TSTP Solution File: KRS010-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KRS010-1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 : 600s
% DateTime : Sun Jul 17 03:24:45 EDT 2022
% Result : Unsatisfiable 0.74s 1.16s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KRS010-1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 7 07:23:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.74/1.01 ============================== Prover9 ===============================
% 0.74/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.74/1.01 Process 10228 was started by sandbox on n029.cluster.edu,
% 0.74/1.01 Tue Jun 7 07:23:36 2022
% 0.74/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_10075_n029.cluster.edu".
% 0.74/1.01 ============================== end of head ===========================
% 0.74/1.01
% 0.74/1.01 ============================== INPUT =================================
% 0.74/1.01
% 0.74/1.01 % Reading from file /tmp/Prover9_10075_n029.cluster.edu
% 0.74/1.01
% 0.74/1.01 set(prolog_style_variables).
% 0.74/1.01 set(auto2).
% 0.74/1.01 % set(auto2) -> set(auto).
% 0.74/1.01 % set(auto) -> set(auto_inference).
% 0.74/1.01 % set(auto) -> set(auto_setup).
% 0.74/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.74/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.74/1.01 % set(auto) -> set(auto_limits).
% 0.74/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.74/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.74/1.01 % set(auto) -> set(auto_denials).
% 0.74/1.01 % set(auto) -> set(auto_process).
% 0.74/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.74/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.74/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.74/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.74/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.74/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.74/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.74/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.74/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.74/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.74/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.74/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.74/1.01 % set(auto2) -> assign(stats, some).
% 0.74/1.01 % set(auto2) -> clear(echo_input).
% 0.74/1.01 % set(auto2) -> set(quiet).
% 0.74/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.74/1.01 % set(auto2) -> clear(print_given).
% 0.74/1.01 assign(lrs_ticks,-1).
% 0.74/1.01 assign(sos_limit,10000).
% 0.74/1.01 assign(order,kbo).
% 0.74/1.01 set(lex_order_vars).
% 0.74/1.01 clear(print_given).
% 0.74/1.01
% 0.74/1.01 % formulas(sos). % not echoed (31 formulas)
% 0.74/1.01
% 0.74/1.01 ============================== end of input ==========================
% 0.74/1.01
% 0.74/1.01 % From the command line: assign(max_seconds, 300).
% 0.74/1.01
% 0.74/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.74/1.01
% 0.74/1.01 % Formulas that are not ordinary clauses:
% 0.74/1.01
% 0.74/1.01 ============================== end of process non-clausal formulas ===
% 0.74/1.01
% 0.74/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.74/1.01
% 0.74/1.01 ============================== PREDICATE ELIMINATION =================
% 0.74/1.01 1 r3least(A) | -e(A) # label(clause_7) # label(axiom). [assumption].
% 0.74/1.01 2 e(exist) # label(clause_1) # label(negated_conjecture). [assumption].
% 0.74/1.01 Derived: r3least(exist). [resolve(1,b,2,a)].
% 0.74/1.01 3 a(A) | -e(B) | -r(B,A) # label(clause_8) # label(axiom). [assumption].
% 0.74/1.01 Derived: a(A) | -r(exist,A). [resolve(3,b,2,a)].
% 0.74/1.01 4 e(A) | c(u1r2(A)) | -a(u1r1(A)) | -r3least(A) # label(clause_10) # label(axiom). [assumption].
% 0.74/1.01 Derived: c(u1r2(A)) | -a(u1r1(A)) | -r3least(A) | a(B) | -r(A,B). [resolve(4,a,3,b)].
% 0.74/1.01 5 e(A) | c(u1r3(A)) | -a(u1r1(A)) | -r3least(A) # label(clause_11) # label(axiom). [assumption].
% 0.74/1.01 Derived: c(u1r3(A)) | -a(u1r1(A)) | -r3least(A) | a(B) | -r(A,B). [resolve(5,a,3,b)].
% 0.74/1.01 6 e(A) | r(A,u1r2(A)) | -a(u1r1(A)) | -r3least(A) # label(clause_12) # label(axiom). [assumption].
% 0.74/1.01 Derived: r(A,u1r2(A)) | -a(u1r1(A)) | -r3least(A) | a(B) | -r(A,B). [resolve(6,a,3,b)].
% 0.74/1.01 7 e(A) | r(A,u1r3(A)) | -a(u1r1(A)) | -r3least(A) # label(clause_13) # label(axiom). [assumption].
