%------------------------------------------------------------------------------ % File : Prover9---1109a % Problem : SWX224-1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : tptp2X_and_run_prover9 %d %s % Computer : n012.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 02:38:08 PM UTC 2026 % Result : Unsatisfiable 66.81s 67.16s % Output : Refutation 66.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.07 % Problem : SWX224-1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.07 % Command : tptp2X_and_run_prover9 %d %s % 0.07/0.25 % Computer : n012.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Wed Apr 29 02:17:30 EDT 2026 % 0.07/0.25 % CPUTime : % 26.71/27.11 ============================== Prover9 =============================== % 26.71/27.11 Prover9 (32) version 2009-11A, November 2009. % 26.71/27.11 Process 11522 was started by sandbox2 on n012.cluster.edu, % 26.71/27.11 Wed Apr 29 02:17:31 2026 % 26.71/27.11 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_11369_n012.cluster.edu". % 26.71/27.11 ============================== end of head =========================== % 26.71/27.11 % 26.71/27.11 ============================== INPUT ================================= % 26.71/27.11 % 26.71/27.11 % Reading from file /tmp/Prover9_11369_n012.cluster.edu % 26.71/27.11 % 26.71/27.11 set(prolog_style_variables). % 26.71/27.11 set(auto2). % 26.71/27.11 % set(auto2) -> set(auto). % 26.71/27.11 % set(auto) -> set(auto_inference). % 26.71/27.11 % set(auto) -> set(auto_setup). % 26.71/27.11 % set(auto_setup) -> set(predicate_elim). % 26.71/27.11 % set(auto_setup) -> assign(eq_defs, unfold). % 26.71/27.11 % set(auto) -> set(auto_limits). % 26.71/27.11 % set(auto_limits) -> assign(max_weight, "100.000"). % 26.71/27.11 % set(auto_limits) -> assign(sos_limit, 20000). % 26.71/27.11 % set(auto) -> set(auto_denials). % 26.71/27.11 % set(auto) -> set(auto_process). % 26.71/27.11 % set(auto2) -> assign(new_constants, 1). % 26.71/27.11 % set(auto2) -> assign(fold_denial_max, 3). % 26.71/27.11 % set(auto2) -> assign(max_weight, "200.000"). % 26.71/27.11 % set(auto2) -> assign(max_hours, 1). % 26.71/27.11 % assign(max_hours, 1) -> assign(max_seconds, 3600). % 26.71/27.11 % set(auto2) -> assign(max_seconds, 0). % 26.71/27.11 % set(auto2) -> assign(max_minutes, 5). % 26.71/27.11 % assign(max_minutes, 5) -> assign(max_seconds, 300). % 26.71/27.11 % set(auto2) -> set(sort_initial_sos). % 26.71/27.11 % set(auto2) -> assign(sos_limit, -1). % 26.71/27.11 % set(auto2) -> assign(lrs_ticks, 3000). % 26.71/27.11 % set(auto2) -> assign(max_megs, 400). % 26.71/27.11 % set(auto2) -> assign(stats, some). % 26.71/27.11 % set(auto2) -> clear(echo_input). % 26.71/27.11 % set(auto2) -> set(quiet). % 26.71/27.11 % set(auto2) -> clear(print_initial_clauses). % 26.71/27.11 % set(auto2) -> clear(print_given). % 26.71/27.11 assign(lrs_ticks,-1). % 26.71/27.11 assign(sos_limit,10000). % 26.71/27.11 assign(order,kbo). % 26.71/27.11 set(lex_order_vars). % 26.71/27.11 clear(print_given). % 26.71/27.11 % 26.71/27.11 % formulas(sos). % not echoed (51 formulas) % 26.71/27.11 % 26.71/27.11 ============================== end of input ========================== % 26.71/27.11 % 26.71/27.11 % From the command line: assign(max_seconds, 300). % 26.71/27.11 % 26.71/27.11 ============================== PROCESS NON-CLAUSAL FORMULAS ========== % 26.71/27.11 % 26.71/27.11 % Formulas that are not ordinary clauses: % 26.71/27.11 % 26.71/27.11 ============================== end of process non-clausal formulas === % 26.71/27.11 % 26.71/27.11 ============================== PROCESS INITIAL CLAUSES =============== % 26.71/27.11 % 26.71/27.11 ============================== PREDICATE ELIMINATION ================= % 26.71/27.11 % 26.71/27.11 ============================== end predicate elimination ============= % 26.71/27.11 % 26.71/27.11 Auto_denials: % 26.71/27.11 % copying label goal to answer in negative clause % 26.71/27.11 % 26.71/27.11 Term ordering decisions: % 26.71/27.11 Function symbol KB weights: bfalse=1. btrue=1. a=1. b=1. c=1. zero=1. nil=1. nothing=1. eq=1. eq3=1. arr=1. eq2=1. index=1. andb=1. cons=1. eq4=1. lam=1. var=1. suc=1. notb=1. just=1. sat_synth_w=1. app=1. tc=1. aux=1. % 26.71/27.11 % 26.71/27.11 ============================== end of process initial clauses ======== % 26.71/27.11 % 26.71/27.11 ============================== CLAUSES FOR SEARCH ==================== % 26.71/27.11 % 26.71/27.11 ============================== end of clauses for search ============= % 26.71/27.11 % 26.71/27.11 ============================== SEARCH ================================ % 26.71/27.11 % 26.71/27.11 % Starting search at 0.01 seconds. % 26.71/27.11 % 26.71/27.11 Low Water (keep): wt=49.000, iters=3454 % 26.71/27.11 % 26.71/27.11 Low Water (keep): wt=43.000, iters=3343 % 26.71/27.11 % 26.71/27.11 Low Water (keep): wt=42.000, iters=3344 % 26.71/27.11 % 26.71/27.11 Low Water (keep): wt=41.000, iters=3375 % 26.71/27.11 % 26.71/27.11 Low Water (keep): wt=39.000, iters=3375 % 26.71/27.11 % 26.71/27.11 Low Water (keep): wt=38.000, iters=3344 % 26.71/27.11 % 26.71/27.11 Low Water (keep): wt=36.000, iters=3440 % 26.71/27.11 % 26.71/27.11 Low Water (keep): wt=35.000, iters=3334 % 26.71/27.11 % 26.71/27.11 Low Water (keep): wt=34.000, iters=3443 % 26.71/27.11 % 26.71/27.11 Low Water (keep): wt=33.000, iters=3333 % 26.71/27.11 % 26.71/27.11 Low Water (keep): wt=32.000, iters=3393 % 26.71/27.11 % 26.71/27.11 Low Water (keep): wt=31.000, iters=3353 % 26.71/27.11 % 26.71/27.11 Low Water (keep): wt=30.000, iters=3352 % 26.71/27.11 % 26.71/27.11 Low Water (keep): wt=29.000, iters=3449 % 26.71/27.11 % 26.71/27.11 Low Water (keep): wt=28.000, iters=3342 % 26.71/27.11 % 26.71/27.11 Low Water (keep): wt=27.000, iters=3340 % 26.71/27.11 % 26.71/27.11 Low Water (displace): id=5649, wt=53.000 % 26.71/27.11 % 26.71/27.11 Low Water (displace): id=8689, wt=48.000 % 26.71/27.11 % 26.71/27.11 Low Water (displace): id=5408, wt=46.000 % 26.71/27.11 % 26.71/27.11 Low Water (displace): id=19779, wt=32.000 % 26.71/27.11 % 26.71/27.11 Low Water (displace): id=26339, wt=28.000 % 26.71/27.11 % 26.71/27.11 Low Water (displace): id=26527, wt=27.000 % 26.71/27.11 % 26.71/27.11 Low Water (displace): id=27015, wt=25.000 % 26.71/27.11 % 26.71/27.11 Low Water (keep): wt=26.000, iters=3434 % 26.71/27.11 % 26.71/27.11 Low Water (keep): wt=25.000, iters=3333 % 66.81/67.16 % 66.81/67.16 ============================== PROOF ================================= % 66.81/67.16 % SZS status Unsatisfiable % 66.81/67.16 % SZS output start Refutation % 66.81/67.16 % 66.81/67.16 % Proof 1 at 63.80 (+ 2.64) seconds: goal. % 66.81/67.16 % Length of proof is 28. % 66.81/67.16 % Level of proof is 6. % 66.81/67.16 % Maximum clause weight is 24.000. % 66.81/67.16 % Given clauses 7096. % 66.81/67.16 % 66.81/67.16 1 notb(btrue) = bfalse # label(axiom_002) # label(axiom). [assumption]. % 66.81/67.16 4 andb(btrue,A) = A # label(axiom_007) # label(axiom). [assumption]. % 66.81/67.16 14 eq(A,A) = btrue # label(axiom_046) # label(axiom). [assumption]. % 66.81/67.16 17 eq4(A,A) = btrue # label(axiom_049) # label(axiom). [assumption]. % 66.81/67.16 32 index(cons(A,B),zero) = just(A) # label(axiom_005) # label(axiom). [assumption]. % 66.81/67.16 41 