%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWV429^2 : TPTP v9.2.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n022.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 09:01:31 AM UTC 2026 % Result : Theorem 0.37s 0.60s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SWV429^2 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.19/0.35 % Computer : n022.cluster.edu % 0.19/0.35 % Model : x86_64 x86_64 % 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.19/0.35 % Memory : 8042.1875MB % 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.19/0.35 % CPULimit : 300 % 0.19/0.35 % WCLimit : 300 % 0.19/0.35 % DateTime : Tue Jun 2 20:17:38 EDT 2026 % 0.19/0.35 % CPUTime : % 0.28/0.51 %----Proving TH0 % 0.37/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.60 % SZS status Theorem % 0.37/0.60 % SZS output start Proof % 0.37/0.60 ( % 0.37/0.60 (declare-sort $$unsorted 0) % 0.37/0.60 (declare-sort tptp.individuals 0) % 0.37/0.60 (declare-const tptp.rel (-> $$unsorted $$unsorted Bool)) % 0.37/0.60 (declare-const tptp.a (-> $$unsorted Bool)) % 0.37/0.60 (declare-const tptp.icl_true (-> $$unsorted Bool)) % 0.37/0.60 (declare-const tptp.icl_false (-> $$unsorted Bool)) % 0.37/0.60 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.37/0.60 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.37/0.60 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.37/0.60 (define tptp.mor () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.60 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.60 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "V" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.37/0.60 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.37/0.60 (define tptp.mbox () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.37/0.60 (define tptp.mdia () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.37/0.60 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.37/0.60 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.37/0.60 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.37/0.60 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.37/0.60 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.37/0.60 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.37/0.60 (define tptp.icl_atom () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ (_ tptp.mbox tptp.rel) _let_2) _let_1))))) % 0.37/0.60 (define tptp.icl_princ () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ _let_2 _let_1))))) % 0.37/0.60 (define tptp.icl_and () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "B" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mand _let_3) _let_2) _let_1)))))) % 0.37/0.60 (define tptp.icl_or () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "B" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor _let_3) _let_2) _let_1)))))) % 0.37/0.60 (define tptp.icl_impl () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "B" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mbox tptp.rel) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.37/0.60 (define tptp.icl_says () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "S" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mbox tptp.rel) (_ (_ tptp.mor _let_3) _let_2)) _let_1)))))) % 0.37/0.60 (define tptp.iclval () (let ((_let_1 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_1) (_ tptp.mvalid _let_1)))) % 0.37/0.60 (define tptp.icl_impl_princ () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "B" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mbox tptp.rel) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.37/0.60 (define @t1 () (@var "A" (-> $$unsorted Bool))) % 0.37/0.60 (define @t2 () (_ tptp.mbox tptp.rel)) % 0.37/0.60 (define @t3 () (@var "B" (-> $$unsorted Bool))) % 0.37/0.60 (define @t4 () (_ @t2 @t3)) % 0.37/0.60 (define @t5 () (_ tptp.icl_princ tptp.a)) % 0.37/0.60 (define @t6 () (not (_ tptp.iclval (_ (_ tptp.icl_impl_princ @t5) @t5)))) % 0.37/0.60 (define @t7 () (@var "X" $$unsorted)) % 0.37/0.60 (define @t8 () (@list @t7)) % 0.37/0.60 (define @t9 () (lambda @t8 false)) % 0.37/0.60 (define @t10 () (lambda @t8 true)) % 0.37/0.60 (define @t11 () (@var "U" $$unsorted)) % 0.37/0.60 (define @t12 () (@var "X" (-> $$unsorted Bool))) % 0.37/0.60 (define @t13 () (_ @t12 @t11)) % 0.37/0.60 (define @t14 () (lambda (@list @t12 @t11) (not @t13))) % 0.37/0.60 (define @t15 () (@var "Y" (-> $$unsorted Bool))) % 0.37/0.60 (define @t16 () (_ @t15 @t11)) % 0.37/0.60 (define @t17 () (@list @t12 @t15 @t11)) % 0.37/0.60 (define @t18 () (lambda @t17 (or @t13 @t16))) % 0.37/0.60 (define @t19 () (lambda @t17 (and @t13 @t16))) % 0.37/0.60 (define @t20 () (@var "__flatten_var_0" $$unsorted)) % 0.37/0.60 (define @t21 () (@var "V" (-> $$unsorted Bool))) % 0.37/0.60 (define @t22 () (@var "U" (-> $$unsorted Bool))) % 0.37/0.60 (define @t23 () (@list @t22 @t21 @t20)) % 0.37/0.60 (define @t24 () (lambda @t23 (_ (_ (_ tptp.mor (_ tptp.mnot @t22)) @t21) @t20))) % 0.37/0.60 (define @t25 () (lambda @t23 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t22) @t21)) (_ (_ tptp.mimpl @t21) @t22)) @t20))) % 0.37/0.60 (define @t26 () (@var "Y" $$unsorted)) % 0.37/0.60 (define @t27 () (@var "P" (-> $$unsorted Bool))) % 0.37/0.60 (define @t28 () (_ @t27 @t26)) % 0.37/0.60 (define @t29 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.37/0.60 (define @t30 () (_ (_ @t29 @t7) @t26)) % 0.37/0.60 (define @t31 () (@list @t26)) % 0.37/0.60 (define @t32 () (forall @t31 (=> @t30 @t28))) % 0.37/0.60 (define @t33 () (@list @t29 @t27 @t7)) % 0.37/0.60 (define @t34 () (lambda @t33 @t32)) % 0.37/0.60 (define @t35 () (lambda @t33 (exists @t31 (and @t30 @t28)))) % 0.37/0.60 (define @t36 () (@var "W" $$unsorted)) % 0.37/0.60 (define @t37 () (@var "X" tptp.individuals)) % 0.37/0.60 (define @t38 