%------------------------------------------------------------------------------
% File : EQP---0.9e
% Problem : SWX204-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_eqp %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 07:00:09 PM UTC 2026
% Result : Unsatisfiable 0.74s 1.13s
% Output : Refutation 0.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 6 RR)
% Number of literals : 20 ( 0 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,plain,
equal(x2(z,A),A),
file('SWX204-1.p',unknown),
[] ).
cnf(2,plain,
equal(s(x2(A,B)),x2(s(A),B)),
inference(flip,[status(thm),theory(equality)],[1]),
[iquote('flip(1)')] ).
cnf(3,plain,
equal(x22(z,A),z),
file('SWX204-1.p',unknown),
[] ).
cnf(4,plain,
equal(x22(s(A),B),x2(B,x22(A,B))),
file('SWX204-1.p',unknown),
[] ).
cnf(5,plain,
equal(mul_idem(A),eq(x22(A,A),A)),
file('SWX204-1.p',unknown),
[] ).
cnf(8,plain,
equal(eq(s(A),s(B)),eq(A,B)),
file('SWX204-1.p',unknown),
[] ).
cnf(10,plain,
equal(eq(s(A),z),bfalse),
file('SWX204-1.p',unknown),
[] ).
cnf(12,plain,
equal(eq2(A,A),btrue),
file('SWX204-1.p',unknown),
[] ).
cnf(13,plain,
~ equal(eq2(eq(x22(A,A),A),bfalse),btrue),
inference(demod,[status(thm),theory(equality)],[5]),
[iquote('demod([5])')] ).
cnf(14,plain,
equal(s(A),x2(s(z),A)),
inference(para,[status(thm),theory(equality)],[1,2]),
[iquote('para(1,2)')] ).
cnf(21,plain,
equal(eq(x2(s(A),B),s(C)),eq(x2(A,B),C)),
inference(para,[status(thm),theory(equality)],[2,8]),
[iquote('para(2,8)')] ).
cnf(25,plain,
equal(eq(x2(s(A),B),z),bfalse),
inference(para,[status(thm),theory(equality)],[2,10]),
[iquote('para(2,10)')] ).
cnf(26,plain,
~ equal(eq2(eq(x2(A,x22(A,s(A))),A),bfalse),btrue),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[4,13]),21]),
[iquote('para(4,13),demod([21])')] ).
cnf(29,plain,
equal(x2(s(z),x2(A,B)),x2(s(A),B)),
inference(para,[status(thm),theory(equality)],[14,2]),
[iquote('para(14,2)')] ).
cnf(30,plain,
equal(x2(s(A),B),x2(s(z),x2(A,B))),
inference(flip,[status(thm),theory(equality)],[29]),
[iquote('flip(29)')] ).
cnf(60,plain,
equal(x2(x2(s(z),A),B),x2(s(z),x2(A,B))),
inference(para,[status(thm),theory(equality)],[14,30]),
[iquote('para(14,30)')] ).
cnf(65,plain,
~ equal(eq2(eq(x2(A,x22(A,x2(s(z),A))),A),bfalse),btrue),
inference(para,[status(thm),theory(equality)],[14,26]),
[iquote('para(14,26)')] ).
cnf(76,plain,
~ equal(eq2(eq(x2(A,x2(s(z),x2(s(A),x22(A,x2(s(z),s(A)))))),A),bfalse),btrue),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[4,65]),60,21]),
[iquote('para(4,65),demod([60,21])')] ).
cnf(87,plain,
~ equal(btrue,btrue),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[3,76]),1,25,12]),
[iquote('para(3,76),demod([1,25,12])')] ).
cnf(88,plain,
$false,
inference(conflict,[status(thm)],[87]),
[iquote('xx_conflict(87)')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX204-1 : TPTP v9.3.0. Released v9.3.0.
% 0.11/0.13 % Command : tptp2X_and_run_eqp %s
% 0.16/0.34 % Computer : n022.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % 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 11:29:35 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.74/1.13 ----- EQP 0.9e, May 2009 -----
% 0.74/1.13 The job began on n022.cluster.edu, Tue May 5 11:29:36 2026
% 0.74/1.13 The command was "./eqp09e".
% 0.74/1.13
% 0.74/1.13 set(prolog_style_variables).
% 0.74/1.13 set(lrpo).
% 0.74/1.13 set(basic_paramod).
