%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SWX186-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 : Tue May 5 07:05:22 PM UTC 2026
% Result : Unsatisfiable 1.88s 2.10s
% Output : Refutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 3 RR)
% Number of literals : 15 ( 14 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 28 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
e_q3(prop_drop_inj2(A,B,C),bfalse) != btrue,
file('SWX186-1.p',unknown),
[] ).
cnf(4,axiom,
A = A,
file('SWX186-1.p',unknown),
[] ).
cnf(6,axiom,
impl(btrue,A) = A,
file('SWX186-1.p',unknown),
[] ).
cnf(9,axiom,
drop(s(A),nil) = nil,
file('SWX186-1.p',unknown),
[] ).
cnf(11,axiom,
drop(s(A),cons(B,C)) = drop(A,C),
file('SWX186-1.p',unknown),
[] ).
cnf(15,axiom,
prop_drop_inj2(A,B,C) = impl(e_q(drop(A,B),drop(A,C)),e_q(B,C)),
file('SWX186-1.p',unknown),
[] ).
cnf(16,plain,
impl(e_q(drop(A,B),drop(A,C)),e_q(B,C)) = prop_drop_inj2(A,B,C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(29,axiom,
e_q(A,A) = btrue,
file('SWX186-1.p',unknown),
[] ).
cnf(33,axiom,
e_q3(A,A) = btrue,
file('SWX186-1.p',unknown),
[] ).
cnf(37,axiom,
e_q(cons(A,B),nil) = bfalse,
file('SWX186-1.p',unknown),
[] ).
cnf(47,plain,
impl(e_q(drop(A,B),drop(s(A),C)),e_q(cons(D,B),C)) = prop_drop_inj2(s(A),cons(D,B),C),
inference(para_into,[status(thm),theory(equality)],[16,11]),
[iquote('para_into,16.1.1.1.1,11.1.1')] ).
cnf(93,plain,
impl(e_q(drop(A,B),nil),bfalse) = prop_drop_inj2(s(A),cons(C,B),nil),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[47,9]),37]),
[iquote('para_into,47.1.1.1.2,9.1.1,demod,37')] ).
cnf(109,plain,
prop_drop_inj2(s(s(A)),cons(B,nil),nil) = bfalse,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[93,9]),29,6])]),
[iquote('para_into,93.1.1.1.1,9.1.1,demod,29,6,flip.1')] ).
cnf(114,plain,
btrue != btrue,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[109,3]),33]),
[iquote('para_from,109.1.1,3.1.1.1,demod,33')] ).
cnf(115,plain,
$false,
inference(binary,[status(thm)],[114,4]),
[iquote('binary,114.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX186-1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.16/0.33 % Computer : n022.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 09:38:51 EDT 2026
% 0.16/0.34 % CPUTime :
% 1.88/2.10 ----- Otter 3.3f, August 2004 -----
% 1.88/2.10 The process was started by sandbox2 on n022.cluster.edu,
% 1.88/2.10 Tue May 5 09:38:51 2026
% 1.88/2.10 The command was "./otter". The process ID is 14362.
% 1.88/2.10
% 1.88/2.10 set(prolog_style_variables).
% 1.88/2.10 set(auto).
% 1.88/2.10 dependent: set(auto1).
% 1.88/2.10 dependent: set(process_input).
% 1.88/2.10 dependent: clear(print_kept).
% 1.88/2.10 dependent: clear(print_new_demod).
% 1.88/2.10 dependent: clear(print_back_demod).
% 1.88/2.10 dependent: clear(print_back_sub).
% 1.88/2.10 dependent: set(control_memory).
% 1.88/2.10 dependent: assign(max_mem, 12000).
% 1.88/2.10 dependent: assign(pick_given_ratio, 4).
% 1.88/2.10 dependent: assign(stats_level, 1).
% 1.88/2.10 dependent: assign(max_seconds, 10800).
% 1.88/2.10 clear(print_given).
% 1.88/2.10
% 1.88/2.10 list(usable).
% 1.88/2.10 0 [] A=A.
% 1.88/2.10 0 [] impl(btrue,Q)=Q.
% 1.88/2.10 0 [] impl(bfalse,Q)=btrue.
% 1.88/2.10 0 [] drop(s(Z),nil)=nil.
% 1.88/2.10 0 [] drop(s(Z),cons(X2,X3))=drop(Z,X3).
% 1.88/2.10 0 [] drop(z,Y)=Y.
% 1.88/2.10 0 [] prop_drop_inj2(X,Y,Z)=impl(e_q(drop(X,Y),drop(X,Z)),e_q(Y,Z)).
% 1.88/2.10 0 [] e_q3(bfalse,btrue)=bfalse.
% 1.88/2.10 0 [] e_q3(btrue,bfalse)=bfalse.
% 1.88/2.10 0 [] e_q2(s(X),s(Y))=e_q2(X,Y).
% 1.88/2.10 0 [] e_q2(s(X),z)=bfalse.
