%------------------------------------------------------------------------------ % File : Prover9---1109a % Problem : MGT080+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : tptp2X_and_run_prover9 %d %s % Computer : n021.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 02:10:27 PM UTC 2026 % Result : Theorem 0.74s 1.06s % Output : Refutation 0.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : MGT080+1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.12 % Command : tptp2X_and_run_prover9 %d %s % 0.16/0.33 % Computer : n021.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.33 % CPULimit : 300 % 0.16/0.33 % WCLimit : 300 % 0.16/0.33 % DateTime : Tue Apr 28 18:49:50 EDT 2026 % 0.16/0.33 % CPUTime : % 0.41/1.02 ============================== Prover9 =============================== % 0.41/1.02 Prover9 (32) version 2009-11A, November 2009. % 0.41/1.02 Process 23465 was started by sandbox2 on n021.cluster.edu, % 0.41/1.02 Tue Apr 28 18:49:51 2026 % 0.41/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_23312_n021.cluster.edu". % 0.41/1.02 ============================== end of head =========================== % 0.41/1.02 % 0.41/1.02 ============================== INPUT ================================= % 0.41/1.02 % 0.41/1.02 % Reading from file /tmp/Prover9_23312_n021.cluster.edu % 0.41/1.02 % 0.41/1.02 set(prolog_style_variables). % 0.41/1.02 set(auto2). % 0.41/1.02 % set(auto2) -> set(auto). % 0.41/1.02 % set(auto) -> set(auto_inference). % 0.41/1.02 % set(auto) -> set(auto_setup). % 0.41/1.02 % set(auto_setup) -> set(predicate_elim). % 0.41/1.02 % set(auto_setup) -> assign(eq_defs, unfold). % 0.41/1.02 % set(auto) -> set(auto_limits). % 0.41/1.02 % set(auto_limits) -> assign(max_weight, "100.000"). % 0.41/1.02 % set(auto_limits) -> assign(sos_limit, 20000). % 0.41/1.02 % set(auto) -> set(auto_denials). % 0.41/1.02 % set(auto) -> set(auto_process). % 0.41/1.02 % set(auto2) -> assign(new_constants, 1). % 0.41/1.02 % set(auto2) -> assign(fold_denial_max, 3). % 0.41/1.02 % set(auto2) -> assign(max_weight, "200.000"). % 0.41/1.02 % set(auto2) -> assign(max_hours, 1). % 0.41/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600). % 0.41/1.02 % set(auto2) -> assign(max_seconds, 0). % 0.41/1.02 % set(auto2) -> assign(max_minutes, 5). % 0.41/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300). % 0.41/1.02 % set(auto2) -> set(sort_initial_sos). % 0.41/1.02 % set(auto2) -> assign(sos_limit, -1). % 0.41/1.02 % set(auto2) -> assign(lrs_ticks, 3000). % 0.41/1.02 % set(auto2) -> assign(max_megs, 400). % 0.41/1.02 % set(auto2) -> assign(stats, some). % 0.41/1.02 % set(auto2) -> clear(echo_input). % 0.41/1.02 % set(auto2) -> set(quiet). % 0.41/1.02 % set(auto2) -> clear(print_initial_clauses). % 0.41/1.02 % set(auto2) -> clear(print_given). % 0.41/1.02 assign(lrs_ticks,-1). % 0.41/1.02 assign(sos_limit,10000). % 0.41/1.02 assign(order,kbo). % 0.41/1.02 set(lex_order_vars). % 0.41/1.02 clear(print_given). % 0.41/1.02 % 0.41/1.02 % formulas(sos). % not echoed (74 formulas) % 0.41/1.02 % 0.41/1.02 ============================== end of input ========================== % 0.41/1.02 % 0.41/1.02 % From the command line: assign(max_seconds, 300). % 0.41/1.02 % 0.41/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ========== % 