%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWV429^1 : 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 : n015.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 0.38s 0.58s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV429^1 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n015.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 20:17:49 EDT 2026 % 0.16/0.35 % CPUTime : % 0.29/0.50 %----Proving TH0 % 0.38/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.58 % SZS status Theorem % 0.38/0.58 % SZS output start Proof % 0.38/0.58 ( % 0.38/0.58 (declare-sort $$unsorted 0) % 0.38/0.58 (declare-sort tptp.individuals 0) % 0.38/0.58 (declare-const tptp.rel (-> $$unsorted $$unsorted Bool)) % 0.38/0.58 (declare-const tptp.a (-> $$unsorted Bool)) % 0.38/0.58 (declare-const tptp.icl_true (-> $$unsorted Bool)) % 0.38/0.58 (declare-const tptp.icl_false (-> $$unsorted Bool)) % 0.38/0.58 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.38/0.58 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.38/0.58 (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)))))) % 0.38/0.58 (define tptp.mor () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.58 (define tptp.mand () (let ((_let_1 (@var "U" $$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))))))) % 0.38/0.58 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "V" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.38/0.58 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.38/0.58 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.38/0.58 (define tptp.mdia () (let ((_let_1 (@var "Y" $$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))))))))) % 0.38/0.58 (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))))))) % 0.38/0.58 (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))))))) % 0.38/0.58 (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)))))) % 0.38/0.58 (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)))))) % 0.38/0.58 (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))))))) % 0.38/0.58 (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))))))) % 0.38/0.58 (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))))) % 0.38/0.58 (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))))) % 0.38/0.58 (define tptp.icl_and () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "B" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mand _let_3) _let_2) _let_1)))))) % 0.38/0.58 (define tptp.icl_or () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.38/0.58 (define tptp.icl_impl () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "B" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mbox tptp.rel) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.38/0.58 (define tptp.icl_says () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.38/0.58 (define tptp.iclval () (let ((_let_1 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_1) (_ tptp.mvalid _let_1)))) % 0.38/0.58 (define tptp.icl_impl_princ () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.38/0.58 (define @t1 () (_ tptp.icl_princ tptp.a)) % 0.38/0.58 (define @t2 () (not (_ tptp.iclval (_ (_ tptp.icl_impl_princ @t1) @t1)))) % 0.38/0.58 (define @t3 () (@var "X" $$unsorted)) % 0.38/0.58 (define @t4 () (@list @t3)) % 0.38/0.58 (define @t5 () (lambda @t4 false)) % 0.38/0.58 (define @t6 () (lambda @t4 true)) % 0.38/0.58 (define @t7 () (@var "U" $$unsorted)) % 0.38/0.58 (define @t8 () (@var "X" (-> $$unsorted Bool))) % 0.38/0.58 (define @t9 () (_ @t8 @t7)) % 0.38/0.58 (define @t10 () (lambda (@list @t8 @t7) (not @t9))) % 0.38/0.58 (define @t11 () (@var "Y" (-> $$unsorted Bool))) % 0.38/0.58 (define @t12 () (_ @t11 @t7)) % 0.38/0.58 (define @t13 () (@list @t8 @t11 @t7)) % 0.38/0.58 (define @t14 () (lambda @t13 (or @t9 @t12))) % 0.38/0.58 (define @t15 () (lambda @t13 (and @t9 @t12))) % 0.38/0.58 (define @t16 () (@var "__flatten_var_0" $$unsorted)) % 0.38/0.58 (define @t17 () (@var "V" (-> $$unsorted Bool))) % 0.38/0.58 (define @t18 () (@var "U" (-> $$unsorted Bool))) % 0.38/0.58 (define @t19 () (@list @t18 @t17 @t16)) % 0.38/0.58 (define @t20 () (lambda @t19 (_ (_ (_ tptp.mor (_ tptp.mnot @t18)) @t17) @t16))) % 0.38/0.58 (define @t21 () (lambda @t19 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t18) @t17)) (_ (_ tptp.mimpl @t17) @t18)) @t16))) % 0.38/0.58 (define @t22 () (@var "Y" $$unsorted)) % 0.38/0.58 (define @t23 () (@var "P" (-> $$unsorted Bool))) % 0.38/0.58 (define @t24 () (_ @t23 @t22)) % 0.38/0.58 (define @t25 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.38/0.58 (define @t26 () (_ (_ @t25 @t3) @t22)) % 0.38/0.58 (define @t27 () (@list @t22)) % 0.38/0.58 (define @t28 () (forall @t27 (=> @t26 @t24))) % 0.38/0.58 (define @t29 () (@list @t25 @t23 @t3)) % 0.38/0.58 (define @t30 () (lambda @t29 @t28)) % 0.38/0.58 (define @t31 () (lambda @t29 (exists @t27 (and @t26 @t24)))) % 0.38/0.58 (define @t32 () (@var "W" $$unsorted)) % 0.38/0.58 (define @t33 () (@var "X" tptp.individuals)) % 0.38/0.58 (define @t34 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.38/0.58 (define @t35 () (_ (_ @t34 @t33) @t32)) % 0.38/0.58 (define @t36 () (@list @t33)) % 0.38/0.58 (define @t37 () (@list @t34 @t32)) % 0.38/0.58 (define @t38 () (lambda @t37 (forall @t36 @t35))) % 0.38/0.58 (define @t39 () (lambda @t37 (exists @t36 @t35))) % 0.38/0.58 (define @t40 () (_ @t23 @t32)) % 0.38/0.58 (define @t41 () (@list @t32)) % 0.38/0.58 (define @t42 () (forall @t41 @t40)) % 0.38/0.58 (define @t43 () (@list @t23)) % 0.38/0.58 (define @t44 () (lambda @t43 @t42)) % 0.38/0.58 (define @t45 () (lambda @t43 (exists @t41 @t40))) % 0.38/0.58 (define @t46 () (not @t40)) % 0.38/0.58 (define @t47 () (lambda @t43 (exists @t41 @t46))) % 0.38/0.58 (define @t48 () (lambda @t43 (forall @t41 @t46))) % 0.38/0.58 (define @t49 () (_ tptp.mbox tptp.rel)) % 0.38/0.58 (define @t50 () (@list @t23 @t16)) % 0.38/0.58 (define @t51 () (lambda @t50 (_ (_ @t49 @t23) @t16))) % 0.38/0.58 (define @t52 () (lambda @t50 (_ @t23 @t16))) % 0.38/0.58 (define @t53 () (@var "B" (-> $$unsorted Bool))) % 0.38/0.58 (define @t54 () (@var "A" (-> $$unsorted Bool))) % 0.38/0.58 (define @t55 () (@list @t54 @t53 @t16)) % 0.38/0.58 (define @t56 () (lambda @t55 (_ (_ (_ tptp.mand @t54) @t53) @t16))) % 0.38/0.58 (define @t57 () (_ tptp.mor @t54)) % 0.38/0.58 (define @t58 () (lambda @t55 (_ (_ @t57 @t53) @t16))) % 0.38/0.58 (define @t59 () (lambda @t55 (_ (_ @t49 (_ (_ tptp.mimpl @t54) @t53)) @t16))) % 0.38/0.58 (define @t60 () (@var "S" (-> $$unsorted Bool))) % 0.38/0.58 (define @t61 () (lambda (@list @t54 @t60 @t16) (_ (_ @t49 (_ @t57 @t60)) @t16))) % 0.38/0.58 (define @t62 () (@list @t8)) % 0.38/0.58 (define @t63 () (lambda @t62 (_ tptp.mvalid @t8))) % 0.38/0.58 (define @t64 () (@var "BOUND_VARIABLE_8045" $$unsorted)) % 0.38/0.58 (define @t65 () (lambda (@list @t64) true)) % 0.38/0.58 (define @t66 () (_ @t65 @t32)) % 0.38/0.58 (define @t67 () (forall @t41 @t66)) % 0.38/0.58 (define @t68 () (forall @t41 (_ @t8 @t32))) % 0.38/0.58 (define @t69 () (lambda @t62 @t68)) % 0.38/0.58 (define @t70 () (@list @t16)) % 0.38/0.58 (define @t71 () (not (tptp.rel @t16 @t22))) % 0.38/0.58 (define @t72 () (tptp.a @t22)) % 0.38/0.58 (define @t73 () (not @t72)) % 0.38/0.58 (define @t74 () (_ tptp.a @t22)) % 0.38/0.58 (define @t75 () (or @t71 @t73 @t74)) % 0.38/0.58 (define @t76 () (lambda @t70 (_ tptp.a @t16))) % 0.38/0.58 (define @t77 () (_ @t76 @t22)) % 0.38/0.58 (define @t78 () (or @t71 @t73 @t77)) % 0.38/0.58 (define @t79 () (forall @t27 @t78)) % 0.38/0.58 (define @t80 () (lambda @t70 @t79)) % 0.38/0.58 (define @t81 () (_ @t53 @t22)) % 0.38/0.58 (define @t82 () (@list @t53 @t16)) % 