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.37/0.60 (define @t39 () (_ (_ @t38 @t37) @t36)) % 0.37/0.60 (define @t40 () (@list @t37)) % 0.37/0.60 (define @t41 () (@list @t38 @t36)) % 0.37/0.60 (define @t42 () (lambda @t41 (forall @t40 @t39))) % 0.37/0.60 (define @t43 () (lambda @t41 (exists @t40 @t39))) % 0.37/0.60 (define @t44 () (_ @t27 @t36)) % 0.37/0.60 (define @t45 () (@list @t36)) % 0.37/0.60 (define @t46 () (forall @t45 @t44)) % 0.37/0.60 (define @t47 () (@list @t27)) % 0.37/0.60 (define @t48 () (lambda @t47 @t46)) % 0.37/0.60 (define @t49 () (lambda @t47 (exists @t45 @t44))) % 0.37/0.60 (define @t50 () (not @t44)) % 0.37/0.60 (define @t51 () (lambda @t47 (exists @t45 @t50))) % 0.37/0.60 (define @t52 () (lambda @t47 (forall @t45 @t50))) % 0.37/0.60 (define @t53 () (@list @t27 @t20)) % 0.37/0.60 (define @t54 () (lambda @t53 (_ (_ @t2 @t27) @t20))) % 0.37/0.60 (define @t55 () (lambda @t53 (_ @t27 @t20))) % 0.37/0.60 (define @t56 () (@list @t1 @t3 @t20)) % 0.37/0.60 (define @t57 () (lambda @t56 (_ (_ (_ tptp.mand @t1) @t3) @t20))) % 0.37/0.60 (define @t58 () (_ tptp.mor @t1)) % 0.37/0.60 (define @t59 () (lambda @t56 (_ (_ @t58 @t3) @t20))) % 0.37/0.60 (define @t60 () (lambda @t56 (_ (_ @t2 (_ (_ tptp.mimpl @t1) @t3)) @t20))) % 0.37/0.60 (define @t61 () (@var "S" (-> $$unsorted Bool))) % 0.37/0.60 (define @t62 () (lambda (@list @t1 @t61 @t20) (_ (_ @t2 (_ @t58 @t61)) @t20))) % 0.37/0.60 (define @t63 () (@list @t12)) % 0.37/0.60 (define @t64 () (lambda @t63 (_ tptp.mvalid @t12))) % 0.37/0.60 (define @t65 () (@var "BOUND_VARIABLE_8190" $$unsorted)) % 0.37/0.60 (define @t66 () (lambda (@list @t65) true)) % 0.37/0.60 (define @t67 () (_ @t66 @t36)) % 0.37/0.60 (define @t68 () (forall @t45 @t67)) % 0.37/0.60 (define @t69 () (forall @t45 (_ @t12 @t36))) % 0.37/0.60 (define @t70 () (lambda @t63 @t69)) % 0.37/0.60 (define @t71 () (@list @t20)) % 0.37/0.60 (define @t72 () (not (tptp.rel @t20 @t26))) % 0.37/0.60 (define @t73 () (tptp.a @t26)) % 0.37/0.60 (define @t74 () (not @t73)) % 0.37/0.60 (define @t75 () (_ tptp.a @t26)) % 0.37/0.60 (define @t76 () (or @t72 @t74 @t75)) % 0.37/0.60 (define @t77 () (lambda @t71 (_ tptp.a @t20))) % 0.37/0.60 (define @t78 () (_ @t77 @t26)) % 0.37/0.60 (define @t79 () (or @t72 @t74 @t78)) % 0.37/0.60 (define @t80 () (forall @t31 @t79)) % 0.37/0.60 (define @t81 () (lambda @t71 @t80)) % 0.37/0.60 (define @t82 () (_ @t3 @t26)) % 0.37/0.60 (define @t83 () (@list @t3 @t20)) % 0.37/0.60 (define @t84 () (_ @t55 tptp.a)) % 0.37/0.60 (define @t85 () (not @t75)) % 0.37/0.60 (define @t86 () (or @t72 @t85 @t82)) % 0.37/0.60 (define @t87 () (not @t78)) % 0.37/0.60 (define @t88 () (or @t72 @t87 @t82)) % 0.37/0.60 (define @t89 () (forall @t31 @t88)) % 0.37/0.60 (define @t90 () (lambda @t83 @t89)) % 0.37/0.60 (define @t91 () (_ @t1 @t26)) % 0.37/0.60 (define @t92 () (not @t91)) % 0.37/0.60 (define @t93 () (forall @t31 (or @t72 @t92 @t82))) % 0.37/0.60 (define @t94 () (lambda @t56 @t93)) % 0.37/0.60 (define @t95 () (not (tptp.rel @t7 @t26))) % 0.37/0.60 (define @t96 () (_ @t3 @t26)) % 0.37/0.60 (define @t97 () (_ @t1 @t26)) % 0.37/0.60 (define @t98 () (not @t97)) % 0.37/0.60 (define @t99 () (or @t95 @t98 @t96)) % 0.37/0.60 (define @t100 () (or @t98 @t96)) % 0.37/0.60 (define @t101 () (not (_ @t1 @t20))) % 0.37/0.60 (define @t102 () (lambda @t71 (or @t101 (_ @t3 @t20)))) % 0.37/0.60 (define @t103 () (_ @t102 @t26)) % 0.37/0.60 (define @t104 () (or @t95 @t103)) % 0.37/0.60 (define @t105 () (forall @t31 @t104)) % 0.37/0.60 (define @t106 () (lambda @t8 @t105)) % 0.37/0.60 (define @t107 () (_ @t27 @t26)) % 0.37/0.60 (define @t108 () (lambda (@list @t27 @t7) (forall @t31 (or @t95 @t107)))) % 0.37/0.60 (define @t109 () (_ @t21 @t20)) % 0.37/0.60 (define @t110 () (lambda (@list @t21 @t20) (or @t101 @t109))) % 0.37/0.60 (define @t111 () (or (not (_ @t22 @t20)) @t109)) % 0.37/0.60 (define @t112 () (_ @t29 @t7 @t26)) % 0.37/0.60 (define @t113 () (not (_ @t22 @t11))) % 0.37/0.60 (define @t114 () (@list @t11)) % 0.37/0.60 (define @t115 () (lambda @t114 (or @t113 (_ @t21 @t11)))) % 0.37/0.60 (define @t116 () (@list @t15 @t11)) % 0.37/0.60 (define @t117 () (lambda @t114 @t113)) % 0.37/0.60 (define @t118 () (_ @t117 @t11)) % 0.37/0.60 (define @t119 () (or @t118 @t16)) % 0.37/0.60 (define @t120 () (lambda @t116 @t119)) % 0.37/0.60 (define @t121 () (not @t30)) % 0.37/0.60 (define @t122 () (or @t121 @t28)) % 0.37/0.60 (define @t123 () (_ @t27 @t36)) % 0.37/0.60 (assume @p1 (= tptp.icl_true tptp.mtrue)) % 0.37/0.60 (assume @p2 (= tptp.icl_false tptp.mfalse)) % 0.37/0.60 (assume @p3 (forall (@list @t1) (_ tptp.mvalid (_ (_ tptp.mimpl (_ @t2 @t1)) @t1)))) % 0.37/0.60 (assume @p4 (forall (@list @t3) (_ tptp.mvalid (_ (_ tptp.mimpl @t4) (_ @t2 @t4))))) % 0.37/0.60 (assume @p5 @t6) % 0.37/0.60 (assume @p6 true) % 0.37/0.60 (step @p7 (= tptp.mfalse @t9) :rule refl :args (@t9)) % 0.37/0.60 (step @p8 (= tptp.mtrue @t10) :rule refl :args (@t10)) % 0.37/0.60 (step @p9 (= tptp.mnot @t14) :rule refl :args (@t14)) % 0.37/0.60 (step @p10 (= tptp.mor @t18) :rule refl :args (@t18)) % 0.37/0.60 (step @p11 (= tptp.mand @t19) :rule refl :args (@t19)) % 0.37/0.60 (step @p12 (= tptp.mimpl @t24) :rule refl :args (@t24)) % 0.37/0.60 (step @p13 (= tptp.miff @t25) :rule refl :args (@t25)) % 0.37/0.60 (step @p14 (= tptp.mbox @t34) :rule refl :args (@t34)) % 0.37/0.60 (step @p15 (= tptp.mdia @t35) :rule refl :args (@t35)) % 0.37/0.60 (step @p16 (= tptp.mall @t42) :rule refl :args (@t42)) % 0.37/0.60 (step @p17 (= tptp.mexists @t43) :rule refl :args (@t43)) % 0.37/0.60 (step @p18 (= tptp.mvalid @t48) :rule refl :args (@t48)) % 0.37/0.60 (step @p19 (= tptp.msatisfiable @t49) :rule refl :args (@t49)) % 0.37/0.60 (step @p20 (= tptp.mcountersatisfiable @t51) :rule refl :args (@t51)) % 0.37/0.60 (step @p21 (= tptp.minvalid @t52) :rule refl :args (@t52)) % 