%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM741^1 : 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 : n001.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 08:40:31 AM UTC 2026 % Result : Theorem 161.77s 162.15s % Output : Proof 161.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM741^1 : TPTP v9.2.1. Released v3.7.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n001.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 12:09:05 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 161.77/162.15 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 161.77/162.15 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 161.77/162.15 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 161.77/162.15 --- Run --ho-elim --full-saturate-quant at 18s... % 161.77/162.15 % SZS status Theorem % 161.77/162.15 % SZS output start Proof % 161.77/162.15 ( % 161.77/162.15 (declare-sort tptp.nat 0) % 161.77/162.15 (declare-sort tptp.frac 0) % 161.77/162.15 (declare-const tptp.z tptp.frac) % 161.77/162.15 (declare-const tptp.less (-> tptp.nat tptp.nat Bool)) % 161.77/162.15 (declare-const tptp.ts (-> tptp.nat tptp.nat tptp.nat)) % 161.77/162.15 (declare-const tptp.num (-> tptp.frac tptp.nat)) % 161.77/162.15 (declare-const tptp.y tptp.frac) % 161.77/162.15 (declare-const tptp.den (-> tptp.frac tptp.nat)) % 161.77/162.15 (declare-const tptp.x tptp.frac) % 161.77/162.15 (define @t1 () (_ tptp.den tptp.x)) % 161.77/162.15 (define @t2 () (_ tptp.ts (_ tptp.num tptp.y))) % 161.77/162.16 (define @t3 () (_ tptp.den tptp.y)) % 161.77/162.16 (define @t4 () (_ tptp.ts (_ tptp.num tptp.x))) % 161.77/162.16 (define @t5 () (_ (_ tptp.less (_ @t4 @t3)) (_ @t2 @t1))) % 161.77/162.16 (define @t6 () (_ tptp.ts (_ tptp.num tptp.z))) % 161.77/162.16 (define @t7 () (_ tptp.den tptp.z)) % 161.77/162.16 (define @t8 () (_ (_ tptp.less (_ @t2 @t7)) (_ @t6 @t3))) % 161.77/162.16 (define @t9 () (@var "Xy" tptp.nat)) % 161.77/162.16 (define @t10 () (@var "Xx" tptp.nat)) % 161.77/162.16 (define @t11 () (_ (_ tptp.less @t10) @t9)) % 161.77/162.16 (define @t12 () (@var "Xz" tptp.nat)) % 161.77/162.16 (define @t13 () (_ tptp.ts @t9)) % 161.77/162.16 (define @t14 () (_ @t13 @t12)) % 161.77/162.16 (define @t15 () (_ tptp.ts @t10)) % 161.77/162.16 (define @t16 () (_ @t15 @t12)) % 161.77/162.16 (define @t17 () (_ tptp.less @t16)) % 161.77/162.16 (define @t18 () (_ @t17 @t14)) % 161.77/162.16 (define @t19 () (@list @t10 @t9 @t12)) % 161.77/162.16 (define @t20 () (forall @t19 (=> @t18 @t11))) % 161.77/162.16 (define @t21 () (@var "Xu" tptp.nat)) % 161.77/162.16 (define @t22 () (_ @t13 @t21)) % 161.77/162.16 (define @t23 () (_ @t17 @t22)) % 161.77/162.16 (define @t24 () (_ (_ tptp.less @t12) @t21)) % 161.77/162.16 (define @t25 () (=> @t24 @t23)) % 161.77/162.16 (define @t26 () (@list @t10 @t9 @t12 @t21)) % 161.77/162.16 (define @t27 () (forall @t26 (=> @t11 @t25))) % 161.77/162.16 (define @t28 () (_ @t13 @t10)) % 161.77/162.16 (define @t29 () (_ @t15 @t9)) % 161.77/162.16 (define @t30 () (= @t29 @t28)) % 161.77/162.16 (define @t31 () (@list @t10 @t9)) % 161.77/162.16 (define @t32 () (forall @t31 @t30)) % 161.77/162.16 (define @t33 () (_ @t15 @t14)) % 161.77/162.16 (define @t34 () (_ (_ tptp.ts @t29) @t12)) % 161.77/162.16 (define @t35 () (= @t34 @t33)) % 161.77/162.16 (define @t36 () (forall @t19 @t35)) % 161.77/162.16 (define @t37 () (not (_ (_ tptp.less (_ @t4 @t7)) (_ @t6 @t1)))) % 161.77/162.16 (define @t38 () (@const 0 (@ho-elim-sort (-> tptp.nat tptp.nat tptp.nat)))) % 161.77/162.16 (define @t39 () (@const 1 (-> (@ho-elim-sort (-> tptp.nat tptp.nat tptp.nat)) tptp.nat (@ho-elim-sort (-> tptp.nat tptp.nat))))) % 161.77/162.16 (define @t40 () (_ @t39 @t38 @t9)) % 161.77/162.16 (define @t41 () (@const 2 (-> (@ho-elim-sort (-> tptp.nat tptp.nat)) tptp.nat tptp.nat))) % 161.77/162.16 (define @t42 () (_ @t39 @t38 @t10)) % 161.77/162.16 (define @t43 () (@const 3 (@ho-elim-sort (-> tptp.nat tptp.nat Bool)))) % 161.77/162.16 (define @t44 () (@const 4 (-> (@ho-elim-sort (-> tptp.nat tptp.nat Bool)) tptp.nat (@ho-elim-sort (-> tptp.nat Bool))))) % 161.77/162.16 (define @t45 () (_ @t44 @t43 (_ @t41 @t42 @t12))) % 161.77/162.16 (define @t46 () (@const 5 (-> (@ho-elim-sort (-> tptp.nat Bool)) tptp.nat Bool))) % 161.77/162.16 (define @t47 () (_ @t46 (_ @t44 @t43 @t10) @t9)) % 161.77/162.16 (define @t48 () (tptp.ts @t9 @t21)) % 161.77/162.16 (define @t49 () (tptp.ts @t10 @t12)) % 161.77/162.16 (define @t50 () (tptp.less @t49 @t48)) % 161.77/162.16 (define @t51 () (tptp.less @t12 @t21)) % 161.77/162.16 (define @t52 () (tptp.less @t10 @t9)) % 161.77/162.16 (define @t53 () (_ tptp.less @t49)) % 161.77/162.16 (define @t54 () (not @t24)) % 161.77/162.16 (define @t55 () (not @t11)) % 161.77/162.16 (define @t56 () (or @t55 @t54 @t23)) % 161.77/162.16 (define @t57 () (@const 6 (@ho-elim-sort (-> tptp.frac tptp.nat)))) % 161.77/162.16 (define @t58 () (@const 7 (-> (@ho-elim-sort (-> tptp.frac tptp.nat)) tptp.frac tptp.nat))) % 161.77/162.16 (define @t59 () (_ @t58 @t57 tptp.x)) % 161.77/162.16 (define @t60 () (@const 8 (@ho-elim-sort (-> tptp.frac tptp.nat)))) % 161.77/162.16 (define @t61 () (_ @t58 @t60 tptp.y)) % 161.77/162.16 (define @t62 () (_ @t39 @t38 @t61)) % 161.77/162.16 (define @t63 () (_ @t41 @t62 @t59)) % 161.77/162.16 (define @t64 () (_ @t58 @t57 tptp.y)) % 161.77/162.16 (define @t65 () (_ @t58 @t60 tptp.x)) % 161.77/162.16 (define @t66 () (_ @t39 @t38 @t65)) % 161.77/162.16 (define @t67 () (_ @t41 @t66 @t64)) % 161.77/162.16 (define @t68 () (_ @t58 @t60 tptp.z)) % 161.77/162.16 (define @t69 () (_ @t39 @t38 @t68)) % 161.77/162.16 (define @t70 () (_ @t41 @t69 @t64)) % 161.77/162.16 (define @t71 () (_ @t58 @t57 tptp.z)) % 161.77/162.16 (define @t72 () (_ @t41 @t62 @t71)) % 161.77/162.16 (define @t73 () (_ @t46 (_ @t44 @t43 @t72) @t70)) % 161.77/162.16 (define @t74 () (_ @t46 (_ @t44 @t43 @t67) @t63)) % 161.77/162.16 (define @t75 () (_ @t46 (_ @t44 @t43 (_ @t41 (_ @t39 @t38 @t72) @t67)) (_ @t41 (_ @t39 @t38 @t70) @t63))) % 161.77/162.16 (define @t76 () (not @t74)) % 161.77/162.16 (define @t77 () (not @t73)) % 161.77/162.16 (define @t78 () (or @t77 @t76 @t75)) % 161.77/162.16 (define @t79 () (_ @t41 @t42 @t9)) % 161.77/162.16 (define @t80 () (_ @t41 @t40 @t10)) % 161.77/162.16 (define @t81 () (forall @t31 (= @t79 @t80))) % 161.77/162.16 (define @t82 () (tptp.ts @t9 @t10)) % 161.77/162.16 (define @t83 () (tptp.ts @t10 @t9)) % 161.77/162.16 (define @t84 () (_ @t39 @t38 (_ @t41 (_ @t39 @t38 @t64) @t68))) % 161.77/162.16 (define @t85 () (_ @t41 (_ @t39 @t38 @t59) @t61)) % 161.77/162.16 (define @t86 () (_ @t41 (_ @t39 @t38 @t79) @t12)) % 161.77/162.16 (define @t87 () (_ @t41 @t40 @t12)) % 161.77/162.16 (define @t88 () (_ @t41 @t42 @t87)) % 161.77/162.16 (define @t89 () (forall @t19 (= @t86 @t88))) % 161.77/162.16 (define @t90 () (tptp.ts @t9 @t12)) % 161.77/162.16 (define @t91 () (tptp.ts @t10 @t90)) % 161.77/162.16 (define @t92 () (tptp.ts @t83 @t12)) % 161.77/162.16 (define @t93 () (_ @t41 @t69 @t85)) % 161.77/162.16 (define @t94 () (_ @t41 @t69 @t59)) % 161.77/162.16 (define @t95 () (_ @t41 (_ @t39 @t38 @t94) @t61)) % 161.77/162.16 (define @t96 () (forall @t19 (= @t88 @t86))) % 161.77/162.16 (define @t97 () (= @t93 @t95)) % 161.77/162.16 (define @t98 () (_ @t39 @t38 @t95)) % 161.77/162.16 (define @t99 () (_ @t41 @t98 @t64)) % 161.77/162.16 (define @t100 () (_ @t39 @t38 @t71)) % 161.77/162.16 (define @t101 () (_ @t41 @t100 @t61)) % 161.77/162.16 (define @t102 () (_ @t39 @t38 @t101)) % 161.77/162.16 (define @t103 () (_ @t41 @t102 @t65)) % 161.77/162.16 (define @t104 () (_ @t44 @t43 (_ @t41 (_ @t39 @t38 @t103) @t64))) % 161.77/162.16 (define @t105 () (_ @t46 @t104 @t99)) % 161.77/162.16 (define @t106 () (tptp.less @t49 @t90)) % 161.77/162.16 (define @t107 () (not @t18)) % 161.77/162.16 (define @t108 () (or @t107 @t11)) % 161.77/162.16 (define @t109 () (_ @t41 @t66 @t71)) % 161.77/162.16 (define @t110 () (_ @t46 (_ @t44 @t43 @t109) @t94)) % 161.77/162.16 (define @t111 () (not (_ @t46 (_ @t44 @t43 (_ @t41 (_ @t39 @t38 @t109) @t61)) @t95))) % 161.77/162.16 (define @t112 () (or @t111 @t110)) % 161.77/162.16 (define @t113 () (@list true false)) % 161.77/162.16 (define @t114 () (_ @t44 @t43 @t103)) % 161.77/162.16 (define @t115 () (_ @t46 @t114 @t95)) % 161.77/162.16 (define @t116 () (not @t105)) % 161.77/162.16 (define @t117 () (or @t116 @t115)) % 161.77/162.16 (assume @p1 @t5) % 161.77/162.16 (assume @p2 @t8) % 161.77/162.16 (assume @p3 @t20) % 161.77/162.16 (assume @p4 @t27) % 161.77/162.16 (assume @p5 @t32) % 161.77/162.16 (assume @p6 @t36) % 161.77/162.16 (assume @p7 @t37) % 161.77/162.16 (assume @p8 true) % 161.77/162.16 (step @p9 :rule evaluate :args ((= false true))) % 161.77/162.16 ; WARNING: add trust step for TRUST % 161.77/162.16 ; trust TRUST PREPROCESS_HO_ELIM % 161.77/162.16 (step @p10 :rule trust :premises () :args ((= (forall @t26 (or (not @t52) (not @t51) @t50)) (forall @t26 (or (not @t47) (not (_ @t46 (_ @t44 @t43 @t12) @t21)) (_ @t46 @t45 (_ @t41 @t40 @t21))))))) % 