%------------------------------------------------------------------------------ % File : Prover9---1109a % Problem : MGT070+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : tptp2X_and_run_prover9 %d %s % Computer : n019.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 Apr 29 02:10:26 PM UTC 2026 % Result : Theorem 0.76s 1.04s % Output : Refutation 0.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : MGT070+1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.12 % Command : tptp2X_and_run_prover9 %d %s % 0.15/0.33 % Computer : n019.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.33 % CPULimit : 300 % 0.15/0.33 % WCLimit : 300 % 0.15/0.33 % DateTime : Tue Apr 28 18:36:58 EDT 2026 % 0.15/0.33 % CPUTime : % 0.76/1.03 ============================== Prover9 =============================== % 0.76/1.03 Prover9 (32) version 2009-11A, November 2009. % 0.76/1.03 Process 15953 was started by sandbox2 on n019.cluster.edu, % 0.76/1.03 Tue Apr 28 18:36:59 2026 % 0.76/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_15800_n019.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_15800_n019.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 (40 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 (all X -less(X,X)) # label(irreflexive) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.03 2 (all X all Y all Z (less(X,Y) & less(Y,Z) -> less(X,Z))) # label(transitive) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.03 3 (all X all Y (less(X,Y) | X = Y | less(Y,X))) # label(trichotomy) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.03 4 (all X all Y (leq(X,Y) <-> less(X,Y) | X = Y)) # label(leq_def) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.03 5 (all X all Y (leq(X,Y) & leq(Y,X) -> X = Y)) # label(leq_antisym) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.03 6 (all X all Y (less(X,Y) -> leq(X,Y))) # label(less_implies_leq) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.03 7 (all X all Y all Z (leq(X,Y) & less(Y,Z) -> less(X,Z))) # label(leq_less_trans) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.03 8 (all X all Y all Z (less(X,Y) & leq(Y,Z) -> less(X,Z))) # label(less_leq_trans) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.03 9 (all X all Y all Z (leq(X,Y) & leq(Y,Z) -> leq(X,Z))) # label(leq_trans) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.03 10 (all X all Y (less(X,Y) -> (exists Z (less(X,Z) & less(Z,Y))))) # label(dense) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.03 11 (all X all A all B (in_closed(X,A,B) <-> leq(A,X) & leq(X,B))) # label(in_closed) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.03 12 (all X all A all B (in_lopen(X,A,B) <-> less(A,X) & leq(X,B))) # label(in_lopen) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.03 13 (all X all A all B (in_ropen(X,A,B) <-> leq(A,X) & less(X,B))) # label(in_ropen) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.03 14 (all X all A all B (in_open(X,A,B) <-> less(A,X) & less(X,B))) # label(in_open) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.03 15 (all I1lo all I1hi all I2lo all I2hi (axis_conflict(I1lo,I1hi,I2lo,I2hi) <-> -(exists X (in_closed(X,I1lo,I1hi) & in_closed(X,I2lo,I2hi))))) # label(axis_conflict_def) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.04 16 (all I1lo all I1hi all I2lo all I2hi (axis_compatible(I1lo,I1hi,I2lo,I2hi) <-> (exists X (in_closed(X,I1lo,I1hi) & in_closed(X,I2lo,I2hi))))) # label(axis_compatible_def) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.04 17 (all I1lo all I1hi all I2lo all I2hi (axis_subsumes(I1lo,I1hi,I2lo,I2hi) <-> (all X (in_closed(X,I1lo,I1hi) -> in_closed(X,I2lo,I2hi))))) # label(axis_subsumes_def) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.04 18 (all V (is_verdict(V) -> V = conflict | V = compatible | V = unknown)) # label(verdict_enum) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.04 19 (all V1 all V2 (is_verdict(V1) & is_verdict(V2) & (V1 = conflict | V2 = conflict) -> box_verdict(V1,V2) = conflict)) # label(box_conflict) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.04 20 (all V1 all V2 (is_verdict(V1) & is_verdict(V2) & V1 = compatible & V2 = compatible -> box_verdict(V1,V2) = compatible)) # label(box_compatible) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.04 21 (all V1 all V2 (is_verdict(V1) & is_verdict(V2) & (V1 = unknown | V2 = unknown) & V1 != conflict & V2 != conflict -> box_verdict(V1,V2) = unknown)) # label(box_unknown) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.04 22 (all V1 all V2 (is_verdict(V1) & is_verdict(V2) -> box_verdict(V1,V2) = conflict | box_verdict(V1,V2) = compatible | box_verdict(V1,V2) = unknown)) # label(box_verdict_total) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.04 23 (all V all InfD all SupD (leq(InfD,V) & leq(V,SupD) -> completion_compatible(V,InfD,SupD))) # label(completion_compat) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.04 24 (all U all V all InfD all SupD (leq(InfD,U) & leq(U,SupD) & leq(InfD,V) & leq(V,SupD) & less(U,V) -> completion_conflict(U,V,InfD,SupD))) # label(completion_conflict) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.04 25 (all U all V all InfD all SupD (leq(InfD,U) & leq(U,SupD) & less(U,V) & leq(V,SupD) -> completion_compatible(U,InfD,SupD))) # label(sharpness_compat) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.04 26 (all U all V all InfD all SupD (leq(InfD,U) & leq(U,SupD) & less(U,V) & leq(V,SupD) -> completion_conflict(U,V,InfD,SupD))) # label(sharpness_conflict) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.04 27 (all A1lo all A1hi all A1plo all A1phi all A2lo all A2hi (axis_subsumes(A1lo,A1hi,A1plo,A1phi) & axis_conflict(A1plo,A1phi,A2lo,A2hi) -> axis_conflict(A1lo,A1hi,A2lo,A2hi))) # label(monotone_conflict) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.04 28 (all A1lo all A1hi all A2lo all A2hi (axis_subsumes(A1lo,A1hi,A2lo,A2hi) -> (all X (in_closed(X,A1lo,A1hi) -> in_closed(X,A2lo,A2hi))))) # label(redundancy) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.04 29 (all X leq(ninf,X)) # label(h_inf_lb) # label(hypothesis) # label(non_clause). [assumption]. % 0.76/1.04 30 (all X leq(X,nsup)) # label(h_sup_ub) # label(hypothesis) # label(non_clause). [assumption]. % 0.76/1.04 31 -(exists V (leq(ninf,V) & leq(V,nsup) & completion_compatible(V,ninf,nsup))) # label(unknown_sound_compatible) # label(negated_conjecture) # label(non_clause). [assumption]. % 0.76/1.04 % 0.76/1.04 ============================== end of process non-clausal formulas === % 0.76/1.04 % 0.76/1.04 ============================== PROCESS INITIAL CLAUSES =============== % 0.76/1.04 % 0.76/1.04 ============================== PREDICATE ELIMINATION ================= % 0.76/1.04 32 -axis_subsumes(A,B,C,D) | -in_closed(E,A,B) | in_closed(E,C,D) # label(axis_subsumes_def) # label(axiom). [clausify(17)]. % 0.76/1.04 33 axis_subsumes(A,B,C,D) | in_closed(f4(A,B,C,D),A,B) # label(axis_subsumes_def) # label(axiom). [clausify(17)]. % 0.76/1.04 Derived: -in_closed(A,B,C) | in_closed(A,D,E) | in_closed(f4(B,C,D,E),B,C). [resolve(32,a,33,a)]. % 0.76/1.04 34 axis_subsumes(A,B,C,D) | -in_closed(f4(A,B,C,D),C,D) # label(axis_subsumes_def) # label(axiom). [clausify(17)]. % 0.76/1.04 Derived: -in_closed(f4(A,B,C,D),C,D) | -in_closed(E,A,B) | in_closed(E,C,D). [resolve(34,a,32,a)]. % 0.76/1.04 35 -axis_subsumes(A,B,C,D) | -in_closed(E,A,B) | in_closed(E,C,D) # label(redundancy) # label(axiom). [clausify(28)]. % 0.76/1.04 36 -axis_subsumes(A,B,C,D) | -axis_conflict(C,D,E,F) | axis_conflict(A,B,E,F) # label(monotone_conflict) # label(axiom). [clausify(27)]. % 0.76/1.04 Derived: -axis_conflict(A,B,C,D) | axis_conflict(E,F,C,D) | in_closed(f4(E,F,A,B),E,F). [resolve(36,a,33,a)]. % 0.76/1.04 Derived: -axis_conflict(A,B,C,D) | axis_conflict(E,F,C,D) | -in_closed(f4(E,F,A,B),A,B). [resolve(36,a,34,a)]. % 0.76/1.04 37 in_lopen(A,B,C) | -less(B,A) | -leq(A,C) # label(in_lopen) # label(axiom). [clausify(12)]. % 0.76/1.04 38 -in_lopen(A,B,C) | less(B,A) # label(in_lopen) # label(axiom). [clausify(12)]. % 0.76/1.04 39 -in_lopen(A,B,C) | leq(A,C) # label(in_lopen) # label(axiom). [clausify(12)]. % 0.76/1.04 40 in_ropen(A,B,C) | -leq(B,A) | -less(A,C) # label(in_ropen) # label(axiom). [clausify(13)]. % 0.76/1.04 41 -in_ropen(A,B,C) | leq(B,A) # label(in_ropen) # label(axiom). [clausify(13)]. % 0.76/1.04 42 -in_ropen(A,B,C) | less(A,C) # label(in_ropen) # label(axiom). [clausify(13)]. % 