0.08/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.08/0.12	% Command  : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 240 THM
0.14/0.33	% Computer : n029.cluster.edu
0.14/0.33	% Model    : x86_64 x86_64
0.14/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.33	% Memory   : 8042.1875MB
0.14/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.14/0.33	% CPULimit : 1920
0.14/0.33	% WCLimit  : 240
0.14/0.33	% DateTime : Sat Sep  6 01:37:07 EDT 2025
0.14/0.34	% CPUTime  : 
0.19/0.48	%----Proving TH0
121.87/122.30	--- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 72s...
121.87/122.30	--- 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 24s...
121.87/122.30	--- 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 24s...
121.87/122.30	--- Run --ho-elim --full-saturate-quant at 14s...
121.87/122.30	% SZS status Theorem
121.87/122.30	% SZS output start Proof
121.87/122.30	(
121.87/122.30	(declare-type tptp.frac ())
121.87/122.30	(declare-const tptp.eq (-> tptp.frac tptp.frac Bool))
121.87/122.30	(declare-const tptp.lessf (-> tptp.frac tptp.frac Bool))
121.87/122.30	(declare-const tptp.x tptp.frac)
121.87/122.30	(declare-const tptp.z tptp.frac)
121.87/122.30	(declare-const tptp.y tptp.frac)
121.87/122.30	(declare-const tptp.u tptp.frac)
121.87/122.30	(declare-const tptp.moref (-> tptp.frac tptp.frac Bool))
121.87/122.30	(declare-const tptp.pf (-> tptp.frac tptp.frac tptp.frac))
121.87/122.30	(define @t1 () (@var "Xz" tptp.frac))
121.87/122.30	(define @t2 () (@var "Xy" tptp.frac))
121.87/122.30	(define @t3 () (_ tptp.pf @t2))
121.87/122.30	(define @t4 () (_ @t3 @t1))
121.87/122.30	(define @t5 () (@var "Xx" tptp.frac))
121.87/122.30	(define @t6 () (_ tptp.pf @t5))
121.87/122.30	(define @t7 () (_ @t6 @t1))
121.87/122.30	(define @t8 () (_ (_ tptp.moref @t7) @t4))
121.87/122.30	(define @t9 () (_ (_ tptp.moref @t5) @t2))
121.87/122.30	(define @t10 () (@list @t5 @t2 @t1))
121.87/122.30	(define @t11 () (forall @t10 (=> @t9 @t8)))
121.87/122.30	(define @t12 () (not (_ (_ tptp.moref (_ (_ tptp.pf tptp.x) tptp.z)) (_ (_ tptp.pf tptp.y) tptp.u))))
121.87/122.30	(define @t13 () (_ tptp.lessf @t5))
121.87/122.30	(define @t14 () (_ @t13 @t1))
121.87/122.30	(define @t15 () (_ tptp.lessf @t2))
121.87/122.30	(define @t16 () (_ @t15 @t1))
121.87/122.30	(define @t17 () (=> @t16 @t14))
121.87/122.30	(define @t18 () (_ @t13 @t2))
121.87/122.30	(define @t19 () (forall @t10 (=> @t18 @t17)))
121.87/122.30	(define @t20 () (_ (_ tptp.moref @t2) @t5))
121.87/122.30	(define @t21 () (@list @t5 @t2))
121.87/122.30	(define @t22 () (forall @t21 (=> @t18 @t20)))
121.87/122.30	(define @t23 () (_ @t15 @t5))
121.87/122.30	(define @t24 () (forall @t21 (=> @t9 @t23)))
121.87/122.30	(define @t25 () (_ (_ tptp.moref tptp.z) tptp.u))
121.87/122.30	(define @t26 () (_ @t3 @t5))
121.87/122.30	(define @t27 () (_ @t6 @t2))
121.87/122.30	(define @t28 () (_ (_ tptp.eq @t27) @t26))