161.77/162.16 (step @p11 :rule refl :args ((tptp.less @t16 @t22))) % 161.77/162.16 (step @p12 :rule refl :args (@t48)) % 161.77/162.16 (step @p13 :rule refl :args (@t49)) % 161.77/162.16 (step @p14 :rule cong :premises (@p13 @p12) :args (@t50)) % 161.77/162.16 (step @p15 :rule trans :premises (@p14 @p11)) % 161.77/162.16 (step @p16 :rule refl :args (tptp.less)) % 161.77/162.16 (step @p17 :rule ho_cong :premises (@p16 @p13)) % 161.77/162.16 (step @p18 :rule ho_cong :premises (@p17 @p12)) % 161.77/162.16 (step @p19 :rule cong :premises (@p18 @p15) :args ((= (_ @t53 @t48) @t50))) % 161.77/162.16 (step @p20 :rule symm :premises (@p19)) % 161.77/162.16 (step @p21 :rule refl :args (@t23)) % 161.77/162.16 (step @p22 :rule eq_resolve :premises (@p21 @p20)) % 161.77/162.16 (step @p23 :rule refl :args (@t22)) % 161.77/162.16 (step @p24 :rule cong :premises (@p23 @p12) :args ((= @t22 @t48))) % 161.77/162.16 (step @p25 :rule symm :premises (@p24)) % 161.77/162.16 (step @p26 :rule eq_resolve :premises (@p23 @p25)) % 161.77/162.16 (step @p27 :rule refl :args (@t16)) % 161.77/162.16 (step @p28 :rule cong :premises (@p27 @p13) :args ((= @t16 @t49))) % 161.77/162.16 (step @p29 :rule symm :premises (@p28)) % 161.77/162.16 (step @p30 :rule eq_resolve :premises (@p27 @p29)) % 161.77/162.16 (step @p31 :rule ho_cong :premises (@p16 @p30)) % 161.77/162.16 (step @p32 :rule ho_cong :premises (@p31 @p26)) % 161.77/162.16 (step @p33 :rule trans :premises (@p32 @p22)) % 161.77/162.16 (step @p34 :rule refl :args (@t51)) % 161.77/162.16 (step @p35 :rule refl :args (@t24)) % 161.77/162.16 (step @p36 :rule cong :premises (@p35 @p34) :args ((= @t24 @t51))) % 161.77/162.16 (step @p37 :rule symm :premises (@p36)) % 161.77/162.16 (step @p38 :rule eq_resolve :premises (@p35 @p37)) % 161.77/162.16 (step @p39 :rule cong :premises (@p38) :args (@t54)) % 161.77/162.16 (step @p40 :rule refl :args (@t52)) % 161.77/162.16 (step @p41 :rule refl :args (@t11)) % 161.77/162.16 (step @p42 :rule cong :premises (@p41 @p40) :args ((= @t11 @t52))) % 161.77/162.16 (step @p43 :rule symm :premises (@p42)) % 161.77/162.16 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 161.77/162.16 (step @p45 :rule cong :premises (@p44) :args (@t55)) % 161.77/162.16 (step @p46 :rule nary_cong :premises (@p45 @p39 @p33) :args (@t56)) % 161.77/162.16 (step @p47 :rule cong :premises (@p46) :args ((forall @t26 @t56))) % 161.77/162.16 (step @p48 :rule aci_norm :args ((= (or @t55 (or @t54 @t23)) @t56))) % 161.77/162.16 (step @p49 :rule bool-impl-elim :args (@t24 @t23)) % 161.77/162.16 (step @p50 :rule refl :args (@t55)) % 161.77/162.16 (step @p51 :rule nary_cong :premises (@p50 @p49) :args ((or @t55 @t25))) % 161.77/162.16 (step @p52 :rule trans :premises (@p51 @p48)) % 161.77/162.16 (step @p53 :rule bool-impl-elim :args (@t11 @t25)) % 161.77/162.16 (step @p54 :rule trans :premises (@p53 @p52)) % 161.77/162.16 (step @p55 :rule cong :premises (@p54) :args (@t27)) % 161.77/162.16 (step @p56 :rule trans :premises (@p55 @p47)) % 