%------------------------------------------------------------------------------ % File : Prover9---1109a % Problem : MGT090+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : tptp2X_and_run_prover9 %d %s % Computer : n031.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 0.86s 1.15s % Output : Refutation 0.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : MGT090+1 : TPTP v9.3.0. Released v9.3.0. % 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s % 0.15/0.34 % Computer : n031.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Apr 28 18:59:17 EDT 2026 % 0.15/0.34 % CPUTime : % 0.86/1.13 ============================== Prover9 =============================== % 0.86/1.13 Prover9 (32) version 2009-11A, November 2009. % 0.86/1.13 Process 32521 was started by sandbox2 on n031.cluster.edu, % 0.86/1.13 Tue Apr 28 18:59:18 2026 % 0.86/1.13 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_32352_n031.cluster.edu". % 0.86/1.13 ============================== end of head =========================== % 0.86/1.13 % 0.86/1.13 ============================== INPUT ================================= % 0.86/1.13 % 0.86/1.13 % Reading from file /tmp/Prover9_32352_n031.cluster.edu % 0.86/1.13 % 0.86/1.13 set(prolog_style_variables). % 0.86/1.13 set(auto2). % 0.86/1.13 % set(auto2) -> set(auto). % 0.86/1.13 % set(auto) -> set(auto_inference). % 0.86/1.13 % set(auto) -> set(auto_setup). % 0.86/1.13 % set(auto_setup) -> set(predicate_elim). % 0.86/1.13 % set(auto_setup) -> assign(eq_defs, unfold). % 0.86/1.13 % set(auto) -> set(auto_limits). % 0.86/1.13 % set(auto_limits) -> assign(max_weight, "100.000"). % 0.86/1.13 % set(auto_limits) -> assign(sos_limit, 20000). % 0.86/1.13 % set(auto) -> set(auto_denials). % 0.86/1.13 % set(auto) -> set(auto_process). % 0.86/1.13 % set(auto2) -> assign(new_constants, 1). % 0.86/1.13 % set(auto2) -> assign(fold_denial_max, 3). % 0.86/1.13 % set(auto2) -> assign(max_weight, "200.000"). % 0.86/1.13 % set(auto2) -> assign(max_hours, 1). % 0.86/1.13 % assign(max_hours, 1) -> assign(max_seconds, 3600). % 0.86/1.13 % set(auto2) -> assign(max_seconds, 0). % 0.86/1.13 % set(auto2) -> assign(max_minutes, 5). % 0.86/1.13 % assign(max_minutes, 5) -> assign(max_seconds, 300). % 0.86/1.13 % set(auto2) -> set(sort_initial_sos). % 0.86/1.13 % set(auto2) -> assign(sos_limit, -1). % 0.86/1.13 % set(auto2) -> assign(lrs_ticks, 3000). % 0.86/1.13 % set(auto2) -> assign(max_megs, 400). % 0.86/1.13 % set(auto2) -> assign(stats, some). % 0.86/1.13 % set(auto2) -> clear(echo_input). % 0.86/1.13 % set(auto2) -> set(quiet). % 0.86/1.13 % set(auto2) -> clear(print_initial_clauses). % 0.86/1.13 % set(auto2) -> clear(print_given). % 0.86/1.13 assign(lrs_ticks,-1). % 0.86/1.13 assign(sos_limit,10000). % 0.86/1.13 assign(order,kbo). % 0.86/1.13 set(lex_order_vars). % 0.86/1.13 clear(print_given). % 0.86/1.13 % 0.86/1.13 % formulas(sos). % not echoed (60 formulas) % 0.86/1.13 % 0.86/1.13 ============================== end of input ========================== % 0.86/1.13 % 0.86/1.13 % From the command line: assign(max_seconds, 300). % 0.86/1.13 % 0.86/1.13 ============================== PROCESS NON-CLAUSAL FORMULAS ========== % 0.86/1.13 % 0.86/1.13 % Formulas that are not ordinary clauses: % 0.86/1.13 1 (all X -less(X,X)) # label(irreflexive) # label(axiom) # label(non_clause). [assumption]. % 0.86/1.13 2 (all X all Y all Z (less(X,Y) & less(Y,Z) -> less(X,Z))) # label(transitive) # label(axiom) # label(non_clause). [assumption]. % 0.86/1.13 3 (all X all Y (less(X,Y) | X = Y | less(Y,X))) # label(trichotomy) # label(axiom) # label(non_clause). [assumption]. % 0.86/1.13 4 (all