%------------------------------------------------------------------------------ % File : Prover9---1109a % Problem : MGT082+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 02:10:28 PM UTC 2026 % Result : Theorem 0.75s 1.04s % Output : Refutation 0.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : MGT082+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 : n019.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 18:51:13 EDT 2026 % 0.16/0.34 % CPUTime : % 0.46/1.01 ============================== Prover9 =============================== % 0.46/1.01 Prover9 (32) version 2009-11A, November 2009. % 0.46/1.01 Process 3874 was started by sandbox on n019.cluster.edu, % 0.46/1.01 Tue Apr 28 18:51:14 2026 % 0.46/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_3721_n019.cluster.edu". % 0.46/1.01 ============================== end of head =========================== % 0.46/1.01 % 0.46/1.01 ============================== INPUT ================================= % 0.46/1.01 % 0.46/1.01 % Reading from file /tmp/Prover9_3721_n019.cluster.edu % 0.46/1.01 % 0.46/1.01 set(prolog_style_variables). % 0.46/1.01 set(auto2). % 0.46/1.01 % set(auto2) -> set(auto). % 0.46/1.01 % set(auto) -> set(auto_inference). % 0.46/1.01 % set(auto) -> set(auto_setup). % 0.46/1.01 % set(auto_setup) -> set(predicate_elim). % 0.46/1.01 % set(auto_setup) -> assign(eq_defs, unfold). % 0.46/1.01 % set(auto) -> set(auto_limits). % 0.46/1.01 % set(auto_limits) -> assign(max_weight, "100.000"). % 0.46/1.01 % set(auto_limits) -> assign(sos_limit, 20000). % 0.46/1.01 % set(auto) -> set(auto_denials). % 0.46/1.01 % set(auto) -> set(auto_process). % 0.46/1.01 % set(auto2) -> assign(new_constants, 1). % 0.46/1.01 % set(auto2) -> assign(fold_denial_max, 3). % 0.46/1.01 % set(auto2) -> assign(max_weight, "200.000"). % 0.46/1.01 % set(auto2) -> assign(max_hours, 1). % 0.46/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600). % 0.46/1.01 % set(auto2) -> assign(max_seconds, 0). % 0.46/1.01 % set(auto2) -> assign(max_minutes, 5). % 0.46/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300). % 0.46/1.01 % set(auto2) -> set(sort_initial_sos). % 0.46/1.01 % set(auto2) -> assign(sos_limit, -1). % 0.46/1.01 % set(auto2) -> assign(lrs_ticks, 3000). % 0.46/1.01 % set(auto2) -> assign(max_megs, 400). % 0.46/1.01 % set(auto2) -> assign(stats, some). % 0.46/1.01 % set(auto2) -> clear(echo_input). % 0.46/1.01 % set(auto2) -> set(quiet). % 0.46/1.01 % set(auto2) -> clear(print_initial_clauses). % 0.46/1.01 % set(auto2) -> clear(print_given). % 0.46/1.01 assign(lrs_ticks,-1). % 0.46/1.01 assign(sos_limit,10000). % 0.46/1.01 assign(order,kbo). % 0.46/1.01 set(lex_order_vars). % 0.46/1.01 clear(print_given). % 0.46/1.01 % 0.46/1.01 % formulas(sos). % not echoed (57 formulas) % 0.46/1.01 % 0.46/1.01 ============================== end of input ========================== % 0.46/1.01 % 0.46/1.01 % From the command line: assign(max_seconds, 300). % 0.46/1.01 % 0.46/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ========== % 0.46/1.01 % 0.46/1.01 % Formulas that are not ordinary clauses: % 0.46/1.01 1 (all X -less(X,X)) # label(irreflexive) # label(axiom) # label(non_clause). [assumption]. % 0.46/1.01 2 (all X all Y all Z (less(X,Y) & less(Y,Z) -> less(X,Z))) # label(transitive) # label(axiom) # label(non_clause). [assumption]. % 0.46/1.01 3 (all X all Y (less(X,Y) | X = Y | less(Y,X))) # label(trichotomy) # label(axiom) # label(non_clause). [assumption]. % 0.46/1.01 4 (all X all Y (leq(X,Y) <-> less(X,Y) | X = Y)) # label(leq_def) # label(axiom) # label(non_clause). [assumption]. % 0.46/1.01 5 (all X all Y (leq(X,Y) & leq(Y,X) -> X = Y)) # label(leq_antisym) # label(axiom) # label(non_clause). [assumption]. % 0.46/1.01 6 (all X all Y (less(X,Y) -> leq(X,Y))) # label(less_implies_leq) # label(axiom) # label(non_clause). [assumption]. % 0.46/1.01 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]. % 0.46/1.01 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]. % 0.46/1.01 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]. % 0.46/1.01 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]. % 0.46/1.01 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]. % 0.46/1.01 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]. % 0.46/1.01 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]. % 0.46/1.01 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]. % 0.46/1.01 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]. % 0.46/1.02 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]. % 0.46/1.02 17 (all V (is_verdict(V) -> V = conflict | V = compatible | V = unknown)) # label(verdict_enum) # label(axiom) # label(non_clause). [assumption]. % 0.46/1.02 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]. % 0.46/1.02 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]. % 0.46/1.02 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]. % 0.46/1.02 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]. % 0.46/1.02 22 --(exists X exists Y exists Z (in_closed(X,v600,v600) & in_closed(X,v601,v601) & less(v300,Y) & in_open(Y,v0,v500) & leq(v16,Z) & in_lopen(Z,v0,v32))) # label(odrl411) # label(negated_conjecture) # label(non_clause). [assumption]. % 0.46/1.02 % 0.46/1.02 ============================== end of process non-clausal formulas === % 0.46/1.02 % 0.46/1.02 ============================== PROCESS INITIAL CLAUSES =============== % 0.46/1.02 % 0.46/1.02 ============================== PREDICATE ELIMINATION ================= % 0.46/1.02 23 -in_open(A,B,C) | less(B,A) # label(in_open) # label(axiom). [clausify(13)]. % 0.46/1.02 24 in_open(c2,v0,v500) # label(odrl411) # label(negated_conjecture). [clausify(22)]. % 0.46/1.02 Derived: less(v0,c2). [resolve(23,a,24,a)]. % 0.46/1.02 25 -in_open(A,B,C) | less(A,C) # label(in_open) # label(axiom). [clausify(13)]. % 0.46/1.02 Derived: less(c2,v500). [resolve(25,a,24,a)]. % 0.46/1.02 26 in_open(A,B,C) | -less(B,A) | -less(A,C) # label(in_open) # label(axiom). [clausify(13)]. % 0.46/1.02 27 -in_lopen(A,B,C) | less(B,A) # label(in_lopen) # label(axiom). [clausify(11)]. % 0.46/1.02 28 in_lopen(c3,v0,v32) # label(odrl411) # label(negated_conjecture). [clausify(22)]. % 0.46/1.02 Derived: less(v0,c3). [resolve(27,a,28,a)]. % 0.46/1.02 29 -in_lopen(A,B,C) | leq(A,C) # label(in_lopen) # label(axiom). [clausify(11)]. % 0.46/1.02 Derived: leq(c3,v32). [resolve(29,a,28,a)]. % 0.46/1.02 30 in_lopen(A,B,C) | -less(B,A) | -leq(A,C) # label(in_lopen) # label(axiom). [clausify(11)]. % 0.46/1.02 31 -axis_conflict(A,B,C,D) | -in_closed(E,A,B) | -in_closed(E,C,D) # label(axis_conflict_def) # label(axiom). [clausify(14)]. % 0.46/1.02 32 axis_conflict(A,B,C,D) | in_closed(f1(A,B,C,D),A,B) # label(axis_conflict_def) # label(axiom). [clausify(14)]. % 0.46/1.02 33 axis_conflict(A,B,C,D) | in_closed(f1(A,B,C,D),C,D) # label(axis_conflict_def) # label(axiom). [clausify(14)]. % 0.46/1.02 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f1(B,C,D,E),B,C). [resolve(31,a,32,a)]. % 0.46/1.02 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f1(B,C,D,E),D,E). [resolve(31,a,33,a)]. % 0.46/1.02 34 -axis_subsumes(A,B,C,D) | -in_closed(E,A,B) | in_closed(E,C,D) # label(axis_subsumes_def) # label(axiom). [clausify(16)]. % 0.46/1.02 35 axis_subsumes(A,B,C,D) | in_closed(f3(A,B,C,D),A,B) # label(axis_subsumes_def) # label(axiom). [clausify(16)]. % 0.46/1.02 Derived: -in_closed(A,B,C) | in_closed(A,D,E) | in_closed(f3(B,C,D,E),B,C). [resolve(34,a,35,a)]. % 0.46/1.02 36 axis_subsumes(A,B,C,D) | -in_closed(f3(A,B,C,D),C,D) # label(axis_subsumes_def) # label(axiom). [clausify(16)]. % 0.46/1.02 Derived: -in_closed(f3(A,B,C,D),C,D) | -in_closed(E,A,B) | in_closed(E,C,D). [resolve(36,a,34,a)]. % 0.46/1.02 37 in_ropen(A,B,C) | -leq(B,A) | -less(A,C) # label(in_ropen) # label(axiom). [clausify(12)]. % 0.46/1.02 38 -in_ropen(A,B,C) | leq(B,A) # label(in_ropen) # label(axiom). [clausify(12)]. % 0.46/1.02 39 -in_ropen(A,B,C) | less(A,C) # label(in_ropen) # label(axiom). [clausify(12)]. % 0.46/1.02 40 axis_compatible(A,B,C,D) | -in_closed(E,A,B) | -in_closed(E,C,D) # label(axis_compatible_def) # label(axiom). [clausify(15)]. % 0.75/1.04 41 -axis_compatible(A,B,C,D) | in_closed(f2(A,B,C,D),A,B) # label(axis_compatible_def) # label(axiom). [clausify(15)]. % 0.75/1.04 42 -axis_compatible(A,B,C,D) | in_closed(f2(A,B,C,D),C,D) # label(axis_compatible_def) # label(axiom). [clausify(15)]. % 0.75/1.04 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f2(B,C,D,E),B,C). [resolve(40,a,41,a)]. % 0.75/1.04 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f2(B,C,D,E),D,E). [resolve(40,a,42,a)]. % 0.75/1.04 % 0.75/1.04 ============================== end predicate elimination ============= % 0.75/1.04 % 0.75/1.04 Auto_denials: (non-Horn, no changes). % 0.75/1.04 % 0.75/1.04 Term ordering decisions: % 0.75/1.04 Function symbol KB weights: conflict=1. v0=1. v600=1. v601=1. unknown=1. v16=1. v300=1. v32=1. v500=1. compatible=1. c1=1. c2=1. c3=1. box_verdict=1. f1=1. f2=1. f3=1. % 0.75/1.04 % 0.75/1.04 ============================== end of process initial clauses ======== % 0.75/1.04 % 0.75/1.04 ============================== CLAUSES FOR SEARCH ==================== % 0.75/1.04 % 0.75/1.04 ============================== end of clauses for search ============= % 0.75/1.04 % 0.75/1.04 ============================== SEARCH ================================ % 0.75/1.04 % 