%------------------------------------------------------------------------------ % File : Prover9---1109a % Problem : SWX217-1 : 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 02:38:07 PM UTC 2026 % Result : Unsatisfiable 0.44s 1.01s % Output : Refutation 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX217-1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.12 % Command : tptp2X_and_run_prover9 %d %s % 0.15/0.33 % Computer : n010.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.33 % CPULimit : 300 % 0.15/0.33 % WCLimit : 300 % 0.15/0.33 % DateTime : Wed Apr 29 01:47:35 EDT 2026 % 0.15/0.33 % CPUTime : % 0.44/1.01 ============================== Prover9 =============================== % 0.44/1.01 Prover9 (32) version 2009-11A, November 2009. % 0.44/1.01 Process 20103 was started by sandbox on n010.cluster.edu, % 0.44/1.01 Wed Apr 29 01:47:36 2026 % 0.44/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_19950_n010.cluster.edu". % 0.44/1.01 ============================== end of head =========================== % 0.44/1.01 % 0.44/1.01 ============================== INPUT ================================= % 0.44/1.01 % 0.44/1.01 % Reading from file /tmp/Prover9_19950_n010.cluster.edu % 0.44/1.01 % 0.44/1.01 set(prolog_style_variables). % 0.44/1.01 set(auto2). % 0.44/1.01 % set(auto2) -> set(auto). % 0.44/1.01 % set(auto) -> set(auto_inference). % 0.44/1.01 % set(auto) -> set(auto_setup). % 0.44/1.01 % set(auto_setup) -> set(predicate_elim). % 0.44/1.01 % set(auto_setup) -> assign(eq_defs, unfold). % 0.44/1.01 % set(auto) -> set(auto_limits). % 0.44/1.01 % set(auto_limits) -> assign(max_weight, "100.000"). % 0.44/1.01 % set(auto_limits) -> assign(sos_limit, 20000). % 0.44/1.01 % set(auto) -> set(auto_denials). % 0.44/1.01 % set(auto) -> set(auto_process). % 0.44/1.01 % set(auto2) -> assign(new_constants, 1). % 0.44/1.01 % set(auto2) -> assign(fold_denial_max, 3). % 0.44/1.01 % set(auto2) -> assign(max_weight, "200.000"). % 0.44/1.01 % set(auto2) -> assign(max_hours, 1). % 0.44/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600). % 0.44/1.01 % set(auto2) -> assign(max_seconds, 0). % 0.44/1.01 % set(auto2) -> assign(max_minutes, 5). % 0.44/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300). % 0.44/1.01 % set(auto2) -> set(sort_initial_sos). % 0.44/1.01 % set(auto2) -> assign(sos_limit, -1). % 0.44/1.01 % set(auto2) -> assign(lrs_ticks, 3000). % 0.44/1.01 % set(auto2) -> assign(max_megs, 400). % 0.44/1.01 % set(auto2) -> assign(stats, some). % 0.44/1.01 % set(auto2) -> clear(echo_input). % 0.44/1.01 % set(auto2) -> set(quiet). % 0.44/1.01 % set(auto2) -> clear(print_initial_clauses). % 0.44/1.01 % set(auto2) -> clear(print_given). % 0.44/1.01 assign(lrs_ticks,-1). % 0.44/1.01 assign(sos_limit,10000). % 0.44/1.01 assign(order,kbo). % 0.44/1.01 set(lex_order_vars). % 0.44/1.01 clear(print_given). % 0.44/1.01 % 0.44/1.01 % formulas(sos). % not echoed (32 formulas) % 0.44/1.01 % 0.44/1.01 ============================== end of input ========================== % 