121.87/122.30	(define @t29 () (forall @t21 @t28))
121.87/122.30	(define @t30 () (@var "Xu" tptp.frac))
121.87/122.30	(define @t31 () (_ (_ tptp.moref @t1) @t30))
121.87/122.30	(define @t32 () (_ (_ tptp.eq @t2) @t30))
121.87/122.30	(define @t33 () (=> @t32 @t31))
121.87/122.30	(define @t34 () (_ (_ tptp.eq @t5) @t1))
121.87/122.30	(define @t35 () (=> @t34 @t33))
121.87/122.30	(define @t36 () (@list @t5 @t2 @t1 @t30))
121.87/122.30	(define @t37 () (forall @t36 (=> @t9 @t35)))
121.87/122.30	(define @t38 () (_ (_ tptp.moref tptp.x) tptp.y))
121.87/122.30	(define @t39 () (@const 0 (@ho-elim-sort (-> tptp.frac tptp.frac Bool))))
121.87/122.30	(define @t40 () (@const 1 (-> (@ho-elim-sort (-> tptp.frac tptp.frac Bool)) tptp.frac (@ho-elim-sort (-> tptp.frac Bool)))))
121.87/122.30	(define @t41 () (@const 2 (-> (@ho-elim-sort (-> tptp.frac Bool)) tptp.frac Bool)))
121.87/122.30	(define @t42 () (@const 3 (@ho-elim-sort (-> tptp.frac tptp.frac Bool))))
121.87/122.30	(define @t43 () (not (_ @t41 (_ @t40 @t39 @t5) @t2)))
121.87/122.30	(define @t44 () (forall @t36 (or @t43 (not (_ @t41 (_ @t40 @t42 @t5) @t1)) (not (_ @t41 (_ @t40 @t42 @t2) @t30)) (_ @t41 (_ @t40 @t39 @t1) @t30))))
121.87/122.30	(define @t45 () (tptp.moref @t1 @t30))
121.87/122.30	(define @t46 () (tptp.eq @t2 @t30))
121.87/122.30	(define @t47 () (tptp.eq @t5 @t1))
121.87/122.30	(define @t48 () (tptp.moref @t5 @t2))
121.87/122.30	(define @t49 () (not @t48))
121.87/122.30	(define @t50 () (not @t32))
121.87/122.30	(define @t51 () (not @t34))
121.87/122.30	(define @t52 () (not @t9))
121.87/122.30	(define @t53 () (or @t52 @t51 @t50 @t31))
121.87/122.30	(define @t54 () (or @t51 @t50 @t31))
121.87/122.30	(define @t55 () (@const 4 (@ho-elim-sort (-> tptp.frac tptp.frac Bool))))
121.87/122.30	(define @t56 () (_ @t40 @t55 @t2))
121.87/122.30	(define @t57 () (tptp.lessf @t2 @t5))
121.87/122.30	(define @t58 () (or @t52 @t23))
121.87/122.30	(define @t59 () (@const 5 (@ho-elim-sort (-> tptp.frac tptp.frac tptp.frac))))
121.87/122.30	(define @t60 () (@const 6 (-> (@ho-elim-sort (-> tptp.frac tptp.frac tptp.frac)) tptp.frac (@ho-elim-sort (-> tptp.frac tptp.frac)))))
121.87/122.30	(define @t61 () (_ @t60 @t59 tptp.y))
121.87/122.30	(define @t62 () (@const 7 (-> (@ho-elim-sort (-> tptp.frac tptp.frac)) tptp.frac tptp.frac)))
121.87/122.30	(define @t63 () (_ @t62 @t61 tptp.u))
121.87/122.30	(define @t64 () (_ @t62 @t61 tptp.z))
121.87/122.30	(define @t65 () (_ @t40 @t55 @t5))
121.87/122.30	(define @t66 () (not (_ @t41 @t65 @t2)))
121.87/122.30	(define @t67 () (tptp.lessf @t5 @t1))
121.87/122.30	(define @t68 () (tptp.lessf @t2 @t1))
121.87/122.30	(define @t69 () (tptp.lessf @t5 @t2))
121.87/122.30	(define @t70 () (not @t69))
121.87/122.30	(define @t71 () (not @t16))
121.87/122.30	(define @t72 () (not @t18))
121.87/122.30	(define @t73 () (or @t72 @t71 @t14))
121.87/122.30	(define @t74 () (_ @t62 (_ @t60 @t59 tptp.x) tptp.z))