161.77/162.16 (step @p57 :rule trans :premises (@p56 @p10)) % 161.77/162.16 (step @p58 :rule eq_resolve :premises (@p4 @p57)) % 161.77/162.16 (step @p59 :rule instantiate :premises (@p58) :args ((@list @t72 @t70 @t67 @t63))) % 161.77/162.16 ; trust TRUST PREPROCESS_HO_ELIM % 161.77/162.16 (step @p60 :rule trust :premises () :args ((= @t8 @t73))) % 161.77/162.16 (step @p61 :rule eq_resolve :premises (@p2 @p60)) % 161.77/162.16 ; trust TRUST PREPROCESS_HO_ELIM % 161.77/162.16 (step @p62 :rule trust :premises () :args ((= @t5 @t74))) % 161.77/162.16 (step @p63 :rule eq_resolve :premises (@p1 @p62)) % 161.77/162.16 (step @p64 :rule cnf_or_pos :args (@t78)) % 161.77/162.16 (step @p65 :rule reordering :premises (@p64) :args ((or @t76 @t77 @t75 (not @t78)))) % 161.77/162.16 (step @p66 :rule chain_m_resolution :premises (@p65 @p63 @p61 @p59) :args (@t75 (@list false false false) (@list @t74 @t73 @t78))) % 161.77/162.16 (step @p67 :rule true_intro :premises (@p66)) % 161.77/162.16 (step @p68 :rule eq-symm :args (@t79 @t80)) % 161.77/162.16 (step @p69 :rule cong :premises (@p68) :args (@t81)) % 161.77/162.16 ; trust TRUST PREPROCESS_HO_ELIM % 161.77/162.16 (step @p70 :rule trust :premises () :args ((= (forall @t31 (= @t83 @t82)) @t81))) % 161.77/162.16 (step @p71 :rule refl :args (@t82)) % 161.77/162.16 (step @p72 :rule refl :args (@t28)) % 161.77/162.16 (step @p73 :rule cong :premises (@p72 @p71) :args ((= @t28 @t82))) % 161.77/162.16 (step @p74 :rule symm :premises (@p73)) % 161.77/162.16 (step @p75 :rule eq_resolve :premises (@p72 @p74)) % 161.77/162.16 (step @p76 :rule refl :args (@t83)) % 161.77/162.16 (step @p77 :rule refl :args (@t29)) % 161.77/162.16 (step @p78 :rule cong :premises (@p77 @p76) :args ((= @t29 @t83))) % 161.77/162.16 (step @p79 :rule symm :premises (@p78)) % 161.77/162.16 (step @p80 :rule eq_resolve :premises (@p77 @p79)) % 161.77/162.16 (step @p81 :rule cong :premises (@p80 @p75) :args (@t30)) % 161.77/162.16 (step @p82 :rule cong :premises (@p81) :args (@t32)) % 161.77/162.16 (step @p83 :rule trans :premises (@p82 @p70 @p69)) % 161.77/162.16 (step @p84 :rule eq_resolve :premises (@p5 @p83)) % 161.77/162.16 (step @p85 :rule instantiate :premises (@p84) :args ((@list @t59 @t61))) % 161.77/162.16 (step @p86 :rule symm :premises (@p85)) % 161.77/162.16 (step @p87 :rule instantiate :premises (@p84) :args ((@list @t64 @t68))) % 161.77/162.16 (step @p88 :rule symm :premises (@p87)) % 161.77/162.16 (step @p89 :rule refl :args (@t38)) % 161.77/162.16 (step @p90 :rule cong :premises (@p89 @p88) :args (@t84)) % 161.77/162.16 (step @p91 :rule cong :premises (@p90 @p86) :args ((_ @t41 @t84 @t85))) % 161.77/162.16 (step @p92 :rule eq-symm :args (@t86 @t88)) % 161.77/162.16 (step @p93 :rule cong :premises (@p92) :args (@t89)) % 161.77/162.16 ; trust TRUST PREPROCESS_HO_ELIM % 161.77/162.16 (step @p94 :rule trust :premises () :args ((= (forall @t19 (= @t92 @t91)) @t89))) % 161.77/162.16 (step @p95 :rule refl :args ((tptp.ts @t10 @t14))) % 161.77/162.16 (step @p96 :rule refl :args (@t90)) % 161.77/162.16 (step @p97 :rule refl :args (@t10)) % 161.77/162.16 (step @p98 :rule cong :premises (@p97 @p96) :args (@t91)) % 161.77/162.16 (step @p99 :rule trans :premises (@p98 @p95)) % 161.77/162.16 (step @p100 :rule refl :args (@t15)) % 161.77/162.16 (step @p101 :rule ho_cong :premises (@p100 @p96)) % 161.77/162.16 (step @p102 :rule cong :premises (@p101 @p99) :args ((= (_ @t15 @t90) @t91))) % 161.77/162.16 (step @p103 :rule symm :premises (@p102)) % 161.77/162.16 (step @p104 :rule refl :args (@t33)) % 161.77/162.16 (step @p105 :rule eq_resolve :premises (@p104 @p103)) % 161.77/162.16 (step @p106 :rule refl :args (@t14)) % 161.77/162.16 (step @p107 :rule cong :premises (@p106 @p96) :args ((= @t14 @t90))) % 161.77/162.16 (step @p108 :rule symm :premises (@p107)) % 161.77/162.16 (step @p109 :rule eq_resolve :premises (@p106 @p108)) % 161.77/162.16 (step @p110 :rule ho_cong :premises (@p100 @p109)) % 161.77/162.16 (step @p111 :rule trans :premises (@p110 @p105)) % 161.77/162.16 (step @p112 :rule refl :args ((tptp.ts @t29 @t12))) % 161.77/162.16 (step @p113 :rule refl :args (@t12)) % 161.77/162.16 (step @p114 :rule cong :premises (@p76 @p113) :args (@t92)) % 161.77/162.16 (step @p115 :rule trans :premises (@p114 @p112)) % 161.77/162.16 (step @p116 :rule refl :args (tptp.ts)) % 161.77/162.16 (step @p117 :rule ho_cong :premises (@p116 @p76)) % 161.77/162.16 (step @p118 :rule ho_cong :premises (@p117 @p113)) % 161.77/162.16 (step @p119 :rule cong :premises (@p118 @p115) :args ((= (_ (_ tptp.ts @t83) @t12) @t92))) % 161.77/162.16 (step @p120 :rule symm :premises (@p119)) % 161.77/162.16 (step @p121 :rule refl :args (@t34)) % 161.77/162.16 (step @p122 :rule eq_resolve :premises (@p121 @p120)) % 161.77/162.16 (step @p123 :rule ho_cong :premises (@p116 @p80)) % 161.77/162.16 (step @p124 :rule ho_cong :premises (@p123 @p113)) % 161.77/162.16 (step @p125 :rule trans :premises (@p124 @p122)) % 161.77/162.16 (step @p126 :rule cong :premises (@p125 @p111) :args (@t35)) % 161.77/162.16 (step @p127 :rule cong :premises (@p126) :args (@t36)) % 161.77/162.16 (step @p128 :rule trans :premises (@p127 @p94 @p93)) % 161.77/162.16 (step @p129 :rule eq_resolve :premises (@p6 @p128)) % 161.77/162.16 (step @p130 :rule instantiate :premises (@p129) :args ((@list @t64 @t68 @t85))) % 161.77/162.16 (step @p131 :rule instantiate :premises (@p84) :args ((@list @t93 @t64))) % 161.77/162.16 (step @p132 :rule symm :premises (@p131)) % 161.77/162.16 (step @p133 :rule refl :args (@t64)) % 161.77/162.16 (step @p134 :rule refl :args (@t69)) % 161.77/162.16 (step @p135 :rule cong :premises (@p134 @p85) :args ((_ @t41 @t69 @t63))) % 161.77/162.16 (step @p136 :rule instantiate :premises (@p129) :args ((@list @t68 @t61 @t59))) % 161.77/162.16 (step @p137 :rule symm :premises (@p136)) % 161.77/162.16 (step @p138 :rule trans :premises (@p137 @p135)) % 161.77/162.16 (step @p139 :rule cong :premises (@p89 @p138) :args ((_ @t39 @t38 (_ @t41 (_ @t39 @t38 (_ @t41 @t69 @t61)) @t59)))) % 161.77/162.16 (step @p140 :rule symm :premises (@p135)) % 161.77/162.16 (step @p141 :rule eq-symm :args (@t93 @t95)) % 161.77/162.16 (step @p142 :rule refl :args (@t96)) % 161.77/162.16 (step @p143 :rule cong :premises (@p142 @p141) :args ((=> @t96 @t97))) % 161.77/162.16 (assume-push @p216 @t96) % 161.77/162.16 (step @p145 :rule instantiate :premises (@p129) :args ((@list @t68 @t59 @t61))) % 161.77/162.16 (step-pop @p217 :rule scope :premises (@p145)) % 161.77/162.16 (step @p146 :rule process_scope :premises (@p217) :args (@t97)) % 161.77/162.16 (step @p148 :rule eq_resolve :premises (@p146 @p143)) % 161.77/162.16 (step @p149 :rule implies_elim :premises (@p148)) % 161.77/162.16 (step @p150 :rule chain_m_resolution :premises (@p149 @p129) :args ((= @t95 @t93) (@list false) (@list @t96))) % 161.77/162.16 (step @p151 :rule trans :premises (@p150 @p140 @p136)) % 161.77/162.16 (step @p152 :rule cong :premises (@p89 @p151) :args (@t98)) % 161.77/162.16 (step @p153 :rule trans :premises (@p152 @p139)) % 161.77/162.16 (step @p154 :rule cong :premises (@p153 @p133) :args (@t99)) % 161.77/162.16 (step @p155 :rule trans :premises (@p154 @p132 @p130 @p91)) % 161.77/162.16 (step @p156 :rule refl :args (@t67)) % 161.77/162.16 (step @p157 :rule instantiate :premises (@p84) :args ((@list @t71 @t61))) % 161.77/162.16 (step @p158 :rule symm :premises (@p157)) % 161.77/162.16 (step @p159 :rule cong :premises (@p89 @p158) :args (@t102)) % 161.77/162.16 (step @p160 :rule cong :premises (@p159 @p156) :args ((_ @t41 @t102 @t67))) % 161.77/162.16 (step @p161 :rule instantiate :premises (@p129) :args ((@list @t101 @t65 @t64))) % 161.77/162.16 (step @p162 :rule symm :premises (@p161)) % 161.77/162.16 (step @p163 :rule trans :premises (@p162 @p160)) % 161.77/162.16 (step @p164 :rule refl :args (@t43)) % 161.77/162.16 (step @p165 :rule cong :premises (@p164 @p163) :args (@t104)) % 161.77/162.16 (step @p166 :rule cong :premises (@p165 @p155) :args (@t105)) % 161.77/162.16 ; trust TRUST PREPROCESS_HO_ELIM % 161.77/162.16 (step @p167 :rule trust :premises () :args ((= (forall @t19 (or (not @t106) @t52)) (forall @t19 (or (not (_ @t46 @t45 @t87)) @t47))))) % 161.77/162.16 (step @p168 :rule refl :args ((tptp.less @t16 @t14))) % 161.77/162.16 (step @p169 :rule cong :premises (@p13 @p96) :args (@t106)) % 161.77/162.16 (step @p170 :rule trans :premises (@p169 @p168)) % 161.77/162.16 (step @p171 :rule ho_cong :premises (@p17 @p96)) % 161.77/162.16 (step @p172 :rule cong :premises (@p171 @p170) :args ((= (_ @t53 @t90) @t106))) % 161.77/162.16 (step @p173 :rule symm :premises (@p172)) % 161.77/162.16 (step @p174 :rule refl :args (@t18)) % 161.77/162.16 (step @p175 :rule eq_resolve :premises (@p174 @p173)) % 161.77/162.16 (step @p176 :rule ho_cong :premises (@p31 @p109)) % 161.77/162.16 (step @p177 :rule trans :premises (@p176 @p175)) % 161.77/162.16 (step @p178 :rule cong :premises (@p177) :args (@t107)) % 161.77/162.16 (step @p179 :rule nary_cong :premises (@p178 @p44) :args (@t108)) % 161.77/162.16 (step @p180 :rule cong :premises (@p179) :args ((forall @t19 @t108))) % 161.77/162.16 (step @p181 :rule bool-impl-elim :args (@t18 @t11)) % 161.77/162.16 (step @p182 :rule cong :premises (@p181) :args (@t20)) % 161.77/162.16 (step @p183 :rule trans :premises (@p182 @p180)) % 161.77/162.16 (step @p184 :rule trans :premises (@p183 @p167)) % 161.77/162.16 (step @p185 :rule eq_resolve :premises (@p3 @p184)) % 161.77/162.16 (step @p186 :rule instantiate :premises (@p185) :args ((@list @t103 @t95 @t64))) % 161.77/162.16 (step @p187 :rule instantiate :premises (@p185) :args ((@list @t109 @t94 @t61))) % 161.77/162.16 ; trust TRUST PREPROCESS_HO_ELIM % 161.77/162.16 (step @p188 :rule trust :premises () :args ((= @t37 (not @t110)))) % 161.77/162.16 (step @p189 :rule eq_resolve :premises (@p7 @p188)) % 161.77/162.16 (step @p190 :rule cnf_or_pos :args (@t112)) % 161.77/162.16 (step @p191 :rule reordering :premises (@p190) :args ((or @t110 @t111 (not @t112)))) % 161.77/162.16 (step @p192 :rule chain_m_resolution :premises (@p191 @p189 @p187) :args (@t111 @t113 (@list @t110 @t112))) % 161.77/162.16 (step @p193 :rule false_intro :premises (@p192)) % 161.77/162.16 (step @p194 :rule refl :args (@t95)) % 161.77/162.16 (step @p195 :rule instantiate :premises (@p84) :args ((@list @t109 @t61))) % 161.77/162.16 (step @p196 :rule instantiate :premises (@p84) :args ((@list @t71 @t65))) % 161.77/162.16 (step @p197 :rule symm :premises (@p196)) % 161.77/162.16 (step @p198 :rule refl :args (@t62)) % 161.77/162.16 (step @p199 :rule cong :premises (@p198 @p197) :args ((_ @t41 @t62 (_ @t41 @t100 @t65)))) % 161.77/162.16 (step @p200 :rule instantiate :premises (@p129) :args ((@list @t61 @t71 @t65))) % 161.77/162.16 (step @p201 :rule symm :premises (@p200)) % 161.77/162.16 (step @p202 :rule refl :args (@t65)) % 161.77/162.16 (step @p203 :rule cong :premises (@p159 @p202) :args (@t103)) % 161.77/162.16 (step @p204 :rule trans :premises (@p203 @p201 @p199 @p195)) % 161.77/162.16 (step @p205 :rule cong :premises (@p164 @p204) :args (@t114)) % 161.77/162.16 (step @p206 :rule cong :premises (@p205 @p194) :args (@t115)) % 161.77/162.16 (step @p207 :rule trans :premises (@p206 @p193)) % 161.77/162.16 (step @p208 :rule false_elim :premises (@p207)) % 161.77/162.16 (step @p209 :rule cnf_or_pos :args (@t117)) % 161.77/162.16 (step @p210 :rule reordering :premises (@p209) :args ((or @t116 @t115 (not @t117)))) % 161.77/162.16 (step @p211 :rule chain_m_resolution :premises (@p210 @p208 @p186) :args (@t116 @t113 (@list @t115 @t117))) % 161.77/162.16 (step @p212 :rule false_intro :premises (@p211)) % 161.77/162.16 (step @p213 :rule symm :premises (@p212)) % 161.77/162.16 (step @p214 :rule trans :premises (@p213 @p166 @p67)) % 161.77/162.16 (step @p215 false :rule eq_resolve :premises (@p214 @p9)) % 161.77/162.16 ) % 161.77/162.16 % SZS output end Proof % 161.77/162.16 % cvc5 exiting %------------------------------------------------------------------------------