% 0.74/1.01 Derived: r(A,u1r3(A)) | -a(u1r1(A)) | -r3least(A) | a(B) | -r(A,B). [resolve(7,a,3,b)].
% 0.74/1.01 8 e(A) | r(A,u1r1(A)) | c(u1r2(A)) | -r3least(A) # label(clause_15) # label(axiom). [assumption].
% 0.74/1.01 Derived: r(A,u1r1(A)) | c(u1r2(A)) | -r3least(A) | a(B) | -r(A,B). [resolve(8,a,3,b)].
% 0.74/1.01 9 e(A) | r(A,u1r1(A)) | c(u1r3(A)) | -r3least(A) # label(clause_16) # label(axiom). [assumption].
% 0.74/1.01 Derived: r(A,u1r1(A)) | c(u1r3(A)) | -r3least(A) | a(B) | -r(A,B). [resolve(9,a,3,b)].
% 0.74/1.01 10 e(A) | -a(u1r1(A)) | -r3least(A) | -equalish(u1r3(A),u1r2(A)) # label(clause_9) # label(axiom). [assumption].
% 0.74/1.01 Derived: -a(u1r1(A)) | -r3least(A) | -equalish(u1r3(A),u1r2(A)) | a(B) | -r(A,B). [resolve(10,a,3,b)].
% 0.74/1.01 11 e(A) | r(A,u1r1(A)) | r(A,u1r2(A)) | -r3least(A) # label(clause_17) # label(axiom). [assumption].
% 0.74/1.01 Derived: r(A,u1r1(A)) | r(A,u1r2(A)) | -r3least(A) | a(B) | -r(A,B). [resolve(11,a,3,b)].
% 0.74/1.01 12 e(A) | r(A,u1r1(A)) | r(A,u1r3(A)) | -r3least(A) # label(clause_18) # label(axiom). [assumption].
% 0.74/1.01 Derived: r(A,u1r1(A)) | r(A,u1r3(A)) | -r3least(A) | a(B) | -r(A,B). [resolve(12,a,3,b)].
% 0.74/1.01 13 e(A) | r(A,u1r1(A)) | -r3least(A) | -equalish(u1r3(A),u1r2(A)) # label(clause_14) # label(axiom). [assumption].
% 0.74/1.01 Derived: r(A,u1r1(A)) | -r3least(A) | -equalish(u1r3(A),u1r2(A)) | a(B) | -r(A,B). [resolve(13,a,3,b)].
% 0.74/1.01 14 equalish(A,B) | -e(C) | -r(C,A) | -r(C,B) | -c(A) | -c(B) # label(clause_6) # label(axiom). [assumption].
% 0.74/1.01 Derived: equalish(A,B) | -r(exist,A) | -r(exist,B) | -c(A) | -c(B). [resolve(14,b,2,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | c(u1r2(C)) | -a(u1r1(C)) | -r3least(C). [resolve(14,b,4,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | c(u1r3(C)) | -a(u1r1(C)) | -r3least(C). [resolve(14,b,5,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | r(C,u1r2(C)) | -a(u1r1(C)) | -r3least(C). [resolve(14,b,6,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | r(C,u1r3(C)) | -a(u1r1(C)) | -r3least(C). [resolve(14,b,7,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | r(C,u1r1(C)) | c(u1r2(C)) | -r3least(C). [resolve(14,b,8,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | r(C,u1r1(C)) | c(u1r3(C)) | -r3least(C). [resolve(14,b,9,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | -a(u1r1(C)) | -r3least(C) | -equalish(u1r3(C),u1r2(C)). [resolve(14,b,10,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | r(C,u1r1(C)) | r(C,u1r2(C)) | -r3least(C). [resolve(14,b,11,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | r(C,u1r1(C)) | r(C,u1r3(C)) | -r3least(C). [resolve(14,b,12,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | r(C,u1r1(C)) | -r3least(C) | -equalish(u1r3(C),u1r2(C)). [resolve(14,b,13,a)].
% 0.74/1.01 15 f(A) | equalish(B,C) | -r(A,B) | -r(A,C) | -d(B) | -d(C) # label(clause_31) # label(axiom). [assumption].
% 0.74/1.01 16 -f(exist) # label(clause_2) # label(negated_conjecture). [assumption].
% 0.74/1.01 17 -f(A) | -equalish(u3r2(A),u3r1(A)) # label(clause_28) # label(axiom). [assumption].