% 1.88/2.10 0 [] e_q2(z,s(X))=bfalse.
% 1.88/2.10 0 [] e_q(X,X)=btrue.
% 1.88/2.10 0 [] e_q2(X,X)=btrue.
% 1.88/2.10 0 [] e_q3(X,X)=btrue.
% 1.88/2.10 0 [] e_q2(X,Z)!=bfalse|e_q(cons(X,Y),cons(Z,X2))=bfalse.
% 1.88/2.10 0 [] e_q2(X,Z)!=btrue|e_q(cons(X,Y),cons(Z,X2))=e_q(Y,X2).
% 1.88/2.10 0 [] e_q(nil,cons(X,Y))=bfalse.
% 1.88/2.10 0 [] e_q(cons(X,Y),nil)=bfalse.
% 1.88/2.10 0 [] e_q3(prop_drop_inj2(X,Y,Z),bfalse)!=btrue.
% 1.88/2.10 end_of_list.
% 1.88/2.10
% 1.88/2.10 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.88/2.10
% 1.88/2.10 This is a Horn set with equality. The strategy will be
% 1.88/2.10 Knuth-Bendix and hyper_res, with positive clauses in
% 1.88/2.10 sos and nonpositive clauses in usable.
% 1.88/2.10
% 1.88/2.10 dependent: set(knuth_bendix).
% 1.88/2.10 dependent: set(anl_eq).
% 1.88/2.10 dependent: set(para_from).
% 1.88/2.10 dependent: set(para_into).
% 1.88/2.10 dependent: clear(para_from_right).
% 1.88/2.10 dependent: clear(para_into_right).
% 1.88/2.10 dependent: set(para_from_vars).
% 1.88/2.10 dependent: set(eq_units_both_ways).
% 1.88/2.10 dependent: set(dynamic_demod_all).
% 1.88/2.10 dependent: set(dynamic_demod).
% 1.88/2.10 dependent: set(order_eq).
% 1.88/2.10 dependent: set(back_demod).
% 1.88/2.10 dependent: set(lrpo).
% 1.88/2.10 dependent: set(hyper_res).
% 1.88/2.10 dependent: clear(order_hyper).
% 1.88/2.10
% 1.88/2.10 ------------> process usable:
% 1.88/2.10 ** KEPT (pick-wt=14): 1 [] e_q2(A,B)!=bfalse|e_q(cons(A,C),cons(B,D))=bfalse.
% 1.88/2.10 ** KEPT (pick-wt=16): 2 [] e_q2(A,B)!=btrue|e_q(cons(A,C),cons(B,D))=e_q(C,D).
% 1.88/2.10 ** KEPT (pick-wt=8): 3 [] e_q3(prop_drop_inj2(A,B,C),bfalse)!=btrue.
% 1.88/2.10
% 1.88/2.10 ------------> process sos:
% 1.88/2.10 ** KEPT (pick-wt=3): 4 [] A=A.
% 1.88/2.10 ** KEPT (pick-wt=5): 5 [] impl(btrue,A)=A.
% 1.88/2.10 ---> New Demodulator: 6 [new_demod,5] impl(btrue,A)=A.
% 1.88/2.10 ** KEPT (pick-wt=5): 7 [] impl(bfalse,A)=btrue.
% 1.88/2.10 ---> New Demodulator: 8 [new_demod,7] impl(bfalse,A)=btrue.
% 1.88/2.10 ** KEPT (pick-wt=6): 9 [] drop(s(A),nil)=nil.
% 1.88/2.10 ---> New Demodulator: 10 [new_demod,9] drop(s(A),nil)=nil.
% 1.88/2.10 ** KEPT (pick-wt=10): 11 [] drop(s(A),cons(B,C))=drop(A,C).
% 1.88/2.10 ---> New Demodulator: 12 [new_demod,11] drop(s(A),cons(B,C))=drop(A,C).
% 1.88/2.10 ** KEPT (pick-wt=5): 13 [] drop(z,A)=A.
% 1.88/2.10 ---> New Demodulator: 14 [new_demod,13] drop(z,A)=A.
% 1.88/2.10 ** KEPT (pick-wt=16): 16 [copy,15,flip.1] impl(e_q(drop(A,B),drop(A,C)),e_q(B,C))=prop_drop_inj2(A,B,C).
% 1.88/2.10 ---> New Demodulator: 17 [new_demod,16] impl(e_q(drop(A,B),drop(A,C)),e_q(B,C))=prop_drop_inj2(A,B,C).
% 1.88/2.10 ** KEPT (pick-wt=5): 18 [] e_q3(bfalse,btrue)=bfalse.
% 1.88/2.10 ---> New Demodulator: 19 [new_demod,18] e_q3(bfalse,btrue)=bfalse.
% 1.88/2.10 ** KEPT (pick-wt=5): 20 [] e_q3(btrue,bfalse)=bfalse.
% 1.88/2.10 ---> New Demodulator: 21 [new_demod,20] e_q3(btrue,bfalse)=bfalse.
