%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : PHI010+1 : TPTP v8.1.0. Released v7.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 13:10:40 EDT 2022
% Result : Theorem 1.88s 2.06s
% Output : Refutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 14 ( 10 unt; 0 nHn; 13 RR)
% Number of literals : 32 ( 9 equ; 19 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(7,axiom,
( ~ property(A)
| ~ object(B)
| ~ object(C)
| ~ is_the(B,A)
| B != C
| exemplifies_property(A,dollar_f1(A,B,C)) ),
file('PHI010+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ property(A)
| ~ object(B)
| ~ object(C)
| ~ is_the(B,A)
| B != C
| dollar_f1(A,B,C) = C ),
file('PHI010+1.p',unknown),
[] ).
cnf(16,axiom,
~ exemplifies_property(dollar_c2,dollar_c1),
file('PHI010+1.p',unknown),
[] ).
cnf(18,plain,
( ~ property(A)
| ~ object(B)
| ~ is_the(B,A)
| B != B
| exemplifies_property(A,dollar_f1(A,B,B)) ),
inference(factor,[status(thm)],[7]),
[iquote('factor,7.2.3')] ).
cnf(21,plain,
( ~ property(A)
| ~ object(B)
| ~ is_the(B,A)
| B != B
| dollar_f1(A,B,B) = B ),
inference(factor,[status(thm)],[9]),
[iquote('factor,9.2.3')] ).
cnf(40,axiom,
A = A,
file('PHI010+1.p',unknown),
[] ).
cnf(42,axiom,
property(dollar_c2),
file('PHI010+1.p',unknown),
[] ).
cnf(43,axiom,
object(dollar_c1),
file('PHI010+1.p',unknown),
[] ).
cnf(44,axiom,
is_the(dollar_c3,dollar_c2),
file('PHI010+1.p',unknown),
[] ).
cnf(46,axiom,
dollar_c3 = dollar_c1,
file('PHI010+1.p',unknown),
[] ).
cnf(47,plain,
is_the(dollar_c1,dollar_c2),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[44]),46]),
[iquote('back_demod,44,demod,46')] ).
cnf(72,plain,
dollar_f1(dollar_c2,dollar_c1,dollar_c1) = dollar_c1,
inference(hyper,[status(thm)],[47,21,42,43,40]),
[iquote('hyper,47,21,42,43,40')] ).
cnf(73,plain,
exemplifies_property(dollar_c2,dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[47,18,42,43,40]),72]),
[iquote('hyper,47,18,42,43,40,demod,72')] ).
cnf(74,plain,
$false,
inference(binary,[status(thm)],[73,16]),
[iquote('binary,73.1,16.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : PHI010+1 : TPTP v8.1.0. Released v7.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.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 02:55:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.85/2.06 ----- Otter 3.3f, August 2004 -----
% 1.85/2.06 The process was started by sandbox2 on n023.cluster.edu,
% 1.85/2.06 Wed Jul 27 02:55:03 2022
% 1.85/2.06 The command was "./otter". The process ID is 9325.
% 1.85/2.06
% 1.85/2.06 set(prolog_style_variables).
% 1.85/2.06 set(auto).
% 1.85/2.06 dependent: set(auto1).
% 1.85/2.06 dependent: set(process_input).
% 1.85/2.06 dependent: clear(print_kept).
% 1.85/2.06 dependent: clear(print_new_demod).
% 1.85/2.06 dependent: clear(print_back_demod).
% 1.85/2.06 dependent: clear(print_back_sub).
% 1.85/2.06 dependent: set(control_memory).
% 1.85/2.06 dependent: assign(max_mem, 12000).
% 1.85/2.06 dependent: assign(pick_given_ratio, 4).
% 1.85/2.06 dependent: assign(stats_level, 1).
% 1.85/2.06 dependent: assign(max_seconds, 10800).
% 1.85/2.06 clear(print_given).
% 1.85/2.06
% 1.85/2.06 formula_list(usable).
% 1.85/2.06 all A (A=A).
% 1.85/2.06 all X (object(X)-> -property(X)).
% 1.85/2.06 all X F (exemplifies_property(F,X)->property(F)&object(X)).
% 1.85/2.06 all X F (is_the(X,F)->property(F)&object(X)).
% 1.85/2.06 all F X W (property(F)&object(X)&object(W)-> (is_the(X,F)&X=W<-> (exists Y (object(Y)&exemplifies_property(F,Y)& (all Z (object(Z)-> (exemplifies_property(F,Z)->Z=Y)))&Y=W)))).
% 1.85/2.06 -(all X F Y (object(X)&property(F)&object(Y)-> (is_the(X,F)&X=Y->exemplifies_property(F,Y)))).
% 1.85/2.06 end_of_list.
% 1.85/2.06
% 1.85/2.06 -------> usable clausifies to:
% 1.85/2.06
% 1.85/2.06 list(usable).
% 1.85/2.06 0 [] A=A.
% 1.85/2.06 0 [] -object(X)| -property(X).
% 1.85/2.06 0 [] -exemplifies_property(F,X)|property(F).