% 0.74/1.13 set(functional_subsume).
% 0.74/1.13 set(ordered_paramod).
% 0.74/1.13 set(prime_paramod).
% 0.74/1.13 set(para_pairs).
% 0.74/1.13 assign(pick_given_ratio,4).
% 0.74/1.13 clear(print_kept).
% 0.74/1.13 clear(print_new_demod).
% 0.74/1.13 clear(print_back_demod).
% 0.74/1.13 clear(print_given).
% 0.74/1.13 assign(max_mem,64000).
% 0.74/1.13 end_of_commands.
% 0.74/1.13
% 0.74/1.13 Usable:
% 0.74/1.13 end_of_list.
% 0.74/1.13
% 0.74/1.13 Sos:
% 0.74/1.13 0 (wt=-1) [] x2(z,A) = A.
% 0.74/1.13 0 (wt=-1) [] x2(s(A),B) = s(x2(A,B)).
% 0.74/1.13 0 (wt=-1) [] x22(z,A) = z.
% 0.74/1.13 0 (wt=-1) [] x22(s(A),B) = x2(B,x22(A,B)).
% 0.74/1.13 0 (wt=-1) [] mul_idem(A) = eq(x22(A,A),A).
% 0.74/1.13 0 (wt=-1) [] eq2(bfalse,btrue) = bfalse.
% 0.74/1.13 0 (wt=-1) [] eq2(btrue,bfalse) = bfalse.
% 0.74/1.13 0 (wt=-1) [] eq(s(A),s(B)) = eq(A,B).
% 0.74/1.13 0 (wt=-1) [] eq(z,s(A)) = bfalse.
% 0.74/1.13 0 (wt=-1) [] eq(s(A),z) = bfalse.
% 0.74/1.13 0 (wt=-1) [] eq(A,A) = btrue.
% 0.74/1.13 0 (wt=-1) [] eq2(A,A) = btrue.
% 0.74/1.13 0 (wt=-1) [] -(eq2(mul_idem(A),bfalse) = btrue).
% 0.74/1.13 end_of_list.
% 0.74/1.13
% 0.74/1.13 Demodulators:
% 0.74/1.13 end_of_list.
% 0.74/1.13
% 0.74/1.13 Passive:
% 0.74/1.13 end_of_list.
% 0.74/1.13
% 0.74/1.13 Starting to process input.
% 0.74/1.13
% 0.74/1.13 ** KEPT: 1 (wt=5) [] x2(z,A) = A.
% 0.74/1.13 1 is a new demodulator.
% 0.74/1.13
% 0.74/1.13 ** KEPT: 2 (wt=9) [flip(1)] s(x2(A,B)) = x2(s(A),B).
% 0.74/1.13 2 is a new demodulator.
% 0.74/1.13
% 0.74/1.13 ** KEPT: 3 (wt=5) [] x22(z,A) = z.
% 0.74/1.13 3 is a new demodulator.
% 0.74/1.13
% 0.74/1.13 ** KEPT: 4 (wt=10) [] x22(s(A),B) = x2(B,x22(A,B)).
% 0.74/1.13 4 is a new demodulator.
% 0.74/1.13
% 0.74/1.13 ** KEPT: 5 (wt=8) [] mul_idem(A) = eq(x22(A,A),A).
% 0.74/1.13 5 is a new demodulator.
% 0.74/1.13
% 0.74/1.13 ** KEPT: 6 (wt=5) [] eq2(bfalse,btrue) = bfalse.
% 0.74/1.13 6 is a new demodulator.
% 0.74/1.13
% 0.74/1.13 ** KEPT: 7 (wt=5) [] eq2(btrue,bfalse) = bfalse.
% 0.74/1.13 7 is a new demodulator.
% 0.74/1.13
% 0.74/1.13 ** KEPT: 8 (wt=9) [] eq(s(A),s(B)) = eq(A,B).
% 0.74/1.13 8 is a new demodulator.
% 0.74/1.13
% 0.74/1.13 ** KEPT: 9 (wt=6) [] eq(z,s(A)) = bfalse.
% 0.74/1.13 9 is a new demodulator.
% 0.74/1.13
% 0.74/1.13 ** KEPT: 10 (wt=6) [] eq(s(A),z) = bfalse.
% 0.74/1.13 10 is a new demodulator.