% 0.74/1.01 18 d(u3r1(A)) | -f(A) # label(clause_26) # label(axiom). [assumption].
% 0.74/1.01 19 d(u3r2(A)) | -f(A) # label(clause_27) # label(axiom). [assumption].
% 0.74/1.01 20 r(A,u3r1(A)) | -f(A) # label(clause_29) # label(axiom). [assumption].
% 0.74/1.01 21 r(A,u3r2(A)) | -f(A) # label(clause_30) # label(axiom). [assumption].
% 0.74/1.01 Derived: equalish(A,B) | -r(exist,A) | -r(exist,B) | -d(A) | -d(B). [resolve(15,a,16,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -d(A) | -d(B) | -equalish(u3r2(C),u3r1(C)). [resolve(15,a,17,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -d(A) | -d(B) | d(u3r1(C)). [resolve(15,a,18,b)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -d(A) | -d(B) | d(u3r2(C)). [resolve(15,a,19,b)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -d(A) | -d(B) | r(C,u3r1(C)). [resolve(15,a,20,b)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -d(A) | -d(B) | r(C,u3r2(C)). [resolve(15,a,21,b)].
% 0.74/1.01 22 r3least(A) | equalish(B,C) | equalish(B,D) | equalish(C,D) | -r(A,B) | -r(A,C) | -r(A,D) # label(clause_25) # label(axiom). [assumption].
% 0.74/1.01 23 -r3least(A) | -equalish(u2r2(A),u2r1(A)) # label(clause_19) # label(axiom). [assumption].
% 0.74/1.01 24 -r3least(A) | -equalish(u2r3(A),u2r1(A)) # label(clause_20) # label(axiom). [assumption].
% 0.74/1.01 25 -r3least(A) | -equalish(u2r3(A),u2r2(A)) # label(clause_21) # label(axiom). [assumption].
% 0.74/1.01 26 r(A,u2r1(A)) | -r3least(A) # label(clause_22) # label(axiom). [assumption].
% 0.74/1.01 27 r(A,u2r2(A)) | -r3least(A) # label(clause_23) # label(axiom). [assumption].
% 0.74/1.01 28 r(A,u2r3(A)) | -r3least(A) # label(clause_24) # label(axiom). [assumption].
% 0.74/1.01 Derived: equalish(A,B) | equalish(A,C) | equalish(B,C) | -r(D,A) | -r(D,B) | -r(D,C) | -equalish(u2r2(D),u2r1(D)). [resolve(22,a,23,a)].
% 0.74/1.01 Derived: equalish(A,B) | equalish(A,C) | equalish(B,C) | -r(D,A) | -r(D,B) | -r(D,C) | -equalish(u2r3(D),u2r1(D)). [resolve(22,a,24,a)].
% 0.74/1.01 Derived: equalish(A,B) | equalish(A,C) | equalish(B,C) | -r(D,A) | -r(D,B) | -r(D,C) | -equalish(u2r3(D),u2r2(D)). [resolve(22,a,25,a)].
% 0.74/1.01 Derived: equalish(A,B) | equalish(A,C) | equalish(B,C) | -r(D,A) | -r(D,B) | -r(D,C) | r(D,u2r1(D)). [resolve(22,a,26,b)].
% 0.74/1.01 Derived: equalish(A,B) | equalish(A,C) | equalish(B,C) | -r(D,A) | -r(D,B) | -r(D,C) | r(D,u2r2(D)). [resolve(22,a,27,b)].
% 0.74/1.01 Derived: equalish(A,B) | equalish(A,C) | equalish(B,C) | -r(D,A) | -r(D,B) | -r(D,C) | r(D,u2r3(D)). [resolve(22,a,28,b)].
% 0.74/1.01 29 r3least(exist). [resolve(1,b,2,a)].
% 0.74/1.01 Derived: -equalish(u2r2(exist),u2r1(exist)). [resolve(29,a,23,a)].
% 0.74/1.01 Derived: -equalish(u2r3(exist),u2r1(exist)). [resolve(29,a,24,a)].
% 0.74/1.01 Derived: -equalish(u2r3(exist),u2r2(exist)). [resolve(29,a,25,a)].
% 0.74/1.01 Derived: r(exist,u2r1(exist)). [resolve(29,a,26,b)].
% 0.74/1.01 Derived: r(exist,u2r2(exist)). [resolve(29,a,27,b)].
