TSTP Solution File: LCL520+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL520+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 13:47:20 EDT 2022
% Result : Theorem 1.56s 1.83s
% Output : Refutation 1.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL520+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 4 15:12:22 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.76/1.03 ============================== Prover9 ===============================
% 0.76/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.76/1.03 Process 20279 was started by sandbox on n006.cluster.edu,
% 0.76/1.03 Mon Jul 4 15:12:23 2022
% 0.76/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_20126_n006.cluster.edu".
% 0.76/1.03 ============================== end of head ===========================
% 0.76/1.03
% 0.76/1.03 ============================== INPUT =================================
% 0.76/1.03
% 0.76/1.03 % Reading from file /tmp/Prover9_20126_n006.cluster.edu
% 0.76/1.03
% 0.76/1.03 set(prolog_style_variables).
% 0.76/1.03 set(auto2).
% 0.76/1.03 % set(auto2) -> set(auto).
% 0.76/1.03 % set(auto) -> set(auto_inference).
% 0.76/1.03 % set(auto) -> set(auto_setup).
% 0.76/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.76/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.76/1.03 % set(auto) -> set(auto_limits).
% 0.76/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.76/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.76/1.03 % set(auto) -> set(auto_denials).
% 0.76/1.03 % set(auto) -> set(auto_process).
% 0.76/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.76/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.76/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.76/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.76/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.76/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.76/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.76/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.76/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.76/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.76/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.76/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.76/1.03 % set(auto2) -> assign(stats, some).
% 0.76/1.03 % set(auto2) -> clear(echo_input).
% 0.76/1.03 % set(auto2) -> set(quiet).
% 0.76/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.76/1.03 % set(auto2) -> clear(print_given).
% 0.76/1.03 assign(lrs_ticks,-1).
% 0.76/1.03 assign(sos_limit,10000).
% 0.76/1.03 assign(order,kbo).
% 0.76/1.03 set(lex_order_vars).
% 0.76/1.03 clear(print_given).
% 0.76/1.03
% 0.76/1.03 % formulas(sos). % not echoed (43 formulas)
% 0.76/1.03
% 0.76/1.03 ============================== end of input ==========================
% 0.76/1.03
% 0.76/1.03 % From the command line: assign(max_seconds, 300).
% 0.76/1.03
% 0.76/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.76/1.03
% 0.76/1.03 % Formulas that are not ordinary clauses:
% 0.76/1.03 1 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 2 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 3 modus_tollens <-> (all X all Y is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))) # label(modus_tollens) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 5 implies_2 <-> (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) # label(implies_2) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 6 implies_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) # label(implies_3) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 9 and_3 <-> (all X all Y is_a_theorem(implies(X,implies(Y,and(X,Y))))) # label(and_3) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 12 or_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))) # label(or_3) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 13 equivalence_1 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(X,Y)))) # label(equivalence_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 14 equivalence_2 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(Y,X)))) # label(equivalence_2) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 15 equivalence_3 <-> (all X all Y is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))) # label(equivalence_3) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 18 kn3 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))) # label(kn3) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 19 cn1 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) # label(cn1) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 25 r4 <-> (all P all Q all R is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))) # label(r4) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 26 r5 <-> (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) # label(r5) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 27 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 28 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 29 op_implies_and -> (all X all Y implies(X,Y) = not(and(X,not(Y)))) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 30 op_implies_or -> (all X all Y implies(X,Y) = or(not(X),Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 31 op_equiv -> (all X all Y equiv(X,Y) = and(implies(X,Y),implies(Y,X))) # label(op_equiv) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83
% 1.56/1.83 ============================== end of process non-clausal formulas ===
% 1.56/1.83
% 1.56/1.83 ============================== PROCESS INITIAL CLAUSES ===============
% 1.56/1.83
% 1.56/1.83 ============================== PREDICATE ELIMINATION =================
% 1.56/1.83
% 1.56/1.83 ============================== end predicate elimination =============
% 1.56/1.83
% 1.56/1.83 Auto_denials: (non-Horn, no changes).
