%------------------------------------------------------------------------------ % File : Prover9---1109a % Problem : MGT092+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : tptp2X_and_run_prover9 %d %s % Computer : n010.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 02:10:29 PM UTC 2026 % Result : Theorem 0.78s 1.10s % Output : Refutation 0.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : MGT092+1 : TPTP v9.3.0. Released v9.3.0. % 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s % 0.16/0.34 % Computer : n010.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 Apr 28 19:22:36 EDT 2026 % 0.16/0.34 % CPUTime : % 0.78/1.09 ============================== Prover9 =============================== % 0.78/1.09 Prover9 (32) version 2009-11A, November 2009. % 0.78/1.09 Process 25093 was started by sandbox on n010.cluster.edu, % 0.78/1.09 Tue Apr 28 19:22:36 2026 % 0.78/1.09 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_24764_n010.cluster.edu". % 0.78/1.09 ============================== end of head =========================== % 0.78/1.09 % 0.78/1.09 ============================== INPUT ================================= % 0.78/1.09 % 0.78/1.09 % Reading from file /tmp/Prover9_24764_n010.cluster.edu % 0.78/1.09 % 0.78/1.09 set(prolog_style_variables). % 0.78/1.09 set(auto2). % 0.78/1.09 % set(auto2) -> set(auto). % 0.78/1.09 % set(auto) -> set(auto_inference). % 0.78/1.09 % set(auto) -> set(auto_setup). % 0.78/1.09 % set(auto_setup) -> set(predicate_elim). % 0.78/1.09 % set(auto_setup) -> assign(eq_defs, unfold). % 0.78/1.09 % set(auto) -> set(auto_limits). % 0.78/1.09 % set(auto_limits) -> assign(max_weight, "100.000"). % 0.78/1.09 % set(auto_limits) -> assign(sos_limit, 20000). % 0.78/1.09 % set(auto) -> set(auto_denials). % 0.78/1.09 % set(auto) -> set(auto_process). % 0.78/1.09 % set(auto2) -> assign(new_constants, 1). % 0.78/1.09 % set(auto2) -> assign(fold_denial_max, 3). % 0.78/1.09 % set(auto2) -> assign(max_weight, "200.000"). % 0.78/1.09 % set(auto2) -> assign(max_hours, 1). % 0.78/1.09 % assign(max_hours, 1) -> assign(max_seconds, 3600). % 0.78/1.09 % set(auto2) -> assign(max_seconds, 0). % 0.78/1.09 % set(auto2) -> assign(max_minutes, 5). % 0.78/1.09 % assign(max_minutes, 5) -> assign(max_seconds, 300). % 0.78/1.09 % set(auto2) -> set(sort_initial_sos). % 0.78/1.09 % set(auto2) -> assign(sos_limit, -1). % 0.78/1.09 % set(auto2) -> assign(lrs_ticks, 3000). % 0.78/1.09 % set(auto2) -> assign(max_megs, 400). % 0.78/1.09 % set(auto2) -> assign(stats, some). % 0.78/1.09 % set(auto2) -> clear(echo_input). % 0.78/1.09 % set(auto2) -> set(quiet). % 0.78/1.09 % set(auto2) -> clear(print_initial_clauses). % 0.78/1.09 % set(auto2) -> clear(print_given). % 0.78/1.09 assign(lrs_ticks,-1). % 0.78/1.09 assign(sos_limit,10000). % 0.78/1.09 assign(order,kbo). % 0.78/1.09 set(lex_order_vars). % 0.78/1.09 clear(print_given). % 0.78/1.09 % 0.78/1.09 % formulas(sos). % not echoed (42 formulas) % 0.78/1.09 % 0.78/1.09 ============================== end of input ========================== % 0.78/1.09 % 0.78/1.09 % From the command line: assign(max_seconds, 300). % 0.78/1.09 % 0.78/1.09 ============================== PROCESS NON-CLAUSAL FORMULAS ========== % 0.78/1.09 % 0.78/1.09 % Formulas that are not ordinary clauses: % 0.78/1.09 1 (all X -less(X,X)) # label(irreflexive) # label(axiom) # label(non_clause). [assumption]. % 0.78/1.09 2 (all X all Y all Z (less(X,Y) & less(Y,Z) -> less(X,Z))) # label(transitive) # label(axiom) # label(non_clause). [assumption]. % 0.78/1.09 3 (all X all Y (less(X,Y) | X = Y | less(Y,X))) # label(trichotomy) # label(axiom) # label(non_clause). [assumption]. % 0.78/1.09 4 (all X all Y (leq(X,Y) <-> less(X,Y) | X = Y)) # label(leq_def) # label(axiom) # label(non_clause). [assumption]. % 0.78/1.09 5 (all X all Y (leq(X,Y) & leq(Y,X) -> X = Y)) # label(leq_antisym) # label(axiom) # label(non_clause). [assumption]. % 0.78/1.09 6 (all X all Y (less(X,Y) -> leq(X,Y))) # label(less_implies_leq) # label(axiom) # label(non_clause). [assumption]. % 0.78/1.09 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]. % 0.78/1.09 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]. % 0.78/1.09 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]. % 0.78/1.09 10 (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]. % 0.78/1.09 11 (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]. % 0.78/1.09 12 (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]. % 0.78/1.09 13 (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]. % 0.78/1.09 14 (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]. % 0.78/1.09 15 (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]. % 0.78/1.09 16 (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]. % 0.78/1.09 17 (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]. % 0.78/1.09 18 (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]. % 0.78/1.09 19 (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]. % 0.78/1.09 20 (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]. % 0.78/1.09 21 (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]. % 0.78/1.09 22 (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]. % 0.78/1.09 23 (all V (is_verdict(V) -> V = conflict | V = compatible | V = unknown)) # label(verdict_enum) # label(axiom) # label(non_clause). [assumption]. % 0.78/1.09 24 (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]. % 0.78/1.09 25 (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]. % 0.78/1.09 26 (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]. % 0.78/1.09 27 (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]. % 0.78/1.09 % 0.78/1.09 ============================== end of process non-clausal formulas === % 0.78/1.09 % 0.78/1.09 ============================== PROCESS INITIAL CLAUSES =============== % 0.78/1.09 % 0.78/1.09 ============================== PREDICATE ELIMINATION ================= % 0.78/1.09 28 -axis_subsumes(A,B,C,D) | -in_closed(E,A,B) | in_closed(E,C,D) # label(redundancy) # label(axiom). [clausify(15)]. % 0.78/1.09 29 axis_subsumes(A,B,C,D) | in_closed(f3(A,B,C,D),A,B) # label(axis_subsumes_def) # label(axiom). [clausify(22)]. % 0.78/1.09 Derived: -in_closed(A,B,C) | in_closed(A,D,E) | in_closed(f3(B,C,D,E),B,C). [resolve(28,a,29,a)]. % 0.78/1.09 30 -axis_subsumes(A,B,C,D) | -in_closed(E,A,B) | in_closed(E,C,D) # label(axis_subsumes_def) # label(axiom). [clausify(22)]. % 0.78/1.09 31 