% 0.74/1.01 Derived: r(exist,u2r3(exist)). [resolve(29,a,28,b)].
% 0.74/1.01 30 c(u1r2(A)) | -a(u1r1(A)) | -r3least(A) | a(B) | -r(A,B). [resolve(4,a,3,b)].
% 0.74/1.01 Derived: c(u1r2(A)) | -a(u1r1(A)) | a(B) | -r(A,B) | equalish(C,D) | equalish(C,E) | equalish(D,E) | -r(A,C) | -r(A,D) | -r(A,E). [resolve(30,c,22,a)].
% 0.74/1.01 Derived: c(u1r2(exist)) | -a(u1r1(exist)) | a(A) | -r(exist,A). [resolve(30,c,29,a)].
% 0.74/1.01 31 c(u1r3(A)) | -a(u1r1(A)) | -r3least(A) | a(B) | -r(A,B). [resolve(5,a,3,b)].
% 0.74/1.01 Derived: c(u1r3(A)) | -a(u1r1(A)) | a(B) | -r(A,B) | equalish(C,D) | equalish(C,E) | equalish(D,E) | -r(A,C) | -r(A,D) | -r(A,E). [resolve(31,c,22,a)].
% 0.74/1.01 Derived: c(u1r3(exist)) | -a(u1r1(exist)) | a(A) | -r(exist,A). [resolve(31,c,29,a)].
% 0.74/1.01 32 r(A,u1r2(A)) | -a(u1r1(A)) | -r3least(A) | a(B) | -r(A,B). [resolve(6,a,3,b)].
% 0.74/1.01 Derived: r(A,u1r2(A)) | -a(u1r1(A)) | a(B) | -r(A,B) | equalish(C,D) | equalish(C,E) | equalish(D,E) | -r(A,C) | -r(A,D) | -r(A,E). [resolve(32,c,22,a)].
% 0.74/1.01 Derived: r(exist,u1r2(exist)) | -a(u1r1(exist)) | a(A) | -r(exist,A). [resolve(32,c,29,a)].
% 0.74/1.01 33 r(A,u1r3(A)) | -a(u1r1(A)) | -r3least(A) | a(B) | -r(A,B). [resolve(7,a,3,b)].
% 0.74/1.01 Derived: r(A,u1r3(A)) | -a(u1r1(A)) | a(B) | -r(A,B) | equalish(C,D) | equalish(C,E) | equalish(D,E) | -r(A,C) | -r(A,D) | -r(A,E). [resolve(33,c,22,a)].
% 0.74/1.01 Derived: r(exist,u1r3(exist)) | -a(u1r1(exist)) | a(A) | -r(exist,A). [resolve(33,c,29,a)].
% 0.74/1.01 34 r(A,u1r1(A)) | c(u1r2(A)) | -r3least(A) | a(B) | -r(A,B). [resolve(8,a,3,b)].
% 0.74/1.01 Derived: r(A,u1r1(A)) | c(u1r2(A)) | a(B) | -r(A,B) | equalish(C,D) | equalish(C,E) | equalish(D,E) | -r(A,C) | -r(A,D) | -r(A,E). [resolve(34,c,22,a)].
% 0.74/1.01 Derived: r(exist,u1r1(exist)) | c(u1r2(exist)) | a(A) | -r(exist,A). [resolve(34,c,29,a)].
% 0.74/1.01 35 r(A,u1r1(A)) | c(u1r3(A)) | -r3least(A) | a(B) | -r(A,B). [resolve(9,a,3,b)].
% 0.74/1.01 Derived: r(A,u1r1(A)) | c(u1r3(A)) | a(B) | -r(A,B) | equalish(C,D) | equalish(C,E) | equalish(D,E) | -r(A,C) | -r(A,D) | -r(A,E). [resolve(35,c,22,a)].
% 0.74/1.01 Derived: r(exist,u1r1(exist)) | c(u1r3(exist)) | a(A) | -r(exist,A). [resolve(35,c,29,a)].
% 0.74/1.01 36 -a(u1r1(A)) | -r3least(A) | -equalish(u1r3(A),u1r2(A)) | a(B) | -r(A,B). [resolve(10,a,3,b)].
% 0.74/1.01 Derived: -a(u1r1(A)) | -equalish(u1r3(A),u1r2(A)) | a(B) | -r(A,B) | equalish(C,D) | equalish(C,E) | equalish(D,E) | -r(A,C) | -r(A,D) | -r(A,E). [resolve(36,b,22,a)].