0.44/1.01 % 0.44/1.01 % From the command line: assign(max_seconds, 300). % 0.44/1.01 % 0.44/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ========== % 0.44/1.01 % 0.44/1.01 % Formulas that are not ordinary clauses: % 0.44/1.01 % 0.44/1.01 ============================== end of process non-clausal formulas === % 0.44/1.01 % 0.44/1.01 ============================== PROCESS INITIAL CLAUSES =============== % 0.44/1.01 % 0.44/1.01 ============================== PREDICATE ELIMINATION ================= % 0.44/1.01 % 0.44/1.01 ============================== end predicate elimination ============= % 0.44/1.01 % 0.44/1.01 Auto_denials: % 0.44/1.01 % copying label goal to answer in negative clause % 0.44/1.01 % 0.44/1.01 Term ordering decisions: % 0.44/1.01 Function symbol KB weights: bfalse=1. zero=1. btrue=1. i=1. o=1. nil=1. cons=1. eq=1. addNat=1. append=1. aux=1. eq2=1. eq3=1. x=1. sat_comm=1. suc=1. half=1. rd=1. shw=1. evenNat=1. double=1. notb=1. % 0.44/1.01 % 0.44/1.01 ============================== end of process initial clauses ======== % 0.44/1.01 % 0.44/1.01 ============================== CLAUSES FOR SEARCH ==================== % 0.44/1.01 % 0.44/1.01 ============================== end of clauses for search ============= % 0.44/1.01 % 0.44/1.01 ============================== SEARCH ================================ % 0.44/1.01 % 0.44/1.01 % Starting search at 0.01 seconds. % 0.44/1.01 % 0.44/1.01 ============================== PROOF ================================= % 0.44/1.01 % SZS status Unsatisfiable % 0.44/1.01 % SZS output start Refutation % 0.44/1.01 % 0.44/1.01 % Proof 1 at 0.03 (+ 0.00) seconds: goal. % 0.44/1.01 % Length of proof is 62. % 0.44/1.01 % Level of proof is 9. % 0.44/1.01 % Maximum clause weight is 21.000. % 0.44/1.01 % Given clauses 115. % 0.44/1.01 % 0.44/1.01 1 notb(btrue) = bfalse # label(axiom_002) # label(axiom). [assumption]. % 0.44/1.01 2 notb(bfalse) = btrue # label(axiom_003) # label(axiom). [assumption]. % 0.44/1.01 3 half(zero) = zero # label(axiom_004) # label(axiom). [assumption]. % 0.44/1.01 4 evenNat(zero) = btrue # label(axiom_007) # label(axiom). [assumption]. % 0.44/1.01 5 shw(zero) = nil # label(axiom_009) # label(axiom). [assumption]. % 0.44/1.01 6 rd(nil) = zero # label(axiom_016) # label(axiom). [assumption]. % 0.44/1.01 7 half(suc(zero)) = zero # label(axiom_005) # label(axiom). [assumption]. % 0.44/1.01 8 append(nil,A) = A # label(axiom_011) # label(axiom). [assumption]. % 0.44/1.01 9 addNat(zero,A) = A # label(axiom_013) # label(axiom). [assumption]. % 0.44/1.01 15 eq2(A,A) = btrue # label(axiom_029) # label(axiom). [assumption]. % 0.44/1.01 17 double(A) = addNat(A,A) # label(axiom_015) # label(axiom). [assumption]. % 0.44/1.01 19 eq(suc(A),zero) = bfalse # label(axiom_027) # label(axiom). [assumption]. % 0.44/1.01 20 evenNat(suc(A)) = notb(evenNat(A)) # label(axiom_008) # label(axiom). [assumption]. % 0.44/1.01 21 notb(evenNat(A)) = evenNat(suc(A)). [copy(20),flip(a)]. % 0.44/1.01 22 