0.37/0.60 (step @p22 (= tptp.icl_atom @t54) :rule refl :args (@t54)) % 0.37/0.60 (step @p23 (= tptp.icl_princ @t55) :rule refl :args (@t55)) % 0.37/0.60 (step @p24 (= tptp.icl_and @t57) :rule refl :args (@t57)) % 0.37/0.60 (step @p25 (= tptp.icl_or @t59) :rule refl :args (@t59)) % 0.37/0.60 (step @p26 (= tptp.icl_impl @t60) :rule refl :args (@t60)) % 0.37/0.60 (step @p27 (= tptp.icl_says @t62) :rule refl :args (@t62)) % 0.37/0.60 (step @p28 (= tptp.iclval @t64) :rule refl :args (@t64)) % 0.37/0.60 (step @p29 (= tptp.icl_impl_princ @t60) :rule refl :args (@t60)) % 0.37/0.60 (step @p30 :rule evaluate :args ((not true))) % 0.37/0.60 (step @p31 :rule quant-unused-vars :args ((= (forall @t45 true) true))) % 0.37/0.60 (step @p32 :rule beta-reduce :args ((= @t67 true))) % 0.37/0.60 (step @p33 :rule cong :premises (@p32) :args (@t68)) % 0.37/0.60 (step @p34 :rule trans :premises (@p33 @p31)) % 0.37/0.60 (step @p35 :rule beta-reduce :args ((= (_ @t70 @t66) @t68))) % 0.37/0.60 (step @p36 :rule trans :premises (@p35 @p34)) % 0.37/0.60 (step @p37 :rule refl :args (@t66)) % 0.37/0.60 (step @p38 :rule symm :premises (@p37)) % 0.37/0.60 (step @p39 :rule alpha_equiv :args ((lambda @t71 true) (@list @t20) (@list @t65))) % 0.37/0.60 (step @p40 :rule trans :premises (@p39 @p38)) % 0.37/0.60 (step @p41 :rule quant-unused-vars :args ((= (forall @t31 true) true))) % 0.37/0.60 (step @p42 :rule bool-or-taut2 :args ((or @t72) @t73 false false)) % 0.37/0.60 (step @p43 :rule cong :premises (@p42) :args ((forall @t31 (or @t72 @t74 @t73)))) % 0.37/0.60 (step @p44 :rule trans :premises (@p43 @p41)) % 0.37/0.60 (step @p45 :rule refl :args (@t73)) % 0.37/0.60 (step @p46 :rule refl :args (@t75)) % 0.37/0.60 (step @p47 :rule cong :premises (@p46 @p45) :args ((= @t75 @t73))) % 0.37/0.60 (step @p48 :rule symm :premises (@p47)) % 0.37/0.60 (step @p49 :rule eq_resolve :premises (@p46 @p48)) % 0.37/0.60 (step @p50 :rule refl :args (@t74)) % 0.37/0.60 (step @p51 :rule refl :args (@t72)) % 0.37/0.60 (step @p52 :rule nary_cong :premises (@p51 @p50 @p49) :args (@t76)) % 0.37/0.60 (step @p53 :rule cong :premises (@p52) :args ((forall @t31 @t76))) % 0.37/0.60 (step @p54 :rule trans :premises (@p53 @p44)) % 0.37/0.60 (step @p55 :rule beta-reduce :args ((= @t78 @t75))) % 0.37/0.60 (step @p56 :rule refl :args (@t74)) % 0.37/0.60 (step @p57 :rule refl :args (@t72)) % 0.37/0.60 (step @p58 :rule nary_cong :premises (@p57 @p56 @p55) :args (@t79)) % 0.37/0.60 (step @p59 :rule cong :premises (@p58) :args (@t80)) % 0.37/0.60 (step @p60 :rule trans :premises (@p59 @p54)) % 0.37/0.60 (step @p61 :rule cong :premises (@p60) :args (@t81)) % 0.37/0.60 (step @p62 :rule trans :premises (@p61 @p40)) % 0.37/0.60 (step @p63 :rule beta-reduce :args ((= (_ (lambda @t83 (forall @t31 (or @t72 @t74 @t82))) @t77) @t81))) % 0.37/0.60 (step @p64 :rule trans :premises (@p63 @p62)) % 0.37/0.60 (step @p65 :rule beta-reduce :args ((= @t84 @t77))) % 0.37/0.60 (step @p66 :rule refl :args (@t82)) % 0.37/0.60 (step @p67 :rule cong :premises (@p49) :args (@t85)) % 0.37/0.60 (step @p68 :rule nary_cong :premises (@p51 @p67 @p66) :args (@t86)) % 0.37/0.60 (step @p69 :rule cong :premises (@p68) :args ((forall @t31 @t86))) % 0.37/0.60 (step @p70 :rule refl :args (@t82)) % 0.37/0.60 (step @p71 :rule cong :premises (@p55) :args (@t87)) % 0.37/0.60 (step @p72 :rule nary_cong :premises (@p57 @p71 @p70) :args (@t88)) % 0.37/0.60 (step @p73 :rule cong :premises (@p72) :args (@t89)) % 0.37/0.60 (step @p74 :rule trans :premises (@p73 @p69)) % 0.37/0.60 (step @p75 :rule cong :premises (@p74) :args (@t90)) % 0.37/0.60 (step @p76 :rule beta-reduce :args ((= (_ @t94 @t77) @t90))) % 0.37/0.60 (step @p77 :rule trans :premises (@p76 @p75)) % 0.37/0.60 (step @p78 :rule refl :args (@t94)) % 0.37/0.60 (step @p79 :rule ho_cong :premises (@p78 @p65)) % 0.37/0.60 (step @p80 :rule trans :premises (@p79 @p77)) % 0.37/0.60 (step @p81 :rule ho_cong :premises (@p80 @p65)) % 0.37/0.60 (step @p82 :rule trans :premises (@p81 @p64)) % 0.37/0.60 (step @p83 :rule refl :args (@t70)) % 0.37/0.60 (step @p84 :rule ho_cong :premises (@p83 @p82)) % 0.37/0.60 (step @p85 :rule trans :premises (@p84 @p36)) % 0.37/0.60 (step @p86 :rule cong :premises (@p85) :args ((not (_ @t70 (_ (_ @t94 @t84) @t84))))) % 0.37/0.60 (step @p87 :rule trans :premises (@p86 @p30)) % 0.37/0.60 (step @p88 :rule refl :args (tptp.a)) % 0.37/0.60 (step @p89 :rule ho_cong :premises (@p23 @p88)) % 0.37/0.60 (step @p90 :rule beta-reduce :args ((= (_ (lambda @t8 (forall @t31 (or @t95 @t92 @t82))) @t20) @t93))) % 0.37/0.60 (step @p91 :rule refl :args (@t20)) % 0.37/0.60 (step @p92 :rule refl :args (@t82)) % 0.37/0.60 (step @p93 :rule refl :args (@t96)) % 0.37/0.60 (step @p94 :rule cong :premises (@p93 @p92) :args ((= @t96 @t82))) % 0.37/0.60 (step @p95 :rule symm :premises (@p94)) % 0.37/0.60 (step @p96 :rule eq_resolve :premises (@p93 @p95)) % 0.37/0.60 (step @p97 :rule refl :args (@t91)) % 0.37/0.60 (step @p98 :rule refl :args (@t97)) % 0.37/0.60 (step @p99 :rule cong :premises (@p98 @p97) :args ((= @t97 @t91))) % 0.37/0.60 (step @p100 :rule symm :premises (@p99)) % 0.37/0.60 (step @p101 :rule eq_resolve :premises (@p98 @p100)) % 0.37/0.60 (step @p102 :rule cong :premises (@p101) :args (@t98)) % 0.37/0.60 (step @p103 :rule refl :args (@t95)) % 0.37/0.60 (step @p104 :rule nary_cong :premises (@p103 @p102 @p96) :args (@t99)) % 0.37/0.60 (step @p105 :rule cong :premises (@p104) :args ((forall @t31 @t99))) % 0.37/0.60 (step @p106 :rule aci_norm :args ((= (or @t95 @t100) @t99))) % 0.37/0.60 (step @p107 :rule beta-reduce :args ((= @t103 @t100))) % 0.37/0.60 (step @p108 :rule refl :args (@t95)) % 0.37/0.60 (step @p109 :rule nary_cong :premises (@p108 @p107) :args (@t104)) % 0.37/0.60 (step @p110 :rule trans :premises (@p109 @p106)) % 0.37/0.60 (step @p111 :rule