%------------------------------------------------------------------------------ % File : Prover9---1109a % Problem : MGT085+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : tptp2X_and_run_prover9 %d %s % Computer : n020.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 02:10:28 PM UTC 2026 % Result : Theorem 0.77s 1.11s % Output : Refutation 0.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : MGT085+1 : TPTP v9.3.0. Released v9.3.0. % 0.13/0.13 % Command : tptp2X_and_run_prover9 %d %s % 0.17/0.34 % Computer : n020.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Apr 28 18:53:34 EDT 2026 % 0.17/0.34 % CPUTime : % 0.77/1.08 ============================== Prover9 =============================== % 0.77/1.08 Prover9 (32) version 2009-11A, November 2009. % 0.77/1.08 Process 26139 was started by sandbox on n020.cluster.edu, % 0.77/1.08 Tue Apr 28 18:53:34 2026 % 0.77/1.08 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25982_n020.cluster.edu". % 0.77/1.08 ============================== end of head =========================== % 0.77/1.08 % 0.77/1.08 ============================== INPUT ================================= % 0.77/1.08 % 0.77/1.08 % Reading from file /tmp/Prover9_25982_n020.cluster.edu % 0.77/1.08 % 0.77/1.08 set(prolog_style_variables). % 0.77/1.08 set(auto2). % 0.77/1.08 % set(auto2) -> set(auto). % 0.77/1.08 % set(auto) -> set(auto_inference). % 0.77/1.08 % set(auto) -> set(auto_setup). % 0.77/1.08 % set(auto_setup) -> set(predicate_elim). % 0.77/1.08 % set(auto_setup) -> assign(eq_defs, unfold). % 0.77/1.08 % set(auto) -> set(auto_limits). % 0.77/1.08 % set(auto_limits) -> assign(max_weight, "100.000"). % 0.77/1.08 % set(auto_limits) -> assign(sos_limit, 20000). % 0.77/1.08 % set(auto) -> set(auto_denials). % 0.77/1.08 % set(auto) -> set(auto_process). % 0.77/1.08 % set(auto2) -> assign(new_constants, 1). % 0.77/1.08 % set(auto2) -> assign(fold_denial_max, 3). % 0.77/1.08 % set(auto2) -> assign(max_weight, "200.000"). % 0.77/1.08 % set(auto2) -> assign(max_hours, 1). % 0.77/1.08 % assign(max_hours, 1) -> assign(max_seconds, 3600). % 0.77/1.08 % set(auto2) -> assign(max_seconds, 0). % 0.77/1.08 % set(auto2) -> assign(max_minutes, 5). % 0.77/1.08 % assign(max_minutes, 5) -> assign(max_seconds, 300). % 0.77/1.08 % set(auto2) -> set(sort_initial_sos). % 0.77/1.08 % set(auto2) -> assign(sos_limit, -1). % 0.77/1.08 % set(auto2) -> assign(lrs_ticks, 3000). % 0.77/1.08 % set(auto2) -> assign(max_megs, 400). % 0.77/1.08 % set(auto2) -> assign(stats, some). % 0.77/1.08 % set(auto2) -> clear(echo_input). % 0.77/1.08 % set(auto2) -> set(quiet). % 0.77/1.08 % set(auto2) -> clear(print_initial_clauses). % 0.77/1.08 % set(auto2) -> clear(print_given). % 0.77/1.08 assign(lrs_ticks,-1). % 0.77/1.08 assign(sos_limit,10000). % 0.77/1.08 assign(order,kbo). % 0.77/1.08 set(lex_order_vars). % 0.77/1.08 clear(print_given). % 0.77/1.08 % 0.77/1.08 % formulas(sos). % not echoed (44 formulas) % 0.77/1.08 % 0.77/1.08 ============================== end of input ========================== % 0.77/1.08 % 0.77/1.08 % From the command line: assign(max_seconds, 300). % 0.77/1.08 % 0.77/1.08 ============================== PROCESS NON-CLAUSAL FORMULAS ========== % 0.77/1.08 % 0.77/1.08 % Formulas that are not ordinary clauses: % 0.77/1.08 1 (all X -less(X,X)) # label(irreflexive) # label(axiom) # label(non_clause). [assumption]. % 0.77/1.08 2 (all X all Y all Z (less(X,Y) & less(Y,Z) -> less(X,Z))) # label(transitive) # label(axiom) # label(non_clause). [assumption]. % 0.77/1.08 3 (all X all Y (less(X,Y) | X = Y | less(Y,X))) # label(trichotomy) # label(axiom) # label(non_clause). [assumption]. % 0.77/1.08 4 (all X all Y (leq(X,Y) <-> less(X,Y) | X = Y)) # label(leq_def) # label(axiom) # label(non_clause). [assumption]. % 0.77/1.08 5 (all X all Y (leq(X,Y) & leq(Y,X) -> X = Y)) # label(leq_antisym) # label(axiom) # label(non_clause). [assumption]. % 0.77/1.08 6 (all X all Y (less(X,Y) -> leq(X,Y))) # label(less_implies_leq) # label(axiom) # label(non_clause). [assumption]. % 0.77/1.08 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]. % 0.77/1.08 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]. % 0.77/1.08 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]. % 0.77/1.08 10 (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]. % 0.77/1.08 11 (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]. % 0.77/1.08 12 (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]. % 0.77/1.08 13 (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]. % 0.77/1.08 14 (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]. % 0.77/1.08 15 (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]. % 0.77/1.09 16 (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]. % 0.77/1.09 17 (all V (is_verdict(V) -> V = conflict | V = compatible | V = unknown)) # label(verdict_enum) # label(axiom) # label(non_clause). [assumption]. % 0.77/1.09 18 (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]. % 0.77/1.09 19 (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]. % 0.77/1.09 20 (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]. % 0.77/1.09 21 (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]. % 0.77/1.09 22 --(exists X exists Y exists Z ((in_lopen(X,v0,v200) | in_lopen(Y,v0,v100) | in_lopen(Z,v0,v50)) & leq(v400,X) & leq(v200,Y) & leq(v100,Z))) # label(odrl445) # label(negated_conjecture) # label(non_clause). [assumption]. % 0.77/1.09 % 0.77/1.09 ============================== end of process non-clausal formulas === % 0.77/1.09 % 0.77/1.09 ============================== PROCESS INITIAL CLAUSES =============== % 0.77/1.09 % 0.77/1.09 ============================== PREDICATE ELIMINATION ================= % 0.77/1.09 23 -axis_conflict(A,B,C,D) | -in_closed(E,A,B) | -in_closed(E,C,D) # label(axis_conflict_def) # label(axiom). [clausify(14)]. % 0.77/1.09 24 axis_conflict(A,B,C,D) | in_closed(f1(A,B,C,D),A,B) # label(axis_conflict_def) # label(axiom). [clausify(14)]. % 0.77/1.09 25 axis_conflict(A,B,C,D) | in_closed(f1(A,B,C,D),C,D) # label(axis_conflict_def) # label(axiom). [clausify(14)]. % 0.77/1.09 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f1(B,C,D,E),B,C). [resolve(23,a,24,a)]. % 0.77/1.09 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f1(B,C,D,E),D,E). [resolve(23,a,25,a)]. % 