half(suc(suc(A))) = suc(half(A)) # label(axiom_006) # label(axiom). [assumption]. % 0.44/1.01 23 rd(cons(o,A)) = double(rd(A)) # label(axiom_018) # label(axiom). [assumption]. % 0.44/1.01 24 addNat(rd(A),rd(A)) = rd(cons(o,A)). [copy(23),rewrite([17(5)]),flip(a)]. % 0.44/1.01 25 shw(suc(A)) = aux(A,evenNat(suc(A))) # label(axiom_010) # label(axiom). [assumption]. % 0.44/1.01 26 aux(A,evenNat(suc(A))) = shw(suc(A)). [copy(25),flip(a)]. % 0.44/1.01 27 addNat(suc(A),B) = suc(addNat(A,B)) # label(axiom_014) # label(axiom). [assumption]. % 0.44/1.01 28 suc(addNat(A,B)) = addNat(suc(A),B). [copy(27),flip(a)]. % 0.44/1.01 29 rd(cons(i,A)) = suc(double(rd(A))) # label(axiom_017) # label(axiom). [assumption]. % 0.44/1.01 30 suc(rd(cons(o,A))) = rd(cons(i,A)). [copy(29),rewrite([17(5),24(6)]),flip(a)]. % 0.44/1.01 31 eq(suc(A),suc(B)) = eq(A,B) # label(axiom_025) # label(axiom). [assumption]. % 0.44/1.01 32 aux(A,btrue) = cons(o,shw(half(suc(A)))) # label(axiom) # label(axiom). [assumption]. % 0.44/1.01 33 cons(o,shw(half(suc(A)))) = aux(A,btrue). [copy(32),flip(a)]. % 0.44/1.01 34 aux(A,bfalse) = cons(i,shw(half(suc(A)))) # label(axiom_001) # label(axiom). [assumption]. % 0.44/1.01 35 cons(i,shw(half(suc(A)))) = aux(A,bfalse). [copy(34),flip(a)]. % 0.44/1.01 36 x(A,B) = rd(append(shw(A),shw(B))) # label(axiom_019) # label(axiom). [assumption]. % 0.44/1.01 37 append(cons(A,B),C) = cons(A,append(B,C)) # label(axiom_012) # label(axiom). [assumption]. % 0.44/1.01 38 sat_comm(A,B) = eq(x(A,B),x(B,A)) # label(axiom_020) # label(axiom). [assumption]. % 0.44/1.01 39 sat_comm(A,B) = eq(rd(append(shw(A),shw(B))),rd(append(shw(B),shw(A)))). [copy(38),rewrite([36(2),36(6)])]. % 0.44/1.01 40 eq2(sat_comm(A,B),bfalse) != btrue # label(goal) # label(negated_conjecture) # answer(goal). [assumption]. % 0.44/1.01 41 eq2(eq(rd(append(shw(A),shw(B))),rd(append(shw(B),shw(A)))),bfalse) != btrue # answer(goal). [copy(40),rewrite([39(1)])]. % 0.44/1.01 42 evenNat(suc(zero)) = bfalse. [para(4(a,1),21(a,1,1)),rewrite([1(2)]),flip(a)]. % 0.44/1.01 43 rd(cons(o,nil)) = zero. [para(6(a,1),24(a,1,1)),rewrite([6(3),9(3)]),flip(a)]. % 0.44/1.01 44 addNat(suc(zero),A) = suc(A). [para(9(a,1),28(a,1,1)),flip(a)]. % 0.44/1.01 48 addNat(suc(rd(A)),rd(A)) = rd(cons(i,A)). [para(24(a,1),28(a,1,1)),rewrite([30(4)]),flip(a)]. % 0.44/1.01 59 cons(o,shw(suc(half(A)))) = aux(suc(A),btrue). [para(22(a,1),33(a,1,2,1))]. % 0.44/1.01 61 suc(rd(aux(A,btrue))) = rd(aux(A,bfalse)). [para(33(a,1),30(a,1,1,1)),rewrite([35(9)])]. % 0.44/1.01 63 aux(zero,bfalse) = cons(i,nil). [para(7(a,1),35(a,1,2,1)),rewrite([5(3)]),flip(a)]. % 0.44/1.01 64 cons(i,shw(suc(half(A)))) = aux(suc(A),bfalse). [para(22(a,1),35(a,1,2,1))]. % 0.44/1.01 72 evenNat(suc(suc(zero))) = btrue. [para(42(a,1),21(a,1,1)),rewrite([2(2)]),flip(a)]. % 0.44/1.01 73 shw(suc(zero)) = cons(i,nil). [para(42(a,1),26(a,1,2)),rewrite([63(3)]),flip(a)]. % 0.44/1.01 75 rd(cons(i,nil)) = suc(zero). [para(43(a,1),30(a,1,1)),flip(a)]. % 0.44/1.01 77 shw(suc(suc(zero))) = aux(suc(zero),btrue). [para(72(a,1),26(a,1,2)),flip(a)]. % 