%------------------------------------------------------------------------------ % File : Prover9---1109a % Problem : MGT093+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : tptp2X_and_run_prover9 %d %s % Computer : n026.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 0.75s 1.08s % Output : Refutation 0.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : MGT093+1 : TPTP v9.3.0. Released v9.3.0. % 0.08/0.15 % Command : tptp2X_and_run_prover9 %d %s % 0.19/0.36 % Computer : n026.cluster.edu % 0.19/0.36 % Model : x86_64 x86_64 % 0.19/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.19/0.36 % Memory : 8042.1875MB % 0.19/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.19/0.36 % CPULimit : 300 % 0.19/0.36 % WCLimit : 300 % 0.19/0.36 % DateTime : Tue Apr 28 19:00:53 EDT 2026 % 0.19/0.36 % CPUTime : % 0.75/1.07 ============================== Prover9 =============================== % 0.75/1.07 Prover9 (32) version 2009-11A, November 2009. % 0.75/1.07 Process 7302 was started by sandbox2 on n026.cluster.edu, % 0.75/1.07 Tue Apr 28 19:00:54 2026 % 0.75/1.07 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7149_n026.cluster.edu". % 0.75/1.07 ============================== end of head =========================== % 0.75/1.07 % 0.75/1.07 ============================== INPUT ================================= % 0.75/1.07 % 0.75/1.07 % Reading from file /tmp/Prover9_7149_n026.cluster.edu % 0.75/1.07 % 0.75/1.07 set(prolog_style_variables). % 0.75/1.07 set(auto2). % 0.75/1.07 % set(auto2) -> set(auto). % 0.75/1.07 % set(auto) -> set(auto_inference). % 0.75/1.07 % set(auto) -> set(auto_setup). % 0.75/1.07 % set(auto_setup) -> set(predicate_elim). % 0.75/1.07 % set(auto_setup) -> assign(eq_defs, unfold). % 0.75/1.07 % set(auto) -> set(auto_limits). % 0.75/1.07 % set(auto_limits) -> assign(max_weight, "100.000"). % 0.75/1.07 % set(auto_limits) -> assign(sos_limit, 20000). % 0.75/1.07 % set(auto) -> set(auto_denials). % 0.75/1.07 % set(auto) -> set(auto_process). % 0.75/1.07 % set(auto2) -> assign(new_constants, 1). % 0.75/1.07 % set(auto2) -> assign(fold_denial_max, 3). % 0.75/1.07 % set(auto2) -> assign(max_weight, "200.000"). % 0.75/1.07 % set(auto2) -> assign(max_hours, 1). % 0.75/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600). % 0.75/1.07 % set(auto2) -> assign(max_seconds, 0). % 0.75/1.07 % set(auto2) -> assign(max_minutes, 5). % 0.75/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300). % 0.75/1.07 % set(auto2) -> set(sort_initial_sos). % 0.75/1.07 % set(auto2) -> assign(sos_limit, -1). % 0.75/1.07 % set(auto2) -> assign(lrs_ticks, 3000). % 0.75/1.07 % set(auto2) -> assign(max_megs, 400). % 0.75/1.07 % set(auto2) -> assign(stats, some). % 0.75/1.07 % set(auto2) -> clear(echo_input). % 0.75/1.07 % set(auto2) -> set(quiet). % 0.75/1.07 % set(auto2) -> clear(print_initial_clauses). % 0.75/1.07 % set(auto2) -> clear(print_given). % 0.75/1.07 assign(lrs_ticks,-1). % 0.75/1.07 assign(sos_limit,10000). % 0.75/1.07 assign(order,kbo). % 0.75/1.07 set(lex_order_vars). % 0.75/1.07 clear(print_given). % 0.75/1.07 % 0.75/1.07 % formulas(sos). % not echoed (37 formulas) % 0.75/1.07 % 0.75/1.07 ============================== end of input ========================== % 0.75/1.07 % 