0.41/1.02 % 0.41/1.02 % Formulas that are not ordinary clauses: % 0.41/1.02 1 (all X -less(X,X)) # label(irreflexive) # label(axiom) # label(non_clause). [assumption]. % 0.41/1.02 2 (all X all Y all Z (less(X,Y) & less(Y,Z) -> less(X,Z))) # label(transitive) # label(axiom) # label(non_clause). [assumption]. % 0.41/1.02 3 (all X all Y (less(X,Y) | X = Y | less(Y,X))) # label(trichotomy) # label(axiom) # label(non_clause). [assumption]. % 0.41/1.02 4 (all X all Y (leq(X,Y) <-> less(X,Y) | X = Y)) # label(leq_def) # label(axiom) # label(non_clause). [assumption]. % 0.41/1.02 5 (all X all Y (leq(X,Y) & leq(Y,X) -> X = Y)) # label(leq_antisym) # label(axiom) # label(non_clause). [assumption]. % 0.41/1.02 6 (all X all Y (less(X,Y) -> leq(X,Y))) # label(less_implies_leq) # label(axiom) # label(non_clause). [assumption]. % 0.41/1.02 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]. % 0.41/1.02 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]. % 0.41/1.02 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]. % 0.41/1.02 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]. % 0.41/1.02 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]. % 0.41/1.02 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]. % 0.41/1.02 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]. % 0.41/1.02 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]. % 0.41/1.02 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]. % 0.41/1.02 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]. % 0.41/1.02 17 (all V (is_verdict(V) -> V = conflict | V = compatible | V = unknown)) # label(verdict_enum) # label(axiom) # label(non_clause). [assumption]. % 0.41/1.02 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]. % 0.41/1.02 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]. % 0.41/1.02 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]. % 0.41/1.02 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]. % 0.41/1.02 22 --(exists X exists Y exists Z exists W (in_closed(X,v600,v600) & in_closed(X,v800,v800) & less(v100,Y) & in_open(Y,v0,v500) & leq(v8,Z) & in_lopen(Z,v0,v32) & in_lopen(W,v0,v300) & leq(v150,W))) # label(odrl365) # label(negated_conjecture) # label(non_clause). [assumption]. % 0.41/1.02 % 0.41/1.02 ============================== end of process non-clausal formulas === % 0.41/1.02 % 0.41/1.02 ============================== PROCESS INITIAL CLAUSES =============== % 0.41/1.02 % 0.41/1.02 ============================== PREDICATE ELIMINATION ================= % 0.41/1.02 23 -in_open(A,B,C) | less(B,A) # label(in_open) # label(axiom). [clausify(13)]. % 0.41/1.02 24 in_open(c2,v0,v500) # label(odrl365) # label(negated_conjecture). [clausify(22)]. % 0.41/1.02 Derived: less(v0,c2). [resolve(23,a,24,a)]. % 0.41/1.02 25 -in_open(A,B,C) | less(A,C) # label(in_open) # label(axiom). [clausify(13)]. % 0.41/1.02 Derived: less(c2,v500). [resolve(25,a,24,a)]. % 0.41/1.02 26 in_open(A,B,C) | -less(B,A) | -less(A,C) # label(in_open) # label(axiom). [clausify(13)]. % 0.41/1.02 27 -in_lopen(A,B,C) | less(B,A) # label(in_lopen) # label(axiom). [clausify(11)]. % 0.41/1.02 28 in_lopen(c3,v0,v32) # label(odrl365) # label(negated_conjecture). [clausify(22)]. % 0.41/1.02 29 in_lopen(c4,v0,v300) # label(odrl365) # label(negated_conjecture). [clausify(22)]. % 