0.44/1.01 78 addNat(suc(suc(zero)),A) = suc(suc(A)). [para(44(a,1),28(a,1,1)),flip(a)]. % 0.44/1.01 82 eq2(eq(rd(append(shw(A),cons(i,nil))),rd(cons(i,shw(A)))),bfalse) != btrue # answer(goal). [para(73(a,1),41(a,1,1,1,1,2)),rewrite([73(9),37(11),8(10)])]. % 0.44/1.01 83 rd(cons(o,cons(i,nil))) = suc(suc(zero)). [para(75(a,1),24(a,1,1)),rewrite([75(6),44(5)]),flip(a)]. % 0.44/1.01 121 eq2(eq(rd(append(aux(suc(zero),btrue),cons(i,nil))),rd(cons(i,aux(suc(zero),btrue)))),bfalse) != btrue # answer(goal). [para(77(a,1),82(a,1,1,1,1,1)),rewrite([77(14)])]. % 0.44/1.01 122 addNat(suc(suc(suc(zero))),A) = suc(suc(suc(A))). [para(78(a,1),28(a,1,1)),flip(a)]. % 0.44/1.01 162 rd(cons(i,cons(o,cons(i,nil)))) = suc(suc(suc(suc(suc(zero))))). [para(83(a,1),48(a,1,1,1)),rewrite([83(10),122(8)]),flip(a)]. % 0.44/1.01 200 cons(o,cons(i,nil)) = aux(suc(zero),btrue). [para(3(a,1),59(a,1,2,1,1)),rewrite([73(4)])]. % 0.44/1.01 204 rd(cons(i,aux(suc(zero),btrue))) = suc(suc(suc(suc(suc(zero))))). [back_rewrite(162),rewrite([200(6)])]. % 0.44/1.01 206 rd(aux(suc(zero),btrue)) = suc(suc(zero)). [back_rewrite(83),rewrite([200(5)])]. % 0.44/1.01 207 eq2(eq(rd(append(aux(suc(zero),btrue),cons(i,nil))),suc(suc(suc(suc(suc(zero)))))),bfalse) != btrue # answer(goal). [back_rewrite(121),rewrite([204(16)])]. % 0.44/1.01 211 rd(aux(suc(zero),bfalse)) = suc(suc(suc(zero))). [para(206(a,1),61(a,1,1)),flip(a)]. % 0.44/1.01 212 append(aux(suc(zero),btrue),A) = cons(o,cons(i,A)). [para(200(a,1),37(a,1,1)),rewrite([37(10),8(9)])]. % 0.44/1.01 214 eq2(eq(rd(cons(o,cons(i,cons(i,nil)))),suc(suc(suc(suc(suc(zero)))))),bfalse) != btrue # answer(goal). [back_rewrite(207),rewrite([212(8)])]. % 0.44/1.01 227 rd(cons(o,aux(suc(zero),bfalse))) = suc(suc(suc(suc(suc(suc(zero)))))). [para(211(a,1),24(a,1,1)),rewrite([211(9),122(9)]),flip(a)]. % 0.44/1.01 229 cons(i,cons(i,nil)) = aux(suc(zero),bfalse). [para(3(a,1),64(a,1,2,1,1)),rewrite([73(4)])]. % 0.44/1.01 237 $F # answer(goal). [back_rewrite(214),rewrite([229(6),227(7),31(14),31(12),31(10),31(8),31(6),19(4),15(3)]),xx(a)]. % 0.44/1.01 % 0.44/1.01 % SZS output end Refutation % 0.44/1.01 ============================== end of proof ========================== % 0.44/1.01 % 0.44/1.01 ============================== STATISTICS ============================ % 0.44/1.01 % 0.44/1.01 Given=115. Generated=653. Kept=227. proofs=1. % 0.44/1.01 Usable=93. Sos=90. Demods=142. Limbo=8, Disabled=68. Hints=0. % 0.44/1.01 Megabytes=0.34. % 0.44/1.01 User_CPU=0.03, System_CPU=0.00, Wall_clock=0. % 0.44/1.01 % 0.44/1.01 ============================== end of statistics ===================== % 0.44/1.01 % 0.44/1.01 ============================== end of search ========================= % 0.44/1.01 % 0.44/1.01 THEOREM PROVED % 0.44/1.01 % SZS status Unsatisfiable % 0.44/1.01 % 0.44/1.01 Exiting with 1 proof. % 0.44/1.01 % 0.44/1.01 Process 20103 exit (max_proofs) Wed Apr 29 01:47:36 2026 % 0.44/1.01 Prover9 interrupted %------------------------------------------------------------------------------