%------------------------------------------------------------------------------
% File : EQP---0.9e
% Problem : SWX206-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_eqp %s
% Computer : n002.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 07:00:10 PM UTC 2026
% Result : Unsatisfiable 0.75s 1.13s
% Output : Refutation 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 10 ( 10 unt; 0 nHn; 4 RR)
% Number of literals : 10 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 7 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,plain,
equal(impl(btrue,A),A),
file('SWX206-1.p',unknown),
[] ).
cnf(3,plain,
equal(x2(z,A),A),
file('SWX206-1.p',unknown),
[] ).
cnf(5,plain,
equal(plus_not_idem(A),impl(eq(x2(A,A),A),eq2(btrue,bfalse))),
file('SWX206-1.p',unknown),
[] ).
cnf(7,plain,
equal(eq2(btrue,bfalse),bfalse),
file('SWX206-1.p',unknown),
[] ).
cnf(8,plain,
equal(plus_not_idem(A),impl(eq(x2(A,A),A),bfalse)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[5]),7]),
[iquote('back_demod(5),demod([7])')] ).
cnf(12,plain,
equal(eq(A,A),btrue),
file('SWX206-1.p',unknown),
[] ).
cnf(13,plain,
equal(eq2(A,A),btrue),
file('SWX206-1.p',unknown),
[] ).
cnf(14,plain,
~ equal(eq2(impl(eq(x2(A,A),A),bfalse),bfalse),btrue),
inference(demod,[status(thm),theory(equality)],[8]),
[iquote('demod([8])')] ).
cnf(27,plain,
~ equal(btrue,btrue),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[3,14]),12,1,13]),
[iquote('para(3,14),demod([12,1,13])')] ).
cnf(28,plain,
$false,
inference(conflict,[status(thm)],[27]),
[iquote('xx_conflict(27)')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWX206-1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : tptp2X_and_run_eqp %s
% 0.18/0.35 % Computer : n002.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue May 5 11:34:01 EDT 2026
% 0.18/0.35 % CPUTime :
% 0.75/1.13 ----- EQP 0.9e, May 2009 -----
% 0.75/1.13 The job began on n002.cluster.edu, Tue May 5 11:34:02 2026
% 0.75/1.13 The command was "./eqp09e".
% 0.75/1.13
% 0.75/1.13 set(prolog_style_variables).
% 0.75/1.13 set(lrpo).
% 0.75/1.13 set(basic_paramod).
% 0.75/1.13 set(functional_subsume).
% 0.75/1.13 set(ordered_paramod).
% 0.75/1.13 set(prime_paramod).
% 0.75/1.13 set(para_pairs).
% 0.75/1.13 assign(pick_given_ratio,4).
% 0.75/1.13 clear(print_kept).
% 0.75/1.13 clear(print_new_demod).
% 0.75/1.13 clear(print_back_demod).
% 0.75/1.13 clear(print_given).
% 0.75/1.13 assign(max_mem,64000).
% 0.75/1.13 end_of_commands.
% 0.75/1.13
% 0.75/1.13 Usable:
% 0.75/1.13 end_of_list.
% 0.75/1.13
% 0.75/1.13 Sos:
% 0.75/1.13 0 (wt=-1) [] impl(btrue,A) = A.
% 0.75/1.13 0 (wt=-1) [] impl(bfalse,A) = btrue.
% 0.75/1.13 0 (wt=-1) [] x2(z,A) = A.
% 0.75/1.13 0 (wt=-1) [] x2(s(A),B) = s(x2(A,B)).
% 0.75/1.13 0 (wt=-1) [] plus_not_idem(A) = impl(eq(x2(A,A),A),eq2(btrue,bfalse)).
% 0.75/1.13 0 (wt=-1) [] eq2(bfalse,btrue) = bfalse.
% 0.75/1.13 0 (wt=-1) [] eq2(btrue,bfalse) = bfalse.
% 0.75/1.13 0 (wt=-1) [] eq(s(A),s(B)) = eq(A,B).