0.41/1.02 Derived: less(v0,c3). [resolve(27,a,28,a)]. % 0.41/1.02 Derived: less(v0,c4). [resolve(27,a,29,a)]. % 0.41/1.02 30 -in_lopen(A,B,C) | leq(A,C) # label(in_lopen) # label(axiom). [clausify(11)]. % 0.41/1.02 Derived: leq(c3,v32). [resolve(30,a,28,a)]. % 0.41/1.02 Derived: leq(c4,v300). [resolve(30,a,29,a)]. % 0.41/1.02 31 in_lopen(A,B,C) | -less(B,A) | -leq(A,C) # label(in_lopen) # label(axiom). [clausify(11)]. % 0.41/1.02 32 -axis_conflict(A,B,C,D) | -in_closed(E,A,B) | -in_closed(E,C,D) # label(axis_conflict_def) # label(axiom). [clausify(14)]. % 0.41/1.02 33 axis_conflict(A,B,C,D) | in_closed(f1(A,B,C,D),A,B) # label(axis_conflict_def) # label(axiom). [clausify(14)]. % 0.41/1.02 34 axis_conflict(A,B,C,D) | in_closed(f1(A,B,C,D),C,D) # label(axis_conflict_def) # label(axiom). [clausify(14)]. % 0.41/1.02 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f1(B,C,D,E),B,C). [resolve(32,a,33,a)]. % 0.41/1.02 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f1(B,C,D,E),D,E). [resolve(32,a,34,a)]. % 0.41/1.02 35 -axis_subsumes(A,B,C,D) | -in_closed(E,A,B) | in_closed(E,C,D) # label(axis_subsumes_def) # label(axiom). [clausify(16)]. % 0.41/1.02 36 axis_subsumes(A,B,C,D) | in_closed(f3(A,B,C,D),A,B) # label(axis_subsumes_def) # label(axiom). [clausify(16)]. % 0.41/1.02 Derived: -in_closed(A,B,C) | in_closed(A,D,E) | in_closed(f3(B,C,D,E),B,C). [resolve(35,a,36,a)]. % 0.41/1.02 37 axis_subsumes(A,B,C,D) | -in_closed(f3(A,B,C,D),C,D) # label(axis_subsumes_def) # label(axiom). [clausify(16)]. % 0.41/1.02 Derived: -in_closed(f3(A,B,C,D),C,D) | -in_closed(E,A,B) | in_closed(E,C,D). [resolve(37,a,35,a)]. % 0.41/1.02 38 in_ropen(A,B,C) | -leq(B,A) | -less(A,C) # label(in_ropen) # label(axiom). [clausify(12)]. % 0.41/1.02 39 -in_ropen(A,B,C) | leq(B,A) # label(in_ropen) # label(axiom). [clausify(12)]. % 0.74/1.06 40 -in_ropen(A,B,C) | less(A,C) # label(in_ropen) # label(axiom). [clausify(12)]. % 0.74/1.06 41 axis_compatible(A,B,C,D) | -in_closed(E,A,B) | -in_closed(E,C,D) # label(axis_compatible_def) # label(axiom). [clausify(15)]. % 0.74/1.06 42 -axis_compatible(A,B,C,D) | in_closed(f2(A,B,C,D),A,B) # label(axis_compatible_def) # label(axiom). [clausify(15)]. % 0.74/1.06 43 -axis_compatible(A,B,C,D) | in_closed(f2(A,B,C,D),C,D) # label(axis_compatible_def) # label(axiom). [clausify(15)]. % 0.74/1.06 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f2(B,C,D,E),B,C). [resolve(41,a,42,a)]. % 0.74/1.06 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f2(B,C,D,E),D,E). [resolve(41,a,43,a)]. % 0.74/1.06 % 0.74/1.06 ============================== end predicate elimination ============= % 0.74/1.06 % 0.74/1.06 Auto_denials: (non-Horn, no changes). % 0.74/1.06 % 0.74/1.06 Term ordering decisions: % 0.74/1.06 Function symbol KB weights: conflict=1. v0=1. v600=1. v800=1. v100=1. v150=1. v300=1. v32=1. v500=1. v8=1. unknown=1. compatible=1. c1=1. c2=1. c3=1. c4=1. box_verdict=1. f1=1. f2=1. f3=1. % 0.74/1.06 % 0.74/1.06 ============================== end of process initial clauses ======== % 0.74/1.06 % 0.74/1.06 ============================== CLAUSES FOR SEARCH ==================== % 0.74/1.06 % 0.74/1.06 ============================== end of clauses for search ============= % 0.74/1.06 % 0.74/1.06 ============================== SEARCH ================================ % 0.74/1.06 % 0.74/1.06 % Starting search at 0.02 seconds. % 0.74/1.06 % 0.74/1.06 ============================== PROOF ================================= % 0.74/1.06 % SZS status Theorem % 0.74/1.06 % SZS output start Refutation % 0.74/1.06 % 0.74/1.06 % Proof 1 at 0.05 (+ 0.01) seconds. % 0.74/1.06 % Length of proof is 19. % 0.74/1.06 % Level of proof is 4. % 0.74/1.06 % Maximum clause weight is 9.000. % 0.74/1.06 % Given clauses 163. % 0.74/1.06 % 0.74/1.06 1 (all X -less(X,X)) # label(irreflexive) # label(axiom) # label(non_clause). [assumption]. % 0.74/1.06 5 (all X all Y (leq(X,Y) & leq(Y,X) -> X = Y)) # label(leq_antisym) # label(axiom) # label(non_clause). [assumption]. % 0.74/1.06 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]. % 0.74/1.06 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]. % 0.74/1.06 22 --(exists X exists Y exists Z exists W (in_closed(X,v600,v600) & in_closed(X,v800,v800) & less(v100,Y) & in_open(Y,v0,v500) & leq(v8,Z) & in_lopen(Z,v0,v32) & in_lopen(W,v0,v300) & leq(v150,W))) # label(odrl365) # label(negated_conjecture) # label(non_clause). [assumption]. % 0.74/1.06 82 less(v600,v800) # label(ord_v600_v800) # label(axiom). [assumption]. % 0.74/1.06 86 in_closed(c1,v600,v600) # label(odrl365) # label(negated_conjecture). [clausify(22)]. % 0.74/1.06 87 in_closed(c1,v800,v800) # label(odrl365) # label(negated_conjecture). [clausify(22)]. % 0.74/1.06 89 -less(A,A) # label(irreflexive) # label(axiom). [clausify(1)]. % 0.74/1.06 97 -in_closed(A,B,C) | leq(B,A) # label(in_closed) # label(axiom). [clausify(10)]. % 0.74/1.06 98 -in_closed(A,B,C) | leq(A,C) # label(in_closed) # label(axiom). [clausify(10)]. % 0.74/1.06 101 -leq(A,B) | -leq(B,A) | B = A # label(leq_antisym) # label(axiom). [clausify(5)]. % 0.74/1.06 102 -leq(A,B) | -less(B,C) | less(A,C) # label(leq_less_trans) # label(axiom). [clausify(7)]. % 0.74/1.06 179 leq(v800,c1). [resolve(97,a,87,a)]. % 0.74/1.06 181 leq(c1,v800). [resolve(98,a,87,a)]. % 0.74/1.06 182 leq(c1,v600). [resolve(98,a,86,a)]. % 0.74/1.06 305 -leq(v800,v600). [ur(102,b,82,a,c,89,a)]. % 0.74/1.06 633 c1 = v800. [resolve(179,a,101,b),flip(b),unit_del(a,181)]. % 0.74/1.06 644 $F. [back_rewrite(182),rewrite([633(1)]),unit_del(a,305)]. % 0.74/1.06 % 0.74/1.06 % SZS output end Refutation % 0.74/1.06 ============================== end of proof ========================== % 0.74/1.06 % 0.74/1.06 ============================== STATISTICS ============================ % 0.74/1.06 % 0.74/1.06 Given=163. Generated=1684. Kept=592. proofs=1. % 0.74/1.06 Usable=163. Sos=384. Demods=4. Limbo=11, Disabled=145. Hints=0. % 0.74/1.06 Megabytes=0.51. % 0.74/1.06 User_CPU=0.05, System_CPU=0.01, Wall_clock=0. % 0.74/1.06 % 0.74/1.06 ============================== end of statistics ===================== % 0.74/1.06 % 0.74/1.06 ============================== end of search ========================= % 0.74/1.06 % 0.74/1.06 THEOREM PROVED % 0.74/1.06 % SZS status Theorem % 0.74/1.06 % 0.74/1.06 Exiting with 1 proof. % 0.74/1.06 % 0.74/1.06 Process 23465 exit (max_proofs) Tue Apr 28 18:49:51 2026 % 0.74/1.06 Prover9 interrupted %------------------------------------------------------------------------------