X all Y (leq(X,Y) <-> less(X,Y) | X = Y)) # label(leq_def) # label(axiom) # label(non_clause). [assumption]. % 0.86/1.13 5 (all X all Y (leq(X,Y) & leq(Y,X) -> X = Y)) # label(leq_antisym) # label(axiom) # label(non_clause). [assumption]. % 0.86/1.13 6 (all X all Y (less(X,Y) -> leq(X,Y))) # label(less_implies_leq) # label(axiom) # label(non_clause). [assumption]. % 0.86/1.13 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]. % 0.86/1.13 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]. % 0.86/1.13 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]. % 0.86/1.13 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]. % 0.86/1.13 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]. % 0.86/1.13 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]. % 0.86/1.13 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]. % 0.86/1.13 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]. % 0.86/1.13 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]. % 0.86/1.13 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]. % 0.86/1.13 17 (all V (is_verdict(V) -> V = conflict | V = compatible | V = unknown)) # label(verdict_enum) # label(axiom) # label(non_clause). [assumption]. % 0.86/1.13 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]. % 0.86/1.13 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]. % 0.86/1.13 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]. % 0.86/1.13 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]. % 0.86/1.13 22 (all V all InfD all SupD (wf(eq,V,InfD,SupD) <-> leq(InfD,V) & leq(V,SupD))) # label(wf_eq) # label(axiom) # label(non_clause). [assumption]. % 0.86/1.13 23 (all V all InfD all SupD (wf(lteq,V,InfD,SupD) <-> leq(InfD,V) & leq(V,SupD))) # label(wf_lteq) # label(axiom) # label(non_clause). [assumption]. % 0.86/1.13 24 (all V all InfD all SupD (wf(gteq,V,InfD,SupD) <-> leq(InfD,V) & leq(V,SupD))) # label(wf_gteq) # label(axiom) # label(non_clause). [assumption]. % 0.86/1.13 25 (all V all InfD all SupD (wf(lt,V,InfD,SupD) <-> leq(InfD,V) & leq(V,SupD) & V != InfD)) # label(wf_lt) # label(axiom) # label(non_clause). [assumption]. % 0.86/1.13 26 (all V all InfD all SupD (wf(gt,V,InfD,SupD) <-> leq(InfD,V) & leq(V,SupD) & V != SupD)) # label(wf_gt) # label(axiom) # label(non_clause). [assumption]. % 0.86/1.13 27 (all V all InfD all SupD (wf(eq,V,InfD,SupD) -> sem_nonempty(eq,V,InfD,SupD))) # label(nonempty_eq) # label(axiom) # label(non_clause). [assumption]. % 0.86/1.13 28 (all V all InfD all SupD (wf(lteq,V,InfD,SupD) -> sem_nonempty(lteq,V,InfD,SupD))) # label(nonempty_lteq) # label(axiom) # label(non_clause). [assumption]. % 0.86/1.13 29 (all V all InfD all SupD (wf(gteq,V,InfD,SupD) -> sem_nonempty(gteq,V,InfD,SupD))) # label(nonempty_gteq) # label(axiom) # label(non_clause). [assumption]. % 0.86/1.13 30 (all V all InfD all SupD (wf(lt,V,InfD,SupD) -> sem_nonempty(lt,V,InfD,SupD))) # label(nonempty_lt) # label(axiom) # label(non_clause). [assumption]. % 0.86/1.13 31 (all V all InfD all SupD (wf(gt,V,InfD,SupD) -> sem_nonempty(gt,V,InfD,SupD))) # label(nonempty_gt) # label(axiom) # label(non_clause). [assumption]. % 0.86/1.13 32 (all Op (is_op(Op) -> Op = eq | Op = lt | Op = lteq | Op = gt | Op = gteq)) # label(op_enum) # label(axiom) # label(non_clause). [assumption]. % 0.86/1.13 % 0.86/1.13 ============================== end of process non-clausal formulas === % 0.86/1.13 % 0.86/1.13 ============================== PROCESS INITIAL CLAUSES =============== % 0.86/1.13 % 0.86/1.13 ============================== PREDICATE ELIMINATION ================= % 0.86/1.13 33 -is_op(A) | A = eq | A = lt | A = lteq | A = gt | A = gteq # label(op_enum) # label(axiom). [clausify(32)]. % 0.86/1.13 34 is_op(eq) # label(op_eq_is_op) # label(axiom). [assumption]. % 0.86/1.13 35 is_op(lt) # label(op_lt_is_op) # label(axiom). [assumption]. % 0.86/1.13 36 is_op(lteq) # label(op_lteq_is_op) # label(axiom). [assumption]. % 0.86/1.13 37 is_op(gt) # label(op_gt_is_op) # label(axiom). [assumption]. % 0.86/1.13 38 is_op(gteq) # label(op_gteq_is_op) # label(axiom). [assumption]. % 0.86/1.13 Derived: eq = eq | eq = lt | eq = lteq | eq = gt | eq = gteq. [resolve(33,a,34,a)]. % 0.86/1.13 Derived: lt = eq | lt = lt | lt = lteq | lt = gt | lt = gteq. [resolve(33,a,35,a)]. % 0.86/1.13 Derived: lteq = eq | lteq = lt | lteq = lteq | lteq = gt | lteq = gteq. [resolve(33,a,36,a)]. % 0.86/1.13 Derived: gt = eq | gt = lt | gt = lteq | gt = gt | gt = gteq. [resolve(33,a,37,a)]. % 0.86/1.13 Derived: gteq = eq | gteq = lt | gteq = lteq | gteq = gt | gteq = gteq. [resolve(33,a,38,a)]. % 0.86/1.15 39 -axis_conflict(A,B,C,D) | -in_closed(E,A,B) | -in_closed(E,C,D) # label(axis_conflict_def) # label(axiom). [clausify(14)]. % 0.86/1.15 40 axis_conflict(A,B,C,D) | in_closed(f1(A,B,C,D),A,B) # label(axis_conflict_def) # label(axiom). [clausify(14)]. % 0.86/1.15 41 axis_conflict(A,B,C,D) | in_closed(f1(A,B,C,D),C,D) # label(axis_conflict_def) # label(axiom). [clausify(14)]. % 0.86/1.15 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f1(B,C,D,E),B,C). [resolve(39,a,40,a)]. % 0.86/1.15 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f1(B,C,D,E),D,E). [resolve(39,a,41,a)]. % 0.86/1.15 42 -axis_subsumes(A,B,C,D) | -in_closed(E,A,B) | in_closed(E,C,D) # label(axis_subsumes_def) # label(axiom). [clausify(16)]. % 0.86/1.15 43 axis_subsumes(A,B,C,D) | in_closed(f3(A,B,C,D),A,B) # label(axis_subsumes_def) # label(axiom). [clausify(16)]. % 0.86/1.15 Derived: -in_closed(A,B,C) | in_closed(A,D,E) | in_closed(f3(B,C,D,E),B,C). [resolve(42,a,43,a)]. % 0.86/1.15 44 axis_subsumes(A,B,C,D) | -in_closed(f3(A,B,C,D),C,D) # label(axis_subsumes_def) # label(axiom). [clausify(16)]. % 0.86/1.15 Derived: -in_closed(f3(A,B,C,D),C,D) | -in_closed(E,A,B) | in_closed(E,C,D). [resolve(44,a,42,a)]. % 0.86/1.15 45 in_lopen(A,B,C) | -less(B,A) | -leq(A,C) # label(in_lopen) # label(axiom). [clausify(11)]. % 0.86/1.15 46 -in_lopen(A,B,C) | less(B,A) # label(in_lopen) # label(axiom). [clausify(11)]. % 0.86/1.15 47 -in_lopen(A,B,C) | leq(A,C) # label(in_lopen) # label(axiom). [clausify(11)]. % 0.86/1.15 48 in_ropen(A,B,C) | -leq(B,A) | -less(A,C) # label(in_ropen) # label(axiom). [clausify(12)]. % 0.86/1.15 49 -in_ropen(A,B,C) | leq(B,A) # label(in_ropen) # label(axiom). [clausify(12)]. % 0.86/1.15 50 -in_ropen(A,B,C) | less(A,C) # label(in_ropen) # label(axiom). [clausify(12)]. % 0.86/1.15 51 in_open(A,B,C) | -less(B,A) | -less(A,C) # label(in_open) # label(axiom). [clausify(13)]. % 0.86/1.15 52 -in_open(A,B,C) | less(B,A) # label(in_open) # label(axiom). [clausify(13)]. % 0.86/1.15 53 -in_open(A,B,C) | less(A,C) # label(in_open) # label(axiom). [clausify(13)]. % 0.86/1.15 54 axis_compatible(A,B,C,D) | -in_closed(E,A,B) | -in_closed(E,C,D) # label(axis_compatible_def) # label(axiom). [clausify(15)]. % 0.86/1.15 55 -axis_compatible(A,B,C,D) | in_closed(f2(A,B,C,D),A,B) # label(axis_compatible_def) # label(axiom). [clausify(15)]. % 0.86/1.15 56 -axis_compatible(A,B,C,D) | in_closed(f2(A,B,C,D),C,D) # label(axis_compatible_def) # label(axiom). [clausify(15)]. % 0.86/1.15 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f2(B,C,D,E),B,C). [resolve(54,a,55,a)]. % 0.86/1.15 Derived: -in_closed(A,B,C) | -in_closed(A,D,E) | in_closed(f2(B,C,D,E),D,E). [resolve(54,a,56,a)]. % 