%------------------------------------------------------------------------------ % File : Prover9---1109a % Problem : MGT106+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 02:10:30 PM UTC 2026 % Result : Unsatisfiable 0.78s 1.08s % Output : Refutation 0.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : MGT106+1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.12 % Command : tptp2X_and_run_prover9 %d %s % 0.14/0.33 % Computer : n010.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.33 % CPULimit : 300 % 0.14/0.33 % WCLimit : 300 % 0.14/0.33 % DateTime : Tue Apr 28 19:21:21 EDT 2026 % 0.14/0.33 % CPUTime : % 0.78/1.07 ============================== Prover9 =============================== % 0.78/1.07 Prover9 (32) version 2009-11A, November 2009. % 0.78/1.07 Process 18386 was started by sandbox2 on n010.cluster.edu, % 0.78/1.07 Tue Apr 28 19:21:21 2026 % 0.78/1.07 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_17981_n010.cluster.edu". % 0.78/1.07 ============================== end of head =========================== % 0.78/1.07 % 0.78/1.07 ============================== INPUT ================================= % 0.78/1.07 % 0.78/1.07 % Reading from file /tmp/Prover9_17981_n010.cluster.edu % 0.78/1.07 % 0.78/1.07 set(prolog_style_variables). % 0.78/1.07 set(auto2). % 0.78/1.07 % set(auto2) -> set(auto). % 0.78/1.07 % set(auto) -> set(auto_inference). % 0.78/1.07 % set(auto) -> set(auto_setup). % 0.78/1.07 % set(auto_setup) -> set(predicate_elim). % 0.78/1.07 % set(auto_setup) -> assign(eq_defs, unfold). % 0.78/1.07 % set(auto) -> set(auto_limits). % 0.78/1.07 % set(auto_limits) -> assign(max_weight, "100.000"). % 0.78/1.07 % set(auto_limits) -> assign(sos_limit, 20000). % 0.78/1.07 % set(auto) -> set(auto_denials). % 0.78/1.07 % set(auto) -> set(auto_process). % 0.78/1.07 % set(auto2) -> assign(new_constants, 1). % 0.78/1.07 % set(auto2) -> assign(fold_denial_max, 3). % 0.78/1.07 % set(auto2) -> assign(max_weight, "200.000"). % 0.78/1.07 % set(auto2) -> assign(max_hours, 1). % 0.78/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600). % 0.78/1.07 % set(auto2) -> assign(max_seconds, 0). % 0.78/1.07 % set(auto2) -> assign(max_minutes, 5). % 0.78/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300). % 0.78/1.07 % set(auto2) -> set(sort_initial_sos). % 0.78/1.07 % set(auto2) -> assign(sos_limit, -1). % 0.78/1.07 % set(auto2) -> assign(lrs_ticks, 3000). % 0.78/1.07 % set(auto2) -> assign(max_megs, 400). % 0.78/1.07 % set(auto2) -> assign(stats, some). % 0.78/1.07 % set(auto2) -> clear(echo_input). % 0.78/1.07 % set(auto2) -> set(quiet). % 0.78/1.07 % set(auto2) -> clear(print_initial_clauses). % 0.78/1.07 % set(auto2) -> clear(print_given). % 0.78/1.07 assign(lrs_ticks,-1). % 0.78/1.07 assign(sos_limit,10000). % 0.78/1.07 assign(order,kbo). % 0.78/1.07 set(lex_order_vars). % 0.78/1.07 clear(print_given). % 0.78/1.07 % 0.78/1.07 % formulas(sos). % not echoed (36 formulas) % 0.78/1.07 % 0.78/1.07 ============================== end of input ========================== % 0.78/1.07 % 0.78/1.07 % From the command line: assign(max_seconds, 300). % 0.78/1.07 % 