%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : QUA002^1 : TPTP v9.2.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n029.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 08:44:39 AM UTC 2026 % Result : Theorem 0.37s 0.57s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : QUA002^1 : TPTP v9.2.1. Released v4.1.0. % 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 : n029.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 13:20:17 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.49 %----Proving TH0 % 0.37/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.57 % SZS status Theorem % 0.37/0.57 % SZS output start Proof % 0.37/0.57 ( % 0.37/0.57 (declare-sort $$unsorted 0) % 0.37/0.57 (declare-const tptp.sup (-> (-> $$unsorted Bool) $$unsorted)) % 0.37/0.57 (declare-const tptp.multiplication (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.57 (declare-const tptp.one $$unsorted) % 0.37/0.57 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.zero $$unsorted) % 0.37/0.57 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.37/0.57 (define tptp.union () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.57 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.37/0.57 (define tptp.supset () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "F" (-> (-> $$unsorted Bool) Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (and (_ _let_3 _let_2) (= (_ tptp.sup _let_2) _let_1)))))))) % 0.37/0.57 (define tptp.unionset () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "F" (-> (-> $$unsorted Bool) Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (and (_ _let_3 _let_2) (_ _let_2 _let_1)))))))) % 0.37/0.57 (define tptp.addition () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (lambda (@list _let_2 _let_1) (_ tptp.sup (_ (_ tptp.union (_ tptp.singleton _let_2)) (_ tptp.singleton _let_1))))))) % 0.37/0.57 (define tptp.crossmult () (let ((_let_1 (@var "Y1" $$unsorted))) (let ((_let_2 (@var "X1" $$unsorted))) (let ((_let_3 (@var "A" $$unsorted))) (let ((_let_4 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_5 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_5 _let_4 _let_3) (exists (@list _let_2 _let_1) (and (_ _let_5 _let_2) (_ _let_4 _let_1) (= _let_3 (_ (_ tptp.multiplication _let_2) _let_1))))))))))) % 0.37/0.57 (define @t1 () (@var "X" $$unsorted)) % 0.37/0.57 (define @t2 () (_ tptp.singleton @t1)) % 0.37/0.57 (define @t3 () (@list @t1)) % 0.37/0.57 (define @t4 () (@var "X" (-> (-> $$unsorted Bool) Bool))) % 0.37/0.57 (define @t5 () (@var "X2" $$unsorted)) % 0.37/0.57 (define @t6 () (@var "X1" $$unsorted)) % 0.37/0.57 (define @t7 () (_ (_ tptp.addition @t6) @t5)) % 0.37/0.57 (define @t8 () (@list @t6 @t5)) % 0.37/0.57 (define @t9 () (@var "Y" (-> $$unsorted Bool))) % 0.37/0.57 (define @t10 () (@var "X" (-> $$unsorted Bool))) % 0.37/0.57 (define @t11 () (_ tptp.sup @t9)) % 0.37/0.57 (define @t12 () (= @t7 (_ (_ tptp.addition @t5) @t6))) % 0.37/0.57 (define @t13 () (forall @t8 @t12)) % 0.37/0.57 (define @t14 () (not @t13)) % 0.37/0.57 (define @t15 () (lambda @t3 false)) % 0.37/0.57 (define @t16 () (@var "U" $$unsorted)) % 0.37/0.57 (define @t17 () (_ @t9 @t16)) % 0.37/0.57 (define @t18 () (lambda (@list @t10 @t9 @t16) (or (_ @t10 @t16) @t17))) % 0.37/0.57 (define @t19 () (@list @t1 @t16)) % 0.37/0.57 (define @t20 () (lambda @t19 (= @t16 @t1))) % 0.37/0.57 (define @t21 () (@var "F" (-> (-> $$unsorted Bool) Bool))) % 0.37/0.57 (define @t22 () (_ @t21 @t9)) % 0.37/0.57 (define @t23 () (@list @t9)) % 0.37/0.57 (define @t24 () (@list @t21 @t1)) % 0.37/0.57 (define @t25 () (lambda @t24 (exists @t23 (and @t22 (= @t11 @t1))))) % 0.37/0.57 (define @t26 () (lambda @t24 (exists @t23 (and @t22 (_ @t9 @t1))))) % 0.37/0.57 (define @t27 () (@var "Y" $$unsorted)) % 0.37/0.57 (define @t28 () (@list @t1 @t27)) % 0.37/0.57 (define @t29 () (lambda @t28 (_ tptp.sup (_ (_ tptp.union @t2) (_ tptp.singleton @t27))))) % 0.37/0.57 (define @t30 () (@var "Y1" $$unsorted)) % 0.37/0.57 (define @t31 () (@var "A" $$unsorted)) % 0.37/0.57 (define @t32 () (lambda (@list @t10 @t9 @t31) (exists (@list @t6 @t30) (and (_ @t10 @t6) (_ @t9 @t30) (= @t31 (_ (_ tptp.multiplication @t6) @t30)))))) % 0.37/0.57 (define @t33 () (= @t16 @t6)) % 0.37/0.57 (define @t34 () (= @t16 @t5)) % 0.37/0.57 (define @t35 () (@list @t16)) % 0.37/0.57 (define @t36 () (lambda @t35 (or @t34 @t33))) % 0.37/0.57 (define @t37 () (tptp.sup @t36)) % 0.37/0.57 (define @t38 () (_ tptp.sup @t36)) % 0.37/0.57 (define @t39 () (lambda @t35 (or @t33 @t34))) % 0.37/0.57 (define @t40 () (tptp.sup @t39)) % 0.37/0.57 (define @t41 () (_ tptp.sup @t39)) % 0.37/0.57 (define @t42 () (= @t41 @t38)) % 0.37/0.57 (define @t43 () (= @t16 @t27)) % 0.37/0.57 (define @t44 () (@list @t27)) % 0.37/0.57 (define @t45 () (or (= @t5 @t16) @t43)) % 0.37/0.57 (define @t46 () (lambda @t35 @t45)) % 0.37/0.57 (define @t47 () (lambda @t44 (_ tptp.sup @t46))) % 0.37/0.57 (define @t48 () (= @t1 @t16)) % 0.37/0.57 (define @t49 () (lambda @t28 (_ tptp.sup (lambda @t35 (or @t48 @t43))))) % 0.37/0.57 (define @t50 () (_ @t49 @t5)) % 0.37/0.57 (define @t51 () (or (= @t6 @t16) @t43)) % 0.37/0.57 (define @t52 () (lambda @t35 @t51)) % 0.37/0.57 (define @t53 () (lambda @t44 (_ tptp.sup @t52))) % 0.37/0.57 (define @t54 () (_ @t49 @t6)) % 0.37/0.57 (define @t55 () (= (_ @t54 @t5) (_ @t50 @t6))) % 0.37/0.57 (define @t56 () (forall @t8 @t55)) % 0.37/0.57 (define @t57 () (lambda @t35 @t43)) % 0.37/0.57 (define @t58 () (_ @t57 @t16)) % 0.37/0.57 (define @t59 () (or @t48 @t58)) % 0.37/0.57 (define @t60 () (lambda @t35 @t59)) % 0.37/0.57 (define @t61 () (@list @t9 @t16)) % 0.37/0.57 (define @t62 () (lambda @t35 (= @t27 @t16))) % 0.37/0.57 (define @t63 () (lambda @t19 @t48)) % 0.37/0.57 (define @t64 () (lambda @t35 @t48)) % 0.37/0.57 (define @t65 () (_ @t64 @t16)) % 0.37/0.57 (define @t66 () (or @t65 @t17)) % 0.37/0.57 (define @t67 () (lambda @t61 @t66)) % 0.37/0.57 (define @t68 () (forall @t8 (= @t40 @t37))) % 0.37/0.57 (define @t69 () (@quantifiers_skolemize @t68 1)) % 0.37/0.57 (define @t70 () (= @t16 @t69)) % 0.37/0.57 (define @t71 () (@quantifiers_skolemize @t68 0)) % 0.37/0.57 (define @t72 () (= @t16 @t71)) % 0.37/0.57 (define @t73 () (lambda @t35 (or @t72 @t70))) % 0.37/0.57 (define @t74 () (@purify @t73)) % 0.37/0.57 (define @t75 () (tptp.sup @t74)) % 0.37/0.57 (define @t76 () (lambda @t35 (or @t70 @t72))) % 0.37/0.57 (define @t77 () (@purify @t76)) % 0.37/0.57 (define @t78 () (tptp.sup @t77)) % 0.37/0.57 (define @t79 () (= @t78 @t75)) % 0.37/0.57 (define @t80 () (not @t79)) % 0.37/0.57 (define @t81 () (not @t68)) % 0.37/0.57 (define @t82 () (tptp.sup @t76)) % 0.37/0.57 (define @t83 () (tptp.sup @t73)) % 0.37/0.57 (define @t84 () (= @t83 @t82)) % 0.37/0.57 (define @t85 () (not @t84)) % 0.37/0.57 (define @t86 () (@list true)) % 0.37/0.57 (define @t87 () (= @t77 @t74)) % 0.37/0.57 (define @t88 () (not @t87)) % 0.37/0.57 (define @t89 () (@const 0 $$unsorted)) % 0.37/0.57 (define @t90 () (= @t71 @t89)) % 0.37/0.57 (define @t91 () (= @t69 @t89)) % 0.37/0.57 (define @t92 () (or @t91 @t90)) % 0.37/0.57 (define @t93 () (or @t90 @t91)) % 0.37/0.57 (define @t94 () (= @t93 @t92)) % 0.37/0.57 (define @t95 () (= @t89 @t69)) % 0.37/0.57 (define @t96 () (= @t89 @t71)) % 0.37/0.57 (define @t97 () (or @t96 @t95)) % 0.37/0.57 (define @t98 () (_ @t73 @t89)) % 0.37/0.57 (define @t99 () (_ @t74 @t89)) % 0.37/0.57 (define @t100 () (or @t95 @t96)) % 0.37/0.57 (define @t101 () (_ @t76 @t89)) % 0.37/0.57 (define @t102 () (_ @t77 @t89)) % 0.37/0.57 (define @t103 () (= @t102 @t99)) % 0.37/0.57 (define @t104 () (not @t103)) % 0.37/0.57 (define @t105 () (or @t87 @t104)) % 0.37/0.57 (define @t106 () (@list true false false)) % 0.37/0.57 (define @t107 () (@list @t94 @t92 @t93)) % 0.37/0.57 (define @t108 () (not @t93)) % 0.37/0.57 (define @t109 () (@list true true)) % 0.37/0.57 (define @t110 () (@list @t90 @t91)) % 0.37/0.57 (define @t111 () (not @t92)) % 0.37/0.57 (assume @p1 (= (_ tptp.sup tptp.emptyset) tptp.zero)) % 0.37/0.57 (assume @p2 (forall @t3 (= (_ tptp.sup @t2) @t1))) % 0.37/0.57 (assume @p3 (forall (@list @t4) (= (_ tptp.sup (_ tptp.supset @t4)) (_ tptp.sup (_ tptp.unionset @t4))))) % 0.37/0.57 (assume @p4 (forall @t8 (= (_ (_ tptp.leq @t6) @t5) (= @t7 @t5)))) % 0.37/0.57 (assume @p5 (forall (@list @t10 @t9) (= (_ (_ tptp.multiplication (_ tptp.sup @t10)) @t11) (_ tptp.sup (_ (_ tptp.crossmult @t10) @t9))))) % 0.37/0.57 (assume @p6 (forall @t3 (= (_ (_ tptp.multiplication @t1) tptp.one) @t1))) % 0.37/0.57 (assume @p7 (forall @t3 (= (_ (_ tptp.multiplication tptp.one) @t1) @t1))) % 0.37/0.57 (assume @p8 @t14) % 0.37/0.57 (assume @p9 true) % 0.37/0.57 (step @p10 (= tptp.emptyset @t15) :rule refl :args (@t15)) % 0.37/0.57 (step @p11 (= tptp.union @t18) :rule refl :args (@t18)) % 0.37/0.57 (step @p12 (= tptp.singleton @t20) :rule refl :args (@t20)) % 0.37/0.57 (step @p13 (= tptp.supset @t25) :rule refl :args (@t25)) % 0.37/0.57 (step @p14 (= tptp.unionset @t26) :rule refl :args (@t26)) % 0.37/0.57 (step @p15 (= tptp.addition @t29) :rule refl :args (@t29)) % 0.37/0.57 (step @p16 (= tptp.crossmult @t32) :rule refl :args (@t32)) % 0.37/0.57 (step @p17 :rule refl :args (@t37)) % 0.37/0.57 (step @p18 :rule refl :args (@t38)) % 0.37/0.57 (step @p19 :rule cong :premises (@p18 @p17) :args ((= @t38 @t37))) % 0.37/0.57 (step @p20 :rule symm :premises (@p19)) % 0.37/0.57 (step @p21 :rule eq_resolve :premises (@p18 @p20)) % 0.37/0.57 (step @p22 :rule refl :args (@t40)) % 0.37/0.57 (step @p23 :rule refl :args (@t41)) % 0.37/0.57 (step @p24 :rule cong :premises (@p23 @p22) :args ((= @t41 @t40))) % 0.37/0.57 (step @p25 :rule symm :premises (@p24)) % 0.37/0.57 (step @p26 :rule eq_resolve :premises (@p23 @p25)) % 0.37/0.57 (step @p27 :rule cong :premises (@p26 @p21) :args (@t42)) % 0.37/0.57 (step @p28 :rule cong :premises (@p27) :args ((forall @t8 @t42))) % 0.37/0.57 (step @p29 :rule beta-reduce :args ((= (_ (lambda @t44 (_ tptp.sup (lambda @t35 (or @t34 @t43)))) @t6) @t38))) % 0.37/0.57 (step @p30 :rule refl :args (@t6)) % 0.37/0.57 (step @p31 :rule refl :args (@t43)) % 0.37/0.57 (step @p32 :rule eq-symm :args (@t5 @t16)) % 0.37/0.57 (step @p33 :rule nary_cong :premises (@p32 @p31) :args (@t45)) % 0.37/0.57 (step @p34 :rule cong :premises (@p33) :args (@t46)) % 0.37/0.57 (step @p35 :rule refl :args (tptp.sup)) % 0.37/0.57 (step @p36 :rule ho_cong :premises (@p35 @p34)) % 0.37/0.57 (step @p37 :rule cong :premises (@p36) :args (@t47)) % 0.37/0.57 (step @p38 :rule beta-reduce :args ((= @t50 @t47))) % 0.37/0.57 (step @p39 :rule trans :premises (@p38 @p37)) % 0.37/0.57 (step @p40 :rule ho_cong :premises (@p39 @p30)) % 0.37/0.57 (step @p41 :rule trans :premises (@p40 @p29)) % 0.37/0.57 (step @p42 :rule beta-reduce :args ((= (_ (lambda @t44 (_ tptp.sup (lambda @t35 (or @t33 @t43)))) @t5) @t41))) % 0.37/0.57 (step @p43 :rule refl :args (@t5)) % 0.37/0.57 (step @p44 :rule eq-symm :args (@t6 @t16)) % 0.37/0.57 (step @p45 :rule nary_cong :premises (@p44 @p31) :args (@t51)) % 0.37/0.57 (step @p46 :rule cong :premises (@p45) :args (@t52)) % 0.37/0.57 (step @p47 :rule ho_cong :premises (@p35 @p46)) % 0.37/0.57 (step @p48 :rule cong :premises (@p47) :args (@t53)) % 0.37/0.57 (step @p49 :rule beta-reduce :args ((= @t54 @t53))) % 0.37/0.57 (step @p50 :rule trans :premises (@p49 @p48)) % 0.37/0.57 (step @p51 :rule ho_cong :premises (@p50 @p43)) % 0.37/0.57 (step @p52 :rule trans :premises (@p51 @p42)) % 0.37/0.57 (step @p53 :rule cong :premises (@p52 @p41) :args (@t55)) % 0.37/0.57 (step @p54 :rule cong :premises (@p53) :args (@t56)) % 0.37/0.57 (step @p55 :rule trans :premises (@p54 @p28)) % 0.37/0.57 (step @p56 :rule cong :premises (@p55) :args ((not @t56))) % 0.37/0.57 (step @p57 :rule beta-reduce :args ((= @t58 @t43))) % 0.37/0.57 (step @p58 :rule refl :args (@t48)) % 0.37/0.57 (step @p59 :rule nary_cong :premises (@p58 @p57) :args (@t59)) % 0.37/0.57 (step @p60 :rule cong :premises (@p59) :args (@t60)) % 0.37/0.57 (step @p61 :rule beta-reduce :args ((= (_ (lambda @t61 (or @t48 @t17)) @t57) @t60))) % 0.37/0.57 (step @p62 :rule trans :premises (@p61 @p60)) % 0.37/0.57 (step @p63 :rule eq-symm :args (@t27 @t16)) % 0.37/0.57 (step @p64 :rule cong :premises (@p63) :args (@t62)) % 0.37/0.57 (step @p65 :rule beta-reduce :args ((= (_ @t63 @t27) @t62))) % 0.37/0.57 (step @p66 :rule trans :premises (@p65 @p64)) % 0.37/0.57 (step @p67 :rule refl :args (@t17)) % 0.37/0.57 (step @p68 :rule beta-reduce :args ((= @t65 @t48))) % 0.37/0.57 (step @p69 :rule nary_cong :premises (@p68 @p67) :args (@t66)) % 0.37/0.57 (step @p70 :rule cong :premises (@p69) :args (@t67)) % 0.37/0.57 (step @p71 :rule beta-reduce :args ((= (_ @t18 @t64) @t67))) % 0.37/0.57 (step @p72 :rule trans :premises (@p71 @p70)) % 0.37/0.57 (step @p73 :rule beta-reduce :args ((= (_ @t63 @t1) @t64))) % 0.37/0.57 (step @p74 :rule refl :args (@t18)) % 0.37/0.57 (step @p75 :rule ho_cong :premises (@p74 @p73)) % 0.37/0.57 (step @p76 :rule trans :premises (@p75 @p72)) % 0.37/0.57 (step @p77 :rule ho_cong :premises (@p76 @p66)) % 0.37/0.57 (step @p78 :rule trans :premises (@p77 @p62)) % 0.37/0.57 (step @p79 :rule ho_cong :premises (@p35 @p78)) % 0.37/0.57 (step @p80 :rule refl :args (@t27)) % 0.37/0.57 (step @p81 :rule eq-symm :args (@t16 @t1)) % 0.37/0.57 (step @p82 :rule cong :premises (@p81) :args (@t20)) % 0.37/0.57 (step @p83 :rule trans :premises (@p12 @p82)) % 0.37/0.57 (step @p84 :rule ho_cong :premises (@p83 @p80)) % 0.37/0.57 (step @p85 :rule refl :args (@t1)) % 0.37/0.57 (step @p86 :rule ho_cong :premises (@p83 @p85)) % 0.37/0.57 (step @p87 :rule ho_cong :premises (@p11 @p86)) % 0.37/0.57 (step @p88 :rule ho_cong :premises (@p87 @p84)) % 0.37/0.57 (step @p89 :rule ho_cong :premises (@p35 @p88)) % 0.37/0.57 (step @p90 :rule trans :premises (@p89 @p79)) % 0.37/0.57 (step @p91 :rule cong :premises (@p90) :args (@t29)) % 0.37/0.57 (step @p92 :rule trans :premises (@p15 @p91)) % 0.37/0.57 (step @p93 :rule ho_cong :premises (@p92 @p43)) % 0.37/0.57 (step @p94 :rule ho_cong :premises (@p93 @p30)) % 0.37/0.57 (step @p95 :rule ho_cong :premises (@p92 @p30)) % 0.37/0.57 (step @p96 :rule ho_cong :premises (@p95 @p43)) % 0.37/0.57 (step @p97 :rule cong :premises (@p96 @p94) :args (@t12)) % 0.37/0.57 (step @p98 :rule cong :premises (@p97) :args (@t13)) % 0.37/0.57 (step @p99 :rule cong :premises (@p98) :args (@t14)) % 0.37/0.57 (step @p100 :rule trans :premises (@p99 @p56)) % 0.37/0.57 (step @p101 :rule eq_resolve :premises (@p8 @p100)) % 0.37/0.57 (step @p102 :rule refl :args (@t80)) % 0.37/0.57 (step @p103 :rule bool-double-not-elim :args (@t68)) % 0.37/0.57 (step @p104 :rule nary_cong :premises (@p103 @p102) :args ((or (not @t81) @t80))) % 0.37/0.57 (step @p105 :rule eq-symm :args (@t75 @t78)) % 0.37/0.57 (step @p106 :rule eq-refl :args (@t76)) % 0.37/0.57 (step @p107 :rule skolem_intro :args (@t77)) % 0.37/0.57 (step @p108 :rule refl :args (@t76)) % 0.37/0.57 (step @p109 :rule cong :premises (@p108 @p107) :args ((= @t76 @t77))) % 0.37/0.57 (step @p110 :rule trans :premises (@p109 @p106)) % 0.37/0.57 (step @p111 :rule true_elim :premises (@p110)) % 0.37/0.57 (step @p112 :rule cong :premises (@p111) :args (@t82)) % 0.37/0.57 (step @p113 :rule eq-refl :args (@t73)) % 0.37/0.57 (step @p114 :rule skolem_intro :args (@t74)) % 0.37/0.57 (step @p115 :rule refl :args (@t73)) % 0.37/0.57 (step @p116 :rule cong :premises (@p115 @p114) :args ((= @t73 @t74))) % 0.37/0.57 (step @p117 :rule trans :premises (@p116 @p113)) % 0.37/0.57 (step @p118 :rule true_elim :premises (@p117)) % 0.37/0.57 (step @p119 :rule cong :premises (@p118) :args (@t83)) % 0.37/0.57 (step @p120 :rule cong :premises (@p119 @p112) :args (@t84)) % 0.37/0.57 (step @p121 :rule trans :premises (@p120 @p105)) % 0.37/0.57 (step @p122 :rule cong :premises (@p121) :args (@t85)) % 0.37/0.57 (step @p123 :rule refl :args (@t81)) % 0.37/0.57 (step @p124 :rule cong :premises (@p123 @p122) :args ((=> @t81 @t85))) % 0.37/0.57 (assume-push @p196 @t81) % 0.37/0.57 (step @p126 :rule skolemize :premises (@p101)) % 0.37/0.57 (step-pop @p197 :rule scope :premises (@p126)) % 0.37/0.57 (step @p127 :rule process_scope :premises (@p197) :args (@t85)) % 0.37/0.57 (step @p129 :rule eq_resolve :premises (@p127 @p124)) % 0.37/0.57 (step @p130 :rule implies_elim :premises (@p129)) % 0.37/0.57 (step @p131 :rule eq_resolve :premises (@p130 @p104)) % 0.37/0.57 (step @p132 :rule chain_m_resolution :premises (@p131 @p101) :args (@t80 @t86 (@list @t68))) % 0.37/0.57 (assume-push @p198 @t87) % 0.37/0.57 (assume-push @p199 @t87) % 0.37/0.57 (step @p135 :rule cong :premises (@p198) :args (@t78)) % 0.37/0.57 (step-pop @p200 :rule scope :premises (@p135)) % 0.37/0.57 (step @p136 :rule process_scope :premises (@p200) :args (@t79)) % 0.37/0.57 (step @p138 :rule modus_ponens :premises (@p198 @p136)) % 0.37/0.57 (step-pop @p201 :rule scope :premises (@p138)) % 0.37/0.57 (step @p139 :rule process_scope :premises (@p201) :args (@t79)) % 0.37/0.57 (step @p141 :rule implies_elim :premises (@p139)) % 0.37/0.57 (step @p142 :rule reordering :premises (@p141) :args ((or @t79 @t88))) % 0.37/0.57 (step @p143 :rule chain_m_resolution :premises (@p142 @p132) :args (@t88 @t86 (@list @t79))) % 0.37/0.57 (step @p144 :rule aci_norm :args (@t94)) % 0.37/0.57 (step @p145 :rule symm :premises (@p144)) % 0.37/0.57 (step @p146 :rule cong :premises (@p145 @p144) :args ((= @t92 @t93))) % 0.37/0.57 (step @p147 :rule eq-refl :args (@t93)) % 0.37/0.57 (step @p148 :rule refl :args (@t93)) % 0.37/0.57 (step @p149 :rule eq-symm :args (@t89 @t69)) % 0.37/0.57 (step @p150 :rule eq-symm :args (@t89 @t71)) % 0.37/0.57 (step @p151 :rule nary_cong :premises (@p150 @p149) :args (@t97)) % 0.37/0.57 (step @p152 :rule beta-reduce :args ((= @t98 @t97))) % 0.37/0.57 (step @p153 :rule trans :premises (@p152 @p151)) % 0.37/0.57 (step @p154 :rule cong :premises (@p153 @p148) :args ((= @t98 @t93))) % 0.37/0.57 (step @p155 :rule trans :premises (@p154 @p147)) % 0.37/0.57 (step @p156 :rule refl :args (@t89)) % 0.37/0.57 (step @p157 :rule ho_cong :premises (@p114 @p156)) % 0.37/0.57 (step @p158 :rule cong :premises (@p157 @p148) :args ((= @t99 @t93))) % 0.37/0.57 (step @p159 :rule trans :premises (@p158 @p155)) % 0.37/0.57 (step @p160 :rule true_elim :premises (@p159)) % 0.37/0.57 (step @p161 :rule eq-refl :args (@t92)) % 0.37/0.57 (step @p162 :rule refl :args (@t92)) % 0.37/0.57 (step @p163 :rule nary_cong :premises (@p149 @p150) :args (@t100)) % 0.37/0.57 (step @p164 :rule beta-reduce :args ((= @t101 @t100))) % 0.37/0.57 (step @p165 :rule trans :premises (@p164 @p163)) % 0.37/0.57 (step @p166 :rule cong :premises (@p165 @p162) :args ((= @t101 @t92))) % 0.37/0.57 (step @p167 :rule trans :premises (@p166 @p161)) % 0.37/0.57 (step @p168 :rule ho_cong :premises (@p107 @p156)) % 0.37/0.57 (step @p169 :rule cong :premises (@p168 @p162) :args ((= @t102 @t92))) % 0.37/0.57 (step @p170 :rule trans :premises (@p169 @p167)) % 0.37/0.57 (step @p171 :rule true_elim :premises (@p170)) % 0.37/0.57 (step @p172 :rule cong :premises (@p171 @p160) :args (@t103)) % 0.37/0.57 (step @p173 :rule trans :premises (@p172 @p146)) % 0.37/0.57 (step @p174 :rule cong :premises (@p173) :args (@t104)) % 0.37/0.57 (step @p175 :rule refl :args (@t87)) % 0.37/0.57 (step @p176 :rule nary_cong :premises (@p175 @p174) :args (@t105)) % 0.37/0.57 ; WARNING: add trust step for TRUST % 0.37/0.57 ; trust TRUST THEORY_LEMMA % 0.37/0.57 (step @p177 :rule trust :premises () :args (@t105)) % 0.37/0.57 (step @p178 :rule eq_resolve :premises (@p177 @p176)) % 0.37/0.57 (step @p179 :rule chain_m_resolution :premises (@p178 @p143) :args ((not @t94) @t86 (@list @t87))) % 0.37/0.57 (step @p180 :rule cnf_or_neg :args (@t93 1)) % 0.37/0.57 (step @p181 :rule cnf_or_neg :args (@t92 0)) % 0.37/0.57 (step @p182 :rule cnf_equiv_neg2 :args (@t94)) % 0.37/0.57 (step @p183 :rule chain_m_resolution :premises (@p182 @p179 @p181 @p180) :args ((not @t91) @t106 @t107)) % 0.37/0.57 (step @p184 :rule cnf_or_neg :args (@t93 0)) % 0.37/0.57 (step @p185 :rule cnf_or_neg :args (@t92 1)) % 0.37/0.57 (step @p186 :rule chain_m_resolution :premises (@p182 @p179 @p185 @p184) :args ((not @t90) @t106 @t107)) % 0.37/0.57 (step @p187 :rule cnf_or_pos :args (@t93)) % 0.37/0.57 (step @p188 :rule reordering :premises (@p187) :args ((or @t90 @t91 @t108))) % 0.37/0.57 (step @p189 :rule chain_m_resolution :premises (@p188 @p186 @p183) :args (@t108 @t109 @t110)) % 0.37/0.57 (step @p190 :rule cnf_or_pos :args (@t92)) % 0.37/0.57 (step @p191 :rule reordering :premises (@p190) :args ((or @t90 @t91 @t111))) % 0.37/0.57 (step @p192 :rule chain_m_resolution :premises (@p191 @p186 @p183) :args (@t111 @t109 @t110)) % 0.37/0.57 (step @p193 :rule cnf_equiv_neg1 :args (@t94)) % 0.37/0.57 (step @p194 :rule reordering :premises (@p193) :args ((or @t93 @t92 @t94))) % 0.37/0.57 (step @p195 false :rule chain_m_resolution :premises (@p194 @p192 @p189 @p179) :args (false (@list true true true) (@list @t92 @t93 @t94))) % 0.37/0.57 ) % 0.37/0.57 % SZS output end Proof % 0.37/0.57 % cvc5 exiting %------------------------------------------------------------------------------