121.87/122.30	(define @t75 () (_ @t60 @t59 @t2))
121.87/122.30	(define @t76 () (_ @t60 @t59 @t5))
121.87/122.30	(define @t77 () (tptp.pf @t2 @t1))
121.87/122.30	(define @t78 () (tptp.pf @t5 @t1))
121.87/122.30	(define @t79 () (tptp.moref @t78 @t77))
121.87/122.30	(define @t80 () (or @t52 @t8))
121.87/122.30	(define @t81 () (_ @t41 (_ @t40 @t39 tptp.x) tptp.y))
121.87/122.30	(define @t82 () (_ @t40 @t39 @t74))
121.87/122.30	(define @t83 () (_ @t41 @t82 @t64))
121.87/122.30	(define @t84 () (not @t81))
121.87/122.30	(define @t85 () (or @t84 @t83))
121.87/122.30	(define @t86 () (@list false false))
121.87/122.30	(define @t87 () (_ @t41 (_ @t40 @t55 @t64) @t74))
121.87/122.30	(define @t88 () (not @t83))
121.87/122.30	(define @t89 () (or @t88 @t87))
121.87/122.30	(define @t90 () (tptp.moref @t2 @t5))
121.87/122.30	(define @t91 () (or @t72 @t20))
121.87/122.30	(define @t92 () (_ @t41 @t82 @t63))
121.87/122.30	(define @t93 () (_ @t40 @t55 @t63))
121.87/122.30	(define @t94 () (_ @t41 @t93 @t74))
121.87/122.30	(define @t95 () (not @t94))
121.87/122.30	(define @t96 () (or @t95 @t92))
121.87/122.30	(define @t97 () (@list true false))
121.87/122.30	(define @t98 () (not @t87))
121.87/122.30	(define @t99 () (_ @t41 @t93 @t64))
121.87/122.30	(define @t100 () (not @t99))
121.87/122.30	(define @t101 () (or @t100 @t98 @t94))
121.87/122.30	(define @t102 () (_ @t41 (_ @t40 @t39 @t64) @t63))
121.87/122.30	(define @t103 () (not @t102))
121.87/122.30	(define @t104 () (or @t103 @t99))
121.87/122.30	(define @t105 () (tptp.pf @t2 @t5))
121.87/122.30	(define @t106 () (tptp.pf @t5 @t2))
121.87/122.30	(define @t107 () (tptp.eq @t106 @t105))
121.87/122.30	(define @t108 () (_ @t41 (_ @t40 @t39 tptp.z) tptp.u))
121.87/122.30	(define @t109 () (_ @t62 (_ @t60 @t59 tptp.u) tptp.y))
121.87/122.30	(define @t110 () (_ @t62 (_ @t60 @t59 tptp.z) tptp.y))
121.87/122.30	(define @t111 () (_ @t41 (_ @t40 @t39 @t110) @t109))
121.87/122.30	(define @t112 () (not @t108))
121.87/122.30	(define @t113 () (or @t112 @t111))
121.87/122.30	(define @t114 () (_ @t41 (_ @t40 @t42 @t109) @t63))
121.87/122.30	(define @t115 () (not @t114))
121.87/122.30	(define @t116 () (_ @t41 (_ @t40 @t42 @t110) @t64))
121.87/122.30	(define @t117 () (not @t116))
121.87/122.30	(define @t118 () (not @t111))
121.87/122.30	(define @t119 () (or @t118 @t117 @t115 @t102))
121.87/122.30	(assume @p1 @t11)
121.87/122.30	(assume @p2 @t12)
121.87/122.30	(assume @p3 @t19)
121.87/122.30	(assume @p4 @t22)
121.87/122.30	(assume @p5 @t24)
121.87/122.30	(assume @p6 @t25)
121.87/122.30	(assume @p7 @t29)
121.87/122.30	(assume @p8 @t37)
121.87/122.30	(assume @p9 @t38)
121.87/122.30	(assume @p10 true)
121.87/122.30	; WARNING: add trust step for TRUST
121.87/122.30	; trust TRUST PREPROCESS_HO_ELIM
121.87/122.30	(step @p11 :rule trust :premises () :args ((= (forall @t36 (or @t49 (not @t47) (not @t46) @t45)) @t44)))
121.87/122.30	(step @p12 :rule refl :args (@t45))
121.87/122.30	(step @p13 :rule refl :args (@t31))
