TSTP Solution File: SYN415+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SYN415+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 13:24:29 EDT 2022
% Result : Theorem 2.68s 2.93s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of clauses : 57 ( 9 unt; 33 nHn; 56 RR)
% Number of literals : 143 ( 41 equ; 50 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 30 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ f(A)
| ~ f(B)
| A = B
| f(dollar_c2) ),
file('SYN415+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ f(A)
| ~ f(B)
| A = B
| ~ f(C)
| dollar_c2 = C ),
file('SYN415+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ f(A)
| f(dollar_c4)
| ~ f(B)
| f(dollar_f1(B)) ),
file('SYN415+1.p',unknown),
[] ).
cnf(5,plain,
( ~ f(A)
| f(dollar_c4)
| f(dollar_f1(A)) ),
inference(factor_simp,[status(thm)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,factor_simp')] ).
cnf(6,axiom,
( ~ f(A)
| f(dollar_c4)
| ~ f(B)
| B != dollar_f1(B) ),
file('SYN415+1.p',unknown),
[] ).
cnf(7,plain,
( ~ f(A)
| f(dollar_c4)
| dollar_f1(A) != A ),
inference(factor_simp,[status(thm)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,factor_simp')] ).
cnf(8,axiom,
( ~ f(A)
| f(dollar_c3)
| ~ f(B)
| f(dollar_f1(B)) ),
file('SYN415+1.p',unknown),
[] ).
cnf(9,plain,
( ~ f(A)
| f(dollar_c3)
| f(dollar_f1(A)) ),
inference(factor_simp,[status(thm)],[inference(copy,[status(thm)],[8])]),
[iquote('copy,8,factor_simp')] ).
cnf(10,axiom,
( ~ f(A)
| f(dollar_c3)
| ~ f(B)
| B != dollar_f1(B) ),
file('SYN415+1.p',unknown),
[] ).
cnf(11,plain,
( ~ f(A)
| f(dollar_c3)
| dollar_f1(A) != A ),
inference(factor_simp,[status(thm)],[inference(copy,[status(thm)],[10])]),
[iquote('copy,10,factor_simp')] ).
cnf(12,axiom,
( ~ f(A)
| dollar_c4 != dollar_c3
| ~ f(B)
| f(dollar_f1(B)) ),
file('SYN415+1.p',unknown),
[] ).
cnf(13,plain,
( ~ f(A)
| dollar_c4 != dollar_c3
| f(dollar_f1(A)) ),
inference(factor_simp,[status(thm)],[inference(copy,[status(thm)],[12])]),
[iquote('copy,12,factor_simp')] ).
cnf(14,axiom,
( ~ f(A)
| dollar_c4 != dollar_c3
| ~ f(B)
| B != dollar_f1(B) ),
file('SYN415+1.p',unknown),
[] ).
cnf(15,plain,
( ~ f(A)
| dollar_c4 != dollar_c3
| dollar_f1(A) != A ),
inference(factor_simp,[status(thm)],[inference(copy,[status(thm)],[14])]),
[iquote('copy,14,factor_simp')] ).
cnf(20,plain,
( ~ f(dollar_c2)
| ~ f(A)
| dollar_c2 = A ),
inference(factor_simp,[status(thm)],[inference(factor,[status(thm)],[3])]),
[iquote('factor,3.3.5,factor_simp')] ).
cnf(23,axiom,
A = A,
file('SYN415+1.p',unknown),
[] ).
cnf(24,axiom,
( f(dollar_c1)
| f(dollar_c2) ),
file('SYN415+1.p',unknown),
[] ).
cnf(25,plain,
( f(dollar_c2)
| f(dollar_c3)
| f(dollar_f1(dollar_c1)) ),
inference(hyper,[status(thm)],[24,9]),
[iquote('hyper,24,9')] ).
cnf(26,plain,
( f(dollar_c2)
| f(dollar_c4)
| f(dollar_f1(dollar_c1)) ),
inference(hyper,[status(thm)],[24,5]),
[iquote('hyper,24,5')] ).
