%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM680^1 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 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 Jun 3 08:40:21 AM UTC 2026 % Result : Theorem 0.14s 0.37s % Output : Proof 0.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : NUM680^1 : TPTP v9.2.1. Released v3.7.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 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 : Tue Jun 2 11:51:03 EDT 2026 % 0.07/0.25 % CPUTime : % 0.14/0.33 %----Proving TH0 % 0.14/0.37 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.14/0.37 % SZS status Theorem % 0.14/0.37 % SZS output start Proof % 0.14/0.37 ( % 0.14/0.37 (declare-sort tptp.nat 0) % 0.14/0.37 (declare-const tptp.more (-> tptp.nat tptp.nat Bool)) % 0.14/0.37 (declare-const tptp.x tptp.nat) % 0.14/0.37 (declare-const tptp.pl (-> tptp.nat tptp.nat tptp.nat)) % 0.14/0.37 (declare-const tptp.y tptp.nat) % 0.14/0.37 (declare-const tptp.less (-> tptp.nat tptp.nat Bool)) % 0.14/0.37 (declare-const tptp.z tptp.nat) % 0.14/0.37 (define @t1 () (_ (_ tptp.pl tptp.y) tptp.z)) % 0.14/0.37 (define @t2 () (_ (_ tptp.pl tptp.x) tptp.z)) % 0.14/0.37 (define @t3 () (_ (_ tptp.more @t2) @t1)) % 0.14/0.37 (define @t4 () (@var "Xa" Bool)) % 0.14/0.37 (define @t5 () (@var "Xy" tptp.nat)) % 0.14/0.37 (define @t6 () (@var "Xx" tptp.nat)) % 0.14/0.37 (define @t7 () (= @t6 @t5)) % 0.14/0.37 (define @t8 () (not @t7)) % 0.14/0.37 (define @t9 () (_ (_ tptp.less @t6) @t5)) % 0.14/0.37 (define @t10 () (=> @t9 @t8)) % 0.14/0.37 (define @t11 () (not @t10)) % 0.14/0.37 (define @t12 () (not @t9)) % 0.14/0.37 (define @t13 () (_ (_ tptp.more @t6) @t5)) % 0.14/0.37 (define @t14 () (=> @t13 @t12)) % 0.14/0.37 (define @t15 () (=> @t14 @t11)) % 0.14/0.37 (define @t16 () (not @t15)) % 0.14/0.37 (define @t17 () (not @t13)) % 0.14/0.37 (define @t18 () (=> @t7 @t17)) % 0.14/0.37 (define @t19 () (=> @t18 (not @t16))) % 0.14/0.37 (define @t20 () (not @t19)) % 0.14/0.37 (define @t21 () (@list @t6 @t5)) % 0.14/0.37 (define @t22 () (forall @t21 @t20)) % 0.14/0.37 (define @t23 () (@var "Xz" tptp.nat)) % 0.14/0.37 (define @t24 () (_ (_ tptp.pl @t5) @t23)) % 0.14/0.37 (define @t25 () (_ (_ tptp.pl @t6) @t23)) % 0.14/0.37 (define @t26 () (@list @t6 @t5 @t23)) % 0.14/0.37 (define @t27 () (_ (_ tptp.less @t25) @t24)) % 0.14/0.37 (define @t28 () (forall @t26 (=> @t9 @t27))) % 0.14/0.37 (define @t29 () (=> @t17 @t9)) % 0.14/0.37 (define @t30 () (forall @t21 (=> @t8 @t29))) % 0.14/0.37 (define @t31 () (_ (_ tptp.more tptp.x) tptp.y)) % 0.14/0.37 (define @t32 () (not @t31)) % 0.14/0.37 (define @t33 () (tptp.pl @t5 @t23)) % 0.14/0.37 (define @t34 () (tptp.pl @t6 @t23)) % 0.14/0.37 (define @t35 () (tptp.less @t34 @t33)) % 0.14/0.37 (define @t36 () (tptp.less @t6 @t5)) % 0.14/0.37 (define @t37 () (or @t12 @t27)) % 0.14/0.37 (define @t38 () (tptp.more @t6 @t5)) % 0.14/0.37 (define @t39 () (or @t7 @t13 @t9)) % 0.14/0.37 (define @t40 () (@var "BOUND_VARIABLE_7509" tptp.nat)) % 0.14/0.37 (define @t41 () (not (tptp.less @t40 @t40))) % 0.14/0.37 (define @t42 () (not (= @t40 @t40))) % 0.14/0.37 (define @t43 () (or @t41 @t42)) % 0.14/0.37 (define @t44 () (@list @t40)) % 0.14/0.37 (define @t45 () (@var "BOUND_VARIABLE_7507" tptp.nat)) % 0.14/0.37 (define @t46 () (not (= @t45 @t40))) % 0.14/0.37 (define @t47 () (tptp.less @t45 @t40)) % 0.14/0.37 (define @t48 () (not @t47)) % 0.14/0.37 (define @t49 () (or @t46 @t48 @t46)) % 0.14/0.37 (define @t50 () (@list @t45)) % 0.14/0.37 (define @t51 () (or @t48 @t46)) % 0.14/0.37 (define @t52 () (forall @t50 @t51)) % 0.14/0.37 (define @t53 () (forall @t44 @t52)) % 0.14/0.37 (define @t54 () (forall (@list @t40 @t45) @t51)) % 0.14/0.37 (define @t55 () (@list @t45 @t40)) % 0.14/0.37 (define @t56 () (_ (_ tptp.less @t45) @t40)) % 0.14/0.37 (define @t57 () (not @t56)) % 0.14/0.37 (define @t58 () (or @t57 @t46)) % 0.14/0.37 (define @t59 () (forall @t55 @t58)) % 0.14/0.37 (define @t60 () (@var "BOUND_VARIABLE_7496" tptp.nat)) % 0.14/0.37 (define @t61 () (@var "BOUND_VARIABLE_7494" tptp.nat)) % 0.14/0.37 (define @t62 () (tptp.less @t61 @t60)) % 0.14/0.37 (define @t63 () (_ (_ tptp.less @t61) @t60)) % 0.14/0.37 (define @t64 () (not @t63)) % 0.14/0.37 (define @t65 () (tptp.more @t61 @t60)) % 0.14/0.37 (define @t66 () (_ (_ tptp.more @t61) @t60)) % 0.14/0.37 (define @t67 () (not @t66)) % 0.14/0.37 (define @t68 () (or @t67 @t64)) % 0.14/0.37 (define @t69 () (forall (@list @t61 @t60) @t68)) % 0.14/0.37 (define @t70 () (@var "BOUND_VARIABLE_7484" tptp.nat)) % 0.14/0.37 (define @t71 () (not (tptp.more @t70 @t70))) % 0.14/0.37 (define @t72 () (not (= @t70 @t70))) % 0.14/0.37 (define @t73 () (or @t72 @t71)) % 0.14/0.37 (define @t74 () (@list @t70)) % 0.14/0.37 (define @t75 () (@var "BOUND_VARIABLE_7482" tptp.nat)) % 0.14/0.37 (define @t76 () (tptp.more @t75 @t70)) % 0.14/0.37 (define @t77 () (not @t76)) % 0.14/0.37 (define @t78 () (not (= @t75 @t70))) % 0.14/0.37 (define @t79 () (or @t78 @t78 @t77)) % 0.14/0.37 (define @t80 () (@list @t75)) % 0.14/0.37 (define @t81 () (or @t78 @t77)) % 0.14/0.37 (define @t82 () (forall @t80 @t81)) % 0.14/0.37 (define @t83 () (forall @t74 @t82)) % 0.14/0.37 (define @t84 () (forall (@list @t70 @t75) @t81)) % 0.14/0.37 (define @t85 () (@list @t75 @t70)) % 0.14/0.37 (define @t86 () (_ (_ tptp.more @t75) @t70)) % 0.14/0.37 (define @t87 () (not @t86)) % 0.14/0.37 (define @t88 () (or @t78 @t87)) % 0.14/0.37 (define @t89 () (forall @t85 @t88)) % 0.14/0.37 (define @t90 () (or @t12 @t8)) % 0.14/0.37 (define @t91 () (forall @t21 @t90)) % 0.14/0.37 (define @t92 () (@list @t6 @t5)) % 0.14/0.37 (define @t93 () (or @t17 @t12)) % 0.14/0.37 (define @t94 () (forall @t21 @t93)) % 0.14/0.37 (define @t95 () (or @t8 @t17)) % 0.14/0.37 (define @t96 () (forall @t21 @t95)) % 0.14/0.37 (define @t97 () (and @t96 @t94 @t91)) % 0.14/0.37 (define @t98 () (and @t95 @t93 @t90)) % 0.14/0.37 (define @t99 () (tptp.pl tptp.x tptp.z)) % 0.14/0.37 (define @t100 () (tptp.pl tptp.y tptp.z)) % 0.14/0.37 (define @t101 () (tptp.more @t99 @t100)) % 0.14/0.37 (define @t102 () (tptp.more @t99 @t99)) % 0.14/0.37 (define @t103 () (= tptp.x tptp.y)) % 0.14/0.37 (define @t104 () (not @t103)) % 0.14/0.37 (define @t105 () (not @t101)) % 0.14/0.37 (define @t106 () (not @t102)) % 0.14/0.37 (define @t107 () (and @t106 @t103 @t101)) % 0.14/0.37 (define @t108 () (tptp.more tptp.x tptp.y)) % 0.14/0.37 (define @t109 () (tptp.less tptp.x tptp.y)) % 0.14/0.37 (define @t110 () (or @t103 @t108 @t109)) % 0.14/0.37 (define @t111 () (tptp.less @t99 @t100)) % 0.14/0.37 (define @t112 () (not @t111)) % 0.14/0.37 (define @t113 () (or @t105 @t112)) % 0.14/0.37 (define @t114 () (not @t109)) % 0.14/0.37 (define @t115 () (or @t114 @t111)) % 0.14/0.37 (define @t116 () (not @t115)) % 0.14/0.37 (define @t117 () (@list true false)) % 0.14/0.37 (define @t118 () (forall @t26 (or (not @t36) @t35))) % 0.14/0.37 (assume @p1 @t3) % 0.14/0.37 (assume @p2 (forall (@list @t4) (=> (not (not @t4)) @t4))) % 0.14/0.37 (assume @p3 @t22) % 0.14/0.37 (assume @p4 (forall @t26 (=> @t7 (= @t25 @t24)))) % 0.14/0.37 (assume @p5 @t28) % 0.14/0.37 (assume @p6 @t30) % 0.14/0.37 (assume @p7 @t32) % 0.14/0.37 (assume @p8 true) % 0.14/0.37 (step @p9 :rule refl :args ((tptp.less @t25 @t24))) % 0.14/0.37 (step @p10 :rule refl :args (@t33)) % 0.14/0.37 (step @p11 :rule refl :args (@t34)) % 0.14/0.37 (step @p12 :rule cong :premises (@p11 @p10) :args (@t35)) % 0.14/0.37 (step @p13 :rule trans :premises (@p12 @p9)) % 0.14/0.37 (step @p14 :rule refl :args (tptp.less)) % 0.14/0.37 (step @p15 :rule ho_cong :premises (@p14 @p11)) % 0.14/0.37 (step @p16 :rule ho_cong :premises (@p15 @p10)) % 0.14/0.37 (step @p17 :rule cong :premises (@p16 @p13) :args ((= (_ (_ tptp.less @t34) @t33) @t35))) % 0.14/0.37 (step @p18 :rule symm :premises (@p17)) % 0.14/0.37 (step @p19 :rule refl :args (@t27)) % 0.14/0.37 (step @p20 :rule eq_resolve :premises (@p19 @p18)) % 0.14/0.37 (step @p21 :rule refl :args (@t24)) % 0.14/0.37 (step @p22 :rule cong :premises (@p21 @p10) :args ((= @t24 @t33))) % 0.14/0.37 (step @p23 :rule symm :premises (@p22)) % 0.14/0.37 (step @p24 :rule eq_resolve :premises (@p21 @p23)) % 0.14/0.37 (step @p25 :rule refl :args (@t25)) % 0.14/0.37 (step @p26 :rule cong :premises (@p25 @p11) :args ((= @t25 @t34))) % 0.14/0.37 (step @p27 :rule symm :premises (@p26)) % 0.14/0.37 (step @p28 :rule eq_resolve :premises (@p25 @p27)) % 0.14/0.37 (step @p29 :rule ho_cong :premises (@p14 @p28)) % 0.14/0.37 (step @p30 :rule ho_cong :premises (@p29 @p24)) % 0.14/0.37 (step @p31 :rule trans :premises (@p30 @p20)) % 0.14/0.37 (step @p32 :rule refl :args (@t36)) % 0.14/0.37 (step @p33 :rule refl :args (@t9)) % 0.14/0.37 (step @p34 :rule cong :premises (@p33 @p32) :args ((= @t9 @t36))) % 0.14/0.37 (step @p35 :rule symm :premises (@p34)) % 0.14/0.37 (step @p36 :rule eq_resolve :premises (@p33 @p35)) % 0.14/0.37 (step @p37 :rule cong :premises (@p36) :args (@t12)) % 0.14/0.37 (step @p38 :rule nary_cong :premises (@p37 @p31) :args (@t37)) % 0.14/0.37 (step @p39 :rule cong :premises (@p38) :args ((forall @t26 @t37))) % 0.14/0.37 (step @p40 :rule bool-impl-elim :args (@t9 @t27)) % 0.14/0.37 (step @p41 :rule cong :premises (@p40) :args (@t28)) % 0.14/0.37 (step @p42 :rule trans :premises (@p41 @p39)) % 0.14/0.37 (step @p43 :rule eq_resolve :premises (@p5 @p42)) % 0.14/0.37 (step @p44 :rule refl :args (@t38)) % 0.14/0.37 (step @p45 :rule refl :args (@t13)) % 0.14/0.37 (step @p46 :rule cong :premises (@p45 @p44) :args ((= @t13 @t38))) % 0.14/0.37 (step @p47 :rule symm :premises (@p46)) % 0.14/0.37 (step @p48 :rule eq_resolve :premises (@p45 @p47)) % 0.14/0.37 (step @p49 :rule refl :args (@t7)) % 0.14/0.37 (step @p50 :rule nary_cong :premises (@p49 @p48 @p36) :args (@t39)) % 0.14/0.37 (step @p51 :rule cong :premises (@p50) :args ((forall @t21 @t39))) % 0.14/0.37 (step @p52 :rule aci_norm :args ((= (or @t7 (or @t13 @t9)) @t39))) % 0.14/0.37 (step @p53 :rule bool-double-not-elim :args (@t13)) % 0.14/0.37 (step @p54 :rule nary_cong :premises (@p53 @p33) :args ((or (not @t17) @t9))) % 0.14/0.37 (step @p55 :rule bool-impl-elim :args (@t17 @t9)) % 0.14/0.37 (step @p56 :rule trans :premises (@p55 @p54)) % 0.14/0.37 (step @p57 :rule nary_cong :premises (@p49 @p56) :args ((or @t7 @t29))) % 0.14/0.37 (step @p58 :rule trans :premises (@p57 @p52)) % 0.14/0.37 (step @p59 :rule refl :args (@t29)) % 0.14/0.37 (step @p60 :rule bool-double-not-elim :args (@t7)) % 0.14/0.37 (step @p61 :rule nary_cong :premises (@p60 @p59) :args ((or (not @t8) @t29))) % 0.14/0.37 (step @p62 :rule bool-impl-elim :args (@t8 @t29)) % 0.14/0.37 (step @p63 :rule trans :premises (@p62 @p61)) % 0.14/0.37 (step @p64 :rule trans :premises (@p63 @p58)) % 0.14/0.37 (step @p65 :rule cong :premises (@p64) :args (@t30)) % 0.14/0.37 (step @p66 :rule trans :premises (@p65 @p51)) % 0.14/0.37 (step @p67 :rule eq_resolve :premises (@p6 @p66)) % 0.14/0.37 (step @p68 :rule instantiate :premises (@p67) :args ((@list tptp.x tptp.y))) % 0.14/0.37 (step @p69 :rule aci_norm :args ((= (or @t41 false) @t41))) % 0.14/0.37 (step @p70 :rule evaluate :args ((not true))) % 0.14/0.37 (step @p71 :rule eq-refl :args (@t40)) % 0.14/0.37 (step @p72 :rule cong :premises (@p71) :args (@t42)) % 0.14/0.37 (step @p73 :rule trans :premises (@p72 @p70)) % 0.14/0.37 (step @p74 :rule refl :args (@t41)) % 0.14/0.37 (step @p75 :rule nary_cong :premises (@p74 @p73) :args (@t43)) % 0.14/0.37 (step @p76 :rule trans :premises (@p75 @p69)) % 0.14/0.37 (step @p77 :rule cong :premises (@p76) :args ((forall @t44 @t43))) % 0.14/0.37 (step @p78 :rule quant-var-elim-eq :args ((= (forall @t50 @t49) @t43))) % 0.14/0.37 (step @p79 :rule aci_norm :args ((= @t51 @t49))) % 0.14/0.37 (step @p80 :rule cong :premises (@p79) :args (@t52)) % 0.14/0.37 (step @p81 :rule trans :premises (@p80 @p78)) % 0.14/0.37 (step @p82 :rule cong :premises (@p81) :args (@t53)) % 