aux(A,B,C,just(D)) = eq(D,B) # label(axiom_001) # label(axiom). [assumption]. % 66.81/67.16 42 index(cons(A,B),suc(C)) = index(B,C) # label(axiom_006) # label(axiom). [assumption]. % 66.81/67.16 43 tc(A,var(B),C) = aux(A,C,B,index(A,B)) # label(axiom_014) # label(axiom). [assumption]. % 66.81/67.16 44 aux(A,B,C,index(A,C)) = tc(A,var(C),B). [copy(43),flip(a)]. % 66.81/67.16 45 tc(A,lam(B),arr(C,D)) = tc(cons(C,A),B,D) # label(axiom_010) # label(axiom). [assumption]. % 66.81/67.16 46 sat_synth_w(A) = notb(tc(nil,A,arr(arr(a,arr(a,b)),arr(a,b)))) # label(axiom_015) # label(axiom). [assumption]. % 66.81/67.16 47 tc(A,app(B,C,D),E) = andb(tc(A,B,arr(D,E)),tc(A,C,D)) # label(axiom_009) # label(axiom). [assumption]. % 66.81/67.16 48 andb(tc(A,B,arr(C,D)),tc(A,E,C)) = tc(A,app(B,E,C),D). [copy(47),flip(a)]. % 66.81/67.16 49 eq4(sat_synth_w(A),bfalse) != btrue # label(goal) # label(negated_conjecture) # answer(goal). [assumption]. % 66.81/67.16 50 eq4(notb(tc(nil,A,arr(arr(a,arr(a,b)),arr(a,b)))),bfalse) != btrue # answer(goal). [copy(49),rewrite([46(1)])]. % 66.81/67.16 52 eq(A,B) != btrue | eq(arr(A,C),arr(B,D)) = eq(C,D) # label(axiom_028) # label(axiom). [assumption]. % 66.81/67.16 60 tc(cons(A,B),var(zero),C) = eq(A,C). [para(32(a,1),44(a,1,4)),rewrite([41(4)]),flip(a)]. % 66.81/67.16 61 aux(cons(A,B),C,suc(D),index(B,D)) = tc(cons(A,B),var(suc(D)),C). [para(42(a,1),44(a,1,4))]. % 66.81/67.16 67 eq4(notb(tc(cons(arr(a,arr(a,b)),nil),A,arr(a,b))),bfalse) != btrue # answer(goal). [para(45(a,1),50(a,1,1,1))]. % 66.81/67.16 81 eq(arr(A,B),arr(A,C)) = eq(B,C). [hyper(52,a,14,a)]. % 66.81/67.16 134 eq4(notb(tc(cons(a,cons(arr(a,arr(a,b)),nil)),A,b)),bfalse) != btrue # answer(goal). [para(45(a,1),67(a,1,1,1))]. % 66.81/67.16 140 andb(tc(cons(A,B),C,arr(D,E)),eq(A,D)) = tc(cons(A,B),app(C,var(zero),D),E). [para(60(a,1),48(a,1,2))]. % 66.81/67.16 147 tc(cons(A,cons(B,C)),var(suc(zero)),D) = eq(B,D). [para(32(a,1),61(a,1,4)),rewrite([41(6)]),flip(a)]. % 66.81/67.16 1695 tc(cons(A,B),app(C,var(zero),A),D) = andb(tc(cons(A,B),C,arr(A,D)),btrue). [para(14(a,1),140(a,1,2)),flip(a)]. % 66.81/67.16 1724 tc(cons(A,cons(B,C)),app(var(suc(zero)),var(zero),D),E) = andb(eq(B,arr(D,E)),eq(A,D)). [para(147(a,1),140(a,1,1)),flip(a)]. % 66.81/67.16 14206 eq4(notb(andb(tc(cons(a,cons(arr(a,arr(a,b)),nil)),A,arr(a,b)),btrue)),bfalse) != btrue # answer(goal). [para(1695(a,1),134(a,1,1,1))]. % 66.81/67.16 35642 tc(cons(A,cons(arr(B,C),D)),app(var(suc(zero)),var(zero),B),E) = andb(eq(C,E),eq(A,B)). [para(81(a,1),1724(a,2,1))]. % 66.81/67.16 39899 $F # answer(goal). [para(35642(a,1),14206(a,1,1,1,1)),rewrite([14(7),14(4),4(3),4(3),1(2),17(3)]),xx(a)]. % 66.81/67.16 % 66.81/67.16 % SZS output end Refutation % 66.81/67.16 ============================== end of proof ========================== % 66.81/67.16 % 66.81/67.16 ============================== STATISTICS ============================ % 66.81/67.16 % 66.81/67.16 Given=7096. Generated=4040233. Kept=39894. proofs=1. % 66.81/67.16 Usable=5061. Sos=9215. Demods=6700. Limbo=2, Disabled=25667. Hints=0. % 66.81/67.16 Megabytes=41.20. % 66.81/67.16 User_CPU=63.80, System_CPU=2.64, Wall_clock=66. % 66.81/67.16 % 66.81/67.16 ============================== end of statistics ===================== % 66.81/67.16 % 66.81/67.16 ============================== end of search ========================= % 66.81/67.16 % 66.81/67.16 THEOREM PROVED % 66.81/67.16 % SZS status Unsatisfiable % 66.81/67.16 % 66.81/67.16 Exiting with 1 proof. % 66.81/67.16 % 66.81/67.16 Process 11522 exit (max_proofs) Wed Apr 29 02:18:37 2026 % 66.81/67.16 Prover9 interrupted %------------------------------------------------------------------------------