cnf(36,plain,
( f(dollar_c2)
| f(dollar_c3)
| dollar_f1(dollar_c1) = dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[25,2,24])])]),
[iquote('hyper,25,2,24,factor_simp,factor_simp')] ).
cnf(44,plain,
( f(dollar_c2)
| f(dollar_f1(dollar_c1))
| dollar_c4 = dollar_c3 ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[26,2,25])])])]),
[iquote('hyper,26,2,25,factor_simp,factor_simp,factor_simp')] ).
cnf(136,plain,
( ~ f(dollar_c1)
| f(dollar_c3)
| f(dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[36,11]),23])]),
[iquote('para_from,36.3.1,11.3.1,unit_del,23,factor_simp')] ).
cnf(148,plain,
( f(dollar_c3)
| f(dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[136,24])]),
[iquote('hyper,136,24,factor_simp')] ).
cnf(173,plain,
( f(dollar_c3)
| f(dollar_f1(dollar_c2)) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[148,9])]),
[iquote('hyper,148,9,factor_simp')] ).
cnf(188,plain,
( f(dollar_c3)
| dollar_f1(dollar_c2) = dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[173,20,148])]),
[iquote('hyper,173,20,148,factor_simp')] ).
cnf(212,plain,
( ~ f(A)
| f(dollar_f1(A))
| f(dollar_c2)
| f(dollar_f1(dollar_c1)) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[44,13]),23]),
[iquote('para_from,44.3.1,13.2.1,unit_del,23')] ).
cnf(213,plain,
( ~ f(dollar_c1)
| f(dollar_f1(dollar_c1))
| f(dollar_c2) ),
inference(factor,[status(thm)],[212]),
[iquote('factor,212.2.4')] ).
cnf(226,plain,
( ~ f(dollar_c2)
| f(dollar_c3) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[188,11]),23])]),
[iquote('para_from,188.2.1,11.3.1,unit_del,23,factor_simp')] ).
cnf(228,plain,
f(dollar_c3),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[226,148])]),
[iquote('hyper,226,148,factor_simp')] ).
cnf(233,plain,
( f(dollar_c4)
| f(dollar_f1(dollar_c3)) ),
inference(hyper,[status(thm)],[228,5]),
[iquote('hyper,228,5')] ).
cnf(449,plain,
( f(dollar_f1(dollar_c1))
| f(dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[213,24])]),
[iquote('hyper,213,24,factor_simp')] ).
cnf(556,plain,
( f(dollar_c2)
| dollar_f1(dollar_c1) = dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[449,2,24])])]),
[iquote('hyper,449,2,24,factor_simp,factor_simp')] ).
cnf(599,plain,
( ~ f(dollar_c1)
| f(dollar_c4)
| f(dollar_c2) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[556,7]),23]),
[iquote('para_from,556.2.1,7.3.1,unit_del,23')] ).
cnf(646,plain,
( f(dollar_c4)
| f(dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[599,24])]),
[iquote('hyper,599,24,factor_simp')] ).
cnf(667,plain,
( f(dollar_c2)
| dollar_c4 = dollar_c3 ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[646,2,228])]),
[iquote('hyper,646,2,228,factor_simp')] ).
cnf(671,plain,
( f(dollar_c4)
| dollar_f1(dollar_c3) = dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[646,20,233])]),
[iquote('hyper,646,20,233,factor_simp')] ).
cnf(673,plain,
( f(dollar_c4)
| dollar_c3 = dollar_c2 ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[646,20,228])]),
[iquote('hyper,646,20,228,flip.2')] ).
cnf(680,plain,
( dollar_c4 = dollar_c3
| dollar_c3 = dollar_c2 ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[667,20,228])]),
[iquote('hyper,667,20,228,flip.2')] ).
cnf(745,plain,
( f(dollar_c4)
| dollar_c3 != dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[671,7]),228])]),
[iquote('para_from,671.2.1,7.3.1,unit_del,228,factor_simp')] ).