% 0.74/1.01 Derived: -a(u1r1(exist)) | -equalish(u1r3(exist),u1r2(exist)) | a(A) | -r(exist,A). [resolve(36,b,29,a)].
% 0.74/1.01 37 r(A,u1r1(A)) | r(A,u1r2(A)) | -r3least(A) | a(B) | -r(A,B). [resolve(11,a,3,b)].
% 0.74/1.01 Derived: r(A,u1r1(A)) | r(A,u1r2(A)) | a(B) | -r(A,B) | equalish(C,D) | equalish(C,E) | equalish(D,E) | -r(A,C) | -r(A,D) | -r(A,E). [resolve(37,c,22,a)].
% 0.74/1.01 Derived: r(exist,u1r1(exist)) | r(exist,u1r2(exist)) | a(A) | -r(exist,A). [resolve(37,c,29,a)].
% 0.74/1.01 38 r(A,u1r1(A)) | r(A,u1r3(A)) | -r3least(A) | a(B) | -r(A,B). [resolve(12,a,3,b)].
% 0.74/1.01 Derived: r(A,u1r1(A)) | r(A,u1r3(A)) | a(B) | -r(A,B) | equalish(C,D) | equalish(C,E) | equalish(D,E) | -r(A,C) | -r(A,D) | -r(A,E). [resolve(38,c,22,a)].
% 0.74/1.01 Derived: r(exist,u1r1(exist)) | r(exist,u1r3(exist)) | a(A) | -r(exist,A). [resolve(38,c,29,a)].
% 0.74/1.01 39 r(A,u1r1(A)) | -r3least(A) | -equalish(u1r3(A),u1r2(A)) | a(B) | -r(A,B). [resolve(13,a,3,b)].
% 0.74/1.01 Derived: r(A,u1r1(A)) | -equalish(u1r3(A),u1r2(A)) | a(B) | -r(A,B) | equalish(C,D) | equalish(C,E) | equalish(D,E) | -r(A,C) | -r(A,D) | -r(A,E). [resolve(39,b,22,a)].
% 0.74/1.01 Derived: r(exist,u1r1(exist)) | -equalish(u1r3(exist),u1r2(exist)) | a(A) | -r(exist,A). [resolve(39,b,29,a)].
% 0.74/1.01 40 equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | c(u1r2(C)) | -a(u1r1(C)) | -r3least(C). [resolve(14,b,4,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | c(u1r2(C)) | -a(u1r1(C)) | equalish(D,E) | equalish(D,F) | equalish(E,F) | -r(C,D) | -r(C,E) | -r(C,F). [resolve(40,h,22,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(exist,A) | -r(exist,B) | -c(A) | -c(B) | c(u1r2(exist)) | -a(u1r1(exist)). [resolve(40,h,29,a)].
% 0.74/1.01 41 equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | c(u1r3(C)) | -a(u1r1(C)) | -r3least(C). [resolve(14,b,5,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | c(u1r3(C)) | -a(u1r1(C)) | equalish(D,E) | equalish(D,F) | equalish(E,F) | -r(C,D) | -r(C,E) | -r(C,F). [resolve(41,h,22,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(exist,A) | -r(exist,B) | -c(A) | -c(B) | c(u1r3(exist)) | -a(u1r1(exist)). [resolve(41,h,29,a)].
% 0.74/1.01 42 equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | r(C,u1r2(C)) | -a(u1r1(C)) | -r3least(C). [resolve(14,b,6,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | r(C,u1r2(C)) | -a(u1r1(C)) | equalish(D,E) | equalish(D,F) | equalish(E,F) | -r(C,D) | -r(C,E) | -r(C,F). [resolve(42,h,22,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(exist,A) | -r(exist,B) | -c(A) | -c(B) | r(exist,u1r2(exist)) | -a(u1r1(exist)). [resolve(42,h,29,a)].
% 0.74/1.01 43 equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | r(C,u1r3(C)) | -a(u1r1(C)) | -r3least(C). [resolve(14,b,7,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | r(C,u1r3(C)) | -a(u1r1(C)) | equalish(D,E) | equalish(D,F) | equalish(E,F) | -r(C,D) | -r(C,E) | -r(C,F). [resolve(43,h,22,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(exist,A) | -r(exist,B) | -c(A) | -c(B) | r(exist,u1r3(exist)) | -a(u1r1(exist)). [resolve(43,h,29,a)].
