%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM737^1 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n014.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 08:40:30 AM UTC 2026 % Result : Theorem 162.05s 162.44s % Output : Proof 162.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM737^1 : TPTP v9.2.1. Released v3.7.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n014.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 12:07:13 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 162.05/162.44 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 162.05/162.44 --- 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... % 162.05/162.44 --- 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... % 162.05/162.44 --- Run --ho-elim --full-saturate-quant at 18s... % 162.05/162.44 % SZS status Theorem % 162.05/162.44 % SZS output start Proof % 162.05/162.44 ( % 162.05/162.44 (declare-sort tptp.nat 0) % 162.05/162.44 (declare-sort tptp.frac 0) % 162.05/162.44 (declare-const tptp.u tptp.frac) % 162.05/162.44 (declare-const tptp.z tptp.frac) % 162.05/162.44 (declare-const tptp.more (-> tptp.nat tptp.nat Bool)) % 162.05/162.44 (declare-const tptp.ts (-> tptp.nat tptp.nat tptp.nat)) % 162.05/162.44 (declare-const tptp.num (-> tptp.frac tptp.nat)) % 162.05/162.44 (declare-const tptp.y tptp.frac) % 162.05/162.44 (declare-const tptp.den (-> tptp.frac tptp.nat)) % 162.05/162.44 (declare-const tptp.x tptp.frac) % 162.05/162.44 (define @t1 () (_ tptp.den tptp.x)) % 162.05/162.44 (define @t2 () (_ tptp.ts (_ tptp.num tptp.y))) % 162.05/162.44 (define @t3 () (_ tptp.den tptp.y)) % 162.05/162.44 (define @t4 () (_ tptp.ts (_ tptp.num tptp.x))) % 162.05/162.44 (define @t5 () (_ (_ tptp.more (_ @t4 @t3)) (_ @t2 @t1))) % 162.05/162.44 (define @t6 () (_ tptp.ts (_ tptp.num tptp.z))) % 162.05/162.44 (define @t7 () (_ tptp.den tptp.z)) % 162.05/162.44 (define @t8 () (= (_ @t4 @t7) (_ @t6 @t1))) % 162.05/162.44 (define @t9 () (_ tptp.ts (_ tptp.num tptp.u))) % 162.05/162.44 (define @t10 () (_ tptp.den tptp.u)) % 162.05/162.44 (define @t11 () (= (_ @t2 @t10) (_ @t9 @t3))) % 162.05/162.44 (define @t12 () (@var "Xy" tptp.nat)) % 162.05/162.44 (define @t13 () (@var "Xx" tptp.nat)) % 162.05/162.44 (define @t14 () (_ (_ tptp.more @t13) @t12)) % 162.05/162.44 (define @t15 () (@var "Xz" tptp.nat)) % 162.05/162.44 (define @t16 () (_ tptp.ts @t12)) % 162.05/162.44 (define @t17 () (_ @t16 @t15)) % 162.05/162.44 (define @t18 () (_ tptp.ts @t13)) % 162.05/162.44 (define @t19 () (_ @t18 @t15)) % 162.05/162.44 (define @t20 () (_ (_ tptp.more @t19) @t17)) % 162.05/162.44 (define @t21 () (@list @t13 @t12 @t15)) % 162.05/162.44 (define @t22 () (forall @t21 (=> @t20 @t14))) % 162.05/162.44 (define @t23 () (_ tptp.ts @t15)) % 162.05/162.44 (define @t24 () (_ @t23 @t12)) % 162.05/162.44 (define @t25 () (_ @t23 @t13)) % 162.05/162.44 (define @t26 () (_ (_ tptp.more @t25) @t24)) % 162.05/162.44 (define @t27 () (forall @t21 (=> @t14 @t26))) % 162.05/162.44 (define @t28 () (_ @t16 @t13)) % 162.05/162.44 (define @t29 () (_ @t18 @t12)) % 162.05/162.44 (define @t30 () (= @t29 @t28)) % 162.05/162.44 (define @t31 () (@list @t13 @t12)) % 162.05/162.44 (define @t32 () (forall @t31 @t30)) % 162.05/162.44 (define @t33 () (_ @t18 @t17)) % 162.05/162.44 (define @t34 () (_ (_ tptp.ts @t29) @t15)) % 162.05/162.44 (define @t35 () (= @t34 @t33)) % 162.05/162.44 (define @t36 () (forall @t21 @t35)) % 162.05/162.44 (define @t37 () (@var "Xy" tptp.frac)) % 162.05/162.44 (define @t38 () (@var "Xx" tptp.frac)) % 162.05/162.44 (define @t39 () (_ (_ tptp.ts (_ tptp.num @t38)) (_ tptp.den @t37))) % 162.05/162.44 (define @t40 () (_ (_ tptp.ts (_ tptp.num @t37)) (_ tptp.den @t38))) % 162.05/162.44 (define @t41 () (not (_ (_ tptp.more (_ @t6 @t10)) (_ @t9 @t7)))) % 162.05/162.44 (define @t42 () (@const 0 (@ho-elim-sort (-> tptp.nat tptp.nat Bool)))) % 162.05/162.44 (define @t43 () (@const 1 (-> (@ho-elim-sort (-> tptp.nat tptp.nat Bool)) tptp.nat (@ho-elim-sort (-> tptp.nat Bool))))) % 162.05/162.44 (define @t44 () (@const 2 (-> (@ho-elim-sort (-> tptp.nat Bool)) tptp.nat Bool))) % 162.05/162.44 (define @t45 () (_ @t44 (_ @t43 @t42 @t13) @t12)) % 162.05/162.44 (define @t46 () (@const 3 (@ho-elim-sort (-> tptp.nat tptp.nat tptp.nat)))) % 162.05/162.44 (define @t47 () (@const 4 (-> (@ho-elim-sort (-> tptp.nat tptp.nat tptp.nat)) tptp.nat (@ho-elim-sort (-> tptp.nat tptp.nat))))) % 162.05/162.44 (define @t48 () (_ @t47 @t46 @t12)) % 162.05/162.44 (define @t49 () (@const 5 (-> (@ho-elim-sort (-> tptp.nat tptp.nat)) tptp.nat tptp.nat))) % 162.05/162.44 (define @t50 () (_ @t49 @t48 @t15)) % 162.05/162.44 (define @t51 () (_ @t47 @t46 @t13)) % 162.05/162.44 (define @t52 () (tptp.more @t13 @t12)) % 162.05/162.44 (define @t53 () (tptp.ts @t12 @t15)) % 162.05/162.44 (define @t54 () (tptp.ts @t13 @t15)) % 162.05/162.44 (define @t55 () (tptp.more @t54 @t53)) % 162.05/162.44 (define @t56 () (not @t20)) % 162.05/162.44 (define @t57 () (or @t56 @t14)) % 162.05/162.44 (define @t58 () (@const 6 (@ho-elim-sort (-> tptp.frac tptp.nat)))) % 162.05/162.44 (define @t59 () (@const 7 (-> (@ho-elim-sort (-> tptp.frac tptp.nat)) tptp.frac tptp.nat))) % 162.05/162.44 (define @t60 () (_ @t59 @t58 tptp.x)) % 162.05/162.44 (define @t61 () (@const 8 (@ho-elim-sort (-> tptp.frac tptp.nat)))) % 162.05/162.44 (define @t62 () (_ @t59 @t61 tptp.y)) % 162.05/162.44 (define @t63 () (_ @t47 @t46 @t62)) % 162.05/162.44 (define @t64 () (_ @t49 @t63 @t60)) % 162.05/162.44 (define @t65 () (_ @t59 @t58 tptp.z)) % 162.05/162.44 (define @t66 () (_ @t59 @t61 tptp.u)) % 162.05/162.44 (define @t67 () (_ @t47 @t46 @t66)) % 162.05/162.44 (define @t68 () (_ @t49 @t67 @t65)) % 162.05/162.44 (define @t69 () (_ @t59 @t58 tptp.u)) % 162.05/162.44 (define @t70 () (_ @t59 @t61 tptp.z)) % 162.05/162.44 (define @t71 () (_ @t47 @t46 @t70)) % 162.05/162.44 (define @t72 () (_ @t49 @t71 @t69)) % 162.05/162.44 (define @t73 () (_ @t44 (_ @t43 @t42 @t72) @t68)) % 162.05/162.44 (define @t74 () (_ @t47 @t46 @t68)) % 162.05/162.44 (define @t75 () (_ @t49 @t74 @t64)) % 162.05/162.44 (define @t76 () (_ @t47 @t46 @t72)) % 162.05/162.44 (define @t77 () (not (_ @t44 (_ @t43 @t42 (_ @t49 @t76 @t64)) @t75))) % 162.05/162.44 (define @t78 () (or @t77 @t73)) % 162.05/162.44 (define @t79 () (_ @t49 @t51 @t12)) % 162.05/162.44 (define @t80 () (_ @t49 @t48 @t13)) % 162.05/162.44 (define @t81 () (forall @t31 (= @t79 @t80))) % 162.05/162.44 (define @t82 () (tptp.ts @t12 @t13)) % 162.05/162.44 (define @t83 () (tptp.ts @t13 @t12)) % 162.05/162.44 (define @t84 () (_ @t47 @t46 @t69)) % 162.05/162.44 (define @t85 () (_ @t47 @t46 (_ @t49 @t84 @t70))) % 162.05/162.44 (define @t86 () (_ @t49 (_ @t47 @t46 @t60) @t62)) % 162.05/162.44 (define @t87 () (_ @t49 (_ @t47 @t46 @t79) @t15)) % 162.05/162.44 (define @t88 () (_ @t49 @t51 @t50)) % 162.05/162.44 (define @t89 () (forall @t21 (= @t87 @t88))) % 162.05/162.44 (define @t90 () (tptp.ts @t13 @t53)) % 162.05/162.44 (define @t91 () (tptp.ts @t83 @t15)) % 162.05/162.44 (define @t92 () (_ @t59 @t61 tptp.x)) % 162.05/162.44 (define @t93 () (_ @t47 @t46 @t92)) % 162.05/162.44 (define @t94 () (_ @t49 @t93 @t65)) % 162.05/162.44 (define @t95 () (_ @t49 @t71 @t60)) % 162.05/162.44 (define @t96 () (_ @t47 @t46 @t65)) % 162.05/162.44 (define @t97 () (_ @t49 @t96 @t92)) % 162.05/162.44 (define @t98 () (_ @t47 @t46 @t97)) % 162.05/162.44 (define @t99 () (_ @t49 @t98 @t62)) % 162.05/162.44 (define @t100 () (_ @t47 @t46 (_ @t49 @t63 @t65))) % 162.05/162.44 (define @t101 () (_ @t49 @t100 @t92)) % 162.05/162.44 (define @t102 () (_ @t47 @t46 @t94)) % 162.05/162.44 (define @t103 () (_ @t49 @t93 (_ @t49 @t84 @t65))) % 162.05/162.44 (define @t104 () (_ @t49 @t98 @t69)) % 162.05/162.44 (define @t105 () (_ @t47 @t46 @t104)) % 162.05/162.44 (define @t106 () (_ @t49 @t63 @t69)) % 162.05/162.44 (define @t107 () (_ @t59 @t58 tptp.y)) % 162.05/162.44 (define @t108 () (_ @t49 @t67 @t107)) % 162.05/162.44 (define @t109 () (_ @t47 @t46 (_ @t49 @t74 @t92))) % 162.05/162.44 (define @t110 () (_ @t49 @t93 @t107)) % 162.05/162.44 (define @t111 () (_ @t43 @t42 (_ @t49 @t74 @t110))) % 162.05/162.44 (define @t112 () (_ @t44 @t111 @t75)) % 162.05/162.44 (define @t113 () (_ @t47 @t46 @t15)) % 162.05/162.44 (define @t114 () (tptp.ts @t15 @t12)) % 162.05/162.44 (define @t115 () (tptp.ts @t15 @t13)) % 162.05/162.44 (define @t116 () (tptp.more @t115 @t114)) % 162.05/162.44 (define @t117 () (not @t14)) % 162.05/162.44 (define @t118 () (or @t117 @t26)) % 162.05/162.44 (define @t119 () (_ @t44 (_ @t43 @t42 @t110) @t64)) % 162.05/162.44 (define @t120 () (not @t119)) % 162.05/162.44 (define @t121 () (or @t120 @t112)) % 162.05/162.44 (assume @p1 @t5) % 162.05/162.44 (assume @p2 @t8) % 162.05/162.44 (assume @p3 @t11) % 162.05/162.44 (assume @p4 @t22) % 162.05/162.44 (assume @p5 @t27) % 162.05/162.44 (assume @p6 @t32) % 162.05/162.44 (assume @p7 @t36) % 162.05/162.44 (assume @p8 (forall (@list @t38 @t37) (=> (= @t39 @t40) (= @t40 @t39)))) % 162.05/162.44 (assume @p9 @t41) % 162.05/162.44 (assume @p10 true) % 162.05/162.44 (step @p11 :rule evaluate :args ((= true false))) % 162.05/162.44 ; WARNING: add trust step for TRUST % 162.05/162.44 ; trust TRUST PREPROCESS_HO_ELIM % 162.05/162.44 (step @p12 :rule trust :premises () :args ((= (forall @t21 (or (not @t55) @t52)) (forall @t21 (or (not (_ @t44 (_ @t43 @t42 (_ @t49 @t51 @t15)) @t50)) @t45))))) % 162.05/162.44 (step @p13 :rule refl :args (@t52)) % 162.05/162.44 (step @p14 :rule refl :args (@t14)) % 162.05/162.44 (step @p15 :rule cong :premises (@p14 @p13) :args ((= @t14 @t52))) % 162.05/162.44 (step @p16 :rule symm :premises (@p15)) % 162.05/162.44 (step @p17 :rule eq_resolve :premises (@p14 @p16)) % 162.05/162.44 (step @p18 :rule refl :args ((tptp.more @t19 @t17))) % 162.05/162.44 (step @p19 :rule refl :args (@t53)) % 162.05/162.44 (step @p20 :rule refl :args (@t54)) % 162.05/162.44 (step @p21 :rule cong :premises (@p20 @p19) :args (@t55)) % 162.05/162.44 (step @p22 :rule trans :premises (@p21 @p18)) % 162.05/162.44 (step @p23 :rule refl :args (tptp.more)) % 162.05/162.44 (step @p24 :rule ho_cong :premises (@p23 @p20)) % 162.05/162.44 (step @p25 :rule ho_cong :premises (@p24 @p19)) % 162.05/162.44 (step @p26 :rule