0.76/1.04 43 in_open(A,B,C) | -less(B,A) | -less(A,C) # label(in_open) # label(axiom). [clausify(14)]. % 0.76/1.04 44 -in_open(A,B,C) | less(B,A) # label(in_open) # label(axiom). [clausify(14)]. % 0.76/1.04 45 -in_open(A,B,C) | less(A,C) # label(in_open) # label(axiom). [clausify(14)]. % 0.76/1.04 46 axis_compatible(A,B,C,D) | -in_closed(E,A,B) | -in_closed(E,C,D) # label(axis_compatible_def) # label(axiom). [clausify(16)]. % 0.76/1.04 47 -axis_compatible(A,B,C,D) | in_closed(f3(A,B,C,D),A,B) # label(axis_compatible_def) # label(axiom). [clausify(16)]. % 0.76/1.04 48 -axis_compatible(A,B,C,D) | in_closed(f3(A,B,C,D),C,D) # label(axis_compatible_def) # label(axiom). [clausify(16)]. % 0.76/1.04 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f3(B,C,D,E),B,C). [resolve(46,a,47,a)]. % 0.76/1.04 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f3(B,C,D,E),D,E). [resolve(46,a,48,a)]. % 0.76/1.04 % 0.76/1.04 ============================== end predicate elimination ============= % 0.76/1.04 % 0.76/1.04 Auto_denials: (non-Horn, no changes). % 0.76/1.04 % 0.76/1.04 Term ordering decisions: % 0.76/1.04 Function symbol KB weights: conflict=1. unknown=1. compatible=1. n0=1. ninf=1. nsup=1. box_verdict=1. f1=1. f2=1. f3=1. f4=1. % 0.76/1.04 % 0.76/1.04 ============================== end of process initial clauses ======== % 0.76/1.04 % 0.76/1.04 ============================== CLAUSES FOR SEARCH ==================== % 0.76/1.04 % 0.76/1.04 ============================== end of clauses for search ============= % 0.76/1.04 % 0.76/1.04 ============================== SEARCH ================================ % 0.76/1.04 % 0.76/1.04 % Starting search at 0.02 seconds. % 0.76/1.04 % 0.76/1.04 ============================== PROOF ================================= % 0.76/1.04 % SZS status Theorem % 0.76/1.04 % SZS output start Refutation % 0.76/1.04 % 0.76/1.04 % Proof 1 at 0.02 (+ 0.00) seconds. % 0.76/1.04 % Length of proof is 10. % 0.76/1.04 % Level of proof is 3. % 0.76/1.04 % Maximum clause weight is 10.000. % 0.76/1.04 % Given clauses 31. % 0.76/1.04 % 0.76/1.04 23 (all V all InfD all SupD (leq(InfD,V) & leq(V,SupD) -> completion_compatible(V,InfD,SupD))) # label(completion_compat) # label(axiom) # label(non_clause). [assumption]. % 0.76/1.04 29 (all X leq(ninf,X)) # label(h_inf_lb) # label(hypothesis) # label(non_clause). [assumption]. % 0.76/1.04 30 (all X leq(X,nsup)) # label(h_sup_ub) # label(hypothesis) # label(non_clause). [assumption]. % 0.76/1.04 31 -(exists V (leq(ninf,V) & leq(V,nsup) & completion_compatible(V,ninf,nsup))) # label(unknown_sound_compatible) # label(negated_conjecture) # label(non_clause). [assumption]. % 0.76/1.04 54 leq(ninf,A) # label(h_inf_lb) # label(hypothesis). [clausify(29)]. % 0.76/1.04 55 leq(A,nsup) # label(h_sup_ub) # label(hypothesis). [clausify(30)]. % 0.76/1.04 66 -leq(ninf,A) | -leq(A,nsup) | -completion_compatible(A,ninf,nsup) # label(unknown_sound_compatible) # label(negated_conjecture). [clausify(31)]. % 0.76/1.04 67 -completion_compatible(A,ninf,nsup). [copy(66),unit_del(a,54),unit_del(b,55)]. % 0.76/1.04 82 -leq(A,B) | -leq(B,C) | completion_compatible(B,A,C) # label(completion_compat) # label(axiom). [clausify(23)]. % 0.76/1.04 163 $F. [ur(82,b,55,a,c,67,a),unit_del(a,54)]. % 0.76/1.04 % 0.76/1.04 % SZS output end Refutation % 0.76/1.04 ============================== end of proof ========================== % 0.76/1.04 % 0.76/1.04 ============================== STATISTICS ============================ % 0.76/1.04 % 0.76/1.04 Given=31. Generated=145. Kept=105. proofs=1. % 0.76/1.04 Usable=31. Sos=63. Demods=1. Limbo=4, Disabled=72. Hints=0. % 0.76/1.04 Megabytes=0.16. % 0.76/1.04 User_CPU=0.02, System_CPU=0.00, Wall_clock=0. % 0.76/1.04 % 0.76/1.04 ============================== end of statistics ===================== % 0.76/1.04 % 0.76/1.04 ============================== end of search ========================= % 0.76/1.04 % 0.76/1.04 THEOREM PROVED % 0.76/1.04 % SZS status Theorem % 0.76/1.04 % 0.76/1.04 Exiting with 1 proof. % 0.76/1.04 % 0.76/1.04 Process 15953 exit (max_proofs) Tue Apr 28 18:36:59 2026 % 0.76/1.04 Prover9 interrupted %------------------------------------------------------------------------------