% 0.74/1.01 44 equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | r(C,u1r1(C)) | c(u1r2(C)) | -r3least(C). [resolve(14,b,8,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | r(C,u1r1(C)) | c(u1r2(C)) | equalish(D,E) | equalish(D,F) | equalish(E,F) | -r(C,D) | -r(C,E) | -r(C,F). [resolve(44,h,22,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(exist,A) | -r(exist,B) | -c(A) | -c(B) | r(exist,u1r1(exist)) | c(u1r2(exist)). [resolve(44,h,29,a)].
% 0.74/1.01 45 equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | r(C,u1r1(C)) | c(u1r3(C)) | -r3least(C). [resolve(14,b,9,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | r(C,u1r1(C)) | c(u1r3(C)) | equalish(D,E) | equalish(D,F) | equalish(E,F) | -r(C,D) | -r(C,E) | -r(C,F). [resolve(45,h,22,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(exist,A) | -r(exist,B) | -c(A) | -c(B) | r(exist,u1r1(exist)) | c(u1r3(exist)). [resolve(45,h,29,a)].
% 0.74/1.01 46 equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | -a(u1r1(C)) | -r3least(C) | -equalish(u1r3(C),u1r2(C)). [resolve(14,b,10,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | -a(u1r1(C)) | -equalish(u1r3(C),u1r2(C)) | equalish(D,E) | equalish(D,F) | equalish(E,F) | -r(C,D) | -r(C,E) | -r(C,F). [resolve(46,g,22,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(exist,A) | -r(exist,B) | -c(A) | -c(B) | -a(u1r1(exist)) | -equalish(u1r3(exist),u1r2(exist)). [resolve(46,g,29,a)].
% 0.74/1.01 47 equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | r(C,u1r1(C)) | r(C,u1r2(C)) | -r3least(C). [resolve(14,b,11,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | r(C,u1r1(C)) | r(C,u1r2(C)) | equalish(D,E) | equalish(D,F) | equalish(E,F) | -r(C,D) | -r(C,E) | -r(C,F). [resolve(47,h,22,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(exist,A) | -r(exist,B) | -c(A) | -c(B) | r(exist,u1r1(exist)) | r(exist,u1r2(exist)). [resolve(47,h,29,a)].
% 0.74/1.01 48 equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | r(C,u1r1(C)) | r(C,u1r3(C)) | -r3least(C). [resolve(14,b,12,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | r(C,u1r1(C)) | r(C,u1r3(C)) | equalish(D,E) | equalish(D,F) | equalish(E,F) | -r(C,D) | -r(C,E) | -r(C,F). [resolve(48,h,22,a)].
% 0.74/1.01 Derived: equalish(A,B) | -r(exist,A) | -r(exist,B) | -c(A) | -c(B) | r(exist,u1r1(exist)) | r(exist,u1r3(exist)). [resolve(48,h,29,a)].
% 0.74/1.16 49 equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | r(C,u1r1(C)) | -r3least(C) | -equalish(u1r3(C),u1r2(C)). [resolve(14,b,13,a)].
% 0.74/1.16 Derived: equalish(A,B) | -r(C,A) | -r(C,B) | -c(A) | -c(B) | r(C,u1r1(C)) | -equalish(u1r3(C),u1r2(C)) | equalish(D,E) | equalish(D,F) | equalish(E,F) | -r(C,D) | -r(C,E) | -r(C,F). [resolve(49,g,22,a)].
% 0.74/1.16 Derived: equalish(A,B) | -r(exist,A) | -r(exist,B) | -c(A) | -c(B) | r(exist,u1r1(exist)) | -equalish(u1r3(exist),u1r2(exist)). [resolve(49,g,29,a)].
% 0.74/1.16
% 0.74/1.16 ============================== end predicate elimination =============
% 0.74/1.16
% 0.74/1.16 Auto_denials: (non-Horn, no changes).
% 0.74/1.16
% 0.74/1.16 Term ordering decisions:
% 0.74/1.16 Function symbol KB weights: exist=1. u1r1=1. u1r2=1. u1r3=1. u2r1=1. u2r2=1. u2r3=1. u3r1=1. u3r2=1.