% 0.75/1.13 0 (wt=-1) [] eq(z,s(A)) = bfalse.
% 0.75/1.13 0 (wt=-1) [] eq(s(A),z) = bfalse.
% 0.75/1.13 0 (wt=-1) [] eq(A,A) = btrue.
% 0.75/1.13 0 (wt=-1) [] eq2(A,A) = btrue.
% 0.75/1.13 0 (wt=-1) [] -(eq2(plus_not_idem(A),bfalse) = btrue).
% 0.75/1.13 end_of_list.
% 0.75/1.13
% 0.75/1.13 Demodulators:
% 0.75/1.13 end_of_list.
% 0.75/1.13
% 0.75/1.13 Passive:
% 0.75/1.13 end_of_list.
% 0.75/1.13
% 0.75/1.13 Starting to process input.
% 0.75/1.13
% 0.75/1.13 ** KEPT: 1 (wt=5) [] impl(btrue,A) = A.
% 0.75/1.13 1 is a new demodulator.
% 0.75/1.13
% 0.75/1.13 ** KEPT: 2 (wt=5) [] impl(bfalse,A) = btrue.
% 0.75/1.13 2 is a new demodulator.
% 0.75/1.13
% 0.75/1.13 ** KEPT: 3 (wt=5) [] x2(z,A) = A.
% 0.75/1.13 3 is a new demodulator.
% 0.75/1.13
% 0.75/1.13 ** KEPT: 4 (wt=9) [flip(1)] s(x2(A,B)) = x2(s(A),B).
% 0.75/1.13 4 is a new demodulator.
% 0.75/1.13
% 0.75/1.13 ** KEPT: 5 (wt=12) [] plus_not_idem(A) = impl(eq(x2(A,A),A),eq2(btrue,bfalse)).
% 0.75/1.13 5 is a new demodulator.
% 0.75/1.13
% 0.75/1.13 ** KEPT: 6 (wt=5) [] eq2(bfalse,btrue) = bfalse.
% 0.75/1.13 6 is a new demodulator.
% 0.75/1.13
% 0.75/1.13 ** KEPT: 7 (wt=5) [] eq2(btrue,bfalse) = bfalse.
% 0.75/1.13 7 is a new demodulator.
% 0.75/1.13 -> 7 back demodulating 5.
% 0.75/1.13
% 0.75/1.13 ** KEPT: 8 (wt=10) [back_demod(5),demod([7])] plus_not_idem(A) = impl(eq(x2(A,A),A),bfalse).
% 0.75/1.13 8 is a new demodulator.
% 0.75/1.13
% 0.75/1.13 ** KEPT: 9 (wt=9) [] eq(s(A),s(B)) = eq(A,B).
% 0.75/1.13 9 is a new demodulator.
% 0.75/1.13
% 0.75/1.13 ** KEPT: 10 (wt=6) [] eq(z,s(A)) = bfalse.
% 0.75/1.13 10 is a new demodulator.
% 0.75/1.13
% 0.75/1.13 ** KEPT: 11 (wt=6) [] eq(s(A),z) = bfalse.
% 0.75/1.13 11 is a new demodulator.
% 0.75/1.13
% 0.75/1.13 ** KEPT: 12 (wt=5) [] eq(A,A) = btrue.
% 0.75/1.13 12 is a new demodulator.
% 0.75/1.13
% 0.75/1.13 ** KEPT: 13 (wt=5) [] eq2(A,A) = btrue.
% 0.75/1.13 13 is a new demodulator.
% 0.75/1.13
% 0.75/1.13 ** KEPT: 14 (wt=11) [demod([8])] -(eq2(impl(eq(x2(A,A),A),bfalse),bfalse) = btrue).
% 0.75/1.13 ---------------- PROOF FOUND ----------------
% 0.75/1.13 % SZS status Unsatisfiable
% 0.75/1.13
% 0.75/1.13
% 0.75/1.13 After processing input:
% 0.75/1.13
% 0.75/1.13 Usable:
% 0.75/1.13 end_of_list.