cong :premises (@p110) :args (@t105)) % 0.37/0.60 (step @p112 :rule trans :premises (@p111 @p105)) % 0.37/0.60 (step @p113 :rule cong :premises (@p112) :args (@t106)) % 0.37/0.60 (step @p114 :rule beta-reduce :args ((= (_ @t108 @t102) @t106))) % 0.37/0.60 (step @p115 :rule trans :premises (@p114 @p113)) % 0.37/0.60 (step @p116 :rule beta-reduce :args ((= (_ @t110 @t3) @t102))) % 0.37/0.60 (step @p117 :rule refl :args (@t3)) % 0.37/0.60 (step @p118 :rule beta-reduce :args ((= (_ (lambda @t23 @t111) @t1) @t110))) % 0.37/0.60 (step @p119 :rule ho_cong :premises (@p118 @p117)) % 0.37/0.60 (step @p120 :rule trans :premises (@p119 @p116)) % 0.37/0.60 (step @p121 :rule beta-reduce :args ((= (_ (lambda @t33 (forall @t31 (or (not @t112) @t107))) tptp.rel) @t108))) % 0.37/0.60 (step @p122 :rule ho_cong :premises (@p121 @p120)) % 0.37/0.60 (step @p123 :rule trans :premises (@p122 @p115)) % 0.37/0.60 (step @p124 :rule ho_cong :premises (@p123 @p91)) % 0.37/0.60 (step @p125 :rule trans :premises (@p124 @p90)) % 0.37/0.60 (step @p126 :rule refl :args (@t1)) % 0.37/0.60 (step @p127 :rule beta-reduce :args ((= (_ @t115 @t20) @t111))) % 0.37/0.60 (step @p128 :rule beta-reduce :args ((= (_ (lambda @t116 (or @t113 @t16)) @t21) @t115))) % 0.37/0.60 (step @p129 :rule refl :args (@t21)) % 0.37/0.60 (step @p130 :rule refl :args (@t16)) % 0.37/0.60 (step @p131 :rule beta-reduce :args ((= @t118 @t113))) % 0.37/0.60 (step @p132 :rule nary_cong :premises (@p131 @p130) :args (@t119)) % 0.37/0.60 (step @p133 :rule cong :premises (@p132) :args (@t120)) % 0.37/0.60 (step @p134 :rule beta-reduce :args ((= (_ @t18 @t117) @t120))) % 0.37/0.60 (step @p135 :rule trans :premises (@p134 @p133)) % 0.37/0.60 (step @p136 :rule beta-reduce :args ((= (_ @t14 @t22) @t117))) % 0.37/0.60 (step @p137 :rule refl :args (@t18)) % 0.37/0.60 (step @p138 :rule ho_cong :premises (@p137 @p136)) % 0.37/0.60 (step @p139 :rule trans :premises (@p138 @p135)) % 0.37/0.60 (step @p140 :rule ho_cong :premises (@p139 @p129)) % 0.37/0.60 (step @p141 :rule trans :premises (@p140 @p128)) % 0.37/0.60 (step @p142 :rule ho_cong :premises (@p141 @p91)) % 0.37/0.60 (step @p143 :rule trans :premises (@p142 @p127)) % 0.37/0.60 (step @p144 :rule refl :args (@t22)) % 0.37/0.60 (step @p145 :rule ho_cong :premises (@p9 @p144)) % 0.37/0.60 (step @p146 :rule ho_cong :premises (@p10 @p145)) % 0.37/0.60 (step @p147 :rule ho_cong :premises (@p146 @p129)) % 0.37/0.60 (step @p148 :rule ho_cong :premises (@p147 @p91)) % 0.37/0.60 (step @p149 :rule trans :premises (@p148 @p143)) % 0.37/0.60 (step @p150 :rule cong :premises (@p149) :args (@t24)) % 0.37/0.60 (step @p151 :rule trans :premises (@p12 @p150)) % 0.37/0.60 (step @p152 :rule ho_cong :premises (@p151 @p126)) % 0.37/0.60 (step @p153 :rule ho_cong :premises (@p152 @p117)) % 0.37/0.60 (step @p154 :rule refl :args (tptp.rel)) % 0.37/0.60 (step @p155 :rule refl :args (@t107)) % 0.37/0.60 (step @p156 :rule refl :args (@t28)) % 0.37/0.60 (step @p157 :rule cong :premises (@p156 @p155) :args ((= @t28 @t107))) % 0.37/0.60 (step @p158 :rule symm :premises (@p157)) % 0.37/0.60 (step @p159 :rule eq_resolve :premises (@p156 @p158)) % 0.37/0.60 (step @p160 :rule refl :args (@t112)) % 0.37/0.60 (step @p161 :rule refl :args (@t30)) % 0.37/0.60 (step @p162 :rule cong :premises (@p161 @p160) :args ((= @t30 @t112))) % 0.37/0.60 (step @p163 :rule symm :premises (@p162)) % 0.37/0.60 (step @p164 :rule eq_resolve :premises (@p161 @p163)) % 0.37/0.60 (step @p165 :rule cong :premises (@p164) :args (@t121)) % 0.37/0.60 (step @p166 :rule nary_cong :premises (@p165 @p159) :args (@t122)) % 0.37/0.60 (step @p167 :rule cong :premises (@p166) :args ((forall @t31 @t122))) % 0.37/0.60 (step @p168 :rule bool-impl-elim :args (@t30 @t28)) % 0.37/0.60 (step @p169 :rule cong :premises (@p168) :args (@t32)) % 0.37/0.60 (step @p170 :rule trans :premises (@p169 @p167)) % 0.37/0.60 (step @p171 :rule cong :premises (@p170) :args (@t34)) % 0.37/0.60 (step @p172 :rule trans :premises (@p14 @p171)) % 0.37/0.60 (step @p173 :rule ho_cong :premises (@p172 @p154)) % 0.37/0.60 (step @p174 :rule ho_cong :premises (@p173 @p153)) % 0.37/0.60 (step @p175 :rule ho_cong :premises (@p174 @p91)) % 0.37/0.60 (step @p176 :rule trans :premises (@p175 @p125)) % 0.37/0.60 (step @p177 :rule cong :premises (@p176) :args (@t60)) % 0.37/0.60 (step @p178 :rule trans :premises (@p29 @p177)) % 0.37/0.60 (step @p179 :rule ho_cong :premises (@p178 @p89)) % 0.37/0.60 (step @p180 :rule ho_cong :premises (@p179 @p89)) % 0.37/0.60 (step @p181 :rule beta-reduce :args ((= (_ (lambda @t47 (forall @t45 @t123)) @t12) @t69))) % 0.37/0.60 (step @p182 :rule refl :args (@t12)) % 0.37/0.60 (step @p183 :rule refl :args (@t123)) % 0.37/0.60 (step @p184 :rule refl :args (@t44)) % 0.37/0.60 (step @p185 :rule cong :premises (@p184 @p183) :args ((= @t44 @t123))) % 0.37/0.60 (step @p186 :rule symm :premises (@p185)) % 0.37/0.60 (step @p187 :rule eq_resolve :premises (@p184 @p186)) % 0.37/0.60 (step @p188 :rule cong :premises (@p187) :args (@t46)) % 0.37/0.60 (step @p189 :rule cong :premises (@p188) :args (@t48)) % 0.37/0.60 (step @p190 :rule trans :premises (@p18 @p189)) % 0.37/0.60 (step @p191 :rule ho_cong :premises (@p190 @p182)) % 0.37/0.60 (step @p192 :rule trans :premises (@p191 @p181)) % 0.37/0.60 (step @p193 :rule cong :premises (@p192) :args (@t64)) % 0.37/0.60 (step @p194 :rule trans :premises (@p28 @p193)) % 0.37/0.60 (step @p195 :rule ho_cong :premises (@p194 @p180)) % 0.37/0.60 (step @p196 :rule cong :premises (@p195) :args (@t6)) % 0.37/0.60 (step @p197 :rule trans :premises (@p196 @p87)) % 0.37/0.60 (step @p198 false :rule eq_resolve :premises (@p5 @p197)) % 0.37/0.60 ) % 0.37/0.60 % SZS output end Proof % 0.37/0.60 % cvc5 exiting %------------------------------------------------------------------------------