%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU619^2 : 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 : n008.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 08:52:27 AM UTC 2026 % Result : Theorem 0.45s 0.64s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU619^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n008.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 17:43:33 EDT 2026 % 0.17/0.35 % CPUTime : % 0.33/0.50 %----Proving TH0 % 0.45/0.64 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.45/0.64 % SZS status Theorem % 0.45/0.64 % SZS output start Proof % 0.45/0.64 ( % 0.45/0.64 (declare-sort $$unsorted 0) % 0.45/0.64 (declare-const tptp.emptyset $$unsorted) % 0.45/0.64 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.setunion (-> $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.45/0.64 (declare-const tptp.setukpairIR Bool) % 0.45/0.64 (declare-const tptp.setukpairIL Bool) % 0.45/0.64 (define tptp.iskpair () (let ((_let_1 (@var "Xy" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (_ tptp.setadjoin _let_2))) (let ((_let_4 (@var "A" $$unsorted))) (let ((_let_5 (_ tptp.setunion _let_4))) (lambda (@list _let_4) (exists (@list _let_2) (and (_ (_ tptp.in _let_2) _let_5) (exists (@list _let_1) (and (_ (_ tptp.in _let_1) _let_5) (= _let_4 (_ (_ tptp.setadjoin (_ _let_3 tptp.emptyset)) (_ (_ tptp.setadjoin (_ _let_3 (_ (_ tptp.setadjoin _let_1) tptp.emptyset))) tptp.emptyset)))))))))))))) % 0.45/0.64 (define @t1 () (@var "Xy" $$unsorted)) % 0.45/0.64 (define @t2 () (_ (_ tptp.setadjoin @t1) tptp.emptyset)) % 0.45/0.64 (define @t3 () (@var "Xx" $$unsorted)) % 0.45/0.64 (define @t4 () (_ tptp.setadjoin @t3)) % 0.45/0.64 (define @t5 () (_ @t4 @t2)) % 0.45/0.64 (define @t6 () (_ (_ tptp.setadjoin @t5) tptp.emptyset)) % 0.45/0.64 (define @t7 () (_ @t4 tptp.emptyset)) % 0.45/0.64 (define @t8 () (_ (_ tptp.setadjoin @t7) @t6)) % 0.45/0.64 (define @t9 () (_ tptp.setunion @t8)) % 0.45/0.64 (define @t10 () (_ tptp.in @t3)) % 0.45/0.64 (define @t11 () (_ @t10 @t9)) % 0.45/0.64 (define @t12 () (@list @t3 @t1)) % 0.45/0.64 (define @t13 () (forall @t12 @t11)) % 0.45/0.64 (define @t14 () (= tptp.setukpairIL @t13)) % 0.45/0.64 (define @t15 () (_ tptp.in @t1)) % 0.45/0.64 (define @t16 () (_ @t15 @t9)) % 0.45/0.64 (define @t17 () (forall @t12 @t16)) % 0.45/0.64 (define @t18 () (= tptp.setukpairIR @t17)) % 0.45/0.64 (define @t19 () (forall @t12 (_ tptp.iskpair @t8))) % 0.45/0.64 (define @t20 () (=> tptp.setukpairIR @t19)) % 0.45/0.64 (define @t21 () (=> tptp.setukpairIL @t20)) % 0.45/0.64 (define @t22 () (not @t21)) % 0.45/0.64 (define @t23 () (@var "A" $$unsorted)) % 0.45/0.64 (define @t24 () (= @t23 @t8)) % 0.45/0.64 (define @t25 () (_ tptp.setunion @t23)) % 0.45/0.64 (define @t26 () (_ @t15 @t25)) % 0.45/0.64 (define @t27 () (and @t26 @t24)) % 0.45/0.64 (define @t28 () (@list @t1)) % 0.45/0.64 (define @t29 () (exists @t28 @t27)) % 0.45/0.64 (define @t30 () (_ @t10 @t25)) % 0.45/0.64 (define @t31 () (and @t30 @t29)) % 0.45/0.64 (define @t32 () (@list @t3)) % 0.45/0.64 (define @t33 () (exists @t32 @t31)) % 0.45/0.64 (define @t34 () (@list @t23)) % 0.45/0.64 (define @t35 () (lambda @t34 @t33)) % 0.45/0.64 (define @t36 () (@var "BOUND_VARIABLE_7480" $$unsorted)) % 0.45/0.64 (define @t37 () (tptp.setadjoin @t36 tptp.emptyset)) % 0.45/0.64 (define @t38 () (@var "BOUND_VARIABLE_7540" $$unsorted)) % 0.45/0.64 (define @t39 () (tptp.setadjoin (tptp.setadjoin @t38 tptp.emptyset) (tptp.setadjoin (tptp.setadjoin @t38 @t37) tptp.emptyset))) % 0.45/0.64 (define @t40 () (tptp.setadjoin @t1 tptp.emptyset)) % 0.45/0.64 (define @t41 () (tptp.setadjoin @t3 @t40)) % 0.45/0.64 (define @t42 () (tptp.setadjoin @t41 tptp.emptyset)) % 0.45/0.64 (define @t43 () (tptp.setadjoin @t3 tptp.emptyset)) % 0.45/0.64 (define @t44 () (tptp.setadjoin @t43 @t42)) % 0.45/0.64 (define @t45 () (tptp.setunion @t44)) % 0.45/0.64 (define @t46 () (@list @t38 @t36)) % 0.45/0.64 (define @t47 () (forall @t12 (not (forall @t46 (or (not (tptp.in @t38 @t45)) (not (tptp.in @t36 @t45)) (not (= @t44 @t39))))))) % 0.45/0.64 (define @t48 () (tptp.setunion @t8)) % 0.45/0.64 (define @t49 () (tptp.in @t1 @t45)) % 0.45/0.64 (define @t50 () (=> tptp.setukpairIR @t47)) % 0.45/0.64 (define @t51 () (tptp.in @t3 @t45)) % 0.45/0.64 (define @t52 () (=> tptp.setukpairIL @t50)) % 0.45/0.64 (define @t53 () (= @t8 @t39)) % 0.45/0.64 (define @t54 () (not @t53)) % 0.45/0.64 (define @t55 () (tptp.in @t36 @t48)) % 0.45/0.64 (define @t56 () (not @t55)) % 0.45/0.64 (define @t57 () (tptp.in @t38 @t48)) % 0.45/0.64 (define @t58 () (not @t57)) % 0.45/0.64 (define @t59 () (or @t58 @t56 @t54)) % 0.45/0.64 (define @t60 () (forall @t46 @t59)) % 0.45/0.64 (define @t61 () (not @t60)) % 0.45/0.64 (define @t62 () (tptp.setunion @t23)) % 0.45/0.64 (define @t63 () (not (tptp.in @t36 @t62))) % 0.45/0.64 (define @t64 () (not (= @t23 (tptp.setadjoin @t43 (tptp.setadjoin (tptp.setadjoin @t3 @t37) tptp.emptyset))))) % 0.45/0.64 (define @t65 () (tptp.in @t3 @t62)) % 0.45/0.64 (define @t66 () (not @t65)) % 0.45/0.64 (define @t67 () (or @t66 @t63 @t64)) % 0.45/0.64 (define @t68 () (@list @t3 @t36)) % 0.45/0.64 (define @t69 () (forall @t68 @t67)) % 0.45/0.64 (define @t70 () (not @t69)) % 0.45/0.64 (define @t71 () (lambda @t34 @t70)) % 0.45/0.64 (define @t72 () (forall @t12 (_ @t71 @t8))) % 0.45/0.64 (define @t73 () (=> tptp.setukpairIR @t72)) % 0.45/0.64 (define @t74 () (=> tptp.setukpairIL @t73)) % 0.45/0.64 (define @t75 () (or @t63 @t64)) % 0.45/0.64 (define @t76 () (or @t66 @t75)) % 0.45/0.64 (define @t77 () (forall @t68 @t76)) % 0.45/0.64 (define @t78 () (@list @t36)) % 0.45/0.64 (define @t79 () (forall @t78 @t76)) % 0.45/0.64 (define @t80 () (forall @t78 @t75)) % 0.45/0.64 (define @t81 () (or @t66 @t80)) % 0.45/0.64 (define @t82 () (tptp.in @t1 @t62)) % 0.45/0.64 (define @t83 () (forall @t28 (or (not @t82) (not (= @t23 @t44))))) % 0.45/0.64 (define @t84 () (not @t30)) % 0.45/0.64 (define @t85 () (or @t84 @t83)) % 0.45/0.64 (define @t86 () (not @t83)) % 0.45/0.64 (define @t87 () (and @t30 @t86)) % 0.45/0.64 (define @t88 () (forall @t32 (not @t87))) % 0.45/0.64 (define @t89 () (not @t88)) % 0.45/0.64 (define @t90 () (not @t24)) % 0.45/0.64 (define @t91 () (not @t26)) % 0.45/0.64 (define @t92 () (or @t91 @t90)) % 0.45/0.64 (define @t93 () (forall @t28 (not @t27))) % 0.45/0.64 (define @t94 () (not @t93)) % 0.45/0.64 (define @t95 () (@quantifiers_skolemize @t47 1)) % 0.45/0.64 (define @t96 () (@quantifiers_skolemize @t47 0)) % 0.45/0.64 (define @t97 () (tptp.setadjoin (tptp.setadjoin @t96 tptp.emptyset) (tptp.setadjoin (tptp.setadjoin @t96 (tptp.setadjoin @t95 tptp.emptyset)) tptp.emptyset))) % 0.45/0.64 (define @t98 () (tptp.setunion @t97)) % 0.45/0.64 (define @t99 () (not (tptp.in @t36 @t98))) % 0.45/0.64 (define @t100 () (not (tptp.in @t38 @t98))) % 0.45/0.64 (define @t101 () (forall @t46 (or @t100 @t99 (not (= @t39 @t97))))) % 0.45/0.64 (define @t102 () (not @t47)) % 0.45/0.64 (define @t103 () (not (= @t97 @t39))) % 0.45/0.64 (define @t104 () (or @t100 @t99 @t103)) % 0.45/0.64 (define @t105 () (forall @t46 @t104)) % 0.45/0.64 (define @t106 () (not (not @t105))) % 0.45/0.64 (define @t107 () (tptp.in @t95 @t98)) % 0.45/0.64 (define @t108 () (not @t107)) % 0.45/0.64 (define @t109 () (tptp.in @t96 @t98)) % 0.45/0.64 (define @t110 () (not @t109)) % 0.45/0.64 (define @t111 () (or @t110 @t108)) % 0.45/0.64 (define @t112 () (not (= @t97 @t97))) % 0.45/0.64 (define @t113 () (or @t110 @t108 @t112)) % 0.45/0.64 (define @t114 () (@list @t96 @t95)) % 0.45/0.64 (assume @p1 @t14) % 0.45/0.64 (assume @p2 @t18) % 0.45/0.64 (assume @p3 @t22) % 0.45/0.64 (assume @p4 true) % 0.45/0.64 (step @p5 (= tptp.iskpair @t35) :rule refl :args (@t35)) % 0.45/0.64 (step @p6 :rule refl :args (@t47)) % 0.45/0.64 (step @p7 :rule refl :args ((tptp.in @t1 @t9))) % 0.45/0.64 (step @p8 :rule refl :args (@t48)) % 0.45/0.64 (step @p9 :rule refl :args ((tptp.setadjoin @t7 @t6))) % 0.45/0.64 (step @p10 :rule refl :args ((tptp.setadjoin @t5 tptp.emptyset))) % 0.45/0.64 (step @p11 :rule refl :args (tptp.emptyset)) % 0.45/0.64 (step @p12 :rule refl :args ((tptp.setadjoin @t3 @t2))) % 0.45/0.64 (step @p13 :rule refl :args (@t40)) % 0.45/0.64 (step @p14 :rule refl :args (@t3)) % 0.45/0.64 (step @p15 :rule cong :premises (@p14 @p13) :args (@t41)) % 0.45/0.64 (step @p16 :rule trans :premises (@p15 @p12)) % 0.45/0.64 (step @p17 :rule cong :premises (@p16 @p11) :args (@t42)) % 0.45/0.64 (step @p18 :rule trans :premises (@p17 @p10)) % 0.45/0.64 (step @p19 :rule refl :args (@t43)) % 0.45/0.64 (step @p20 :rule cong :premises (@p19 @p18) :args (@t44)) % 0.45/0.64 (step @p21 :rule trans :premises (@p20 @p9)) % 0.45/0.64 (step @p22 :rule cong :premises (@p21) :args (@t45)) % 0.45/0.64 (step @p23 :rule trans :premises (@p22 @p8)) % 0.45/0.64 (step @p24 :rule refl :args (@t1)) % 0.45/0.64 (step @p25 :rule cong :premises (@p24 @p23) :args (@t49)) % 0.45/0.64 (step @p26 :rule trans :premises (@p25 @p7)) % 0.45/0.64 (step @p27 :rule refl :args (@t15)) % 0.45/0.64 (step @p28 :rule ho_cong :premises (@p27 @p23)) % 0.45/0.64 (step @p29 :rule cong :premises (@p28 @p26) :args ((= (_ @t15 @t45) @t49))) % 0.45/0.64 (step @p30 :rule symm :premises (@p29)) % 0.45/0.64 (step @p31 :rule refl :args (@t16)) % 0.45/0.64 (step @p32 :rule eq_resolve :premises (@p31 @p30)) % 0.45/0.64 (step @p33 :rule refl :args (tptp.setunion)) % 0.45/0.64 (step @p34 :rule ho_cong :premises (@p33 @p21)) % 0.45/0.64 (step @p35 :rule cong :premises (@p34 @p23) :args ((= (_ tptp.setunion @t44) @t45))) % 0.45/0.64 (step @p36 :rule symm :premises (@p35)) % 0.45/0.64 (step @p37 :rule refl :args (@t9)) % 0.45/0.64 (step @p38 :rule eq_resolve :premises (@p37 @p36)) % 0.45/0.64 (step @p39 :rule refl :args (tptp.setadjoin)) % 0.45/0.64 (step @p40 :rule ho_cong :premises (@p39 @p19)) % 0.45/0.64 (step @p41 :rule ho_cong :premises (@p40 @p18)) % 0.45/0.64 (step @p42 :rule cong :premises (@p41 @p21) :args ((= (_ (_ tptp.setadjoin @t43) @t42) @t44))) % 0.45/0.64 (step @p43 :rule symm :premises (@p42)) % 0.45/0.64 (step @p44 :rule refl :args (@t8)) % 0.45/0.64 (step @p45 :rule eq_resolve :premises (@p44 @p43)) % 0.45/0.64 (step @p46 :rule ho_cong :premises (@p39 @p16)) % 0.45/0.64 (step @p47 :rule ho_cong :premises (@p46 @p11)) % 0.45/0.64 (step @p48 :rule cong :premises (@p47 @p18) :args ((= (_ (_ tptp.setadjoin @t41) tptp.emptyset) @t42))) % 0.45/0.64 (step @p49 :rule symm :premises (@p48)) % 0.45/0.64 (step @p50 :rule refl :args (@t6)) % 0.45/0.64 (step @p51 :rule eq_resolve :premises (@p50 @p49)) % 0.45/0.64 (step @p52 :rule refl :args (@t4)) % 0.45/0.64 (step @p53 :rule ho_cong :premises (@p52 @p13)) % 0.45/0.64 (step @p54 :rule cong :premises (@p53 @p16) :args ((= (_ @t4 @t40) @t41))) % 0.45/0.64 (step @p55 :rule symm :premises (@p54)) % 0.45/0.64 (step @p56 :rule refl :args (@t5)) % 0.45/0.64 (step @p57 :rule eq_resolve :premises (@p56 @p55)) % 0.45/0.64 (step @p58 :rule refl :args (@t2)) % 0.45/0.64 (step @p59 :rule cong :premises (@p58 @p13) :args ((= @t2 @t40))) % 0.45/0.64 (step @p60 :rule symm :premises (@p59)) % 0.45/0.64 (step @p61 :rule eq_resolve :premises (@p58 @p60)) % 0.45/0.64 (step @p62 :rule ho_cong :premises (@p52 @p61)) % 0.45/0.64 (step @p63 :rule trans :premises (@p62 @p57)) % 0.45/0.64 (step @p64 :rule ho_cong :premises (@p39 @p63)) % 0.45/0.64 (step @p65 :rule ho_cong :premises (@p64 @p11)) % 0.45/0.64 (step @p66 :rule trans :premises (@p65 @p51)) % 0.45/0.64 (step @p67 :rule refl :args (@t7)) % 0.45/0.64 (step @p68 :rule cong :premises (@p67 @p19) :args ((= @t7 @t43))) % 0.45/0.64 (step @p69 :rule symm :premises (@p68)) % 0.45/0.64 (step @p70 :rule eq_resolve :premises (@p67 @p69)) % 0.45/0.64 (step @p71 :rule ho_cong :premises (@p39 @p70)) % 0.45/0.64 (step @p72 :rule ho_cong :premises (@p71 @p66)) % 0.45/0.64 (step @p73 :rule trans :premises (@p72 @p45)) % 0.45/0.64 (step @p74 :rule ho_cong :premises (@p33 @p73)) % 0.45/0.64 (step @p75 :rule trans :premises (@p74 @p38)) % 0.45/0.64 (step @p76 :rule ho_cong :premises (@p27 @p75)) % 0.45/0.64 (step @p77 :rule trans :premises (@p76 @p32)) % 0.45/0.64 (step @p78 :rule cong :premises (@p77) :args (@t17)) % 0.45/0.64 (step @p79 :rule refl :args (tptp.setukpairIR)) % 0.45/0.64 (step @p80 :rule cong :premises (@p79 @p78) :args (@t18)) % 0.45/0.64 (step @p81 :rule eq_resolve :premises (@p2 @p80)) % 0.45/0.64 (step @p82 :rule cong :premises (@p81 @p6) :args (@t50)) % 0.45/0.64 (step @p83 :rule refl :args ((tptp.in @t3 @t9))) % 0.45/0.64 (step @p84 :rule cong :premises (@p14 @p23) :args (@t51)) % 0.45/0.64 (step @p85 :rule trans :premises (@p84 @p83)) % 0.45/0.64 (step @p86 :rule refl :args (@t10)) % 0.45/0.64 (step @p87 :rule ho_cong :premises (@p86 @p23)) % 0.45/0.64 (step @p88 :rule cong :premises (@p87 @p85) :args ((= (_ @t10 @t45) @t51))) % 0.45/0.64 (step @p89 :rule symm :premises (@p88)) % 0.45/0.64 (step @p90 :rule refl :args (@t11)) % 0.45/0.64 (step @p91 :rule eq_resolve :premises (@p90 @p89)) % 0.45/0.64 (step @p92 :rule ho_cong :premises (@p86 @p75)) % 0.45/0.64 (step @p93 :rule trans :premises (@p92 @p91)) % 0.45/0.64 (step @p94 :rule cong :premises (@p93) :args (@t13)) % 0.45/0.64 (step @p95 :rule refl :args (tptp.setukpairIL)) % 0.45/0.64 (step @p96 :rule cong :premises (@p95 @p94) :args (@t14)) % 0.45/0.64 (step @p97 :rule eq_resolve :premises (@p1 @p96)) % 0.45/0.64 (step @p98 :rule cong :premises (@p97 @p82) :args (@t52)) % 0.45/0.64 (step @p99 :rule cong :premises (@p98) :args ((not @t52))) % 0.45/0.64 (step @p100 :rule refl :args (@t39)) % 0.45/0.64 (step @p101 :rule cong :premises (@p73 @p100) :args (@t53)) % 0.45/0.64 (step @p102 :rule cong :premises (@p101) :args (@t54)) % 0.45/0.64 (step @p103 :rule cong :premises (@p73) :args (@t48)) % 0.45/0.64 (step @p104 :rule refl :args (@t36)) % 0.45/0.64 (step @p105 :rule cong :premises (@p104 @p103) :args (@t55)) % 0.45/0.64 (step @p106 :rule cong :premises (@p105) :args (@t56)) % 0.45/0.64 (step @p107 :rule refl :args (@t38)) % 0.45/0.64 (step @p108 :rule cong :premises (@p107 @p103) :args (@t57)) % 0.45/0.64 (step @p109 :rule cong :premises (@p108) :args (@t58)) % 0.45/0.64 (step @p110 :rule nary_cong :premises (@p109 @p106 @p102) :args (@t59)) % 0.45/0.64 (step @p111 :rule cong :premises (@p110) :args (@t60)) % 0.45/0.64 (step @p112 :rule cong :premises (@p111) :args (@t61)) % 0.45/0.64 (step @p113 :rule beta-reduce :args ((= (_ (lambda @t34 (not (forall @t46 (or (not (tptp.in @t38 @t62)) @t63 (not (= @t23 @t39)))))) @t8) @t61))) % 0.45/0.64 (step @p114 :rule trans :premises (@p113 @p112)) % 0.45/0.64 (step @p115 :rule alpha_equiv :args (@t69 (@list @t3) (@list @t38))) % 0.45/0.64 (step @p116 :rule cong :premises (@p115) :args (@t70)) % 0.45/0.64 (step @p117 :rule cong :premises (@p116) :args (@t71)) % 0.45/0.64 (step @p118 :rule ho_cong :premises (@p117 @p44)) % 0.45/0.64 (step @p119 :rule trans :premises (@p118 @p114)) % 0.45/0.64 (step @p120 :rule cong :premises (@p119) :args (@t72)) % 0.45/0.64 (step @p121 :rule cong :premises (@p79 @p120) :args (@t73)) % 0.45/0.64 (step @p122 :rule cong :premises (@p95 @p121) :args (@t74)) % 0.45/0.64 (step @p123 :rule cong :premises (@p122) :args ((not @t74))) % 0.45/0.64 (step @p124 :rule refl :args (@t8)) % 0.45/0.64 (step @p125 :rule aci_norm :args ((= @t76 @t67))) % 0.45/0.64 (step @p126 :rule cong :premises (@p125) :args (@t77)) % 0.45/0.64 (step @p127 :rule quant-merge-prenex :args ((= (forall @t32 @t79) @t77))) % 0.45/0.64 (step @p128 :rule alpha_equiv :args (@t80 (@list @t36) (@list @t1))) % 0.45/0.64 (step @p129 :rule refl :args (@t66)) % 0.45/0.64 (step @p130 :rule nary_cong :premises (@p129 @p128) :args (@t81)) % 0.45/0.64 (step @p131 :rule quant-miniscope-or :args ((= @t79 @t81))) % 0.45/0.64 (step @p132 :rule trans :premises (@p131 @p130)) % 0.45/0.64 (step @p133 :rule symm :premises (@p132)) % 0.45/0.64 (step @p134 :rule cong :premises (@p133) :args ((forall @t32 (or @t66 @t83)))) % 0.45/0.64 (step @p135 :rule trans :premises (@p134 @p127)) % 0.45/0.64 (step @p136 :rule trans :premises (@p135 @p126)) % 0.45/0.64 (step @p137 :rule refl :args (@t83)) % 0.45/0.64 (step @p138 :rule refl :args ((tptp.in @t3 @t25))) % 0.45/0.64 (step @p139 :rule refl :args (@t62)) % 0.45/0.64 (step @p140 :rule cong :premises (@p14 @p139) :args (@t65)) % 0.45/0.64 (step @p141 :rule trans :premises (@p140 @p138)) % 0.45/0.64 (step @p142 :rule ho_cong :premises (@p86 @p139)) % 0.45/0.64 (step @p143 :rule cong :premises (@p142 @p141) :args ((= (_ @t10 @t62) @t65))) % 0.45/0.64 (step @p144 :rule symm :premises (@p143)) % 0.45/0.64 (step @p145 :rule refl :args (@t30)) % 0.45/0.64 (step @p146 :rule eq_resolve :premises (@p145 @p144)) % 0.45/0.64 (step @p147 :rule refl :args (@t25)) % 0.45/0.64 (step @p148 :rule cong :premises (@p147 @p139) :args ((= @t25 @t62))) % 0.45/0.64 (step @p149 :rule symm :premises (@p148)) % 0.45/0.64 (step @p150 :rule eq_resolve :premises (@p147 @p149)) % 0.45/0.64 (step @p151 :rule ho_cong :premises (@p86 @p150)) % 0.45/0.64 (step @p152 :rule trans :premises (@p151 @p146)) % 0.45/0.64 (step @p153 :rule cong :premises (@p152) :args (@t84)) % 0.45/0.64 (step @p154 :rule nary_cong :premises (@p153 @p137) :args (@t85)) % 0.45/0.64 (step @p155 :rule cong :premises (@p154) :args ((forall @t32 @t85))) % 0.45/0.64 (step @p156 :rule trans :premises (@p155 @p136)) % 0.45/0.64 (step @p157 :rule bool-double-not-elim :args (@t83)) % 0.45/0.64 (step @p158 :rule refl :args (@t84)) % 0.45/0.64 (step @p159 :rule nary_cong :premises (@p158 @p157) :args ((or @t84 (not @t86)))) % 0.45/0.64 (step @p160 :rule bool-and-de-morgan :args (@t30 @t86 true)) % 0.45/0.64 (step @p161 :rule trans :premises (@p160 @p159)) % 0.45/0.64 (step @p162 :rule cong :premises (@p161) :args (@t88)) % 0.45/0.64 (step @p163 :rule trans :premises (@p162 @p156)) % 0.45/0.64 (step @p164 :rule cong :premises (@p163) :args (@t89)) % 0.45/0.64 (step @p165 :rule exists-elim :args ((= (exists @t32 @t87) @t89))) % 0.45/0.64 (step @p166 :rule trans :premises (@p165 @p164)) % 0.45/0.64 (step @p167 :rule refl :args (@t23)) % 0.45/0.64 (step @p168 :rule cong :premises (@p167 @p73) :args (@t24)) % 0.45/0.64 (step @p169 :rule cong :premises (@p168) :args (@t90)) % 0.45/0.64 (step @p170 :rule refl :args ((tptp.in @t1 @t25))) % 0.45/0.64 (step @p171 :rule cong :premises (@p24 @p139) :args (@t82)) % 0.45/0.64 (step @p172 :rule trans :premises (@p171 @p170)) % 0.45/0.64 (step @p173 :rule ho_cong :premises (@p27 @p139)) % 0.45/0.64 (step @p174 :rule cong :premises (@p173 @p172) :args ((= (_ @t15 @t62) @t82))) % 0.45/0.64 (step @p175 :rule symm :premises (@p174)) % 0.45/0.64 (step @p176 :rule refl :args (@t26)) % 0.45/0.64 (step @p177 :rule eq_resolve :premises (@p176 @p175)) % 0.45/0.64 (step @p178 :rule ho_cong :premises (@p27 @p150)) % 0.45/0.64 (step @p179 :rule trans :premises (@p178 @p177)) % 0.45/0.64 (step @p180 :rule cong :premises (@p179) :args (@t91)) % 0.45/0.64 (step @p181 :rule nary_cong :premises (@p180 @p169) :args (@t92)) % 0.45/0.64 (step @p182 :rule cong :premises (@p181) :args ((forall @t28 @t92))) % 0.45/0.64 (step @p183 :rule bool-and-de-morgan :args (@t26 @t24 true)) % 0.45/0.64 (step @p184 :rule cong :premises (@p183) :args (@t93)) % 0.45/0.64 (step @p185 :rule trans :premises (@p184 @p182)) % 0.45/0.64 (step @p186 :rule cong :premises (@p185) :args (@t94)) % 0.45/0.64 (step @p187 :rule exists-elim :args ((= @t29 @t94))) % 0.45/0.64 (step @p188 :rule trans :premises (@p187 @p186)) % 0.45/0.64 (step @p189 :rule refl :args (@t30)) % 0.45/0.64 (step @p190 :rule nary_cong :premises (@p189 @p188) :args (@t31)) % 0.45/0.64 (step @p191 :rule cong :premises (@p190) :args (@t33)) % 0.45/0.64 (step @p192 :rule trans :premises (@p191 @p166)) % 0.45/0.64 (step @p193 :rule cong :premises (@p192) :args (@t35)) % 0.45/0.64 (step @p194 :rule trans :premises (@p5 @p193)) % 0.45/0.64 (step @p195 :rule ho_cong :premises (@p194 @p124)) % 0.45/0.64 (step @p196 :rule cong :premises (@p195) :args (@t19)) % 0.45/0.64 (step @p197 :rule cong :premises (@p79 @p196) :args (@t20)) % 0.45/0.64 (step @p198 :rule cong :premises (@p95 @p197) :args (@t21)) % 0.45/0.64 (step @p199 :rule cong :premises (@p198) :args (@t22)) % 0.45/0.64 (step @p200 :rule trans :premises (@p199 @p123)) % 0.45/0.64 (step @p201 :rule trans :premises (@p200 @p99)) % 0.45/0.64 (step @p202 :rule eq_resolve :premises (@p3 @p201)) % 0.45/0.64 (step @p203 :rule not_implies_elim2 :premises (@p202)) % 0.45/0.64 (step @p204 :rule not_implies_elim2 :premises (@p203)) % 0.45/0.64 (step @p205 :rule refl :args (@t101)) % 0.45/0.64 (step @p206 :rule bool-double-not-elim :args (@t47)) % 0.45/0.64 (step @p207 :rule nary_cong :premises (@p206 @p205) :args ((or (not @t102) @t101))) % 0.45/0.64 (step @p208 :rule eq-symm :args (@t97 @t39)) % 0.45/0.64 (step @p209 :rule cong :premises (@p208) :args (@t103)) % 0.45/0.64 (step @p210 :rule refl :args (@t99)) % 0.45/0.64 (step @p211 :rule refl :args (@t100)) % 0.45/0.64 (step @p212 :rule nary_cong :premises (@p211 @p210 @p209) :args (@t104)) % 0.45/0.64 (step @p213 :rule cong :premises (@p212) :args (@t105)) % 0.45/0.64 (step @p214 :rule bool-double-not-elim :args (@t105)) % 0.45/0.64 (step @p215 :rule trans :premises (@p214 @p213)) % 0.45/0.64 (step @p216 :rule refl :args (@t102)) % 0.45/0.64 (step @p217 :rule cong :premises (@p216 @p215) :args ((=> @t102 @t106))) % 0.45/0.64 (assume-push @p250 @t102) % 0.45/0.64 (step @p219 :rule skolemize :premises (@p204)) % 0.45/0.64 (step-pop @p251 :rule scope :premises (@p219)) % 0.45/0.64 (step @p220 :rule process_scope :premises (@p251) :args (@t106)) % 0.45/0.64 (step @p222 :rule eq_resolve :premises (@p220 @p217)) % 0.45/0.64 (step @p223 :rule implies_elim :premises (@p222)) % 0.45/0.64 (step @p224 :rule eq_resolve :premises (@p223 @p207)) % 0.45/0.64 (step @p225 :rule chain_m_resolution :premises (@p224 @p204) :args (@t101 (@list true) (@list @t47))) % 0.45/0.64 (step @p226 :rule aci_norm :args ((= (or @t110 @t108 false) @t111))) % 0.45/0.64 (step @p227 :rule evaluate :args ((not true))) % 0.45/0.64 (step @p228 :rule eq-refl :args (@t97)) % 0.45/0.64 (step @p229 :rule cong :premises (@p228) :args (@t112)) % 0.45/0.64 (step @p230 :rule trans :premises (@p229 @p227)) % 0.45/0.64 (step @p231 :rule refl :args (@t108)) % 0.45/0.64 (step @p232 :rule refl :args (@t110)) % 0.45/0.64 (step @p233 :rule nary_cong :premises (@p232 @p231 @p230) :args (@t113)) % 0.45/0.64 (step @p234 :rule trans :premises (@p233 @p226)) % 0.45/0.64 (step @p235 :rule cong :premises (@p205 @p234) :args ((=> @t101 @t113))) % 0.45/0.64 (assume-push @p252 @t101) % 0.45/0.64 (step @p237 :rule instantiate :premises (@p225) :args (@t114)) % 0.45/0.64 (step-pop @p253 :rule scope :premises (@p237)) % 0.45/0.64 (step @p238 :rule process_scope :premises (@p253) :args (@t113)) % 0.45/0.64 (step @p240 :rule eq_resolve :premises (@p238 @p235)) % 0.45/0.64 (step @p241 :rule implies_elim :premises (@p240)) % 0.45/0.64 (step @p242 :rule chain_m_resolution :premises (@p241 @p225) :args (@t111 (@list false) (@list @t101))) % 0.45/0.64 (step @p243 :rule not_implies_elim1 :premises (@p202)) % 0.45/0.64 (step @p244 :rule instantiate :premises (@p243) :args (@t114)) % 0.45/0.64 (step @p245 :rule not_implies_elim1 :premises (@p203)) % 0.45/0.64 (step @p246 :rule instantiate :premises (@p245) :args (@t114)) % 0.45/0.64 (step @p247 :rule cnf_or_pos :args (@t111)) % 0.45/0.64 (step @p248 :rule reordering :premises (@p247) :args ((or @t110 @t108 (not @t111)))) % 0.45/0.64 (step @p249 false :rule chain_m_resolution :premises (@p248 @p246 @p244 @p242) :args (false (@list false false false) (@list @t107 @t109 @t111))) % 0.45/0.64 ) % 0.45/0.64 % SZS output end Proof % 0.45/0.64 % cvc5 exiting %------------------------------------------------------------------------------