0.86/1.15 % 0.86/1.15 ============================== end predicate elimination ============= % 0.86/1.15 % 0.86/1.15 Auto_denials: (non-Horn, no changes). % 0.86/1.15 % 0.86/1.15 Term ordering decisions: % 0.86/1.15 Function symbol KB weights: eq=1. gt=1. gteq=1. lt=1. lteq=1. conflict=1. unknown=1. compatible=1. v600=1. v0=1. v1200=1. box_verdict=1. f1=1. f2=1. f3=1. % 0.86/1.15 % 0.86/1.15 ============================== end of process initial clauses ======== % 0.86/1.15 % 0.86/1.15 ============================== CLAUSES FOR SEARCH ==================== % 0.86/1.15 % 0.86/1.15 ============================== end of clauses for search ============= % 0.86/1.15 % 0.86/1.15 ============================== SEARCH ================================ % 0.86/1.15 % 0.86/1.15 % Starting search at 0.02 seconds. % 0.86/1.15 % 0.86/1.15 ============================== PROOF ================================= % 0.86/1.15 % SZS status Theorem % 0.86/1.15 % SZS output start Refutation % 0.86/1.15 % 0.86/1.15 % Proof 1 at 0.03 (+ 0.00) seconds. % 0.86/1.15 % Length of proof is 17. % 0.86/1.15 % Level of proof is 4. % 0.86/1.15 % Maximum clause weight is 14.000. % 0.86/1.15 % Given clauses 82. % 0.86/1.15 % 0.86/1.15 1 (all X -less(X,X)) # label(irreflexive) # label(axiom) # label(non_clause). [assumption]. % 0.86/1.15 4 (all X all Y (leq(X,Y) <-> less(X,Y) | X = Y)) # label(leq_def) # label(axiom) # label(non_clause). [assumption]. % 0.86/1.15 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]. % 0.86/1.15 25 (all V all InfD all SupD (wf(lt,V,InfD,SupD) <-> leq(InfD,V) & leq(V,SupD) & V != InfD)) # label(wf_lt) # label(axiom) # label(non_clause). [assumption]. % 0.86/1.15 60 less(v0,v600) # label(ord_v0_v600) # label(axiom). [assumption]. % 0.86/1.15 61 less(v600,v1200) # label(ord_v600_v1200) # label(axiom). [assumption]. % 0.86/1.15 63 -less(A,A) # label(irreflexive) # label(axiom). [clausify(1)]. % 0.86/1.15 85 -wf(lt,v600,v0,v1200) # label(odrl613) # label(negated_conjecture). [assumption]. % 0.86/1.15 88 leq(A,B) | -less(A,B) # label(leq_def) # label(axiom). [clausify(4)]. % 0.86/1.15 89 leq(A,B) | B != A # label(leq_def) # label(axiom). [clausify(4)]. % 0.86/1.15 105 -leq(A,B) | -less(B,C) | less(A,C) # label(leq_less_trans) # label(axiom). [clausify(7)]. % 0.86/1.15 118 wf(lt,A,B,C) | -leq(B,A) | -leq(A,C) | B = A # label(wf_lt) # label(axiom). [clausify(25)]. % 0.86/1.15 151 leq(v600,v1200). [resolve(88,b,61,a)]. % 0.86/1.15 152 leq(v0,v600). [resolve(88,b,60,a)]. % 0.86/1.15 173 -leq(v600,v0). [ur(105,b,60,a,c,63,a)]. % 0.86/1.15 226 v0 != v600. [ur(89,a,173,a)]. % 0.86/1.15 291 $F. [ur(118,a,85,a,c,151,a,d,226,a),unit_del(a,152)]. % 0.86/1.15 % 0.86/1.15 % SZS output end Refutation % 0.86/1.15 ============================== end of proof ========================== % 0.86/1.15 % 0.86/1.15 ============================== STATISTICS ============================ % 0.86/1.15 % 0.86/1.15 Given=82. Generated=332. Kept=216. proofs=1. % 0.86/1.15 Usable=82. Sos=128. Demods=3. Limbo=0, Disabled=107. Hints=0. % 0.86/1.15 Megabytes=0.25. % 0.86/1.15 User_CPU=0.03, System_CPU=0.00, Wall_clock=0. % 0.86/1.15 % 0.86/1.15 ============================== end of statistics ===================== % 0.86/1.15 % 0.86/1.15 ============================== end of search ========================= % 0.86/1.15 % 0.86/1.15 THEOREM PROVED % 0.86/1.15 % SZS status Theorem % 0.86/1.15 % 0.86/1.15 Exiting with 1 proof. % 0.86/1.15 % 0.86/1.15 Process 32521 exit (max_proofs) Tue Apr 28 18:59:18 2026 % 0.86/1.15 Prover9 interrupted %------------------------------------------------------------------------------