121.87/122.30	(step @p14 :rule cong :premises (@p13 @p12) :args ((= @t31 @t45)))
121.87/122.30	(step @p15 :rule symm :premises (@p14))
121.87/122.30	(step @p16 :rule eq_resolve :premises (@p13 @p15))
121.87/122.30	(step @p17 :rule refl :args (@t46))
121.87/122.30	(step @p18 :rule refl :args (@t32))
121.87/122.30	(step @p19 :rule cong :premises (@p18 @p17) :args ((= @t32 @t46)))
121.87/122.30	(step @p20 :rule symm :premises (@p19))
121.87/122.30	(step @p21 :rule eq_resolve :premises (@p18 @p20))
121.87/122.30	(step @p22 :rule cong :premises (@p21) :args (@t50))
121.87/122.30	(step @p23 :rule refl :args (@t47))
121.87/122.30	(step @p24 :rule refl :args (@t34))
121.87/122.30	(step @p25 :rule cong :premises (@p24 @p23) :args ((= @t34 @t47)))
121.87/122.30	(step @p26 :rule symm :premises (@p25))
121.87/122.30	(step @p27 :rule eq_resolve :premises (@p24 @p26))
121.87/122.30	(step @p28 :rule cong :premises (@p27) :args (@t51))
121.87/122.30	(step @p29 :rule refl :args (@t48))
121.87/122.30	(step @p30 :rule refl :args (@t9))
121.87/122.30	(step @p31 :rule cong :premises (@p30 @p29) :args ((= @t9 @t48)))
121.87/122.30	(step @p32 :rule symm :premises (@p31))
121.87/122.30	(step @p33 :rule eq_resolve :premises (@p30 @p32))
121.87/122.30	(step @p34 :rule cong :premises (@p33) :args (@t52))
121.87/122.30	(step @p35 :rule nary_cong :premises (@p34 @p28 @p22 @p16) :args (@t53))
121.87/122.30	(step @p36 :rule cong :premises (@p35) :args ((forall @t36 @t53)))
121.87/122.30	(step @p37 :rule aci_norm :args ((= (or @t52 @t54) @t53)))
121.87/122.30	(step @p38 :rule aci_norm :args ((= (or @t51 (or @t50 @t31)) @t54)))
121.87/122.30	(step @p39 :rule bool-impl-elim :args (@t32 @t31))
121.87/122.30	(step @p40 :rule refl :args (@t51))
121.87/122.30	(step @p41 :rule nary_cong :premises (@p40 @p39) :args ((or @t51 @t33)))
121.87/122.30	(step @p42 :rule trans :premises (@p41 @p38))
121.87/122.30	(step @p43 :rule bool-impl-elim :args (@t34 @t33))
121.87/122.30	(step @p44 :rule trans :premises (@p43 @p42))
121.87/122.30	(step @p45 :rule refl :args (@t52))
121.87/122.30	(step @p46 :rule nary_cong :premises (@p45 @p44) :args ((or @t52 @t35)))
121.87/122.30	(step @p47 :rule trans :premises (@p46 @p37))
121.87/122.30	(step @p48 :rule bool-impl-elim :args (@t9 @t35))
121.87/122.30	(step @p49 :rule trans :premises (@p48 @p47))
121.87/122.30	(step @p50 :rule cong :premises (@p49) :args (@t37))
121.87/122.30	(step @p51 :rule trans :premises (@p50 @p36))
121.87/122.30	(step @p52 :rule trans :premises (@p51 @p11))
121.87/122.30	(step @p53 :rule eq_resolve :premises (@p8 @p52))
121.87/122.30	; trust TRUST PREPROCESS_HO_ELIM
121.87/122.30	(step @p54 :rule trust :premises () :args ((= (forall @t21 (or @t49 @t57)) (forall @t21 (or @t43 (_ @t41 @t56 @t5))))))
121.87/122.30	(step @p55 :rule refl :args (@t57))
121.87/122.30	(step @p56 :rule refl :args (@t23))