0.75/1.04 % Starting search at 0.02 seconds. % 0.75/1.04 % 0.75/1.04 ============================== PROOF ================================= % 0.75/1.04 % SZS status Theorem % 0.75/1.04 % SZS output start Refutation % 0.75/1.04 % 0.75/1.04 % Proof 1 at 0.04 (+ 0.01) seconds. % 0.75/1.04 % Length of proof is 19. % 0.75/1.04 % Level of proof is 4. % 0.75/1.04 % Maximum clause weight is 9.000. % 0.75/1.04 % Given clauses 118. % 0.75/1.04 % 0.75/1.04 1 (all X -less(X,X)) # label(irreflexive) # label(axiom) # label(non_clause). [assumption]. % 0.75/1.04 5 (all X all Y (leq(X,Y) & leq(Y,X) -> X = Y)) # label(leq_antisym) # label(axiom) # label(non_clause). [assumption]. % 0.75/1.04 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]. % 0.75/1.04 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]. % 0.75/1.04 22 --(exists X exists Y exists Z (in_closed(X,v600,v600) & in_closed(X,v601,v601) & less(v300,Y) & in_open(Y,v0,v500) & leq(v16,Z) & in_lopen(Z,v0,v32))) # label(odrl411) # label(negated_conjecture) # label(non_clause). [assumption]. % 0.75/1.04 66 less(v600,v601) # label(ord_v600_v601) # label(axiom). [assumption]. % 0.75/1.04 69 in_closed(c1,v600,v600) # label(odrl411) # label(negated_conjecture). [clausify(22)]. % 0.75/1.04 70 in_closed(c1,v601,v601) # label(odrl411) # label(negated_conjecture). [clausify(22)]. % 0.75/1.04 72 -less(A,A) # label(irreflexive) # label(axiom). [clausify(1)]. % 0.75/1.04 80 -in_closed(A,B,C) | leq(B,A) # label(in_closed) # label(axiom). [clausify(10)]. % 0.75/1.04 81 -in_closed(A,B,C) | leq(A,C) # label(in_closed) # label(axiom). [clausify(10)]. % 0.75/1.04 84 -leq(A,B) | -leq(B,A) | B = A # label(leq_antisym) # label(axiom). [clausify(5)]. % 0.75/1.04 85 -leq(A,B) | -less(B,C) | less(A,C) # label(leq_less_trans) # label(axiom). [clausify(7)]. % 0.75/1.04 145 leq(v601,c1). [resolve(80,a,70,a)]. % 0.75/1.04 147 leq(c1,v601). [resolve(81,a,70,a)]. % 0.75/1.04 148 leq(c1,v600). [resolve(81,a,69,a)]. % 0.75/1.04 223 -leq(v601,v600). [ur(85,b,66,a,c,72,a)]. % 0.75/1.04 454 c1 = v601. [resolve(145,a,84,b),flip(b),unit_del(a,147)]. % 0.75/1.04 465 $F. [back_rewrite(148),rewrite([454(1)]),unit_del(a,223)]. % 0.75/1.04 % 0.75/1.04 % SZS output end Refutation % 0.75/1.04 ============================== end of proof ========================== % 0.75/1.04 % 0.75/1.04 ============================== STATISTICS ============================ % 0.75/1.04 % 0.75/1.04 Given=118. Generated=1053. Kept=414. proofs=1. % 0.75/1.04 Usable=118. Sos=251. Demods=4. Limbo=11, Disabled=124. Hints=0. % 0.75/1.04 Megabytes=0.36. % 0.75/1.04 User_CPU=0.04, System_CPU=0.01, Wall_clock=0. % 0.75/1.04 % 0.75/1.04 ============================== end of statistics ===================== % 0.75/1.04 % 0.75/1.04 ============================== end of search ========================= % 0.75/1.04 % 0.75/1.04 THEOREM PROVED % 0.75/1.04 % SZS status Theorem % 0.75/1.04 % 0.75/1.04 Exiting with 1 proof. % 0.75/1.04 % 0.75/1.04 Process 3874 exit (max_proofs) Tue Apr 28 18:51:14 2026 % 0.75/1.04 Prover9 interrupted %------------------------------------------------------------------------------