% 1.85/2.06 0 [] -exemplifies_property(F,X)|object(X).
% 1.85/2.06 0 [] -is_the(X,F)|property(F).
% 1.85/2.06 0 [] -is_the(X,F)|object(X).
% 1.85/2.06 0 [] -property(F)| -object(X)| -object(W)| -is_the(X,F)|X!=W|object($f1(F,X,W)).
% 1.85/2.06 0 [] -property(F)| -object(X)| -object(W)| -is_the(X,F)|X!=W|exemplifies_property(F,$f1(F,X,W)).
% 1.85/2.06 0 [] -property(F)| -object(X)| -object(W)| -is_the(X,F)|X!=W| -object(Z)| -exemplifies_property(F,Z)|Z=$f1(F,X,W).
% 1.85/2.06 0 [] -property(F)| -object(X)| -object(W)| -is_the(X,F)|X!=W|$f1(F,X,W)=W.
% 1.85/2.06 0 [] -property(F)| -object(X)| -object(W)|is_the(X,F)| -object(Y)| -exemplifies_property(F,Y)|object($f2(F,X,W,Y))|Y!=W.
% 1.85/2.06 0 [] -property(F)| -object(X)| -object(W)|is_the(X,F)| -object(Y)| -exemplifies_property(F,Y)|exemplifies_property(F,$f2(F,X,W,Y))|Y!=W.
% 1.85/2.06 0 [] -property(F)| -object(X)| -object(W)|is_the(X,F)| -object(Y)| -exemplifies_property(F,Y)|$f2(F,X,W,Y)!=Y|Y!=W.
% 1.85/2.06 0 [] -property(F)| -object(X)| -object(W)|X=W| -object(Y)| -exemplifies_property(F,Y)|object($f2(F,X,W,Y))|Y!=W.
% 1.85/2.06 0 [] -property(F)| -object(X)| -object(W)|X=W| -object(Y)| -exemplifies_property(F,Y)|exemplifies_property(F,$f2(F,X,W,Y))|Y!=W.
% 1.85/2.06 0 [] -property(F)| -object(X)| -object(W)|X=W| -object(Y)| -exemplifies_property(F,Y)|$f2(F,X,W,Y)!=Y|Y!=W.
% 1.85/2.06 0 [] object($c3).
% 1.85/2.06 0 [] property($c2).
% 1.85/2.06 0 [] object($c1).
% 1.85/2.06 0 [] is_the($c3,$c2).
% 1.85/2.06 0 [] $c3=$c1.
% 1.85/2.06 0 [] -exemplifies_property($c2,$c1).
% 1.85/2.06 end_of_list.
% 1.85/2.06
% 1.85/2.06 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 1.85/2.06
% 1.85/2.06 This ia a non-Horn set with equality. The strategy will be
% 1.85/2.06 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.85/2.06 deletion, with positive clauses in sos and nonpositive
% 1.85/2.06 clauses in usable.
% 1.85/2.06
% 1.85/2.06 dependent: set(knuth_bendix).
% 1.85/2.06 dependent: set(anl_eq).
% 1.85/2.06 dependent: set(para_from).
% 1.85/2.06 dependent: set(para_into).
% 1.85/2.06 dependent: clear(para_from_right).
% 1.85/2.06 dependent: clear(para_into_right).
% 1.85/2.06 dependent: set(para_from_vars).
% 1.85/2.06 dependent: set(eq_units_both_ways).
% 1.85/2.06 dependent: set(dynamic_demod_all).
% 1.85/2.06 dependent: set(dynamic_demod).
% 1.85/2.06 dependent: set(order_eq).
% 1.85/2.06 dependent: set(back_demod).
% 1.85/2.06 dependent: set(lrpo).
% 1.85/2.06 dependent: set(hyper_res).
% 1.85/2.06 dependent: set(unit_deletion).
% 1.85/2.06 dependent: set(factor).
% 1.85/2.06
% 1.85/2.06 ------------> process usable:
% 1.85/2.06 ** KEPT (pick-wt=4): 1 [] -object(A)| -property(A).
% 1.85/2.06 ** KEPT (pick-wt=5): 2 [] -exemplifies_property(A,B)|property(A).
% 1.85/2.06 ** KEPT (pick-wt=5): 3 [] -exemplifies_property(A,B)|object(B).
% 1.85/2.06 ** KEPT (pick-wt=5): 4 [] -is_the(A,B)|property(B).
% 1.85/2.06 ** KEPT (pick-wt=5): 5 [] -is_the(A,B)|object(A).
% 1.85/2.06 ** KEPT (pick-wt=17): 6 [] -property(A)| -object(B)| -object(C)| -is_the(B,A)|B!=C|object($f1(A,B,C)).
% 1.85/2.06 ** KEPT (pick-wt=18): 7 [] -property(A)| -object(B)| -object(C)| -is_the(B,A)|B!=C|exemplifies_property(A,$f1(A,B,C)).