cnf(749,plain,
f(dollar_c4),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[745,673]),23])]),
[iquote('para_into,745.2.1,673.2.1,unit_del,23,factor_simp')] ).
cnf(751,plain,
( dollar_c4 = dollar_c2
| dollar_c4 = dollar_c3 ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[749,20,667])]),
[iquote('hyper,749,20,667,flip.1')] ).
cnf(760,plain,
( dollar_c3 = dollar_c2
| f(dollar_f1(dollar_c4)) ),
inference(hyper,[status(thm)],[680,13,749]),
[iquote('hyper,680,13,749')] ).
cnf(765,plain,
( A = dollar_c3
| dollar_c3 = dollar_c2
| ~ f(A)
| ~ f(B)
| dollar_c2 = B ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[680,3]),749]),
[iquote('para_into,680.1.1,3.3.1,unit_del,749')] ).
cnf(769,plain,
( dollar_c3 = dollar_c2
| ~ f(dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[765]),228])]),
[iquote('factor,765.1.5,unit_del,228,factor_simp')] ).
cnf(797,plain,
( dollar_c4 = dollar_c2
| f(dollar_f1(dollar_c3)) ),
inference(hyper,[status(thm)],[751,13,228]),
[iquote('hyper,751,13,228')] ).
cnf(852,plain,
( f(dollar_c2)
| f(dollar_f1(dollar_c4)) ),
inference(para_from,[status(thm),theory(equality)],[760,228]),
[iquote('para_from,760.1.1,228.1.1')] ).
cnf(878,plain,
( f(dollar_c2)
| dollar_f1(dollar_c4) = dollar_c4 ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[852,2,749])]),
[iquote('hyper,852,2,749,factor_simp')] ).
cnf(1017,plain,
( ~ f(A)
| dollar_c3 != dollar_c2
| f(dollar_f1(A))
| f(dollar_f1(dollar_c3)) ),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[797,13])]),
[iquote('para_from,797.1.1,13.2.1,flip.2')] ).
cnf(1018,plain,
( dollar_c3 != dollar_c2
| f(dollar_f1(dollar_c3)) ),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[1017]),228]),
[iquote('factor,1017.3.4,unit_del,228')] ).
cnf(1037,plain,
( dollar_c4 != dollar_c3
| f(dollar_c2) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[878,15]),749,23]),
[iquote('para_from,878.2.1,15.3.1,unit_del,749,23')] ).
cnf(1041,plain,
f(dollar_c2),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[1037,667]),23])]),
[iquote('para_into,1037.1.1,667.2.1,unit_del,23,factor_simp')] ).
cnf(1043,plain,
dollar_c3 = dollar_c2,
inference(hyper,[status(thm)],[1041,769]),
[iquote('hyper,1041,769')] ).
cnf(1049,plain,
dollar_c4 = dollar_c2,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1041,20,749])]),
[iquote('hyper,1041,20,749,flip.1')] ).
cnf(1053,plain,
f(dollar_f1(dollar_c2)),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1018]),1043,1043]),23]),
[iquote('back_demod,1018,demod,1043,1043,unit_del,23')] ).
cnf(1067,plain,
( ~ f(A)
| dollar_f1(A) != A ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[15]),1049,1043]),23]),
[iquote('back_demod,15,demod,1049,1043,unit_del,23')] ).
cnf(1073,plain,
dollar_f1(dollar_c2) = dollar_c2,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1053,20,1041])]),
[iquote('hyper,1053,20,1041,flip.1')] ).
cnf(1092,plain,
$false,
inference(hyper,[status(thm)],[1067,1041,1073]),
[iquote('hyper,1067,1041,1073')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.17 % Problem : SYN415+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.17 % Command : otter-tptp-script %s
% 0.12/0.38 % Computer : n018.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8042.1875MB
% 0.12/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Wed Jul 27 11:24:46 EDT 2022
% 0.12/0.38 % CPUTime :
% 2.68/2.93 ----- Otter 3.3f, August 2004 -----
% 2.68/2.93 The process was started by sandbox on n018.cluster.edu,
% 2.68/2.93 Wed Jul 27 11:24:46 2022
% 2.68/2.93 The command was "./otter". The process ID is 7421.