121.87/122.30	(step @p57 :rule cong :premises (@p56 @p55) :args ((= @t23 @t57)))
121.87/122.30	(step @p58 :rule symm :premises (@p57))
121.87/122.30	(step @p59 :rule eq_resolve :premises (@p56 @p58))
121.87/122.30	(step @p60 :rule nary_cong :premises (@p34 @p59) :args (@t58))
121.87/122.30	(step @p61 :rule cong :premises (@p60) :args ((forall @t21 @t58)))
121.87/122.30	(step @p62 :rule bool-impl-elim :args (@t9 @t23))
121.87/122.30	(step @p63 :rule cong :premises (@p62) :args (@t24))
121.87/122.30	(step @p64 :rule trans :premises (@p63 @p61))
121.87/122.30	(step @p65 :rule trans :premises (@p64 @p54))
121.87/122.30	(step @p66 :rule eq_resolve :premises (@p5 @p65))
121.87/122.30	(step @p67 :rule instantiate :premises (@p66) :args ((@list @t64 @t63)))
121.87/122.30	; trust TRUST PREPROCESS_HO_ELIM
121.87/122.30	(step @p68 :rule trust :premises () :args ((= (forall @t10 (or @t70 (not @t68) @t67)) (forall @t10 (or @t66 (not (_ @t41 @t56 @t1)) (_ @t41 @t65 @t1))))))
121.87/122.30	(step @p69 :rule refl :args (@t67))
121.87/122.30	(step @p70 :rule refl :args (@t14))
121.87/122.30	(step @p71 :rule cong :premises (@p70 @p69) :args ((= @t14 @t67)))
121.87/122.30	(step @p72 :rule symm :premises (@p71))
121.87/122.30	(step @p73 :rule eq_resolve :premises (@p70 @p72))
121.87/122.30	(step @p74 :rule refl :args (@t68))
121.87/122.30	(step @p75 :rule refl :args (@t16))
121.87/122.30	(step @p76 :rule cong :premises (@p75 @p74) :args ((= @t16 @t68)))
121.87/122.30	(step @p77 :rule symm :premises (@p76))
121.87/122.30	(step @p78 :rule eq_resolve :premises (@p75 @p77))
121.87/122.30	(step @p79 :rule cong :premises (@p78) :args (@t71))
121.87/122.30	(step @p80 :rule refl :args (@t69))
121.87/122.30	(step @p81 :rule refl :args (@t18))
121.87/122.30	(step @p82 :rule cong :premises (@p81 @p80) :args ((= @t18 @t69)))
121.87/122.30	(step @p83 :rule symm :premises (@p82))
121.87/122.30	(step @p84 :rule eq_resolve :premises (@p81 @p83))
121.87/122.30	(step @p85 :rule cong :premises (@p84) :args (@t72))
121.87/122.30	(step @p86 :rule nary_cong :premises (@p85 @p79 @p73) :args (@t73))
121.87/122.30	(step @p87 :rule cong :premises (@p86) :args ((forall @t10 @t73)))
121.87/122.30	(step @p88 :rule aci_norm :args ((= (or @t72 (or @t71 @t14)) @t73)))
121.87/122.30	(step @p89 :rule bool-impl-elim :args (@t16 @t14))
121.87/122.30	(step @p90 :rule refl :args (@t72))
121.87/122.30	(step @p91 :rule nary_cong :premises (@p90 @p89) :args ((or @t72 @t17)))
121.87/122.30	(step @p92 :rule trans :premises (@p91 @p88))
121.87/122.30	(step @p93 :rule bool-impl-elim :args (@t18 @t17))
121.87/122.30	(step @p94 :rule trans :premises (@p93 @p92))
121.87/122.30	(step @p95 :rule cong :premises (@p94) :args (@t19))
121.87/122.30	(step @p96 :rule trans :premises (@p95 @p87))
121.87/122.30	(step @p97 :rule trans :premises (@p96 @p68))
121.87/122.30	(step @p98 :rule eq_resolve :premises (@p3 @p97))
121.87/122.30	(step @p99 :rule instantiate :premises (@p98) :args ((@list @t63 @t64 @t74)))