0.78/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ========== % 0.78/1.07 % 0.78/1.07 % Formulas that are not ordinary clauses: % 0.78/1.07 1 (all X -less(X,X)) # label(irreflexive) # label(axiom) # label(non_clause). [assumption]. % 0.78/1.07 2 (all X all Y all Z (less(X,Y) & less(Y,Z) -> less(X,Z))) # label(transitive) # label(axiom) # label(non_clause). [assumption]. % 0.78/1.07 3 (all X all Y (less(X,Y) | X = Y | less(Y,X))) # label(trichotomy) # label(axiom) # label(non_clause). [assumption]. % 0.78/1.07 4 (all X all Y (leq(X,Y) <-> less(X,Y) | X = Y)) # label(leq_def) # label(axiom) # label(non_clause). [assumption]. % 0.78/1.07 5 (all X all Y (leq(X,Y) & leq(Y,X) -> X = Y)) # label(leq_antisym) # label(axiom) # label(non_clause). [assumption]. % 0.78/1.07 6 (all X all Y (less(X,Y) -> leq(X,Y))) # label(less_implies_leq) # label(axiom) # label(non_clause). [assumption]. % 0.78/1.07 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]. % 0.78/1.07 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]. % 0.78/1.07 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]. % 0.78/1.07 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]. % 0.78/1.07 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]. % 0.78/1.07 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]. % 0.78/1.07 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]. % 0.78/1.07 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]. % 0.78/1.07 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]. % 0.78/1.08 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]. % 0.78/1.08 17 (all V (is_verdict(V) -> V = conflict | V = compatible | V = unknown)) # label(verdict_enum) # label(axiom) # label(non_clause). [assumption]. % 0.78/1.08 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]. % 0.78/1.08 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]. % 0.78/1.08 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]. % 0.78/1.08 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]. % 0.78/1.08 % 0.78/1.08 ============================== end of process non-clausal formulas === % 0.78/1.08 % 0.78/1.08 ============================== PROCESS INITIAL CLAUSES =============== % 0.78/1.08 % 0.78/1.08 ============================== PREDICATE ELIMINATION ================= % 0.78/1.08 22 -in_lopen(A,B,C) | less(B,A) # label(in_lopen) # label(axiom). [clausify(11)]. % 0.78/1.08 23 in_lopen(w,v0,v600) # label(wit_in_lopen) # label(axiom). [assumption]. % 0.78/1.08 Derived: less(v0,w). [resolve(22,a,23,a)]. % 0.78/1.08 24 -in_lopen(A,B,C) | leq(A,C) # label(in_lopen) # label(axiom). [clausify(11)]. % 0.78/1.08 Derived: leq(w,v600). [resolve(24,a,23,a)]. % 0.78/1.08 25 in_lopen(A,B,C) | -less(B,A) | -leq(A,C) # label(in_lopen) # label(axiom). [clausify(11)]. % 0.78/1.08 26 -axis_conflict(A,B,C,D) | -in_closed(E,A,B) | -in_closed(E,C,D) # label(axis_conflict_def) # label(axiom). [clausify(14)]. % 0.78/1.08 27 axis_conflict(A,B,C,D) | in_closed(f1(A,B,C,D),A,B) # label(axis_conflict_def) # label(axiom). [clausify(14)]. % 0.78/1.08 28 axis_conflict(A,B,C,D) | in_closed(f1(A,B,C,D),C,D) # label(axis_conflict_def) # label(axiom). [clausify(14)]. % 