0.75/1.07 % From the command line: assign(max_seconds, 300). % 0.75/1.07 % 0.75/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ========== % 0.75/1.07 % 0.75/1.07 % Formulas that are not ordinary clauses: % 0.75/1.07 1 (all X -less(X,X)) # label(irreflexive) # label(axiom) # label(non_clause). [assumption]. % 0.75/1.07 2 (all X all Y all Z (less(X,Y) & less(Y,Z) -> less(X,Z))) # label(transitive) # label(axiom) # label(non_clause). [assumption]. % 0.75/1.07 3 (all X all Y (less(X,Y) | X = Y | less(Y,X))) # label(trichotomy) # label(axiom) # label(non_clause). [assumption]. % 0.75/1.07 4 (all X all Y (leq(X,Y) <-> less(X,Y) | X = Y)) # label(leq_def) # label(axiom) # label(non_clause). [assumption]. % 0.75/1.07 5 (all X all Y (leq(X,Y) & leq(Y,X) -> X = Y)) # label(leq_antisym) # label(axiom) # label(non_clause). [assumption]. % 0.75/1.07 6 (all X all Y (less(X,Y) -> leq(X,Y))) # label(less_implies_leq) # label(axiom) # label(non_clause). [assumption]. % 0.75/1.07 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]. % 0.75/1.07 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]. % 0.75/1.07 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]. % 0.75/1.07 10 (all V1 all V2 (is_verdict(V1) & is_verdict(V2) & (V1 = compatible | V2 = compatible) -> or_verdict(V1,V2) = compatible)) # label(or_compat) # label(axiom) # label(non_clause). [assumption]. % 0.75/1.07 11 (all V1 all V2 (is_verdict(V1) & is_verdict(V2) & V1 = conflict & V2 = conflict -> or_verdict(V1,V2) = conflict)) # label(or_conflict) # label(axiom) # label(non_clause). [assumption]. % 0.75/1.07 12 (all V1 all V2 (is_verdict(V1) & is_verdict(V2) & V1 != compatible & V2 != compatible & -(V1 = conflict & V2 = conflict) -> or_verdict(V1,V2) = unknown)) # label(or_unknown) # label(axiom) # label(non_clause). [assumption]. % 0.75/1.07 13 (all V1 all V2 (is_verdict(V1) & is_verdict(V2) -> or_verdict(V1,V2) = compatible | or_verdict(V1,V2) = conflict | or_verdict(V1,V2) = unknown)) # label(or_verdict_total) # label(axiom) # label(non_clause). [assumption]. % 0.75/1.07 14 (all Vm all Vr (is_verdict(Vm) & is_verdict(Vr) & Vm = compatible & Vr = conflict -> xone_verdict(Vm,Vr) = compatible)) # label(xone_compat) # label(axiom) # label(non_clause). [assumption]. % 0.75/1.07 15 (all Vm all Vr (is_verdict(Vm) & is_verdict(Vr) & Vm = conflict & Vr = conflict -> xone_verdict(Vm,Vr) = conflict)) # label(xone_conflict) # label(axiom) # label(non_clause). [assumption]. % 0.75/1.07 16 (all Vm all Vr (is_verdict(Vm) & is_verdict(Vr) & -(Vm = compatible & Vr = conflict) & -(Vm = conflict & Vr = conflict) -> xone_verdict(Vm,Vr) = unknown)) # label(xone_unknown) # label(axiom) # label(non_clause). [assumption]. % 0.75/1.07 17 (all Vm all Vr (is_verdict(Vm) & is_verdict(Vr) -> xone_verdict(Vm,Vr) = compatible | xone_verdict(Vm,Vr) = conflict | xone_verdict(Vm,Vr) = unknown)) # label(xone_verdict_total) # label(axiom) # label(non_clause). [assumption]. % 0.75/1.07 18 (all A1lo all A1hi all A2lo all A2hi all B1lo all B1hi all B2lo all B2hi (axis_conflict(A1lo,A1hi,B1lo,B1hi) & axis_conflict(A1lo,A1hi,B2lo,B2hi) & axis_conflict(A2lo,A2hi,B1lo,B1hi) & axis_conflict(A2lo,A2hi,B2lo,B2hi) -> -(exists X ((in_closed(X,A1lo,A1hi) | in_closed(X,A2lo,A2hi)) & (in_closed(X,B1lo,B1hi) | in_closed(X,B2lo,B2hi)))))) # label(or_sound_2branch) # label(axiom) # label(non_clause). [assumption]. % 0.75/1.07 19 (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]. % 0.75/1.07 20 (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]. % 0.75/1.07 21 (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]. % 0.75/1.07 22 (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]. % 0.75/1.07 23 (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]. % 0.75/1.07 24 (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]. % 0.75/1.07 25 (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]. % 0.75/1.07 26 (all V (is_verdict(V) -> V = conflict | V = compatible | V = unknown)) # label(verdict_enum) # label(axiom) # label(non_clause). [assumption]. % 0.75/1.07 27 (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]. % 0.75/1.07 28 (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]. % 0.75/1.07 29 (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]. % 0.75/1.07 30 (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]. % 0.75/1.07 % 0.75/1.07 ============================== end of process non-clausal formulas === % 0.75/1.07 % 0.75/1.07 ============================== PROCESS INITIAL CLAUSES =============== % 0.75/1.07 % 0.75/1.07 ============================== PREDICATE ELIMINATION ================= % 0.75/1.07 31 -axis_subsumes(A,B,C,D) | -in_closed(E,A,B) | in_closed(E,C,D) # label(axis_subsumes_def) # label(axiom). [clausify(25)]. % 0.75/1.07 32 axis_subsumes(A,B,C,D) | in_closed(f3(A,B,C,D),A,B) # label(axis_subsumes_def) # label(axiom). [clausify(25)]. % 0.75/1.07 Derived: -in_closed(A,B,C) | in_closed(A,D,E) | in_closed(f3(B,C,D,E),B,C). [resolve(31,a,32,a)]. % 0.75/1.07 33 axis_subsumes(A,B,C,D) | -in_closed(f3(A,B,C,D),C,D) # label(axis_subsumes_def) # label(axiom). [clausify(25)]. % 0.75/1.08 Derived: -in_closed(f3(A,B,C,D),C,D) | -in_closed(E,A,B) | in_closed(E,C,D). [resolve(33,a,31,a)]. % 0.75/1.08 34 in_lopen(A,B,C) | -less(B,A) | -leq(A,C) # label(in_lopen) # label(axiom). [clausify(20)]. % 0.75/1.08 35 -in_lopen(A,B,C) | less(B,A) # label(in_lopen) # label(axiom). [clausify(20)]. % 0.75/1.08 36 -in_lopen(A,B,C) | leq(A,C) # label(in_lopen) # label(axiom). [clausify(20)]. % 0.75/1.08 37 in_ropen(A,B,C) | -leq(B,A) | -less(A,C) # label(in_ropen) # label(axiom). [clausify(21)]. % 0.75/1.08 38 -in_ropen(A,B,C) | leq(B,A) # label(in_ropen) # label(axiom). [clausify(21)]. % 0.75/1.08 39 -in_ropen(A,B,C) | less(A,C) # label(in_ropen) # label(axiom). [clausify(21)]. % 0.75/1.08 40 in_open(A,B,C) | -less(B,A) | -less(A,C) # label(in_open) # label(axiom). [clausify(22)]. % 0.75/1.08 41 -in_open(A,B,C) | less(B,A) # label(in_open) # label(axiom). [clausify(22)]. % 0.75/1.08 42 -in_open(A,B,C) | less(A,C) # label(in_open) # label(axiom). [clausify(22)]. % 0.75/1.08 43 axis_compatible(A,B,C,D) | -in_closed(E,A,B) | -in_closed(E,C,D) # label(axis_compatible_def) # label(axiom). [clausify(24)]. % 0.75/1.08 44 -axis_compatible(A,B,C,D) | in_closed(f2(A,B,C,D),A,B) # label(axis_compatible_def) # label(axiom). [clausify(24)]. % 0.75/1.08 45 -axis_compatible(A,B,C,D) | in_closed(f2(A,B,C,D),C,D) # label(axis_compatible_def) # label(axiom). [clausify(24)]. % 