% 0.74/1.13
% 0.74/1.13 ** KEPT: 11 (wt=5) [] eq(A,A) = btrue.
% 0.74/1.13 11 is a new demodulator.
% 0.74/1.13
% 0.74/1.13 ** KEPT: 12 (wt=5) [] eq2(A,A) = btrue.
% 0.74/1.13 12 is a new demodulator.
% 0.74/1.13
% 0.74/1.13 ** KEPT: 13 (wt=9) [demod([5])] -(eq2(eq(x22(A,A),A),bfalse) = btrue).
% 0.74/1.13 ---------------- PROOF FOUND ----------------
% 0.74/1.13 % SZS status Unsatisfiable
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 After processing input:
% 0.74/1.13
% 0.74/1.13 Usable:
% 0.74/1.13 end_of_list.
% 0.74/1.13
% 0.74/1.13 Sos:
% 0.74/1.13 1 (wt=5) [] x2(z,A) = A.
% 0.74/1.13 3 (wt=5) [] x22(z,A) = z.
% 0.74/1.13 6 (wt=5) [] eq2(bfalse,btrue) = bfalse.
% 0.74/1.13 7 (wt=5) [] eq2(btrue,bfalse) = bfalse.
% 0.74/1.13 11 (wt=5) [] eq(A,A) = btrue.
% 0.74/1.13 12 (wt=5) [] eq2(A,A) = btrue.
% 0.74/1.13 9 (wt=6) [] eq(z,s(A)) = bfalse.
% 0.74/1.13 10 (wt=6) [] eq(s(A),z) = bfalse.
% 0.74/1.13 5 (wt=8) [] mul_idem(A) = eq(x22(A,A),A).
% 0.74/1.13 2 (wt=9) [flip(1)] s(x2(A,B)) = x2(s(A),B).
% 0.74/1.13 8 (wt=9) [] eq(s(A),s(B)) = eq(A,B).
% 0.74/1.13 13 (wt=9) [demod([5])] -(eq2(eq(x22(A,A),A),bfalse) = btrue).
% 0.74/1.13 4 (wt=10) [] x22(s(A),B) = x2(B,x22(A,B)).
% 0.74/1.13 end_of_list.
% 0.74/1.13
% 0.74/1.13 Demodulators:
% 0.74/1.13 1 (wt=5) [] x2(z,A) = A.
% 0.74/1.13 2 (wt=9) [flip(1)] s(x2(A,B)) = x2(s(A),B).
% 0.74/1.13 3 (wt=5) [] x22(z,A) = z.
% 0.74/1.13 4 (wt=10) [] x22(s(A),B) = x2(B,x22(A,B)).
% 0.74/1.13 5 (wt=8) [] mul_idem(A) = eq(x22(A,A),A).
% 0.74/1.13 6 (wt=5) [] eq2(bfalse,btrue) = bfalse.
% 0.74/1.13 7 (wt=5) [] eq2(btrue,bfalse) = bfalse.
% 0.74/1.13 8 (wt=9) [] eq(s(A),s(B)) = eq(A,B).
% 0.74/1.13 9 (wt=6) [] eq(z,s(A)) = bfalse.
% 0.74/1.13 10 (wt=6) [] eq(s(A),z) = bfalse.
% 0.74/1.13 11 (wt=5) [] eq(A,A) = btrue.
% 0.74/1.13 12 (wt=5) [] eq2(A,A) = btrue.
% 0.74/1.13 end_of_list.
% 0.74/1.13
% 0.74/1.13 Passive:
% 0.74/1.13 end_of_list.
% 0.74/1.13
% 0.74/1.13 UNIT CONFLICT from 87 and x=x at 0.01 seconds.
% 0.74/1.13
% 0.74/1.13 ---------------- PROOF ----------------
% 0.74/1.13 % SZS output start Refutation
% See solution above
% 0.74/1.13 ------------ end of proof -------------
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 ------------- memory usage ------------
% 0.74/1.13 Memory dynamically allocated (tp_alloc): 488.