0.78/1.08 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f1(B,C,D,E),B,C). [resolve(26,a,27,a)]. % 0.78/1.08 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f1(B,C,D,E),D,E). [resolve(26,a,28,a)]. % 0.78/1.08 29 -axis_subsumes(A,B,C,D) | -in_closed(E,A,B) | in_closed(E,C,D) # label(axis_subsumes_def) # label(axiom). [clausify(16)]. % 0.78/1.08 30 axis_subsumes(A,B,C,D) | in_closed(f3(A,B,C,D),A,B) # label(axis_subsumes_def) # label(axiom). [clausify(16)]. % 0.78/1.08 Derived: -in_closed(A,B,C) | in_closed(A,D,E) | in_closed(f3(B,C,D,E),B,C). [resolve(29,a,30,a)]. % 0.78/1.08 31 axis_subsumes(A,B,C,D) | -in_closed(f3(A,B,C,D),C,D) # label(axis_subsumes_def) # label(axiom). [clausify(16)]. % 0.78/1.08 Derived: -in_closed(f3(A,B,C,D),C,D) | -in_closed(E,A,B) | in_closed(E,C,D). [resolve(31,a,29,a)]. % 0.78/1.08 32 in_ropen(A,B,C) | -leq(B,A) | -less(A,C) # label(in_ropen) # label(axiom). [clausify(12)]. % 0.78/1.08 33 -in_ropen(A,B,C) | leq(B,A) # label(in_ropen) # label(axiom). [clausify(12)]. % 0.78/1.08 34 -in_ropen(A,B,C) | less(A,C) # label(in_ropen) # label(axiom). [clausify(12)]. % 0.78/1.08 35 in_open(A,B,C) | -less(B,A) | -less(A,C) # label(in_open) # label(axiom). [clausify(13)]. % 0.78/1.08 36 -in_open(A,B,C) | less(B,A) # label(in_open) # label(axiom). [clausify(13)]. % 0.78/1.08 37 -in_open(A,B,C) | less(A,C) # label(in_open) # label(axiom). [clausify(13)]. % 0.78/1.08 38 axis_compatible(A,B,C,D) | -in_closed(E,A,B) | -in_closed(E,C,D) # label(axis_compatible_def) # label(axiom). [clausify(15)]. % 0.78/1.08 39 -axis_compatible(A,B,C,D) | in_closed(f2(A,B,C,D),A,B) # label(axis_compatible_def) # label(axiom). [clausify(15)]. % 0.78/1.08 40 -axis_compatible(A,B,C,D) | in_closed(f2(A,B,C,D),C,D) # label(axis_compatible_def) # label(axiom). [clausify(15)]. % 0.78/1.08 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f2(B,C,D,E),B,C). [resolve(38,a,39,a)]. % 0.78/1.08 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f2(B,C,D,E),D,E). [resolve(38,a,40,a)]. % 0.78/1.08 % 0.78/1.08 ============================== end predicate elimination ============= % 0.78/1.08 % 0.78/1.08 Auto_denials: (non-Horn, no changes). % 0.78/1.08 % 0.78/1.08 Term ordering decisions: % 0.78/1.08 Function symbol KB weights: conflict=1. unknown=1. compatible=1. v600=1. w=1. v0=1. v800=1. box_verdict=1. f1=1. f2=1. f3=1. % 0.78/1.08 % 0.78/1.08 ============================== end of process initial clauses ======== % 0.78/1.08 % 0.78/1.08 ============================== CLAUSES FOR SEARCH ==================== % 0.78/1.08 % 0.78/1.08 ============================== end of clauses for search ============= % 0.78/1.08 % 0.78/1.08 ============================== SEARCH ================================ % 0.78/1.08 % 0.78/1.08 % Starting search at 0.02 seconds. % 0.78/1.08 % 0.78/1.08 ============================== PROOF ================================= % 0.78/1.08 % SZS status Unsatisfiable % 0.78/1.08 % SZS output start Refutation % 0.78/1.08 % 0.78/1.08 % Proof 1 at 0.02 (+ 0.00) seconds. % 0.78/1.08 % Length of proof is 27. % 0.78/1.08 % Level of proof is 5. % 0.78/1.08 % Maximum clause weight is 9.000. % 