cong :premises (@p25 @p22) :args ((= (_ (_ tptp.more @t54) @t53) @t55))) % 162.05/162.44 (step @p27 :rule symm :premises (@p26)) % 162.05/162.44 (step @p28 :rule refl :args (@t20)) % 162.05/162.44 (step @p29 :rule eq_resolve :premises (@p28 @p27)) % 162.05/162.44 (step @p30 :rule refl :args (@t17)) % 162.05/162.44 (step @p31 :rule cong :premises (@p30 @p19) :args ((= @t17 @t53))) % 162.05/162.44 (step @p32 :rule symm :premises (@p31)) % 162.05/162.44 (step @p33 :rule eq_resolve :premises (@p30 @p32)) % 162.05/162.44 (step @p34 :rule refl :args (@t19)) % 162.05/162.44 (step @p35 :rule cong :premises (@p34 @p20) :args ((= @t19 @t54))) % 162.05/162.44 (step @p36 :rule symm :premises (@p35)) % 162.05/162.44 (step @p37 :rule eq_resolve :premises (@p34 @p36)) % 162.05/162.44 (step @p38 :rule ho_cong :premises (@p23 @p37)) % 162.05/162.44 (step @p39 :rule ho_cong :premises (@p38 @p33)) % 162.05/162.44 (step @p40 :rule trans :premises (@p39 @p29)) % 162.05/162.44 (step @p41 :rule cong :premises (@p40) :args (@t56)) % 162.05/162.44 (step @p42 :rule nary_cong :premises (@p41 @p17) :args (@t57)) % 162.05/162.44 (step @p43 :rule cong :premises (@p42) :args ((forall @t21 @t57))) % 162.05/162.44 (step @p44 :rule bool-impl-elim :args (@t20 @t14)) % 162.05/162.44 (step @p45 :rule cong :premises (@p44) :args (@t22)) % 162.05/162.44 (step @p46 :rule trans :premises (@p45 @p43)) % 162.05/162.44 (step @p47 :rule trans :premises (@p46 @p12)) % 162.05/162.44 (step @p48 :rule eq_resolve :premises (@p4 @p47)) % 162.05/162.44 (step @p49 :rule instantiate :premises (@p48) :args ((@list @t72 @t68 @t64))) % 162.05/162.44 ; trust TRUST PREPROCESS_HO_ELIM % 162.05/162.44 (step @p50 :rule trust :premises () :args ((= @t41 (not @t73)))) % 162.05/162.44 (step @p51 :rule eq_resolve :premises (@p9 @p50)) % 162.05/162.44 (step @p52 :rule cnf_or_pos :args (@t78)) % 162.05/162.44 (step @p53 :rule reordering :premises (@p52) :args ((or @t73 @t77 (not @t78)))) % 162.05/162.44 (step @p54 :rule chain_m_resolution :premises (@p53 @p51 @p49) :args (@t77 (@list true false) (@list @t73 @t78))) % 162.05/162.44 (step @p55 :rule false_intro :premises (@p54)) % 162.05/162.44 (step @p56 :rule refl :args (@t75)) % 162.05/162.44 (step @p57 :rule refl :args (@t64)) % 162.05/162.44 (step @p58 :rule eq-symm :args (@t79 @t80)) % 162.05/162.44 (step @p59 :rule cong :premises (@p58) :args (@t81)) % 162.05/162.44 ; trust TRUST PREPROCESS_HO_ELIM % 162.05/162.44 (step @p60 :rule trust :premises () :args ((= (forall @t31 (= @t83 @t82)) @t81))) % 162.05/162.44 (step @p61 :rule refl :args (@t82)) % 162.05/162.44 (step @p62 :rule refl :args (@t28)) % 162.05/162.44 (step @p63 :rule cong :premises (@p62 @p61) :args ((= @t28 @t82))) % 162.05/162.44 (step @p64 :rule symm :premises (@p63)) % 162.05/162.44 (step @p65 :rule eq_resolve :premises (@p62 @p64)) % 162.05/162.44 (step @p66 :rule refl :args (@t83)) % 162.05/162.44 (step @p67 :rule refl :args (@t29)) % 162.05/162.44 (step @p68 :rule cong :premises (@p67 @p66) :args ((= @t29 @t83))) % 162.05/162.44 (step @p69 :rule symm :premises (@p68)) % 162.05/162.44 (step @p70 :rule eq_resolve :premises (@p67 @p69)) % 162.05/162.44 (step @p71 :rule cong :premises (@p70 @p65) :args (@t30)) % 162.05/162.44 (step @p72 :rule cong :premises (@p71) :args (@t32)) % 162.05/162.44 (step @p73 :rule trans :premises (@p72 @p60 @p59)) % 162.05/162.44 (step @p74 :rule eq_resolve :premises (@p6 @p73)) % 162.05/162.44 (step @p75 :rule instantiate :premises (@p74) :args ((@list @t69 @t70))) % 162.05/162.44 (step @p76 :rule symm :premises (@p75)) % 162.05/162.44 (step @p77 :rule refl :args (@t46)) % 162.05/162.44 (step @p78 :rule cong :premises (@p77 @p76) :args (@t85)) % 162.05/162.44 (step @p79 :rule cong :premises (@p78 @p57) :args ((_ @t49 @t85 @t64))) % 162.05/162.44 (step @p80 :rule instantiate :premises (@p74) :args ((@list @t60 @t62))) % 162.05/162.44 (step @p81 :rule symm :premises (@p80)) % 162.05/162.44 (step @p82 :rule refl :args (@t85)) % 162.05/162.44 (step @p83 :rule cong :premises (@p82 @p81) :args ((_ @t49 @t85 @t86))) % 162.05/162.44 (step @p84 :rule eq-symm :args (@t87 @t88)) % 162.05/162.44 (step @p85 :rule cong :premises (@p84) :args (@t89)) % 162.05/162.44 ; trust TRUST PREPROCESS_HO_ELIM % 162.05/162.44 (step @p86 :rule trust :premises () :args ((= (forall @t21 (= @t91 @t90)) @t89))) % 162.05/162.44 (step @p87 :rule refl :args ((tptp.ts @t13 @t17))) % 162.05/162.44 (step @p88 :rule refl :args (@t13)) % 162.05/162.44 (step @p89 :rule cong :premises (@p88 @p19) :args (@t90)) % 162.05/162.44 (step @p90 :rule trans :premises (@p89 @p87)) % 162.05/162.44 (step @p91 :rule refl :args (@t18)) % 162.05/162.44 (step @p92 :rule ho_cong :premises (@p91 @p19)) % 162.05/162.44 (step @p93 :rule cong :premises (@p92 @p90) :args ((= (_ @t18 @t53) @t90))) % 162.05/162.44 (step @p94 :rule symm :premises (@p93)) % 162.05/162.44 (step @p95 :rule refl :args (@t33)) % 162.05/162.44 (step @p96 :rule eq_resolve :premises (@p95 @p94)) % 162.05/162.44 (step @p97 :rule ho_cong :premises (@p91 @p33)) % 162.05/162.44 (step @p98 :rule trans :premises (@p97 @p96)) % 162.05/162.44 (step @p99 :rule refl :args ((tptp.ts @t29 @t15))) % 162.05/162.44 (step @p100 :rule refl :args (@t15)) % 162.05/162.44 (step @p101 :rule cong :premises (@p66 @p100) :args (@t91)) % 162.05/162.44 (step @p102 :rule trans :premises (@p101 @p99)) % 162.05/162.44 (step @p103 :rule refl :args (tptp.ts)) % 162.05/162.44 (step @p104 :rule ho_cong :premises (@p103 @p66)) % 162.05/162.44 (step @p105 :rule ho_cong :premises (@p104 @p100)) % 162.05/162.44 (step @p106 :rule cong :premises (@p105 @p102) :args ((= (_ (_ tptp.ts @t83) @t15) @t91))) % 162.05/162.44 (step @p107 :rule symm :premises (@p106)) % 162.05/162.44 (step @p108 :rule refl :args (@t34)) % 162.05/162.44 (step @p109 :rule eq_resolve :premises (@p108 @p107)) % 162.05/162.44 (step @p110 :rule ho_cong :premises (@p103 @p70)) % 162.05/162.44 (step @p111 :rule ho_cong :premises (@p110 @p100)) % 162.05/162.44 (step @p112 :rule trans :premises (@p111 @p109)) % 162.05/162.44 (step @p113 :rule cong :premises (@p112 @p98) :args (@t35)) % 162.05/162.44 (step @p114 :rule cong :premises (@p113) :args (@t36)) % 162.05/162.44 (step @p115 :rule trans :premises (@p114 @p86 @p85)) % 162.05/162.44 (step @p116 :rule eq_resolve :premises (@p7 @p115)) % 162.05/162.44 (step @p117 :rule instantiate :premises (@p116) :args ((@list @t69 @t70 @t86))) % 162.05/162.44 (step @p118 :rule instantiate :premises (@p116) :args ((@list @t70 @t60 @t62))) % 162.05/162.44 (step @p119 :rule symm :premises (@p118)) % 162.05/162.44 (step @p120 :rule refl :args (@t62)) % 162.05/162.44 (step @p121 :rule eq-symm :args (@t94 @t95)) % 162.05/162.44 ; trust TRUST PREPROCESS_HO_ELIM % 162.05/162.44 (step @p122 :rule trust :premises () :args ((= @t8 (= @t94 @t95)))) % 162.05/162.44 (step @p123 :rule trans :premises (@p122 @p121)) % 162.05/162.44 (step @p124 :rule eq_resolve :premises (@p2 @p123)) % 162.05/162.44 (step @p125 :rule symm :premises (@p124)) % 162.05/162.44 (step @p126 :rule instantiate :premises (@p74) :args ((@list @t65 @t92))) % 162.05/162.44 (step @p127 :rule symm :premises (@p126)) % 162.05/162.44 (step @p128 :rule trans :premises (@p127 @p125)) % 162.05/162.44 (step @p129 :rule cong :premises (@p77 @p128) :args (@t98)) % 162.05/162.44 (step @p130 :rule cong :premises (@p129 @p120) :args (@t99)) % 162.05/162.44 (step @p131 :rule instantiate :premises (@p116) :args ((@list @t65 @t92 @t62))) % 162.05/162.44 (step @p132 :rule instantiate :premises (@p74) :args ((@list @t92 @t62))) % 162.05/162.44 (step @p133 :rule refl :args (@t96)) % 162.05/162.44 (step @p134 :rule cong :premises (@p133 @p132) :args ((_ @t49 @t96 (_ @t49 @t63 @t92)))) % 162.05/162.44 (step @p135 :rule instantiate :premises (@p116) :args ((@list @t65 @t62 @t92))) % 162.05/162.44 (step @p136 :rule symm :premises (@p135)) % 162.05/162.44 (step @p137 :rule refl :args (@t92)) % 162.05/162.44 (step @p138 :rule instantiate :premises (@p74) :args ((@list @t65 @t62))) % 162.05/162.44 (step @p139 :rule cong :premises (@p77 @p138) :args (@t100)) % 162.05/162.44 (step @p140 :rule cong :premises (@p139 @p137) :args (@t101)) % 162.05/162.44 (step @p141 :rule trans :premises (@p140 @p136 @p134 @p131 @p130 @p119)) % 162.05/162.44 (step @p142 :rule refl :args (@t84)) % 162.05/162.44 (step @p143 :rule cong :premises (@p142 @p141) :args ((_ @t49 @t84 @t101))) % 162.05/162.44 (step @p144 :rule symm :premises (@p140)) % 162.05/162.44 (step @p145 :rule symm :premises (@p134)) % 162.05/162.44 (step @p146 :rule symm :premises (@p131)) % 162.05/162.44 (step @p147 :rule trans :premises (@p146 @p145 @p135 @p144)) % 162.05/162.44 (step @p148 :rule cong :premises (@p142 @p147) :args ((_ @t49 @t84 @t99))) % 162.05/162.44 (step @p149 :rule instantiate :premises (@p116) :args ((@list @t69 @t97 @t62))) % 162.05/162.44 (step @p150 :rule symm :premises (@p149)) % 162.05/162.44 (step @p151 :rule symm :premises (@p128)) % 162.05/162.44 (step @p152 :rule cong :premises (@p142 @p151) :args ((_ @t49 @t84 @t95))) % 162.05/162.44 (step @p153 :rule instantiate :premises (@p116) :args ((@list @t69 @t70 @t60))) % 162.05/162.44 (step @p154 :rule symm :premises (@p153)) % 162.05/162.44 (step @p155 :rule refl :args (@t60)) % 162.05/162.44 (step @p156 :rule symm :premises (@p78)) % 162.05/162.44 (step @p157 :rule cong :premises (@p156 @p155) :args ((_ @t49 @t76 @t60))) % 162.05/162.44 (step @p158 :rule instantiate :premises (@p74) :args ((@list @t72 @t60))) % 162.05/162.44 (step @p159 :rule instantiate :premises (@p116) :args ((@list @t60 @t70 @t69))) % 162.05/162.44 (step @p160 :rule symm :premises (@p159)) % 162.05/162.44 (step @p161 :rule refl :args (@t69)) % 162.05/162.44 (step @p162 :rule instantiate :premises (@p74) :args ((@list @t60 @t70))) % 162.05/162.44 (step @p163 :rule trans :premises (@p127 @p125 @p162)) % 162.05/162.44 (step @p164 :rule cong :premises (@p77 @p163) :args (@t98)) % 162.05/162.44 (step @p165 :rule cong :premises (@p77 @p126) :args (@t102)) % 162.05/162.44 (step @p166 :rule trans :premises (@p165 @p164)) % 162.05/162.44 (step @p167 :rule cong :premises (@p166 @p161) :args ((_ @t49 @t102 @t69))) % 162.05/162.44 (step @p168 :rule