% 0.75/1.13
% 0.75/1.13 Sos:
% 0.75/1.13 1 (wt=5) [] impl(btrue,A) = A.
% 0.75/1.13 2 (wt=5) [] impl(bfalse,A) = btrue.
% 0.75/1.13 3 (wt=5) [] x2(z,A) = A.
% 0.75/1.13 6 (wt=5) [] eq2(bfalse,btrue) = bfalse.
% 0.75/1.13 7 (wt=5) [] eq2(btrue,bfalse) = bfalse.
% 0.75/1.13 12 (wt=5) [] eq(A,A) = btrue.
% 0.75/1.13 13 (wt=5) [] eq2(A,A) = btrue.
% 0.75/1.13 10 (wt=6) [] eq(z,s(A)) = bfalse.
% 0.75/1.13 11 (wt=6) [] eq(s(A),z) = bfalse.
% 0.75/1.13 4 (wt=9) [flip(1)] s(x2(A,B)) = x2(s(A),B).
% 0.75/1.13 9 (wt=9) [] eq(s(A),s(B)) = eq(A,B).
% 0.75/1.13 8 (wt=10) [back_demod(5),demod([7])] plus_not_idem(A) = impl(eq(x2(A,A),A),bfalse).
% 0.75/1.13 14 (wt=11) [demod([8])] -(eq2(impl(eq(x2(A,A),A),bfalse),bfalse) = btrue).
% 0.75/1.13 end_of_list.
% 0.75/1.13
% 0.75/1.13 Demodulators:
% 0.75/1.13 1 (wt=5) [] impl(btrue,A) = A.
% 0.75/1.13 2 (wt=5) [] impl(bfalse,A) = btrue.
% 0.75/1.13 3 (wt=5) [] x2(z,A) = A.
% 0.75/1.13 4 (wt=9) [flip(1)] s(x2(A,B)) = x2(s(A),B).
% 0.75/1.13 6 (wt=5) [] eq2(bfalse,btrue) = bfalse.
% 0.75/1.13 7 (wt=5) [] eq2(btrue,bfalse) = bfalse.
% 0.75/1.13 8 (wt=10) [back_demod(5),demod([7])] plus_not_idem(A) = impl(eq(x2(A,A),A),bfalse).
% 0.75/1.13 9 (wt=9) [] eq(s(A),s(B)) = eq(A,B).
% 0.75/1.13 10 (wt=6) [] eq(z,s(A)) = bfalse.
% 0.75/1.13 11 (wt=6) [] eq(s(A),z) = bfalse.
% 0.75/1.13 12 (wt=5) [] eq(A,A) = btrue.
% 0.75/1.13 13 (wt=5) [] eq2(A,A) = btrue.
% 0.75/1.13 end_of_list.
% 0.75/1.13
% 0.75/1.13 Passive:
% 0.75/1.13 end_of_list.
% 0.75/1.13
% 0.75/1.13 UNIT CONFLICT from 27 and x=x at 0.00 seconds.
% 0.75/1.13
% 0.75/1.13 ---------------- PROOF ----------------
% 0.75/1.13 % SZS output start Refutation
% See solution above
% 0.75/1.13 ------------ end of proof -------------
% 0.75/1.13
% 0.75/1.13
% 0.75/1.13 ------------- memory usage ------------
% 0.75/1.13 Memory dynamically allocated (tp_alloc): 488.