0.78/1.08 % Given clauses 45. % 0.78/1.08 % 0.78/1.08 1 (all X -less(X,X)) # label(irreflexive) # label(axiom) # label(non_clause). [assumption]. % 0.78/1.08 2 (all X all Y all Z (less(X,Y) & less(Y,Z) -> less(X,Z))) # label(transitive) # label(axiom) # label(non_clause). [assumption]. % 0.78/1.08 4 (all X all Y (leq(X,Y) <-> less(X,Y) | X = Y)) # label(leq_def) # label(axiom) # label(non_clause). [assumption]. % 0.78/1.08 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]. % 0.78/1.08 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]. % 0.78/1.08 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]. % 0.78/1.08 23 in_lopen(w,v0,v600) # label(wit_in_lopen) # label(axiom). [assumption]. % 0.78/1.08 24 -in_lopen(A,B,C) | leq(A,C) # label(in_lopen) # label(axiom). [clausify(11)]. % 0.78/1.08 45 less(v600,v800) # label(ord_v600_v800) # label(axiom). [assumption]. % 0.78/1.08 46 leq(v800,w) # label(wit_leq) # label(axiom). [assumption]. % 0.78/1.08 48 -less(A,A) # label(irreflexive) # label(axiom). [clausify(1)]. % 0.78/1.08 55 leq(A,B) | B != A # label(leq_def) # label(axiom). [clausify(4)]. % 0.78/1.08 58 -less(A,B) | -less(B,C) | less(A,C) # label(transitive) # label(axiom). [clausify(2)]. % 0.78/1.08 59 -leq(A,B) | less(A,B) | B = A # label(leq_def) # label(axiom). [clausify(4)]. % 0.78/1.08 61 -leq(A,B) | -less(B,C) | less(A,C) # label(leq_less_trans) # label(axiom). [clausify(7)]. % 0.78/1.08 62 -less(A,B) | -leq(B,C) | less(A,C) # label(less_leq_trans) # label(axiom). [clausify(8)]. % 0.78/1.08 79 leq(w,v600). [resolve(24,a,23,a)]. % 0.78/1.08 97 leq(A,A). [xx_res(55,b)]. % 0.78/1.08 107 -less(v800,v600). [ur(58,b,45,a,c,48,a)]. % 0.78/1.08 109 less(v800,w) | v800 = w. [resolve(59,a,46,a),flip(b)]. % 0.78/1.08 115 -leq(v800,v600). [ur(61,b,45,a,c,48,a)]. % 0.78/1.08 156 less(w,v600) | w = v600. [resolve(79,a,59,a),flip(b)]. % 0.78/1.08 166 -less(v800,w). [ur(62,b,79,a,c,107,a)]. % 0.78/1.08 168 -less(w,v600). [ur(61,a,46,a,c,107,a)]. % 0.78/1.08 170 v800 = w. [back_unit_del(109),unit_del(a,166)]. % 0.78/1.08 171 w = v600. [back_unit_del(156),unit_del(a,168)]. % 0.78/1.08 175 $F. [back_rewrite(115),rewrite([170(1),171(1)]),unit_del(a,97)]. % 0.78/1.08 % 0.78/1.08 % SZS output end Refutation % 0.78/1.08 ============================== end of proof ========================== % 0.78/1.08 % 0.78/1.08 ============================== STATISTICS ============================ % 0.78/1.08 % 0.78/1.08 Given=45. Generated=202. Kept=126. proofs=1. % 0.78/1.08 Usable=45. Sos=60. Demods=5. Limbo=5, Disabled=78. Hints=0. % 0.78/1.08 Megabytes=0.16. % 0.78/1.08 User_CPU=0.02, System_CPU=0.00, Wall_clock=0. % 0.78/1.08 % 0.78/1.08 ============================== end of statistics ===================== % 0.78/1.08 % 0.78/1.08 ============================== end of search ========================= % 0.78/1.08 % 0.78/1.08 THEOREM PROVED % 0.78/1.08 % SZS status Unsatisfiable % 0.78/1.08 % 0.78/1.08 Exiting with 1 proof. % 0.78/1.08 % 0.78/1.08 Process 18386 exit (max_proofs) Tue Apr 28 19:21:21 2026 % 0.78/1.08 Prover9 interrupted %------------------------------------------------------------------------------