instantiate :premises (@p116) :args ((@list @t92 @t65 @t69))) % 162.05/162.44 (step @p169 :rule instantiate :premises (@p74) :args ((@list @t65 @t69))) % 162.05/162.44 (step @p170 :rule refl :args (@t93)) % 162.05/162.44 (step @p171 :rule cong :premises (@p170 @p169) :args (@t103)) % 162.05/162.44 (step @p172 :rule trans :premises (@p171 @p168 @p167 @p160 @p158 @p157 @p154 @p152)) % 162.05/162.44 (step @p173 :rule cong :premises (@p77 @p172) :args ((_ @t47 @t46 @t103))) % 162.05/162.44 (step @p174 :rule symm :premises (@p171)) % 162.05/162.44 (step @p175 :rule symm :premises (@p168)) % 162.05/162.44 (step @p176 :rule symm :premises (@p165)) % 162.05/162.44 (step @p177 :rule cong :premises (@p176 @p161) :args (@t104)) % 162.05/162.44 (step @p178 :rule trans :premises (@p177 @p175 @p174)) % 162.05/162.44 (step @p179 :rule cong :premises (@p77 @p178) :args (@t105)) % 162.05/162.44 (step @p180 :rule trans :premises (@p179 @p173)) % 162.05/162.44 (step @p181 :rule cong :premises (@p180 @p120) :args ((_ @t49 @t105 @t62))) % 162.05/162.44 (step @p182 :rule instantiate :premises (@p116) :args ((@list @t97 @t69 @t62))) % 162.05/162.44 (step @p183 :rule trans :premises (@p182 @p181 @p150 @p148 @p143 @p117 @p83 @p79)) % 162.05/162.44 (step @p184 :rule refl :args (@t42)) % 162.05/162.44 (step @p185 :rule cong :premises (@p184 @p183) :args ((_ @t43 @t42 (_ @t49 @t98 (_ @t49 @t84 @t62))))) % 162.05/162.44 (step @p186 :rule instantiate :premises (@p74) :args ((@list @t69 @t62))) % 162.05/162.44 (step @p187 :rule refl :args (@t98)) % 162.05/162.44 (step @p188 :rule cong :premises (@p187 @p186) :args ((_ @t49 @t98 @t106))) % 162.05/162.44 (step @p189 :rule eq-symm :args (@t106 @t108)) % 162.05/162.44 ; trust TRUST PREPROCESS_HO_ELIM % 162.05/162.44 (step @p190 :rule trust :premises () :args ((= @t11 (= @t106 @t108)))) % 162.05/162.44 (step @p191 :rule trans :premises (@p190 @p189)) % 162.05/162.44 (step @p192 :rule eq_resolve :premises (@p3 @p191)) % 162.05/162.44 (step @p193 :rule cong :premises (@p187 @p192) :args ((_ @t49 @t98 @t108))) % 162.05/162.44 (step @p194 :rule instantiate :premises (@p116) :args ((@list @t97 @t66 @t107))) % 162.05/162.44 (step @p195 :rule symm :premises (@p194)) % 162.05/162.44 (step @p196 :rule refl :args (@t107)) % 162.05/162.44 (step @p197 :rule refl :args (@t66)) % 162.05/162.44 (step @p198 :rule cong :premises (@p165 @p197) :args ((_ @t49 @t102 @t66))) % 162.05/162.44 (step @p199 :rule instantiate :premises (@p116) :args ((@list @t92 @t65 @t66))) % 162.05/162.44 (step @p200 :rule instantiate :premises (@p74) :args ((@list @t65 @t66))) % 162.05/162.44 (step @p201 :rule cong :premises (@p170 @p200) :args ((_ @t49 @t93 @t68))) % 162.05/162.44 (step @p202 :rule instantiate :premises (@p74) :args ((@list @t68 @t92))) % 162.05/162.44 (step @p203 :rule symm :premises (@p202)) % 162.05/162.44 (step @p204 :rule trans :premises (@p203 @p201 @p199 @p198)) % 162.05/162.44 (step @p205 :rule cong :premises (@p77 @p204) :args (@t109)) % 162.05/162.44 (step @p206 :rule cong :premises (@p205 @p196) :args ((_ @t49 @t109 @t107))) % 162.05/162.44 (step @p207 :rule instantiate :premises (@p116) :args ((@list @t68 @t92 @t107))) % 162.05/162.44 (step @p208 :rule trans :premises (@p207 @p206 @p195 @p193 @p188)) % 162.05/162.44 (step @p209 :rule cong :premises (@p184 @p208) :args (@t111)) % 162.05/162.44 (step @p210 :rule trans :premises (@p209 @p185)) % 