axis_subsumes(A,B,C,D) | -in_closed(f3(A,B,C,D),C,D) # label(axis_subsumes_def) # label(axiom). [clausify(22)]. % 0.78/1.09 Derived: -in_closed(f3(A,B,C,D),C,D) | -in_closed(E,A,B) | in_closed(E,C,D). [resolve(31,a,28,a)]. % 0.78/1.09 32 -axis_subsumes(A,B,C,D) | -axis_conflict(C,D,E,F) | axis_conflict(A,B,E,F) # label(monotone_conflict) # label(axiom). [clausify(14)]. % 0.78/1.09 Derived: -axis_conflict(A,B,C,D) | axis_conflict(E,F,C,D) | in_closed(f3(E,F,A,B),E,F). [resolve(32,a,29,a)]. % 0.78/1.09 Derived: -axis_conflict(A,B,C,D) | axis_conflict(E,F,C,D) | -in_closed(f3(E,F,A,B),A,B). [resolve(32,a,31,a)]. % 0.78/1.09 33 in_lopen(A,B,C) | -less(B,A) | -leq(A,C) # label(in_lopen) # label(axiom). [clausify(17)]. % 0.78/1.09 34 -in_lopen(A,B,C) | less(B,A) # label(in_lopen) # label(axiom). [clausify(17)]. % 0.78/1.09 35 -in_lopen(A,B,C) | leq(A,C) # label(in_lopen) # label(axiom). [clausify(17)]. % 0.78/1.10 36 in_ropen(A,B,C) | -leq(B,A) | -less(A,C) # label(in_ropen) # label(axiom). [clausify(18)]. % 0.78/1.10 37 -in_ropen(A,B,C) | leq(B,A) # label(in_ropen) # label(axiom). [clausify(18)]. % 0.78/1.10 38 -in_ropen(A,B,C) | less(A,C) # label(in_ropen) # label(axiom). [clausify(18)]. % 0.78/1.10 39 in_open(A,B,C) | -less(B,A) | -less(A,C) # label(in_open) # label(axiom). [clausify(19)]. % 0.78/1.10 40 -in_open(A,B,C) | less(B,A) # label(in_open) # label(axiom). [clausify(19)]. % 0.78/1.10 41 -in_open(A,B,C) | less(A,C) # label(in_open) # label(axiom). [clausify(19)]. % 0.78/1.10 42 axis_compatible(A,B,C,D) | -in_closed(E,A,B) | -in_closed(E,C,D) # label(axis_compatible_def) # label(axiom). [clausify(21)]. % 0.78/1.10 43 -axis_compatible(A,B,C,D) | in_closed(f2(A,B,C,D),A,B) # label(axis_compatible_def) # label(axiom). [clausify(21)]. % 0.78/1.10 44 -axis_compatible(A,B,C,D) | in_closed(f2(A,B,C,D),C,D) # label(axis_compatible_def) # label(axiom). [clausify(21)]. % 0.78/1.10 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f2(B,C,D,E),B,C). [resolve(42,a,43,a)]. % 0.78/1.10 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f2(B,C,D,E),D,E). [resolve(42,a,44,a)]. % 0.78/1.10 % 0.78/1.10 ============================== end predicate elimination ============= % 0.78/1.10 % 0.78/1.10 Auto_denials: (non-Horn, no changes). % 0.78/1.10 % 0.78/1.10 Term ordering decisions: % 0.78/1.10 Function symbol KB weights: conflict=1. unknown=1. compatible=1. v400=1. v800=1. v0=1. v1200=1. box_verdict=1. f1=1. f2=1. f3=1. % 0.78/1.10 % 0.78/1.10 ============================== end of process initial clauses ======== % 0.78/1.10 % 0.78/1.10 ============================== CLAUSES FOR SEARCH ==================== % 0.78/1.10 % 0.78/1.10 ============================== end of clauses for search ============= % 0.78/1.10 % 0.78/1.10 ============================== SEARCH ================================ % 0.78/1.10 % 0.78/1.10 % Starting search at 0.02 seconds. % 0.78/1.10 % 0.78/1.10 ============================== PROOF ================================= % 0.78/1.10 % SZS status Theorem % 0.78/1.10 % SZS output start Refutation % 0.78/1.10 % 0.78/1.10 % Proof 1 at 0.02 (+ 0.01) seconds. % 0.78/1.10 % Length of proof is 26. % 0.78/1.10 % Level of proof is 6. % 0.78/1.10 % Maximum clause weight is 17.000. % 0.78/1.10 % Given