% 1.56/1.83
% 1.56/1.83 Term ordering decisions:
% 1.56/1.83
% 1.56/1.83 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 1.56/1.83 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. c13=1. c14=1. c15=1. c16=1. c17=1. c18=1. c19=1. c20=1. c21=1. c22=1. c23=1. c24=1. c25=1. c26=1. c27=1. c28=1. c29=1. c30=1. c31=1. c32=1. c33=1. c34=1. c35=1. c36=1. c37=1. c38=1. c39=1. c40=1. c41=1. c42=1. c43=1. c44=1. c45=1. c46=1. c47=1. c48=1. c49=1. c50=1. c51=1. c52=1. c53=1. c54=1. c55=1. implies=1. or=1. and=1. equiv=1. not=0.
% 1.56/1.83
% 1.56/1.83 ============================== end of process initial clauses ========
% 1.56/1.83
% 1.56/1.83 ============================== CLAUSES FOR SEARCH ====================
% 1.56/1.83
% 1.56/1.83 ============================== end of clauses for search =============
% 1.56/1.83
% 1.56/1.83 ============================== SEARCH ================================
% 1.56/1.83
% 1.56/1.83 % Starting search at 0.02 seconds.
% 1.56/1.83
% 1.56/1.83 Low Water (keep): wt=33.000, iters=3501
% 1.56/1.83
% 1.56/1.83 Low Water (keep): wt=32.000, iters=3586
% 1.56/1.83
% 1.56/1.83 Low Water (keep): wt=30.000, iters=3408
% 1.56/1.83
% 1.56/1.83 Low Water (keep): wt=28.000, iters=3336
% 1.56/1.83
% 1.56/1.83 Low Water (keep): wt=27.000, iters=3390
% 1.56/1.83
% 1.56/1.83 Low Water (keep): wt=26.000, iters=3346
% 1.56/1.83
% 1.56/1.83 Low Water (keep): wt=25.000, iters=3495
% 1.56/1.83
% 1.56/1.83 ============================== PROOF =================================
% 1.56/1.83 % SZS status Theorem
% 1.56/1.83 % SZS output start Refutation
% 1.56/1.83
% 1.56/1.83 % Proof 1 at 0.79 (+ 0.03) seconds.
% 1.56/1.83 % Length of proof is 67.
% 1.56/1.83 % Level of proof is 14.
% 1.56/1.83 % Maximum clause weight is 16.000.
% 1.56/1.83 % Given clauses 392.
% 1.56/1.83
% 1.56/1.83 1 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 18 kn3 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))) # label(kn3) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 27 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 28 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 29 op_implies_and -> (all X all Y implies(X,Y) = not(and(X,not(Y)))) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 30 op_implies_or -> (all X all Y implies(X,Y) = or(not(X),Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.83 32 op_or # label(rosser_op_or) # label(axiom). [assumption].
% 1.56/1.83 33 op_implies_and # label(rosser_op_implies_and) # label(axiom). [assumption].
% 1.56/1.83 35 modus_ponens # label(rosser_modus_ponens) # label(axiom). [assumption].
% 1.56/1.83 36 kn1 # label(rosser_kn1) # label(axiom). [assumption].
% 1.56/1.83 37 kn2 # label(rosser_kn2) # label(axiom). [assumption].
% 1.56/1.83 38 kn3 # label(rosser_kn3) # label(axiom). [assumption].
% 1.56/1.83 40 op_implies_or # label(principia_op_implies_or) # label(axiom). [assumption].
% 1.56/1.83 41 op_and # label(principia_op_and) # label(axiom). [assumption].
% 1.56/1.83 42 -r3 # label(principia_r3) # label(negated_conjecture). [assumption].
% 1.56/1.83 53 -kn1 | is_a_theorem(implies(A,and(A,A))) # label(kn1) # label(axiom). [clausify(16)].