% 0.74/1.13 type (bytes each) gets frees in use avail bytes
% 0.74/1.13 sym_ent ( 96) 60 0 60 0 5.6 K
% 0.74/1.13 term ( 16) 8811 7689 1122 32 22.2 K
% 0.74/1.13 gen_ptr ( 8) 6474 2101 4373 19 34.3 K
% 0.74/1.13 context ( 808) 14578 14576 2 5 5.5 K
% 0.74/1.13 trail ( 12) 245 245 0 7 0.1 K
% 0.74/1.13 bt_node ( 68) 6514 6511 3 7 0.7 K
% 0.74/1.13 ac_position (285432) 0 0 0 0 0.0 K
% 0.74/1.13 ac_match_pos (14044) 0 0 0 0 0.0 K
% 0.74/1.13 ac_match_free_vars_pos (4020)
% 0.74/1.13 0 0 0 0 0.0 K
% 0.74/1.13 discrim ( 12) 976 302 674 11 8.0 K
% 0.74/1.13 flat ( 40) 12949 12949 0 20 0.8 K
% 0.74/1.13 discrim_pos ( 12) 539 539 0 1 0.0 K
% 0.74/1.13 fpa_head ( 12) 661 0 661 0 7.7 K
% 0.74/1.13 fpa_tree ( 28) 215 215 0 9 0.2 K
% 0.74/1.13 fpa_pos ( 36) 139 139 0 1 0.0 K
% 0.74/1.13 literal ( 12) 453 366 87 1 1.0 K
% 0.74/1.13 clause ( 24) 453 366 87 1 2.1 K
% 0.74/1.13 list ( 12) 112 56 56 3 0.7 K
% 0.74/1.13 list_pos ( 20) 388 156 232 2 4.6 K
% 0.74/1.13 pair_index ( 40) 2 0 2 0 0.1 K
% 0.74/1.13
% 0.74/1.13 -------------- statistics -------------
% 0.74/1.13 Clauses input 13
% 0.74/1.13 Usable input 0
% 0.74/1.13 Sos input 13
% 0.74/1.13 Demodulators input 0
% 0.74/1.13 Passive input 0
% 0.74/1.13
% 0.74/1.13 Processed BS (before search) 13
% 0.74/1.13 Forward subsumed BS 0
% 0.74/1.13 Kept BS 13
% 0.74/1.13 New demodulators BS 12
% 0.74/1.13 Back demodulated BS 0
% 0.74/1.13
% 0.74/1.13 Clauses or pairs given 982
% 0.74/1.13 Clauses generated 297
% 0.74/1.13 Forward subsumed 223
% 0.74/1.13 Deleted by weight 0
% 0.74/1.13 Deleted by variable count 0
% 0.74/1.13 Kept 74
% 0.74/1.13 New demodulators 41
% 0.74/1.13 Back demodulated 32
% 0.74/1.13 Ordered paramod prunes 0
% 0.74/1.13 Basic paramod prunes 598
% 0.74/1.13 Prime paramod prunes 14
% 0.74/1.13 Semantic prunes 0
% 0.74/1.13
% 0.74/1.13 Rewrite attmepts 3953
% 0.74/1.13 Rewrites 469
% 0.74/1.13
% 0.74/1.13 FPA overloads 0
% 0.74/1.13 FPA underloads 0
% 0.74/1.13
% 0.74/1.13 Usable size 0
% 0.74/1.13 Sos size 54
% 0.74/1.13 Demodulators size 38
% 0.74/1.13 Passive size 0
% 0.74/1.13 Disabled size 32
% 0.74/1.13
% 0.74/1.13 Proofs found 1
% 0.74/1.13
% 0.74/1.13 ----------- times (seconds) ----------- Tue May 5 11:29:36 2026
% 0.74/1.13
% 0.74/1.13 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 0.74/1.13 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 0.74/1.13 wall-clock time 0 (0 hr, 0 min, 0 sec)
% 0.74/1.13 input time 0.00
% 0.74/1.13 paramodulation time 0.00
% 0.74/1.13 demodulation time 0.00
% 0.74/1.13 orient time 0.00
% 0.74/1.13 weigh time 0.00
% 0.74/1.13 forward subsume time 0.00
% 0.74/1.13 back demod find time 0.00
% 0.74/1.13 conflict time 0.00
% 0.74/1.13 LRPO time 0.00
% 0.74/1.13 store clause time 0.00
% 0.74/1.13 disable clause time 0.00
% 0.74/1.13 prime paramod time 0.00
% 0.74/1.13 semantics time 0.00
% 0.74/1.13
% 0.74/1.13 EQP interrupted
%------------------------------------------------------------------------------