162.05/162.44 (step @p211 :rule cong :premises (@p210 @p56) :args (@t112)) % 162.05/162.44 ; trust TRUST PREPROCESS_HO_ELIM % 162.05/162.44 (step @p212 :rule trust :premises () :args ((= (forall @t21 (or (not @t52) @t116)) (forall @t21 (or (not @t45) (_ @t44 (_ @t43 @t42 (_ @t49 @t113 @t13)) (_ @t49 @t113 @t12))))))) % 162.05/162.44 (step @p213 :rule refl :args ((tptp.more @t25 @t24))) % 162.05/162.44 (step @p214 :rule refl :args (@t114)) % 162.05/162.44 (step @p215 :rule refl :args (@t115)) % 162.05/162.44 (step @p216 :rule cong :premises (@p215 @p214) :args (@t116)) % 162.05/162.44 (step @p217 :rule trans :premises (@p216 @p213)) % 162.05/162.44 (step @p218 :rule ho_cong :premises (@p23 @p215)) % 162.05/162.44 (step @p219 :rule ho_cong :premises (@p218 @p214)) % 162.05/162.44 (step @p220 :rule cong :premises (@p219 @p217) :args ((= (_ (_ tptp.more @t115) @t114) @t116))) % 162.05/162.44 (step @p221 :rule symm :premises (@p220)) % 162.05/162.44 (step @p222 :rule refl :args (@t26)) % 162.05/162.44 (step @p223 :rule eq_resolve :premises (@p222 @p221)) % 162.05/162.44 (step @p224 :rule refl :args (@t24)) % 162.05/162.44 (step @p225 :rule cong :premises (@p224 @p214) :args ((= @t24 @t114))) % 162.05/162.44 (step @p226 :rule symm :premises (@p225)) % 162.05/162.44 (step @p227 :rule eq_resolve :premises (@p224 @p226)) % 162.05/162.44 (step @p228 :rule refl :args (@t25)) % 162.05/162.44 (step @p229 :rule cong :premises (@p228 @p215) :args ((= @t25 @t115))) % 162.05/162.44 (step @p230 :rule symm :premises (@p229)) % 162.05/162.44 (step @p231 :rule eq_resolve :premises (@p228 @p230)) % 162.05/162.44 (step @p232 :rule ho_cong :premises (@p23 @p231)) % 162.05/162.44 (step @p233 :rule ho_cong :premises (@p232 @p227)) % 162.05/162.44 (step @p234 :rule trans :premises (@p233 @p223)) % 162.05/162.44 (step @p235 :rule cong :premises (@p17) :args (@t117)) % 162.05/162.44 (step @p236 :rule nary_cong :premises (@p235 @p234) :args (@t118)) % 162.05/162.44 (step @p237 :rule cong :premises (@p236) :args ((forall @t21 @t118))) % 162.05/162.44 (step @p238 :rule bool-impl-elim :args (@t14 @t26)) % 162.05/162.44 (step @p239 :rule cong :premises (@p238) :args (@t27)) % 162.05/162.44 (step @p240 :rule trans :premises (@p239 @p237)) % 162.05/162.44 (step @p241 :rule trans :premises (@p240 @p212)) % 162.05/162.44 (step @p242 :rule eq_resolve :premises (@p5 @p241)) % 162.05/162.44 (step @p243 :rule instantiate :premises (@p242) :args ((@list @t110 @t64 @t68))) % 162.05/162.44 ; trust TRUST PREPROCESS_HO_ELIM % 162.05/162.44 (step @p244 :rule trust :premises () :args ((= @t5 @t119))) % 162.05/162.44 (step @p245 :rule eq_resolve :premises (@p1 @p244)) % 162.05/162.44 (step @p246 :rule cnf_or_pos :args (@t121)) % 162.05/162.44 (step @p247 :rule reordering :premises (@p246) :args ((or @t120 @t112 (not @t121)))) % 162.05/162.44 (step @p248 :rule chain_m_resolution :premises (@p247 @p245 @p243) :args (@t112 (@list false false) (@list @t119 @t121))) % 162.05/162.44 (step @p249 :rule true_intro :premises (@p248)) % 162.05/162.44 (step @p250 :rule symm :premises (@p249)) % 162.05/162.44 (step @p251 :rule trans :premises (@p250 @p211 @p55)) % 162.05/162.44 (step @p252 false :rule eq_resolve :premises (@p251 @p11)) % 162.05/162.45 ) % 162.05/162.45 % SZS output end Proof % 162.05/162.45 % cvc5 exiting %------------------------------------------------------------------------------