0.75/1.08 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f2(B,C,D,E),B,C). [resolve(43,a,44,a)]. % 0.75/1.08 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f2(B,C,D,E),D,E). [resolve(43,a,45,a)]. % 0.75/1.08 % 0.75/1.08 ============================== end predicate elimination ============= % 0.75/1.08 % 0.75/1.08 Auto_denials: (non-Horn, no changes). % 0.75/1.08 % 0.75/1.08 Term ordering decisions: % 0.75/1.08 Function symbol KB weights: conflict=1. compatible=1. unknown=1. box_verdict=1. or_verdict=1. xone_verdict=1. f1=1. f2=1. f3=1. % 0.75/1.08 % 0.75/1.08 ============================== end of process initial clauses ======== % 0.75/1.08 % 0.75/1.08 ============================== CLAUSES FOR SEARCH ==================== % 0.75/1.08 % 0.75/1.08 ============================== end of clauses for search ============= % 0.75/1.08 % 0.75/1.08 ============================== SEARCH ================================ % 0.75/1.08 % 0.75/1.08 % Starting search at 0.02 seconds. % 0.75/1.08 % 0.75/1.08 ============================== PROOF ================================= % 0.75/1.08 % SZS status Theorem % 0.75/1.08 % SZS output start Refutation % 0.75/1.08 % 0.75/1.08 % Proof 1 at 0.02 (+ 0.00) seconds. % 0.75/1.08 % Length of proof is 7. % 0.75/1.08 % Level of proof is 3. % 0.75/1.08 % Maximum clause weight is 15.000. % 0.75/1.08 % Given clauses 31. % 0.75/1.08 % 0.75/1.08 14 (all Vm all Vr (is_verdict(Vm) & is_verdict(Vr) & Vm = compatible & Vr = conflict -> xone_verdict(Vm,Vr) = compatible)) # label(xone_compat) # label(axiom) # label(non_clause). [assumption]. % 0.75/1.08 46 is_verdict(conflict) # label(conflict_is_verdict) # label(axiom). [assumption]. % 0.75/1.08 47 is_verdict(compatible) # label(compatible_is_verdict) # label(axiom). [assumption]. % 0.75/1.08 59 xone_verdict(compatible,conflict) != compatible # label(odrl644) # label(negated_conjecture). [assumption]. % 0.75/1.08 81 -is_verdict(A) | -is_verdict(B) | A != compatible | B != conflict | xone_verdict(A,B) = compatible # label(xone_compat) # label(axiom). [clausify(14)]. % 0.75/1.08 82 -is_verdict(A) | -is_verdict(B) | compatible != A | conflict != B | xone_verdict(A,B) = compatible. [copy(81),flip(c),flip(d)]. % 0.75/1.08 152 $F. [ur(82,b,46,a,c,xx,d,xx,e,59,a),unit_del(a,47)]. % 0.75/1.08 % 0.75/1.08 % SZS output end Refutation % 0.75/1.08 ============================== end of proof ========================== % 0.75/1.08 % 0.75/1.08 ============================== STATISTICS ============================ % 0.75/1.08 % 0.75/1.08 Given=31. Generated=156. Kept=98. proofs=1. % 0.75/1.08 Usable=31. Sos=62. Demods=0. Limbo=2, Disabled=68. Hints=0. % 0.75/1.08 Megabytes=0.17. % 0.75/1.08 User_CPU=0.02, System_CPU=0.00, Wall_clock=0. % 0.75/1.08 % 0.75/1.08 ============================== end of statistics ===================== % 0.75/1.08 % 0.75/1.08 ============================== end of search ========================= % 0.75/1.08 % 0.75/1.08 THEOREM PROVED % 0.75/1.08 % SZS status Theorem % 0.75/1.08 % 0.75/1.08 Exiting with 1 proof. % 0.75/1.08 % 0.75/1.08 Process 7302 exit (max_proofs) Tue Apr 28 19:00:54 2026 % 0.75/1.08 Prover9 interrupted %------------------------------------------------------------------------------