% 2.68/2.93
% 2.68/2.93 set(prolog_style_variables).
% 2.68/2.93 set(auto).
% 2.68/2.93 dependent: set(auto1).
% 2.68/2.93 dependent: set(process_input).
% 2.68/2.93 dependent: clear(print_kept).
% 2.68/2.93 dependent: clear(print_new_demod).
% 2.68/2.93 dependent: clear(print_back_demod).
% 2.68/2.93 dependent: clear(print_back_sub).
% 2.68/2.93 dependent: set(control_memory).
% 2.68/2.93 dependent: assign(max_mem, 12000).
% 2.68/2.93 dependent: assign(pick_given_ratio, 4).
% 2.68/2.93 dependent: assign(stats_level, 1).
% 2.68/2.93 dependent: assign(max_seconds, 10800).
% 2.68/2.93 clear(print_given).
% 2.68/2.93
% 2.68/2.93 formula_list(usable).
% 2.68/2.93 all A (A=A).
% 2.68/2.93 -((exists X f(X))& (all Y Z (f(Y)&f(Z)->Y=Z))<-> (exists U (f(U)& (all V (f(V)->U=V))))).
% 2.68/2.93 end_of_list.
% 2.68/2.93
% 2.68/2.93 -------> usable clausifies to:
% 2.68/2.93
% 2.68/2.93 list(usable).
% 2.68/2.93 0 [] A=A.
% 2.68/2.93 0 [] f($c1)|f($c2).
% 2.68/2.93 0 [] f($c1)| -f(V)|$c2=V.
% 2.68/2.93 0 [] -f(Y)| -f(Z)|Y=Z|f($c2).
% 2.68/2.93 0 [] -f(Y)| -f(Z)|Y=Z| -f(V)|$c2=V.
% 2.68/2.93 0 [] -f(X)|f($c4)| -f(U)|f($f1(U)).
% 2.68/2.93 0 [] -f(X)|f($c4)| -f(U)|U!=$f1(U).
% 2.68/2.93 0 [] -f(X)|f($c3)| -f(U)|f($f1(U)).
% 2.68/2.93 0 [] -f(X)|f($c3)| -f(U)|U!=$f1(U).
% 2.68/2.93 0 [] -f(X)|$c4!=$c3| -f(U)|f($f1(U)).
% 2.68/2.93 0 [] -f(X)|$c4!=$c3| -f(U)|U!=$f1(U).
% 2.68/2.93 end_of_list.
% 2.68/2.93
% 2.68/2.93 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 2.68/2.93
% 2.68/2.93 This ia a non-Horn set with equality. The strategy will be
% 2.68/2.93 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.68/2.93 deletion, with positive clauses in sos and nonpositive
% 2.68/2.93 clauses in usable.
% 2.68/2.93
% 2.68/2.93 dependent: set(knuth_bendix).
% 2.68/2.93 dependent: set(anl_eq).
% 2.68/2.93 dependent: set(para_from).
% 2.68/2.93 dependent: set(para_into).
% 2.68/2.93 dependent: clear(para_from_right).
% 2.68/2.93 dependent: clear(para_into_right).
% 2.68/2.93 dependent: set(para_from_vars).
% 2.68/2.93 dependent: set(eq_units_both_ways).
% 2.68/2.93 dependent: set(dynamic_demod_all).
% 2.68/2.93 dependent: set(dynamic_demod).
% 2.68/2.93 dependent: set(order_eq).
% 2.68/2.93 dependent: set(back_demod).
% 2.68/2.93 dependent: set(lrpo).
% 2.68/2.93 dependent: set(hyper_res).
% 2.68/2.93 dependent: set(unit_deletion).
% 2.68/2.93 dependent: set(factor).