% 0.75/1.14 type (bytes each) gets frees in use avail bytes
% 0.75/1.14 sym_ent ( 96) 61 0 61 0 5.7 K
% 0.75/1.14 term ( 16) 1143 928 215 12 4.3 K
% 0.75/1.14 gen_ptr ( 8) 888 217 671 9 5.3 K
% 0.75/1.14 context ( 808) 1638 1636 2 2 3.2 K
% 0.75/1.14 trail ( 12) 41 41 0 3 0.0 K
% 0.75/1.14 bt_node ( 68) 745 742 3 2 0.3 K
% 0.75/1.14 ac_position (285432) 0 0 0 0 0.0 K
% 0.75/1.14 ac_match_pos (14044) 0 0 0 0 0.0 K
% 0.75/1.14 ac_match_free_vars_pos (4020)
% 0.75/1.14 0 0 0 0 0.0 K
% 0.75/1.14 discrim ( 12) 215 25 190 0 2.2 K
% 0.75/1.14 flat ( 40) 662 662 0 9 0.4 K
% 0.75/1.14 discrim_pos ( 12) 14 14 0 1 0.0 K
% 0.75/1.14 fpa_head ( 12) 179 0 179 0 2.1 K
% 0.75/1.14 fpa_tree ( 28) 56 56 0 9 0.2 K
% 0.75/1.14 fpa_pos ( 36) 47 47 0 1 0.0 K
% 0.75/1.14 literal ( 12) 77 50 27 0 0.3 K
% 0.75/1.14 clause ( 24) 77 50 27 0 0.6 K
% 0.75/1.14 list ( 12) 80 24 56 4 0.7 K
% 0.75/1.14 list_pos ( 20) 118 28 90 0 1.8 K
% 0.75/1.14 pair_index ( 40) 2 0 2 0 0.1 K
% 0.75/1.14
% 0.75/1.14 -------------- statistics -------------
% 0.75/1.14 Clauses input 13
% 0.75/1.14 Usable input 0
% 0.75/1.14 Sos input 13
% 0.75/1.14 Demodulators input 0
% 0.75/1.14 Passive input 0
% 0.75/1.14
% 0.75/1.14 Processed BS (before search) 14
% 0.75/1.14 Forward subsumed BS 0
% 0.75/1.14 Kept BS 14
% 0.75/1.14 New demodulators BS 13
% 0.75/1.14 Back demodulated BS 1
% 0.75/1.14
% 0.75/1.14 Clauses or pairs given 165
% 0.75/1.14 Clauses generated 36
% 0.75/1.14 Forward subsumed 23
% 0.75/1.14 Deleted by weight 0
% 0.75/1.14 Deleted by variable count 0
% 0.75/1.14 Kept 13
% 0.75/1.14 New demodulators 8
% 0.75/1.14 Back demodulated 2
% 0.75/1.14 Ordered paramod prunes 0
% 0.75/1.14 Basic paramod prunes 55
% 0.75/1.14 Prime paramod prunes 0
% 0.75/1.14 Semantic prunes 0
% 0.75/1.14
% 0.75/1.14 Rewrite attmepts 277
% 0.75/1.14 Rewrites 12
% 0.75/1.14
% 0.75/1.14 FPA overloads 0
% 0.75/1.14 FPA underloads 0
% 0.75/1.14
% 0.75/1.14 Usable size 0
% 0.75/1.14 Sos size 23
% 0.75/1.14 Demodulators size 18
% 0.75/1.14 Passive size 0
% 0.75/1.14 Disabled size 3
% 0.75/1.14
% 0.75/1.14 Proofs found 1
% 0.75/1.14
% 0.75/1.14 ----------- times (seconds) ----------- Tue May 5 11:34:02 2026
% 0.75/1.14
% 0.75/1.14 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 0.75/1.14 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 0.75/1.14 wall-clock time 0 (0 hr, 0 min, 0 sec)
% 0.75/1.14 input time 0.00
% 0.75/1.14 paramodulation time 0.00
% 0.75/1.14 demodulation time 0.00
% 0.75/1.14 orient time 0.00
% 0.75/1.14 weigh time 0.00
% 0.75/1.14 forward subsume time 0.00
% 0.75/1.14 back demod find time 0.00
% 0.75/1.14 conflict time 0.00
% 0.75/1.14 LRPO time 0.00
% 0.75/1.14 store clause time 0.00
% 0.75/1.14 disable clause time 0.00
% 0.75/1.14 prime paramod time 0.00
% 0.75/1.14 semantics time 0.00
% 0.75/1.14
% 0.75/1.14 EQP interrupted
%------------------------------------------------------------------------------