121.87/122.30	(step @p100 :rule instantiate :premises (@p66) :args ((@list @t74 @t64)))
121.87/122.30	; trust TRUST PREPROCESS_HO_ELIM
121.87/122.30	(step @p101 :rule trust :premises () :args ((= (forall @t10 (or @t49 @t79)) (forall @t10 (or @t43 (_ @t41 (_ @t40 @t39 (_ @t62 @t76 @t1)) (_ @t62 @t75 @t1)))))))
121.87/122.30	(step @p102 :rule refl :args ((tptp.moref @t7 @t4)))
121.87/122.30	(step @p103 :rule refl :args (@t77))
121.87/122.30	(step @p104 :rule refl :args (@t78))
121.87/122.30	(step @p105 :rule cong :premises (@p104 @p103) :args (@t79))
121.87/122.30	(step @p106 :rule trans :premises (@p105 @p102))
121.87/122.30	(step @p107 :rule refl :args (tptp.moref))
121.87/122.30	(step @p108 :rule ho_cong :premises (@p107 @p104))
121.87/122.30	(step @p109 :rule ho_cong :premises (@p108 @p103))
121.87/122.30	(step @p110 :rule cong :premises (@p109 @p106) :args ((= (_ (_ tptp.moref @t78) @t77) @t79)))
121.87/122.30	(step @p111 :rule symm :premises (@p110))
121.87/122.30	(step @p112 :rule refl :args (@t8))
121.87/122.30	(step @p113 :rule eq_resolve :premises (@p112 @p111))
121.87/122.30	(step @p114 :rule refl :args (@t4))
121.87/122.30	(step @p115 :rule cong :premises (@p114 @p103) :args ((= @t4 @t77)))
121.87/122.30	(step @p116 :rule symm :premises (@p115))
121.87/122.30	(step @p117 :rule eq_resolve :premises (@p114 @p116))
121.87/122.30	(step @p118 :rule refl :args (@t7))
121.87/122.30	(step @p119 :rule cong :premises (@p118 @p104) :args ((= @t7 @t78)))
121.87/122.30	(step @p120 :rule symm :premises (@p119))
121.87/122.30	(step @p121 :rule eq_resolve :premises (@p118 @p120))
121.87/122.30	(step @p122 :rule ho_cong :premises (@p107 @p121))
121.87/122.30	(step @p123 :rule ho_cong :premises (@p122 @p117))
121.87/122.30	(step @p124 :rule trans :premises (@p123 @p113))
121.87/122.30	(step @p125 :rule nary_cong :premises (@p34 @p124) :args (@t80))
121.87/122.30	(step @p126 :rule cong :premises (@p125) :args ((forall @t10 @t80)))
121.87/122.30	(step @p127 :rule bool-impl-elim :args (@t9 @t8))
121.87/122.30	(step @p128 :rule cong :premises (@p127) :args (@t11))
121.87/122.30	(step @p129 :rule trans :premises (@p128 @p126))
121.87/122.30	(step @p130 :rule trans :premises (@p129 @p101))
121.87/122.30	(step @p131 :rule eq_resolve :premises (@p1 @p130))
121.87/122.30	(step @p132 :rule instantiate :premises (@p131) :args ((@list tptp.x tptp.y tptp.z)))
121.87/122.30	; trust TRUST PREPROCESS_HO_ELIM
121.87/122.30	(step @p133 :rule trust :premises () :args ((= @t38 @t81)))
121.87/122.30	(step @p134 :rule eq_resolve :premises (@p9 @p133))
121.87/122.30	(step @p135 :rule cnf_or_pos :args (@t85))
121.87/122.30	(step @p136 :rule reordering :premises (@p135) :args ((or @t84 @t83 (not @t85))))
121.87/122.30	(step @p137 :rule chain_resolution :premises (@p136 @p134 @p132) :args (@t86 (@list @t81 @t85)))
121.87/122.30	(step @p138 :rule cnf_or_pos :args (@t89))