% 2.68/2.93
% 2.68/2.93 ------------> process usable:
% 2.68/2.93 ** KEPT (pick-wt=7): 1 [] f($c1)| -f(A)|$c2=A.
% 2.68/2.93 ** KEPT (pick-wt=9): 2 [] -f(A)| -f(B)|A=B|f($c2).
% 2.68/2.93 ** KEPT (pick-wt=12): 3 [] -f(A)| -f(B)|A=B| -f(C)|$c2=C.
% 2.68/2.93 ** KEPT (pick-wt=7): 5 [copy,4,factor_simp] -f(A)|f($c4)|f($f1(A)).
% 2.68/2.93 ** KEPT (pick-wt=8): 7 [copy,6,factor_simp] -f(A)|f($c4)|$f1(A)!=A.
% 2.68/2.93 ** KEPT (pick-wt=7): 9 [copy,8,factor_simp] -f(A)|f($c3)|f($f1(A)).
% 2.68/2.93 ** KEPT (pick-wt=8): 11 [copy,10,factor_simp] -f(A)|f($c3)|$f1(A)!=A.
% 2.68/2.93 ** KEPT (pick-wt=8): 13 [copy,12,factor_simp] -f(A)|$c4!=$c3|f($f1(A)).
% 2.68/2.93 ** KEPT (pick-wt=9): 15 [copy,14,factor_simp] -f(A)|$c4!=$c3|$f1(A)!=A.
% 2.68/2.93
% 2.68/2.93 ------------> process sos:
% 2.68/2.93 ** KEPT (pick-wt=3): 23 [] A=A.
% 2.68/2.93 ** KEPT (pick-wt=4): 24 [] f($c1)|f($c2).
% 2.68/2.93 Following clause subsumed by 23 during input processing: 0 [copy,23,flip.1] A=A.
% 2.68/2.93 23 back subsumes 22.
% 2.68/2.93 23 back subsumes 21.
% 2.68/2.93 23 back subsumes 17.
% 2.68/2.93 23 back subsumes 16.
% 2.68/2.93
% 2.68/2.93 ======= end of input processing =======
% 2.68/2.93
% 2.68/2.93 =========== start of search ===========
% 2.68/2.93
% 2.68/2.93 -------- PROOF --------
% 2.68/2.93
% 2.68/2.93 -----> EMPTY CLAUSE at 1.01 sec ----> 1092 [hyper,1067,1041,1073] $F.
% 2.68/2.93
% 2.68/2.93 Length of proof is 46. Level of proof is 21.
% 2.68/2.93
% 2.68/2.93 ---------------- PROOF ----------------
% 2.68/2.93 % SZS status Theorem
% 2.68/2.93 % SZS output start Refutation
% See solution above
% 2.68/2.93 ------------ end of proof -------------
% 2.68/2.93
% 2.68/2.93
% 2.68/2.93 Search stopped by max_proofs option.
% 2.68/2.93
% 2.68/2.93
% 2.68/2.93 Search stopped by max_proofs option.
% 2.68/2.93
% 2.68/2.93 ============ end of search ============
% 2.68/2.93
% 2.68/2.93 -------------- statistics -------------
% 2.68/2.93 clauses given 72
% 2.68/2.93 clauses generated 97891
% 2.68/2.93 clauses kept 1082
% 2.68/2.93 clauses forward subsumed 96377
% 2.68/2.93 clauses back subsumed 943
% 2.68/2.93 Kbytes malloced 976
% 2.68/2.93
% 2.68/2.93 ----------- times (seconds) -----------
% 2.68/2.93 user CPU time 1.01 (0 hr, 0 min, 1 sec)
% 2.68/2.93 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.68/2.93 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 2.68/2.93
% 2.68/2.93 That finishes the proof of the theorem.
% 2.68/2.93
% 2.68/2.93 Process 7421 finished Wed Jul 27 11:24:49 2022
% 2.68/2.93 Otter interrupted
% 2.68/2.93 PROOF FOUND
%------------------------------------------------------------------------------