clauses 61. % 0.78/1.10 % 0.78/1.10 1 (all X -less(X,X)) # label(irreflexive) # label(axiom) # label(non_clause). [assumption]. % 0.78/1.10 2 (all X all Y all Z (less(X,Y) & less(Y,Z) -> less(X,Z))) # label(transitive) # label(axiom) # label(non_clause). [assumption]. % 0.78/1.10 3 (all X all Y (less(X,Y) | X = Y | less(Y,X))) # label(trichotomy) # label(axiom) # label(non_clause). [assumption]. % 0.78/1.10 4 (all X all Y (leq(X,Y) <-> less(X,Y) | X = Y)) # label(leq_def) # label(axiom) # label(non_clause). [assumption]. % 0.78/1.10 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]. % 0.78/1.10 13 (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]. % 0.78/1.10 48 less(v0,v400) # label(ord_v0_v400) # label(axiom). [assumption]. % 0.78/1.10 49 less(v400,v800) # label(ord_v400_v800) # label(axiom). [assumption]. % 0.78/1.10 50 less(v800,v1200) # label(ord_v800_v1200) # label(axiom). [assumption]. % 0.78/1.10 51 less(A,B) | B = A | less(B,A) # label(trichotomy) # label(axiom). [clausify(3)]. % 0.78/1.10 54 -less(A,A) # label(irreflexive) # label(axiom). [clausify(1)]. % 0.78/1.10 60 -completion_conflict(v400,v800,v0,v1200) # label(odrl633) # label(negated_conjecture). [assumption]. % 0.78/1.10 62 leq(A,B) | -less(A,B) # label(leq_def) # label(axiom). [clausify(4)]. % 0.78/1.10 63 leq(A,B) | B != A # label(leq_def) # label(axiom). [clausify(4)]. % 0.78/1.10 66 -less(A,B) | -less(B,C) | less(A,C) # label(transitive) # label(axiom). [clausify(2)]. % 0.78/1.10 69 -leq(A,B) | -less(B,C) | less(A,C) # label(leq_less_trans) # label(axiom). [clausify(7)]. % 0.78/1.10 80 -leq(A,B) | -leq(B,C) | -less(B,D) | -leq(D,C) | completion_conflict(B,D,A,C) # label(sharpness_conflict) # label(axiom). [clausify(13)]. % 0.78/1.10 106 leq(v800,v1200). [resolve(62,b,50,a)]. % 0.78/1.10 108 leq(v0,v400). [resolve(62,b,48,a)]. % 0.78/1.10 123 -less(v1200,v800). [ur(66,b,50,a,c,54,a)]. % 0.78/1.10 171 -leq(v1200,v400). [ur(69,b,49,a,c,123,a)]. % 0.78/1.10 172 -less(v1200,v400). [ur(66,b,49,a,c,123,a)]. % 0.78/1.10 190 -leq(v400,v1200). [ur(80,a,108,a,c,49,a,d,106,a,e,60,a)]. % 0.78/1.10 202 v1200 != v400. [ur(63,a,171,a),flip(a)]. % 0.78/1.10 203 less(v400,v1200). [resolve(172,a,51,c),unit_del(b,202)]. % 0.78/1.10 210 $F. [resolve(203,a,62,b),unit_del(a,190)]. % 0.78/1.10 % 0.78/1.10 % SZS output end Refutation % 0.78/1.10 ============================== end of proof ========================== % 0.78/1.10 % 0.78/1.10 ============================== STATISTICS ============================ % 0.78/1.10 % 0.78/1.10 Given=61. Generated=298. Kept=158. proofs=1. % 0.78/1.10 Usable=61. Sos=87. Demods=3. Limbo=5, Disabled=71. Hints=0. % 0.78/1.10 Megabytes=0.20. % 0.78/1.10 User_CPU=0.02, System_CPU=0.01, Wall_clock=0. % 0.78/1.10 % 0.78/1.10 ============================== end of statistics ===================== % 0.78/1.10 % 0.78/1.10 ============================== end of search ========================= % 0.78/1.10 % 0.78/1.10 THEOREM PROVED % 0.78/1.10 % SZS status Theorem % 0.78/1.10 % 0.78/1.10 Exiting with 1 proof. % 0.78/1.10 % 0.78/1.10 Process 25093 exit (max_proofs) Tue Apr 28 19:22:36 2026 % 0.78/1.10 Prover9 interrupted %------------------------------------------------------------------------------