121.87/122.30	(step @p139 :rule reordering :premises (@p138) :args ((or @t88 @t87 (not @t89))))
121.87/122.30	(step @p140 :rule chain_resolution :premises (@p139 @p137 @p100) :args (@t86 (@list @t83 @t89)))
121.87/122.30	; trust TRUST PREPROCESS_HO_ELIM
121.87/122.30	(step @p141 :rule trust :premises () :args ((= (forall @t21 (or @t70 @t90)) (forall @t21 (or @t66 (_ @t41 (_ @t40 @t39 @t2) @t5))))))
121.87/122.30	(step @p142 :rule refl :args (@t90))
121.87/122.30	(step @p143 :rule refl :args (@t20))
121.87/122.30	(step @p144 :rule cong :premises (@p143 @p142) :args ((= @t20 @t90)))
121.87/122.30	(step @p145 :rule symm :premises (@p144))
121.87/122.30	(step @p146 :rule eq_resolve :premises (@p143 @p145))
121.87/122.30	(step @p147 :rule nary_cong :premises (@p85 @p146) :args (@t91))
121.87/122.30	(step @p148 :rule cong :premises (@p147) :args ((forall @t21 @t91)))
121.87/122.30	(step @p149 :rule bool-impl-elim :args (@t18 @t20))
121.87/122.30	(step @p150 :rule cong :premises (@p149) :args (@t22))
121.87/122.30	(step @p151 :rule trans :premises (@p150 @p148))
121.87/122.30	(step @p152 :rule trans :premises (@p151 @p141))
121.87/122.30	(step @p153 :rule eq_resolve :premises (@p4 @p152))
121.87/122.30	(step @p154 :rule instantiate :premises (@p153) :args ((@list @t63 @t74)))
121.87/122.30	; trust TRUST PREPROCESS_HO_ELIM
121.87/122.30	(step @p155 :rule trust :premises () :args ((= @t12 (not @t92))))
121.87/122.30	(step @p156 :rule eq_resolve :premises (@p2 @p155))
121.87/122.30	(step @p157 :rule cnf_or_pos :args (@t96))
121.87/122.30	(step @p158 :rule reordering :premises (@p157) :args ((or @t92 @t95 (not @t96))))
121.87/122.30	(step @p159 :rule chain_resolution :premises (@p158 @p156 @p154) :args (@t97 (@list @t92 @t96)))
121.87/122.30	(step @p160 :rule cnf_or_pos :args (@t101))
121.87/122.30	(step @p161 :rule reordering :premises (@p160) :args ((or @t94 @t98 @t100 (not @t101))))
121.87/122.30	(step @p162 :rule chain_resolution :premises (@p161 @p159 @p140 @p99) :args ((@list true false false) (@list @t94 @t87 @t101)))
121.87/122.30	(step @p163 :rule cnf_or_pos :args (@t104))
121.87/122.30	(step @p164 :rule reordering :premises (@p163) :args ((or @t99 @t103 (not @t104))))
121.87/122.30	(step @p165 :rule chain_resolution :premises (@p164 @p162 @p67) :args (@t97 (@list @t99 @t104)))
121.87/122.30	; trust TRUST PREPROCESS_HO_ELIM
121.87/122.30	(step @p166 :rule trust :premises () :args ((= (forall @t21 @t107) (forall @t21 (_ @t41 (_ @t40 @t42 (_ @t62 @t76 @t2)) (_ @t62 @t75 @t5))))))
121.87/122.30	(step @p167 :rule refl :args ((tptp.eq @t27 @t26)))
121.87/122.30	(step @p168 :rule refl :args (@t105))
121.87/122.30	(step @p169 :rule refl :args (@t106))
121.87/122.30	(step @p170 :rule cong :premises (@p169 @p168) :args (@t107))
121.87/122.30	(step @p171 :rule trans :premises (@p170 @p167))
121.87/122.30	(step @p172 :rule refl :args (tptp.eq))
121.87/122.30	(step @p173 :rule ho_cong :premises (@p172 @p169))