% 1.85/2.06 ** KEPT (pick-wt=23): 8 [] -property(A)| -object(B)| -object(C)| -is_the(B,A)|B!=C| -object(D)| -exemplifies_property(A,D)|D=$f1(A,B,C).
% 1.85/2.06 ** KEPT (pick-wt=18): 9 [] -property(A)| -object(B)| -object(C)| -is_the(B,A)|B!=C|$f1(A,B,C)=C.
% 1.88/2.06 ** KEPT (pick-wt=23): 10 [] -property(A)| -object(B)| -object(C)|is_the(B,A)| -object(D)| -exemplifies_property(A,D)|object($f2(A,B,C,D))|D!=C.
% 1.88/2.06 ** KEPT (pick-wt=24): 11 [] -property(A)| -object(B)| -object(C)|is_the(B,A)| -object(D)| -exemplifies_property(A,D)|exemplifies_property(A,$f2(A,B,C,D))|D!=C.
% 1.88/2.06 ** KEPT (pick-wt=24): 12 [] -property(A)| -object(B)| -object(C)|is_the(B,A)| -object(D)| -exemplifies_property(A,D)|$f2(A,B,C,D)!=D|D!=C.
% 1.88/2.06 ** KEPT (pick-wt=23): 13 [] -property(A)| -object(B)| -object(C)|B=C| -object(D)| -exemplifies_property(A,D)|object($f2(A,B,C,D))|D!=C.
% 1.88/2.06 ** KEPT (pick-wt=24): 14 [] -property(A)| -object(B)| -object(C)|B=C| -object(D)| -exemplifies_property(A,D)|exemplifies_property(A,$f2(A,B,C,D))|D!=C.
% 1.88/2.06 ** KEPT (pick-wt=24): 15 [] -property(A)| -object(B)| -object(C)|B=C| -object(D)| -exemplifies_property(A,D)|$f2(A,B,C,D)!=D|D!=C.
% 1.88/2.06 ** KEPT (pick-wt=3): 16 [] -exemplifies_property($c2,$c1).
% 1.88/2.06
% 1.88/2.06 ------------> process sos:
% 1.88/2.06 ** KEPT (pick-wt=3): 40 [] A=A.
% 1.88/2.06 ** KEPT (pick-wt=2): 41 [] object($c3).
% 1.88/2.06 ** KEPT (pick-wt=2): 42 [] property($c2).
% 1.88/2.06 ** KEPT (pick-wt=2): 43 [] object($c1).
% 1.88/2.06 ** KEPT (pick-wt=3): 44 [] is_the($c3,$c2).
% 1.88/2.06 ** KEPT (pick-wt=3): 45 [] $c3=$c1.
% 1.88/2.06 ---> New Demodulator: 46 [new_demod,45] $c3=$c1.
% 1.88/2.06 Following clause subsumed by 40 during input processing: 0 [copy,40,flip.1] A=A.
% 1.88/2.06 40 back subsumes 35.
% 1.88/2.06 40 back subsumes 33.
% 1.88/2.06 40 back subsumes 31.
% 1.88/2.06 >>>> Starting back demodulation with 46.
% 1.88/2.06 >> back demodulating 44 with 46.
% 1.88/2.06 >> back demodulating 41 with 46.
% 1.88/2.06
% 1.88/2.06 ======= end of input processing =======
% 1.88/2.06
% 1.88/2.06 =========== start of search ===========
% 1.88/2.06
% 1.88/2.06 -------- PROOF --------
% 1.88/2.06
% 1.88/2.06 ----> UNIT CONFLICT at 0.01 sec ----> 74 [binary,73.1,16.1] $F.
% 1.88/2.06
% 1.88/2.06 Length of proof is 5. Level of proof is 3.
% 1.88/2.06
% 1.88/2.06 ---------------- PROOF ----------------
% 1.88/2.06 % SZS status Theorem
% 1.88/2.06 % SZS output start Refutation
% See solution above
% 1.88/2.06 ------------ end of proof -------------
% 1.88/2.06
% 1.88/2.06
% 1.88/2.06 Search stopped by max_proofs option.
% 1.88/2.06
% 1.88/2.06
% 1.88/2.06 Search stopped by max_proofs option.
% 1.88/2.06
% 1.88/2.06 ============ end of search ============
% 1.88/2.06
% 1.88/2.06 -------------- statistics -------------
% 1.88/2.06 clauses given 5
% 1.88/2.06 clauses generated 94
% 1.88/2.06 clauses kept 71
% 1.88/2.06 clauses forward subsumed 33
% 1.88/2.06 clauses back subsumed 3
% 1.88/2.06 Kbytes malloced 976
% 1.88/2.06
% 1.88/2.06 ----------- times (seconds) -----------
% 1.88/2.06 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.88/2.06 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.88/2.06 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.88/2.06
% 1.88/2.06 That finishes the proof of the theorem.
% 1.88/2.06
% 1.88/2.06 Process 9325 finished Wed Jul 27 02:55:05 2022
% 1.88/2.06 Otter interrupted
% 1.88/2.06 PROOF FOUND
%------------------------------------------------------------------------------