%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ANA035-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 12:46:47 EDT 2022
% Result : Unsatisfiable 1.69s 1.90s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 20 ( 16 unt; 0 nHn; 8 RR)
% Number of literals : 24 ( 16 equ; 8 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 38 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) != c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('ANA035-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(A)
| c_times(B,C,A) = c_times(C,B,A) ),
file('ANA035-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(A)
| c_times(B,c_times(C,D,A),A) = c_times(C,c_times(B,D,A),A) ),
file('ANA035-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| c_HOL_Oabs(c_times(B,C,A),A) = c_times(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A) ),
file('ANA035-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_OrderedGroup_Oab__semigroup__mult(A) ),
file('ANA035-2.p',unknown),
[] ).
cnf(7,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA035-2.p',unknown),
[] ).
cnf(8,plain,
class_OrderedGroup_Oab__semigroup__mult(t_b),
inference(hyper,[status(thm)],[7,5]),
[iquote('hyper,7,5')] ).
cnf(10,plain,
c_HOL_Oabs(c_times(A,B,t_b),t_b) = c_times(c_HOL_Oabs(A,t_b),c_HOL_Oabs(B,t_b),t_b),
inference(hyper,[status(thm)],[7,4]),
[iquote('hyper,7,4')] ).
cnf(11,plain,
c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) != c_times(c_times(v_c,v_ca,t_b),c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),10])]),
[iquote('back_demod,1,demod,10,flip.1')] ).
cnf(12,plain,
c_times(A,c_times(B,C,t_b),t_b) = c_times(B,c_times(A,C,t_b),t_b),
inference(hyper,[status(thm)],[8,3]),
[iquote('hyper,8,3')] ).
cnf(13,plain,
c_times(A,B,t_b) = c_times(B,A,t_b),
inference(hyper,[status(thm)],[8,2]),
[iquote('hyper,8,2')] ).
cnf(21,plain,
c_times(A,c_times(B,C,t_b),t_b) = c_times(C,c_times(A,B,t_b),t_b),
inference(para_into,[status(thm),theory(equality)],[12,13]),
[iquote('para_into,12.1.1.2,13.1.1')] ).
cnf(23,plain,
c_times(c_times(A,B,t_b),C,t_b) = c_times(A,c_times(C,B,t_b),t_b),
inference(para_into,[status(thm),theory(equality)],[12,13]),
[iquote('para_into,12.1.1,13.1.1')] ).
cnf(24,plain,
c_times(A,c_times(B,C,t_b),t_b) = c_times(B,c_times(C,A,t_b),t_b),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[21])]),
[iquote('copy,21,flip.1')] ).
cnf(36,plain,
c_times(c_HOL_Oabs(v_g(v_x),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),v_ca,t_b),t_b) != c_times(c_times(v_c,v_ca,t_b),c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(para_from,[status(thm),theory(equality)],[21,11]),
[iquote('para_from,21.1.1,11.1.1')] ).
cnf(49,plain,
c_times(A,c_times(B,c_times(C,D,t_b),t_b),t_b) = c_times(c_times(B,D,t_b),c_times(C,A,t_b),t_b),
inference(para_into,[status(thm),theory(equality)],[24,23]),
[iquote('para_into,24.1.1.2,23.1.1')] ).
cnf(54,plain,
c_times(c_times(A,B,t_b),C,t_b) = c_times(A,c_times(B,C,t_b),t_b),
inference(para_into,[status(thm),theory(equality)],[24,13]),
[iquote('para_into,24.1.1,13.1.1')] ).
cnf(62,plain,
c_times(A,c_times(B,c_times(C,D,t_b),t_b),t_b) = c_times(B,c_times(D,c_times(C,A,t_b),t_b),t_b),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[49]),54]),
[iquote('back_demod,49,demod,54')] ).
cnf(67,plain,
c_times(c_HOL_Oabs(v_g(v_x),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),v_ca,t_b),t_b),t_b) != c_times(v_c,c_times(v_ca,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[36]),54,54]),
[iquote('back_demod,36,demod,54,54')] ).
cnf(68,plain,
$false,
inference(binary,[status(thm)],[67,62]),
[iquote('binary,67.1,62.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ANA035-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 10:17:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.69/1.90 ----- Otter 3.3f, August 2004 -----
% 1.69/1.90 The process was started by sandbox2 on n027.cluster.edu,
% 1.69/1.90 Wed Jul 27 10:17:37 2022
% 1.69/1.90 The command was "./otter". The process ID is 28968.
% 1.69/1.90
% 1.69/1.90 set(prolog_style_variables).
% 1.69/1.90 set(auto).
% 1.69/1.90 dependent: set(auto1).
% 1.69/1.90 dependent: set(process_input).
% 1.69/1.90 dependent: clear(print_kept).
% 1.69/1.90 dependent: clear(print_new_demod).
% 1.69/1.90 dependent: clear(print_back_demod).
% 1.69/1.90 dependent: clear(print_back_sub).
% 1.69/1.90 dependent: set(control_memory).
% 1.69/1.90 dependent: assign(max_mem, 12000).
% 1.69/1.90 dependent: assign(pick_given_ratio, 4).
% 1.69/1.90 dependent: assign(stats_level, 1).