0.77/1.09 26 -axis_subsumes(A,B,C,D) | -in_closed(E,A,B) | in_closed(E,C,D) # label(axis_subsumes_def) # label(axiom). [clausify(16)]. % 0.77/1.09 27 axis_subsumes(A,B,C,D) | in_closed(f3(A,B,C,D),A,B) # label(axis_subsumes_def) # label(axiom). [clausify(16)]. % 0.77/1.09 Derived: -in_closed(A,B,C) | in_closed(A,D,E) | in_closed(f3(B,C,D,E),B,C). [resolve(26,a,27,a)]. % 0.77/1.09 28 axis_subsumes(A,B,C,D) | -in_closed(f3(A,B,C,D),C,D) # label(axis_subsumes_def) # label(axiom). [clausify(16)]. % 0.77/1.09 Derived: -in_closed(f3(A,B,C,D),C,D) | -in_closed(E,A,B) | in_closed(E,C,D). [resolve(28,a,26,a)]. % 0.77/1.09 29 in_ropen(A,B,C) | -leq(B,A) | -less(A,C) # label(in_ropen) # label(axiom). [clausify(12)]. % 0.77/1.09 30 -in_ropen(A,B,C) | leq(B,A) # label(in_ropen) # label(axiom). [clausify(12)]. % 0.77/1.09 31 -in_ropen(A,B,C) | less(A,C) # label(in_ropen) # label(axiom). [clausify(12)]. % 0.77/1.09 32 in_open(A,B,C) | -less(B,A) | -less(A,C) # label(in_open) # label(axiom). [clausify(13)]. % 0.77/1.09 33 -in_open(A,B,C) | less(B,A) # label(in_open) # label(axiom). [clausify(13)]. % 0.77/1.09 34 -in_open(A,B,C) | less(A,C) # label(in_open) # label(axiom). [clausify(13)]. % 0.77/1.09 35 axis_compatible(A,B,C,D) | -in_closed(E,A,B) | -in_closed(E,C,D) # label(axis_compatible_def) # label(axiom). [clausify(15)]. % 0.77/1.09 36 -axis_compatible(A,B,C,D) | in_closed(f2(A,B,C,D),A,B) # label(axis_compatible_def) # label(axiom). [clausify(15)]. % 0.77/1.09 37 -axis_compatible(A,B,C,D) | in_closed(f2(A,B,C,D),C,D) # label(axis_compatible_def) # label(axiom). [clausify(15)]. % 0.77/1.09 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f2(B,C,D,E),B,C). [resolve(35,a,36,a)]. % 0.77/1.09 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f2(B,C,D,E),D,E). [resolve(35,a,37,a)]. % 0.77/1.09 % 0.77/1.09 ============================== end predicate elimination ============= % 0.77/1.09 % 0.77/1.09 Auto_denials: (non-Horn, no changes). % 0.77/1.09 % 0.77/1.09 Term ordering decisions: % 0.77/1.11 Function symbol KB weights: conflict=1. unknown=1. v0=1. compatible=1. v100=1. v200=1. v400=1. v50=1. c1=1. c2=1. c3=1. box_verdict=1. f1=1. f2=1. f3=1. % 0.77/1.11 % 0.77/1.11 ============================== end of process initial clauses ======== % 0.77/1.11 % 0.77/1.11 ============================== CLAUSES FOR SEARCH ==================== % 0.77/1.11 % 0.77/1.11 ============================== end of clauses for search ============= % 0.77/1.11 % 0.77/1.11 ============================== SEARCH ================================ % 0.77/1.11 % 0.77/1.11 % Starting search at 0.02 seconds. % 0.77/1.11 % 0.77/1.11 ============================== PROOF ================================= % 0.77/1.11 % SZS status Theorem % 0.77/1.11 % SZS output start Refutation % 0.77/1.11 % 0.77/1.11 % Proof 1 at 0.05 (+ 0.00) seconds. % 0.77/1.11 % Length of proof is 28. % 0.77/1.11 % Level of proof is 6. % 0.77/1.11 % Maximum clause weight is 12.000. % 0.77/1.11 % Given clauses 138. % 0.77/1.11 % 0.77/1.11 1 (all X -less(X,X)) # label(irreflexive) # label(axiom) # label(non_clause). [assumption]. % 0.77/1.11 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]. % 