% 1.88/2.10 ** KEPT (pick-wt=9): 22 [] e_q2(s(A),s(B))=e_q2(A,B).
% 1.88/2.10 ---> New Demodulator: 23 [new_demod,22] e_q2(s(A),s(B))=e_q2(A,B).
% 1.88/2.10 ** KEPT (pick-wt=6): 24 [] e_q2(s(A),z)=bfalse.
% 1.88/2.10 ---> New Demodulator: 25 [new_demod,24] e_q2(s(A),z)=bfalse.
% 1.88/2.10 ** KEPT (pick-wt=6): 26 [] e_q2(z,s(A))=bfalse.
% 1.88/2.10 ---> New Demodulator: 27 [new_demod,26] e_q2(z,s(A))=bfalse.
% 1.88/2.10 ** KEPT (pick-wt=5): 28 [] e_q(A,A)=btrue.
% 1.88/2.10 ---> New Demodulator: 29 [new_demod,28] e_q(A,A)=btrue.
% 1.88/2.10 ** KEPT (pick-wt=5): 30 [] e_q2(A,A)=btrue.
% 1.88/2.10 ---> New Demodulator: 31 [new_demod,30] e_q2(A,A)=btrue.
% 1.88/2.10 ** KEPT (pick-wt=5): 32 [] e_q3(A,A)=btrue.
% 1.88/2.10 ---> New Demodulator: 33 [new_demod,32] e_q3(A,A)=btrue.
% 1.88/2.10 ** KEPT (pick-wt=7): 34 [] e_q(nil,cons(A,B))=bfalse.
% 1.88/2.10 ---> New Demodulator: 35 [new_demod,34] e_q(nil,cons(A,B))=bfalse.
% 1.88/2.10 ** KEPT (pick-wt=7): 36 [] e_q(cons(A,B),nil)=bfalse.
% 1.88/2.10 ---> New Demodulator: 37 [new_demod,36] e_q(cons(A,B),nil)=bfalse.
% 1.88/2.10 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 1.88/2.10 >>>> Starting back demodulation with 6.
% 1.88/2.10 >>>> Starting back demodulation with 8.
% 1.88/2.10 >>>> Starting back demodulation with 10.
% 1.88/2.10 >>>> Starting back demodulation with 12.
% 1.88/2.10 >>>> Starting back demodulation with 14.
% 1.88/2.10 >>>> Starting back demodulation with 17.
% 1.88/2.10 >>>> Starting back demodulation with 19.
% 1.88/2.10 >>>> Starting back demodulation with 21.
% 1.88/2.10 >>>> Starting back demodulation with 23.
% 1.88/2.10 >>>> Starting back demodulation with 25.
% 1.88/2.10 >>>> Starting back demodulation with 27.
% 1.88/2.10 >>>> Starting back demodulation with 29.
% 1.88/2.10 >>>> Starting back demodulation with 31.
% 1.88/2.10 >>>> Starting back demodulation with 33.
% 1.88/2.10 >>>> Starting back demodulation with 35.
% 1.88/2.10 >>>> Starting back demodulation with 37.
% 1.88/2.10
% 1.88/2.10 ======= end of input processing =======
% 1.88/2.10
% 1.88/2.10 =========== start of search ===========
% 1.88/2.10
% 1.88/2.10 -------- PROOF --------
% 1.88/2.10
% 1.88/2.10 ----> UNIT CONFLICT at 0.00 sec ----> 115 [binary,114.1,4.1] $F.
% 1.88/2.10
% 1.88/2.10 Length of proof is 5. Level of proof is 5.
% 1.88/2.10
% 1.88/2.10 ---------------- PROOF ----------------
% 1.88/2.10 % SZS status Unsatisfiable
% 1.88/2.10 % SZS output start Refutation
% See solution above
% 1.88/2.10 ------------ end of proof -------------
% 1.88/2.10
% 1.88/2.10
% 1.88/2.10 Search stopped by max_proofs option.
% 1.88/2.10
% 1.88/2.10
% 1.88/2.10 Search stopped by max_proofs option.
% 1.88/2.10
% 1.88/2.10 ============ end of search ============
% 1.88/2.10
% 1.88/2.10 -------------- statistics -------------
% 1.88/2.10 clauses given 34
% 1.88/2.10 clauses generated 172
% 1.88/2.10 clauses kept 73
% 1.88/2.10 clauses forward subsumed 125
% 1.88/2.10 clauses back subsumed 1
% 1.88/2.10 Kbytes malloced 1953
% 1.88/2.10
% 1.88/2.10 ----------- times (seconds) -----------
% 1.88/2.10 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.88/2.10 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.88/2.10 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.88/2.10
% 1.88/2.10 That finishes the proof of the theorem.
% 1.88/2.10
% 1.88/2.10 Process 14362 finished Tue May 5 09:38:52 2026
% 1.88/2.10 Otter interrupted
% 1.88/2.10 PROOF FOUND
%------------------------------------------------------------------------------