% 1.56/1.83 54 is_a_theorem(implies(A,and(A,A))). [copy(53),unit_del(a,36)].
% 1.56/1.83 56 -kn2 | is_a_theorem(implies(and(A,B),A)) # label(kn2) # label(axiom). [clausify(17)].
% 1.56/1.83 57 is_a_theorem(implies(and(A,B),A)). [copy(56),unit_del(a,37)].
% 1.56/1.83 69 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 1.56/1.83 70 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(69),unit_del(a,35)].
% 1.56/1.83 77 r3 | -is_a_theorem(implies(or(c48,c49),or(c49,c48))) # label(r3) # label(axiom). [clausify(24)].
% 1.56/1.83 78 -is_a_theorem(implies(or(c48,c49),or(c49,c48))). [copy(77),unit_del(a,42)].
% 1.56/1.83 79 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom). [clausify(30)].
% 1.56/1.83 80 or(not(A),B) = implies(A,B). [copy(79),unit_del(a,40)].
% 1.56/1.83 81 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 1.56/1.83 82 not(and(A,not(B))) = implies(A,B). [copy(81),unit_del(a,33)].
% 1.56/1.83 87 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)].
% 1.56/1.83 88 or(A,B) = implies(not(A),B). [copy(87),rewrite([82(6)]),unit_del(a,32)].
% 1.56/1.83 89 -op_and | and(A,B) = not(or(not(A),not(B))) # label(op_and) # label(axiom). [clausify(28)].
% 1.56/1.83 90 not(implies(not(not(A)),not(B))) = and(A,B). [copy(89),rewrite([88(5)]),flip(b),unit_del(a,41)].
% 1.56/1.83 111 -kn3 | is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))) # label(kn3) # label(axiom). [clausify(18)].
% 1.56/1.83 112 is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))). [copy(111),unit_del(a,38)].
% 1.56/1.83 115 implies(not(not(A)),B) = implies(A,B). [back_rewrite(80),rewrite([88(2)])].
% 1.56/1.83 116 -is_a_theorem(implies(implies(not(c48),c49),implies(not(c49),c48))). [back_rewrite(78),rewrite([88(3),88(7)])].
% 1.56/1.83 125 not(implies(A,not(B))) = and(A,B). [back_rewrite(90),rewrite([115(4)])].
% 1.56/1.83 126 -is_a_theorem(and(A,B)) | is_a_theorem(A). [resolve(70,b,57,a)].
% 1.56/1.83 127 -is_a_theorem(A) | is_a_theorem(and(A,A)). [resolve(70,b,54,a)].
% 1.56/1.83 132 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(and(B,C)),not(and(C,A)))). [resolve(112,a,70,b)].
% 1.56/1.83 133 is_a_theorem(implies(implies(A,B),implies(implies(B,C),not(and(not(C),A))))). [para(82(a,1),112(a,1,2,1))].
% 1.56/1.83 137 is_a_theorem(implies(A,and(not(not(A)),not(not(A))))). [para(115(a,1),54(a,1))].
% 1.56/1.83 138 -is_a_theorem(not(not(A))) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [para(115(a,1),70(b,1))].
% 1.56/1.83 139 implies(not(implies(A,B)),C) = implies(and(A,not(B)),C). [para(82(a,1),115(a,1,1,1))].
% 1.56/1.83 143 -is_a_theorem(and(implies(implies(not(c48),c49),implies(not(c49),c48)),A)). [ur(70,b,57,a,c,116,a)].
% 1.56/1.83 147 not(and(A,and(B,C))) = implies(A,implies(B,not(C))). [para(125(a,1),82(a,1,1,2))].
% 1.56/1.83 148 not(implies(A,implies(B,C))) = and(A,and(B,not(C))). [para(82(a,1),125(a,1,1,2))].
% 1.56/1.83 149 implies(not(and(A,B)),C) = implies(implies(A,not(B)),C). [para(125(a,1),115(a,1,1,1))].