% 0.74/1.16
% 0.74/1.16 ============================== end of process initial clauses ========
% 0.74/1.16
% 0.74/1.16 ============================== CLAUSES FOR SEARCH ====================
% 0.74/1.16
% 0.74/1.16 ============================== end of clauses for search =============
% 0.74/1.16
% 0.74/1.16 ============================== SEARCH ================================
% 0.74/1.16
% 0.74/1.16 % Starting search at 0.08 seconds.
% 0.74/1.16
% 0.74/1.16 ============================== PROOF =================================
% 0.74/1.16 % SZS status Unsatisfiable
% 0.74/1.16 % SZS output start Refutation
% 0.74/1.16
% 0.74/1.16 % Proof 1 at 0.16 (+ 0.00) seconds.
% 0.74/1.16 % Length of proof is 50.
% 0.74/1.16 % Level of proof is 10.
% 0.74/1.16 % Maximum clause weight is 13.000.
% 0.74/1.16 % Given clauses 254.
% 0.74/1.16
% 0.74/1.16 1 r3least(A) | -e(A) # label(clause_7) # label(axiom). [assumption].
% 0.74/1.16 2 e(exist) # label(clause_1) # label(negated_conjecture). [assumption].
% 0.74/1.16 3 a(A) | -e(B) | -r(B,A) # label(clause_8) # label(axiom). [assumption].
% 0.74/1.16 14 equalish(A,B) | -e(C) | -r(C,A) | -r(C,B) | -c(A) | -c(B) # label(clause_6) # label(axiom). [assumption].
% 0.74/1.16 15 f(A) | equalish(B,C) | -r(A,B) | -r(A,C) | -d(B) | -d(C) # label(clause_31) # label(axiom). [assumption].
% 0.74/1.16 16 -f(exist) # label(clause_2) # label(negated_conjecture). [assumption].
% 0.74/1.16 23 -r3least(A) | -equalish(u2r2(A),u2r1(A)) # label(clause_19) # label(axiom). [assumption].
% 0.74/1.16 24 -r3least(A) | -equalish(u2r3(A),u2r1(A)) # label(clause_20) # label(axiom). [assumption].
% 0.74/1.16 25 -r3least(A) | -equalish(u2r3(A),u2r2(A)) # label(clause_21) # label(axiom). [assumption].
% 0.74/1.16 26 r(A,u2r1(A)) | -r3least(A) # label(clause_22) # label(axiom). [assumption].
% 0.74/1.16 27 r(A,u2r2(A)) | -r3least(A) # label(clause_23) # label(axiom). [assumption].
% 0.74/1.16 28 r(A,u2r3(A)) | -r3least(A) # label(clause_24) # label(axiom). [assumption].
% 0.74/1.16 29 r3least(exist). [resolve(1,b,2,a)].
% 0.74/1.16 52 c(A) | d(A) | -a(A) # label(clause_3) # label(axiom). [assumption].
% 0.74/1.16 53 a(A) | -r(exist,A). [resolve(3,b,2,a)].
% 0.74/1.16 54 equalish(A,B) | -r(exist,A) | -r(exist,B) | -c(A) | -c(B). [resolve(14,b,2,a)].
% 0.74/1.16 55 equalish(A,B) | -r(exist,A) | -r(exist,B) | -d(A) | -d(B). [resolve(15,a,16,a)].
% 0.74/1.16 67 -equalish(u2r2(exist),u2r1(exist)). [resolve(29,a,23,a)].
% 0.74/1.16 68 -equalish(u2r3(exist),u2r1(exist)). [resolve(29,a,24,a)].
% 0.74/1.16 69 -equalish(u2r3(exist),u2r2(exist)). [resolve(29,a,25,a)].
% 0.74/1.16 70 r(exist,u2r1(exist)). [resolve(29,a,26,b)].
% 0.74/1.16 71 r(exist,u2r2(exist)). [resolve(29,a,27,b)].
% 0.74/1.16 72 r(exist,u2r3(exist)). [resolve(29,a,28,b)].
% 0.74/1.16 320 equalish(A,u2r1(exist)) | -r(exist,A) | -d(A) | -d(u2r1(exist)). [resolve(70,a,55,c)].
% 0.74/1.16 322 equalish(A,u2r1(exist)) | -r(exist,A) | -c(A) | -c(u2r1(exist)). [resolve(70,a,54,c)].
% 0.74/1.16 324 a(u2r1(exist)). [resolve(70,a,53,b)].