121.87/122.30	(step @p174 :rule ho_cong :premises (@p173 @p168))
121.87/122.30	(step @p175 :rule cong :premises (@p174 @p171) :args ((= (_ (_ tptp.eq @t106) @t105) @t107)))
121.87/122.30	(step @p176 :rule symm :premises (@p175))
121.87/122.30	(step @p177 :rule refl :args (@t28))
121.87/122.30	(step @p178 :rule eq_resolve :premises (@p177 @p176))
121.87/122.30	(step @p179 :rule refl :args (@t26))
121.87/122.30	(step @p180 :rule cong :premises (@p179 @p168) :args ((= @t26 @t105)))
121.87/122.30	(step @p181 :rule symm :premises (@p180))
121.87/122.30	(step @p182 :rule eq_resolve :premises (@p179 @p181))
121.87/122.30	(step @p183 :rule refl :args (@t27))
121.87/122.30	(step @p184 :rule cong :premises (@p183 @p169) :args ((= @t27 @t106)))
121.87/122.30	(step @p185 :rule symm :premises (@p184))
121.87/122.30	(step @p186 :rule eq_resolve :premises (@p183 @p185))
121.87/122.30	(step @p187 :rule ho_cong :premises (@p172 @p186))
121.87/122.30	(step @p188 :rule ho_cong :premises (@p187 @p182))
121.87/122.30	(step @p189 :rule trans :premises (@p188 @p178))
121.87/122.30	(step @p190 :rule cong :premises (@p189) :args (@t29))
121.87/122.30	(step @p191 :rule trans :premises (@p190 @p166))
121.87/122.30	(step @p192 :rule eq_resolve :premises (@p7 @p191))
121.87/122.30	(step @p193 :rule instantiate :premises (@p192) :args ((@list tptp.z tptp.y)))
121.87/122.30	(step @p194 :rule instantiate :premises (@p131) :args ((@list tptp.z tptp.u tptp.y)))
121.87/122.30	; trust TRUST PREPROCESS_HO_ELIM
121.87/122.30	(step @p195 :rule trust :premises () :args ((= @t25 @t108)))
121.87/122.30	(step @p196 :rule eq_resolve :premises (@p6 @p195))
121.87/122.30	(step @p197 :rule cnf_or_pos :args (@t113))
121.87/122.30	(step @p198 :rule reordering :premises (@p197) :args ((or @t112 @t111 (not @t113))))
121.87/122.30	(step @p199 :rule chain_resolution :premises (@p198 @p196 @p194) :args (@t86 (@list @t108 @t113)))
121.87/122.30	(step @p200 :rule instantiate :premises (@p192) :args ((@list tptp.u tptp.y)))
122.08/122.30	(step @p201 :rule cnf_or_pos :args (@t119))
122.08/122.30	(step @p202 :rule reordering :premises (@p201) :args ((or @t115 @t118 @t117 @t102 (not @t119))))
122.08/122.30	(step @p203 :rule chain_resolution :premises (@p202 @p200 @p199 @p193 @p165) :args ((@list false false false true) (@list @t114 @t111 @t116 @t102)))
122.08/122.30	(assume-push @p210 @t44)
122.08/122.30	(step @p205 :rule instantiate :premises (@p53) :args ((@list @t110 @t109 @t64 @t63)))
122.08/122.30	(step-pop @p210 :rule scope :premises (@p205))
122.08/122.30	(step @p206 :rule process_scope :premises (@p210) :args (@t119))
122.08/122.30	(step @p208 :rule implies_elim :premises (@p206))
122.08/122.30	(step @p209 false :rule chain_resolution :premises (@p208 @p203 @p53) :args (@t97 (@list @t119 @t44)))
122.08/122.30	)
122.08/122.30	% SZS output end Proof
122.08/122.31	% cvc5 exiting
122.08/122.31	EOF