0.77/1.11 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]. % 0.77/1.11 11 (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]. % 0.77/1.11 22 --(exists X exists Y exists Z ((in_lopen(X,v0,v200) | in_lopen(Y,v0,v100) | in_lopen(Z,v0,v50)) & leq(v400,X) & leq(v200,Y) & leq(v100,Z))) # label(odrl445) # label(negated_conjecture) # label(non_clause). [assumption]. % 0.77/1.11 45 less(v50,v100) # label(ord_v50_v100) # label(axiom). [assumption]. % 0.77/1.11 48 less(v100,v200) # label(ord_v100_v200) # label(axiom). [assumption]. % 0.77/1.11 50 less(v200,v400) # label(ord_v200_v400) # label(axiom). [assumption]. % 0.77/1.11 51 leq(v400,c1) # label(odrl445) # label(negated_conjecture). [clausify(22)]. % 0.77/1.11 52 leq(v200,c2) # label(odrl445) # label(negated_conjecture). [clausify(22)]. % 0.77/1.11 53 leq(v100,c3) # label(odrl445) # label(negated_conjecture). [clausify(22)]. % 0.77/1.11 55 in_lopen(c1,v0,v200) | in_lopen(c2,v0,v100) | in_lopen(c3,v0,v50) # label(odrl445) # label(negated_conjecture). [clausify(22)]. % 0.77/1.11 56 -less(A,A) # label(irreflexive) # label(axiom). [clausify(1)]. % 0.77/1.11 67 -in_lopen(A,B,C) | leq(A,C) # label(in_lopen) # label(axiom). [clausify(11)]. % 0.77/1.11 71 -leq(A,B) | -less(B,C) | less(A,C) # label(leq_less_trans) # label(axiom). [clausify(7)]. % 0.77/1.11 73 -leq(A,B) | -leq(B,C) | leq(A,C) # label(leq_trans) # label(axiom). [clausify(9)]. % 0.77/1.11 118 leq(c3,v50) | in_lopen(c1,v0,v200) | in_lopen(c2,v0,v100). [resolve(67,a,55,c)]. % 0.77/1.11 162 -leq(v400,v200). [ur(71,b,50,a,c,56,a)]. % 0.77/1.11 164 -leq(v200,v100). [ur(71,b,48,a,c,56,a)]. % 0.77/1.11 167 -leq(v100,v50). [ur(71,b,45,a,c,56,a)]. % 0.77/1.11 289 -leq(c1,v200). [ur(73,a,51,a,c,162,a)]. % 0.77/1.11 321 -leq(c2,v100). [ur(73,a,52,a,c,164,a)]. % 0.77/1.11 337 -leq(c3,v50). [ur(73,a,53,a,c,167,a)]. % 0.77/1.11 342 in_lopen(c1,v0,v200) | in_lopen(c2,v0,v100). [back_unit_del(118),unit_del(a,337)]. % 0.77/1.11 407 -in_lopen(c1,A,v200). [ur(67,b,289,a)]. % 0.77/1.11 411 in_lopen(c2,v0,v100). [back_unit_del(342),unit_del(a,407)]. % 0.77/1.11 441 -in_lopen(c2,A,v100). [ur(67,b,321,a)]. % 0.77/1.11 442 $F. [resolve(441,a,411,a)]. % 0.77/1.11 % 0.77/1.11 % SZS output end Refutation % 0.77/1.11 ============================== end of proof ========================== % 0.77/1.11 % 0.77/1.11 ============================== STATISTICS ============================ % 0.77/1.11 % 0.77/1.11 Given=138. Generated=1089. Kept=396. proofs=1. % 0.77/1.11 Usable=136. Sos=244. Demods=3. Limbo=0, Disabled=86. Hints=0. % 0.77/1.11 Megabytes=0.33. % 0.77/1.11 User_CPU=0.05, System_CPU=0.00, Wall_clock=0. % 0.77/1.11 % 0.77/1.11 ============================== end of statistics ===================== % 0.77/1.11 % 0.77/1.11 ============================== end of search ========================= % 0.77/1.11 % 0.77/1.11 THEOREM PROVED % 0.77/1.11 % SZS status Theorem % 0.77/1.11 % 0.77/1.11 Exiting with 1 proof. % 0.77/1.11 % 0.77/1.11 Process 26139 exit (max_proofs) Tue Apr 28 18:53:34 2026 % 0.77/1.11 Prover9 interrupted %------------------------------------------------------------------------------