% 0.74/1.16 339 equalish(A,u2r2(exist)) | -r(exist,A) | -d(A) | -d(u2r2(exist)). [resolve(71,a,55,c)].
% 0.74/1.16 341 equalish(A,u2r2(exist)) | -r(exist,A) | -c(A) | -c(u2r2(exist)). [resolve(71,a,54,c)].
% 0.74/1.16 343 a(u2r2(exist)). [resolve(71,a,53,b)].
% 0.74/1.16 362 a(u2r3(exist)). [resolve(72,a,53,b)].
% 0.74/1.16 369 -d(u2r3(exist)) | -d(u2r1(exist)). [resolve(320,b,72,a),unit_del(a,68)].
% 0.74/1.16 370 -d(u2r2(exist)) | -d(u2r1(exist)). [resolve(320,b,71,a),unit_del(a,67)].
% 0.74/1.16 371 c(u2r1(exist)) | d(u2r1(exist)). [resolve(324,a,52,c)].
% 0.74/1.16 372 c(u2r2(exist)) | d(u2r2(exist)). [resolve(343,a,52,c)].
% 0.74/1.16 373 c(u2r3(exist)) | d(u2r3(exist)). [resolve(362,a,52,c)].
% 0.74/1.16 374 c(u2r2(exist)) | -d(u2r1(exist)). [resolve(372,b,370,a)].
% 0.74/1.16 375 c(u2r3(exist)) | -d(u2r1(exist)). [resolve(373,b,369,a)].
% 0.74/1.16 376 c(u2r2(exist)) | c(u2r1(exist)). [resolve(374,b,371,b)].
% 0.74/1.16 377 c(u2r3(exist)) | c(u2r1(exist)). [resolve(375,b,371,b)].
% 0.74/1.16 378 -c(u2r3(exist)) | -c(u2r1(exist)). [resolve(322,b,72,a),unit_del(a,68)].
% 0.74/1.16 379 -c(u2r2(exist)) | -c(u2r1(exist)). [resolve(322,b,71,a),unit_del(a,67)].
% 0.74/1.16 385 -d(u2r3(exist)) | -d(u2r2(exist)). [resolve(339,b,72,a),unit_del(a,69)].
% 0.74/1.16 386 -d(u2r2(exist)) | c(u2r3(exist)). [resolve(385,a,373,b)].
% 0.74/1.16 387 c(u2r3(exist)) | c(u2r2(exist)). [resolve(386,a,372,b)].
% 0.74/1.16 388 c(u2r2(exist)) | -c(u2r1(exist)). [resolve(387,a,378,a)].
% 0.74/1.16 390 -c(u2r3(exist)) | -c(u2r2(exist)). [resolve(341,b,72,a),unit_del(a,69)].
% 0.74/1.16 391 -c(u2r2(exist)) | c(u2r1(exist)). [resolve(390,a,377,a)].
% 0.74/1.16 392 c(u2r1(exist)). [resolve(391,a,376,a),merge(b)].
% 0.74/1.16 393 c(u2r2(exist)). [back_unit_del(388),unit_del(b,392)].
% 0.74/1.16 394 $F. [back_unit_del(379),unit_del(a,393),unit_del(b,392)].
% 0.74/1.16
% 0.74/1.16 % SZS output end Refutation
% 0.74/1.16 ============================== end of proof ==========================
% 0.74/1.16
% 0.74/1.16 ============================== STATISTICS ============================
% 0.74/1.16
% 0.74/1.16 Given=254. Generated=3479. Kept=344. proofs=1.
% 0.74/1.16 Usable=245. Sos=6. Demods=0. Limbo=2, Disabled=203. Hints=0.
% 0.74/1.16 Megabytes=0.36.
% 0.74/1.16 User_CPU=0.16, System_CPU=0.00, Wall_clock=0.
% 0.74/1.16
% 0.74/1.16 ============================== end of statistics =====================
% 0.74/1.16
% 0.74/1.16 ============================== end of search =========================
% 0.74/1.16
% 0.74/1.16 THEOREM PROVED
% 0.74/1.16 % SZS status Unsatisfiable
% 0.74/1.16
% 0.74/1.16 Exiting with 1 proof.
% 0.74/1.16
% 0.74/1.16 Process 10228 exit (max_proofs) Tue Jun 7 07:23:36 2022
% 0.74/1.16 Prover9 interrupted
%------------------------------------------------------------------------------