% 1.69/1.90 dependent: assign(max_seconds, 10800).
% 1.69/1.90 clear(print_given).
% 1.69/1.90
% 1.69/1.90 list(usable).
% 1.69/1.90 0 [] A=A.
% 1.69/1.90 0 [] c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b)!=c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b).
% 1.69/1.90 0 [] class_Ring__and__Field_Oordered__idom(t_b).
% 1.69/1.90 0 [] -class_OrderedGroup_Oab__semigroup__mult(T_a)|c_times(V_a,V_b,T_a)=c_times(V_b,V_a,T_a).
% 1.69/1.90 0 [] -class_OrderedGroup_Oab__semigroup__mult(T_a)|c_times(V_a,c_times(V_b,V_c,T_a),T_a)=c_times(V_b,c_times(V_a,V_c,T_a),T_a).
% 1.69/1.90 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a)=c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a).
% 1.69/1.90 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Oab__semigroup__mult(T).
% 1.69/1.90 end_of_list.
% 1.69/1.90
% 1.69/1.90 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.69/1.90
% 1.69/1.90 This is a Horn set with equality. The strategy will be
% 1.69/1.90 Knuth-Bendix and hyper_res, with positive clauses in
% 1.69/1.90 sos and nonpositive clauses in usable.
% 1.69/1.90
% 1.69/1.90 dependent: set(knuth_bendix).
% 1.69/1.90 dependent: set(anl_eq).
% 1.69/1.90 dependent: set(para_from).
% 1.69/1.90 dependent: set(para_into).
% 1.69/1.90 dependent: clear(para_from_right).
% 1.69/1.90 dependent: clear(para_into_right).
% 1.69/1.90 dependent: set(para_from_vars).
% 1.69/1.90 dependent: set(eq_units_both_ways).
% 1.69/1.90 dependent: set(dynamic_demod_all).
% 1.69/1.90 dependent: set(dynamic_demod).
% 1.69/1.90 dependent: set(order_eq).
% 1.69/1.90 dependent: set(back_demod).
% 1.69/1.90 dependent: set(lrpo).
% 1.69/1.90 dependent: set(hyper_res).
% 1.69/1.90 dependent: clear(order_hyper).
% 1.69/1.90
% 1.69/1.90 ------------> process usable:
% 1.69/1.90 ** KEPT (pick-wt=31): 1 [] c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b)!=c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b).
% 1.69/1.90 ** KEPT (pick-wt=11): 2 [] -class_OrderedGroup_Oab__semigroup__mult(A)|c_times(B,C,A)=c_times(C,B,A).
% 1.69/1.90 ** KEPT (pick-wt=17): 3 [] -class_OrderedGroup_Oab__semigroup__mult(A)|c_times(B,c_times(C,D,A),A)=c_times(C,c_times(B,D,A),A).
% 1.69/1.90 ** KEPT (pick-wt=17): 4 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oabs(c_times(B,C,A),A)=c_times(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A).
% 1.69/1.90 ** KEPT (pick-wt=4): 5 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Oab__semigroup__mult(A).
% 1.69/1.90
% 1.69/1.90 ------------> process sos:
% 1.69/1.90 ** KEPT (pick-wt=3): 6 [] A=A.
% 1.69/1.90 ** KEPT (pick-wt=2): 7 [] class_Ring__and__Field_Oordered__idom(t_b).
% 1.69/1.90 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 1.69/1.90
% 1.69/1.90 ======= end of input processing =======
% 1.69/1.90
% 1.69/1.90 =========== start of search ===========
% 1.69/1.90
% 1.69/1.90 -------- PROOF --------
% 1.69/1.90
% 1.69/1.90 ----> UNIT CONFLICT at 0.00 sec ----> 68 [binary,67.1,62.1] $F.
% 1.69/1.90
% 1.69/1.90 Length of proof is 13. Level of proof is 6.
% 1.69/1.90
% 1.69/1.90 ---------------- PROOF ----------------
% 1.69/1.90 % SZS status Unsatisfiable
% 1.69/1.90 % SZS output start Refutation
% See solution above
% 1.69/1.90 ------------ end of proof -------------
% 1.69/1.90
% 1.69/1.90
% 1.69/1.90 Search stopped by max_proofs option.
% 1.69/1.90
% 1.69/1.90
% 1.69/1.90 Search stopped by max_proofs option.
% 1.69/1.90
% 1.69/1.90 ============ end of search ============
% 1.69/1.90
% 1.69/1.90 -------------- statistics -------------
% 1.69/1.90 clauses given 10
% 1.69/1.90 clauses generated 103
% 1.69/1.90 clauses kept 65
% 1.69/1.90 clauses forward subsumed 94
% 1.69/1.90 clauses back subsumed 4
% 1.69/1.90 Kbytes malloced 976
% 1.69/1.90
% 1.69/1.90 ----------- times (seconds) -----------
% 1.69/1.90 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.90 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.90 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.69/1.90
% 1.69/1.90 That finishes the proof of the theorem.
% 1.69/1.90
% 1.69/1.90 Process 28968 finished Wed Jul 27 10:17:38 2022
% 1.69/1.90 Otter interrupted
% 1.69/1.90 PROOF FOUND
%------------------------------------------------------------------------------