0.14/0.37 (step @p83 :rule quant-merge-prenex :args ((= @t53 @t54))) % 0.14/0.37 (step @p84 :rule symm :premises (@p83)) % 0.14/0.37 (step @p85 :rule quant_var_reordering :args ((= (forall @t55 @t51) @t54))) % 0.14/0.37 (step @p86 :rule trans :premises (@p85 @p84 @p82)) % 0.14/0.37 (step @p87 :rule trans :premises (@p86 @p77)) % 0.14/0.37 (step @p88 :rule refl :args (@t46)) % 0.14/0.37 (step @p89 :rule refl :args (@t47)) % 0.14/0.37 (step @p90 :rule refl :args (@t56)) % 0.14/0.37 (step @p91 :rule cong :premises (@p90 @p89) :args ((= @t56 @t47))) % 0.14/0.37 (step @p92 :rule symm :premises (@p91)) % 0.14/0.37 (step @p93 :rule eq_resolve :premises (@p90 @p92)) % 0.14/0.37 (step @p94 :rule cong :premises (@p93) :args (@t57)) % 0.14/0.37 (step @p95 :rule nary_cong :premises (@p94 @p88) :args (@t58)) % 0.14/0.37 (step @p96 :rule cong :premises (@p95) :args (@t59)) % 0.14/0.37 (step @p97 :rule trans :premises (@p96 @p87)) % 0.14/0.37 (step @p98 :rule refl :args (@t62)) % 0.14/0.37 (step @p99 :rule refl :args (@t63)) % 0.14/0.37 (step @p100 :rule cong :premises (@p99 @p98) :args ((= @t63 @t62))) % 0.14/0.37 (step @p101 :rule symm :premises (@p100)) % 0.14/0.37 (step @p102 :rule eq_resolve :premises (@p99 @p101)) % 0.14/0.37 (step @p103 :rule cong :premises (@p102) :args (@t64)) % 0.14/0.37 (step @p104 :rule refl :args (@t65)) % 0.14/0.37 (step @p105 :rule refl :args (@t66)) % 0.14/0.37 (step @p106 :rule cong :premises (@p105 @p104) :args ((= @t66 @t65))) % 0.14/0.37 (step @p107 :rule symm :premises (@p106)) % 0.14/0.37 (step @p108 :rule eq_resolve :premises (@p105 @p107)) % 0.14/0.37 (step @p109 :rule cong :premises (@p108) :args (@t67)) % 0.14/0.37 (step @p110 :rule nary_cong :premises (@p109 @p103) :args (@t68)) % 0.14/0.37 (step @p111 :rule cong :premises (@p110) :args (@t69)) % 0.14/0.37 (step @p112 :rule aci_norm :args ((= (or false @t71) @t71))) % 0.14/0.37 (step @p113 :rule refl :args (@t71)) % 0.14/0.37 (step @p114 :rule eq-refl :args (@t70)) % 0.14/0.37 (step @p115 :rule cong :premises (@p114) :args (@t72)) % 0.14/0.37 (step @p116 :rule trans :premises (@p115 @p70)) % 0.14/0.37 (step @p117 :rule nary_cong :premises (@p116 @p113) :args (@t73)) % 0.14/0.37 (step @p118 :rule trans :premises (@p117 @p112)) % 0.14/0.37 (step @p119 :rule cong :premises (@p118) :args ((forall @t74 @t73))) % 0.14/0.37 (step @p120 :rule quant-var-elim-eq :args ((= (forall @t80 @t79) @t73))) % 0.14/0.37 (step @p121 :rule aci_norm :args ((= @t81 @t79))) % 0.14/0.37 (step @p122 :rule cong :premises (@p121) :args (@t82)) % 0.14/0.37 (step @p123 :rule trans :premises (@p122 @p120)) % 0.14/0.37 (step @p124 :rule cong :premises (@p123) :args (@t83)) % 0.14/0.37 (step @p125 :rule quant-merge-prenex :args ((= @t83 @t84))) % 0.14/0.37 (step @p126 :rule symm :premises (@p125)) % 0.14/0.37 (step @p127 :rule quant_var_reordering :args ((= (forall @t85 @t81) @t84))) % 0.14/0.37 (step @p128 :rule trans :premises (@p127 @p126 @p124)) % 0.14/0.37 (step @p129 :rule trans :premises (@p128 @p119)) % 0.14/0.37 (step @p130 :rule refl :args (@t76)) % 0.14/0.37 (step @p131 :rule refl :args (@t86)) % 0.14/0.37 (step @p132 :rule cong :premises (@p131 @p130) :args ((= @t86 @t76))) % 0.14/0.37 (step @p133 :rule symm :premises (@p132)) % 0.14/0.37 (step @p134 :rule eq_resolve :premises (@p131 @p133)) % 0.14/0.37 (step @p135 :rule cong :premises (@p134) :args (@t87)) % 0.14/0.37 (step @p136 :rule refl :args (@t78)) % 0.14/0.37 (step @p137 :rule nary_cong :premises (@p136 @p135) :args (@t88)) % 0.14/0.37 (step @p138 :rule cong :premises (@p137) :args (@t89)) % 0.14/0.37 (step @p139 :rule trans :premises (@p138 @p129)) % 0.14/0.37 (step @p140 :rule nary_cong :premises (@p139 @p111 @p97) :args ((and @t89 @t69 @t59))) % 0.14/0.37 (step @p141 :rule alpha_equiv :args (@t91 @t92 (@list @t45 @t40))) % 0.14/0.37 (step @p142 :rule alpha_equiv :args (@t94 @t92 (@list @t61 @t60))) % 0.14/0.37 (step @p143 :rule alpha_equiv :args (@t96 @t92 (@list @t75 @t70))) % 0.14/0.37 (step @p144 :rule nary_cong :premises (@p143 @p142 @p141) :args (@t97)) % 0.14/0.37 (step @p145 :rule quant-miniscope-and :args ((= (forall @t21 @t98) @t97))) % 0.14/0.37 (step @p146 :rule trans :premises (@p145 @p144)) % 0.14/0.37 (step @p147 :rule trans :premises (@p146 @p140)) % 0.14/0.37 (step @p148 :rule aci_norm :args ((= (and @t95 (and @t93 @t90)) @t98))) % 0.14/0.37 (step @p149 :rule bool-impl-elim :args (@t9 @t8)) % 0.14/0.37 (step @p150 :rule bool-impl-elim :args (@t13 @t12)) % 0.14/0.37 (step @p151 :rule nary_cong :premises (@p150 @p149) :args ((and @t14 @t10))) % 0.14/0.37 (step @p152 :rule bool-double-not-elim :args (@t10)) % 0.14/0.37 (step @p153 :rule refl :args (@t14)) % 0.14/0.37 (step @p154 :rule nary_cong :premises (@p153 @p152) :args ((and @t14 (not @t11)))) % 0.14/0.37 (step @p155 :rule bool-implies-de-morgan :args (@t14 @t11)) % 0.14/0.37 (step @p156 :rule trans :premises (@p155 @p154)) % 0.14/0.37 (step @p157 :rule trans :premises (@p156 @p151)) % 0.14/0.37 (step @p158 :rule bool-impl-elim :args (@t7 @t17)) % 0.14/0.37 (step @p159 :rule nary_cong :premises (@p158 @p157) :args ((and @t18 @t16))) % 0.14/0.37 (step @p160 :rule trans :premises (@p159 @p148)) % 0.14/0.37 (step @p161 :rule bool-implies-de-morgan :args (@t18 @t15)) % 0.14/0.37 (step @p162 :rule trans :premises (@p161 @p160)) % 0.14/0.37 (step @p163 :rule cong :premises (@p162) :args ((forall @t21 (not (=> @t18 @t15))))) % 0.14/0.37 (step @p164 :rule trans :premises (@p163 @p147)) % 0.14/0.37 (step @p165 :rule bool-double-not-elim :args (@t15)) % 0.14/0.37 (step @p166 :rule refl :args (@t18)) % 0.14/0.37 (step @p167 :rule cong :premises (@p166 @p165) :args (@t19)) % 0.14/0.37 (step @p168 :rule cong :premises (@p167) :args (@t20)) % 0.14/0.37 (step @p169 :rule cong :premises (@p168) :args (@t22)) % 0.14/0.37 (step @p170 :rule trans :premises (@p169 @p164)) % 0.14/0.37 (step @p171 :rule eq_resolve :premises (@p3 @p170)) % 0.14/0.37 (step @p172 :rule and_elim :premises (@p171) :args (0)) % 0.14/0.37 (step @p173 :rule instantiate :premises (@p172) :args ((@list @t99))) % 0.14/0.37 (step @p174 :rule refl :args ((tptp.more @t2 @t1))) % 0.14/0.37 (step @p175 :rule refl :args (@t100)) % 0.14/0.37 (step @p176 :rule refl :args (@t99)) % 0.14/0.37 (step @p177 :rule cong :premises (@p176 @p175) :args (@t101)) % 0.14/0.37 (step @p178 :rule trans :premises (@p177 @p174)) % 0.14/0.37 (step @p179 :rule refl :args (tptp.more)) % 0.14/0.37 (step @p180 :rule ho_cong :premises (@p179 @p176)) % 0.14/0.37 (step @p181 :rule ho_cong :premises (@p180 @p175)) % 0.14/0.37 (step @p182 :rule cong :premises (@p181 @p178) :args ((= (_ (_ tptp.more @t99) @t100) @t101))) % 0.14/0.37 (step @p183 :rule symm :premises (@p182)) % 0.14/0.37 (step @p184 :rule refl :args (@t3)) % 0.14/0.37 (step @p185 :rule eq_resolve :premises (@p184 @p183)) % 0.14/0.37 (step @p186 :rule refl :args (@t1)) % 0.14/0.37 (step @p187 :rule cong :premises (@p186 @p175) :args ((= @t1 @t100))) % 0.14/0.37 (step @p188 :rule symm :premises (@p187)) % 0.14/0.37 (step @p189 :rule eq_resolve :premises (@p186 @p188)) % 0.14/0.37 (step @p190 :rule refl :args (@t2)) % 0.14/0.37 (step @p191 :rule cong :premises (@p190 @p176) :args ((= @t2 @t99))) % 0.14/0.37 (step @p192 :rule symm :premises (@p191)) % 0.14/0.37 (step @p193 :rule eq_resolve :premises (@p190 @p192)) % 0.14/0.37 (step @p194 :rule refl :args (tptp.more)) % 0.14/0.37 (step @p195 :rule ho_cong :premises (@p194 @p193)) % 0.14/0.37 (step @p196 :rule ho_cong :premises (@p195 @p189)) % 0.14/0.37 (step @p197 :rule trans :premises (@p196 @p185)) % 0.14/0.37 (step @p198 :rule eq_resolve :premises (@p1 @p197)) % 0.14/0.37 (step @p199 :rule bool-double-not-elim :args (@t102)) % 0.14/0.37 (step @p200 :rule refl :args (@t104)) % 0.14/0.37 (step @p201 :rule refl :args (@t105)) % 0.14/0.37 (step @p202 :rule nary_cong :premises (@p201 @p200 @p199) :args ((or @t105 @t104 (not @t106)))) % 0.14/0.37 (assume-push @p258 @t106) % 0.14/0.37 (assume-push @p259 @t103) % 0.14/0.37 (assume-push @p260 @t101) % 0.14/0.37 (step @p206 :rule evaluate :args ((= true false))) % 0.14/0.37 (step @p207 :rule false_intro :premises (@p173)) % 0.14/0.37 (step @p208 :rule refl :args (tptp.z)) % 0.14/0.37 (step @p209 :rule symm :premises (@p259)) % 0.14/0.37 (step @p210 :rule cong :premises (@p209 @p208) :args (@t100)) % 0.14/0.37 (step @p211 :rule refl :args (@t99)) % 0.14/0.37 (step @p212 :rule cong :premises (@p211 @p210) :args (@t101)) % 0.14/0.37 (step @p213 :rule true_intro :premises (@p198)) % 0.14/0.37 (step @p214 :rule symm :premises (@p213)) % 0.14/0.37 (step @p215 :rule trans :premises (@p214 @p212 @p207)) % 0.14/0.37 (step @p216 false :rule eq_resolve :premises (@p215 @p206)) % 0.14/0.37 (step-pop @p261 :rule scope :premises (@p216)) % 0.14/0.37 (step-pop @p262 :rule scope :premises (@p261)) % 0.14/0.37 (step-pop @p263 :rule scope :premises (@p262)) % 0.14/0.37 (step @p217 :rule process_scope :premises (@p263) :args (false)) % 0.14/0.37 (assume-push @p264 @t101) % 0.14/0.37 (assume-push @p265 @t103) % 0.14/0.37 (assume-push @p266 @t106) % 0.14/0.37 (step @p224 :rule and_intro :premises (@p173 @p265 @p198)) % 0.14/0.37 (step-pop @p267 :rule scope :premises (@p224)) % 0.14/0.37 (step-pop @p268 :rule scope :premises (@p267)) % 0.14/0.37 (step-pop @p269 :rule scope :premises (@p268)) % 0.14/0.37 (step @p225 :rule process_scope :premises (@p269) :args (@t107)) % 0.14/0.37 (step @p229 :rule implies_elim :premises (@p225)) % 0.14/0.37 (step @p230 :rule resolution :premises (@p229 @p217) :args (true @t107)) % 0.14/0.37 (step @p231 :rule not_and :premises (@p230)) % 0.14/0.37 (step @p232 :rule eq_resolve :premises (@p231 @p202)) % 0.14/0.37 (step @p233 :rule chain_m_resolution :premises (@p232 @p198 @p173) :args (@t104 (@list false true) (@list @t101 @t102))) % 0.14/0.37 (step @p234 :rule refl :args (@t108)) % 0.14/0.37 (step @p235 :rule refl :args (@t31)) % 0.14/0.37 (step @p236 :rule cong :premises (@p235 @p234) :args ((= @t31 @t108))) % 0.14/0.37 (step @p237 :rule symm :premises (@p236)) % 0.14/0.37 (step @p238 :rule eq_resolve :premises (@p235 @p237)) % 0.14/0.37 (step @p239 :rule cong :premises (@p238) :args (@t32)) % 0.14/0.37 (step @p240 :rule eq_resolve :premises (@p7 @p239)) % 0.14/0.37 (step @p241 :rule cnf_or_pos :args (@t110)) % 0.14/0.37 (step @p242 :rule reordering :premises (@p241) :args ((or @t108 @t103 @t109 (not @t110)))) % 0.14/0.37 (step @p243 :rule chain_m_resolution :premises (@p242 @p240 @p233 @p68) :args (@t109 (@list true true false) (@list @t108 @t103 @t110))) % 0.14/0.37 (step @p244 :rule and_elim :premises (@p171) :args (1)) % 0.14/0.37 (step @p245 :rule instantiate :premises (@p244) :args ((@list @t99 @t100))) % 0.14/0.37 (step @p246 :rule cnf_or_pos :args (@t113)) % 0.14/0.37 (step @p247 :rule reordering :premises (@p246) :args ((or @t105 @t112 (not @t113)))) % 0.14/0.37 (step @p248 :rule chain_m_resolution :premises (@p247 @p198 @p245) :args (@t112 (@list false false) (@list @t101 @t113))) % 0.14/0.37 (step @p249 :rule cnf_or_pos :args (@t115)) % 0.14/0.37 (step @p250 :rule reordering :premises (@p249) :args ((or @t111 @t114 @t116))) % 0.14/0.37 (step @p251 :rule chain_m_resolution :premises (@p250 @p248 @p243) :args (@t116 @t117 (@list @t111 @t109))) % 0.14/0.37 (assume-push @p270 @t118) % 0.14/0.37 (step @p253 :rule instantiate :premises (@p43) :args ((@list tptp.x tptp.y tptp.z))) % 0.14/0.37 (step-pop @p271 :rule scope :premises (@p253)) % 0.14/0.37 (step @p254 :rule process_scope :premises (@p271) :args (@t115)) % 0.14/0.37 (step @p256 :rule implies_elim :premises (@p254)) % 0.14/0.37 (step @p257 false :rule chain_m_resolution :premises (@p256 @p251 @p43) :args (false @t117 (@list @t115 @t118))) % 0.14/0.37 ) % 0.14/0.37 % SZS output end Proof % 0.14/0.37 % cvc5 exiting %------------------------------------------------------------------------------