above
% 2.00/2.20 ------------ end of proof -------------
% 2.00/2.20
% 2.00/2.20
% 2.00/2.20 Search stopped by max_proofs option.
% 2.00/2.20
% 2.00/2.20
% 2.00/2.20 Search stopped by max_proofs option.
% 2.00/2.20
% 2.00/2.20 ============ end of search ============
% 2.00/2.20
% 2.00/2.20 -------------- statistics -------------
% 2.00/2.20 clauses given 7
% 2.00/2.20 clauses generated 187
% 2.00/2.20 clauses kept 102
% 2.00/2.20 clauses forward subsumed 113
% 2.00/2.20 clauses back subsumed 1
% 2.00/2.20 Kbytes malloced 976
% 2.00/2.20
% 2.00/2.20 ----------- times (seconds) -----------
% 2.00/2.20 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.00/2.20 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.00/2.20 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 2.00/2.20
% 2.00/2.20 That finishes the proof of the theorem.
% 2.00/2.20
% 2.00/2.20 Process 32514 finished Wed Jul 27 06:20:25 2022
% 2.00/2.20 Otter interrupted
% 2.00/2.20 PROOF FOUND
%------------------------------------------------------------------------------