% 1.56/1.83 150 and(not(not(A)),B) = and(A,B). [para(115(a,1),125(a,1,1)),rewrite([125(3)]),flip(a)].
% 1.56/1.83 155 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,not(C)),not(and(C,A)))). [back_rewrite(132),rewrite([149(7)])].
% 1.56/1.83 157 is_a_theorem(implies(A,and(A,not(not(A))))). [back_rewrite(137),rewrite([150(5)])].
% 1.56/1.83 172 is_a_theorem(and(implies(and(A,B),A),implies(and(A,B),A))). [resolve(127,a,57,a)].
% 1.56/1.83 226 is_a_theorem(implies(A,and(A,not(not(not(not(A))))))). [para(115(a,1),157(a,1)),rewrite([150(7)])].
% 1.56/1.83 249 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(not(C),not(A))))). [para(115(a,1),133(a,1,1)),rewrite([82(7)])].
% 1.56/1.83 287 -is_a_theorem(and(A,B)) | is_a_theorem(not(not(A))). [para(150(a,1),126(a,1))].
% 1.56/1.83 324 -is_a_theorem(implies(implies(not(c48),c49),implies(not(c49),not(not(c48))))). [ur(138,b,157,a,c,143,a),rewrite([148(10),147(11)])].
% 1.56/1.83 551 is_a_theorem(implies(A,and(A,not(not(not(not(not(not(A))))))))). [para(115(a,1),226(a,1)),rewrite([150(9)])].
% 1.56/1.83 612 implies(and(A,not(not(B))),C) = implies(and(A,B),C). [para(125(a,1),139(a,1,1)),flip(a)].
% 1.56/1.83 1194 is_a_theorem(not(not(implies(and(A,B),A)))). [resolve(172,a,287,a)].
% 1.56/1.83 1232 is_a_theorem(not(and(and(not(A),B),A))). [para(125(a,1),1194(a,1,1))].
% 1.56/1.83 1914 is_a_theorem(implies(implies(and(A,A),not(B)),not(and(B,A)))). [resolve(155,a,551,a),rewrite([612(9),612(7),612(5)])].
% 1.56/1.83 3076 -is_a_theorem(not(and(and(A,A),B))) | is_a_theorem(not(and(B,A))). [resolve(1914,a,138,b),rewrite([125(4)])].
% 1.56/1.83 8152 is_a_theorem(implies(A,A)). [resolve(3076,a,1232,a),rewrite([82(3)])].
% 1.56/1.83 8354 -is_a_theorem(implies(implies(A,A),implies(implies(not(c48),c49),implies(not(c49),not(not(c48)))))). [ur(70,a,8152,a,c,324,a)].
% 1.56/1.83 8355 $F. [resolve(8354,a,249,a)].
% 1.56/1.83
% 1.56/1.83 % SZS output end Refutation
% 1.56/1.83 ============================== end of proof ==========================
% 1.56/1.83
% 1.56/1.83 ============================== STATISTICS ============================
% 1.56/1.83
% 1.56/1.83 Given=392. Generated=21442. Kept=8303. proofs=1.
% 1.56/1.83 Usable=346. Sos=6581. Demods=184. Limbo=187, Disabled=1260. Hints=0.
% 1.56/1.83 Megabytes=9.75.
% 1.56/1.83 User_CPU=0.79, System_CPU=0.03, Wall_clock=0.
% 1.56/1.83
% 1.56/1.83 ============================== end of statistics =====================
% 1.56/1.83
% 1.56/1.83 ============================== end of search =========================
% 1.56/1.83
% 1.56/1.83 THEOREM PROVED
% 1.56/1.83 % SZS status Theorem
% 1.56/1.83
% 1.56/1.83 Exiting with 1 proof.
% 1.56/1.83
% 1.56/1.83 Process 20279 exit (max_proofs) Mon Jul 4 15:12:23 2022
% 1.56/1.83 Prover9 interrupted
%------------------------------------------------------------------------------