0.38/0.58 (define @t83 () (_ @t52 tptp.a)) % 0.38/0.58 (define @t84 () (not @t74)) % 0.38/0.58 (define @t85 () (or @t71 @t84 @t81)) % 0.38/0.58 (define @t86 () (not @t77)) % 0.38/0.58 (define @t87 () (or @t71 @t86 @t81)) % 0.38/0.58 (define @t88 () (forall @t27 @t87)) % 0.38/0.58 (define @t89 () (lambda @t82 @t88)) % 0.38/0.58 (define @t90 () (_ @t54 @t22)) % 0.38/0.58 (define @t91 () (not @t90)) % 0.38/0.58 (define @t92 () (forall @t27 (or @t71 @t91 @t81))) % 0.38/0.58 (define @t93 () (lambda @t55 @t92)) % 0.38/0.58 (define @t94 () (not (tptp.rel @t3 @t22))) % 0.38/0.58 (define @t95 () (_ @t53 @t22)) % 0.38/0.58 (define @t96 () (_ @t54 @t22)) % 0.38/0.58 (define @t97 () (not @t96)) % 0.38/0.58 (define @t98 () (or @t94 @t97 @t95)) % 0.38/0.58 (define @t99 () (or @t97 @t95)) % 0.38/0.58 (define @t100 () (not (_ @t54 @t16))) % 0.38/0.58 (define @t101 () (lambda @t70 (or @t100 (_ @t53 @t16)))) % 0.38/0.58 (define @t102 () (_ @t101 @t22)) % 0.38/0.58 (define @t103 () (or @t94 @t102)) % 0.38/0.58 (define @t104 () (forall @t27 @t103)) % 0.38/0.58 (define @t105 () (lambda @t4 @t104)) % 0.38/0.58 (define @t106 () (_ @t23 @t22)) % 0.38/0.58 (define @t107 () (lambda (@list @t23 @t3) (forall @t27 (or @t94 @t106)))) % 0.38/0.58 (define @t108 () (_ @t17 @t16)) % 0.38/0.58 (define @t109 () (lambda (@list @t17 @t16) (or @t100 @t108))) % 0.38/0.58 (define @t110 () (or (not (_ @t18 @t16)) @t108)) % 0.38/0.58 (define @t111 () (_ @t25 @t3 @t22)) % 0.38/0.58 (define @t112 () (not (_ @t18 @t7))) % 0.38/0.58 (define @t113 () (@list @t7)) % 0.38/0.58 (define @t114 () (lambda @t113 (or @t112 (_ @t17 @t7)))) % 0.38/0.58 (define @t115 () (@list @t11 @t7)) % 0.38/0.58 (define @t116 () (lambda @t113 @t112)) % 0.38/0.58 (define @t117 () (_ @t116 @t7)) % 0.38/0.58 (define @t118 () (or @t117 @t12)) % 0.38/0.58 (define @t119 () (lambda @t115 @t118)) % 0.38/0.58 (define @t120 () (not @t26)) % 0.38/0.58 (define @t121 () (or @t120 @t24)) % 0.38/0.58 (define @t122 () (_ @t23 @t32)) % 0.38/0.58 (assume @p1 (= tptp.icl_true tptp.mtrue)) % 0.38/0.58 (assume @p2 (= tptp.icl_false tptp.mfalse)) % 0.38/0.58 (assume @p3 @t2) % 0.38/0.58 (assume @p4 true) % 0.38/0.58 (step @p5 (= tptp.mfalse @t5) :rule refl :args (@t5)) % 0.38/0.58 (step @p6 (= tptp.mtrue @t6) :rule refl :args (@t6)) % 0.38/0.58 (step @p7 (= tptp.mnot @t10) :rule refl :args (@t10)) % 0.38/0.58 (step @p8 (= tptp.mor @t14) :rule refl :args (@t14)) % 0.38/0.58 (step @p9 (= tptp.mand @t15) :rule refl :args (@t15)) % 0.38/0.58 (step @p10 (= tptp.mimpl @t20) :rule refl :args (@t20)) % 0.38/0.58 (step @p11 (= tptp.miff @t21) :rule refl :args (@t21)) % 0.38/0.58 (step @p12 (= tptp.mbox @t30) :rule refl :args (@t30)) % 0.38/0.58 (step @p13 (= tptp.mdia @t31) :rule refl :args (@t31)) % 0.38/0.58 (step @p14 (= tptp.mall @t38) :rule refl :args (@t38)) % 0.38/0.58 (step @p15 (= tptp.mexists @t39) :rule refl :args (@t39)) % 0.38/0.58 (step @p16 (= tptp.mvalid @t44) :rule refl :args (@t44)) % 0.38/0.58 (step @p17 (= tptp.msatisfiable @t45) :rule refl :args (@t45)) % 0.38/0.58 (step @p18 (= tptp.mcountersatisfiable @t47) :rule refl :args (@t47)) % 0.38/0.58 (step @p19 (= tptp.minvalid @t48) :rule refl :args (@t48)) % 0.38/0.58 (step @p20 (= tptp.icl_atom @t51) :rule refl :args (@t51)) % 0.38/0.58 (step @p21 (= tptp.icl_princ @t52) :rule refl :args (@t52)) % 0.38/0.58 (step @p22 (= tptp.icl_and @t56) :rule refl :args (@t56)) % 0.38/0.58 (step @p23 (= tptp.icl_or @t58) :rule refl :args (@t58)) % 0.38/0.58 (step @p24 (= tptp.icl_impl @t59) :rule refl :args (@t59)) % 0.38/0.58 (step @p25 (= tptp.icl_says @t61) :rule refl :args (@t61)) % 0.38/0.58 (step @p26 (= tptp.iclval @t63) :rule refl :args (@t63)) % 0.38/0.58 (step @p27 (= tptp.icl_impl_princ @t59) :rule refl :args (@t59)) % 0.38/0.58 (step @p28 :rule evaluate :args ((not true))) % 0.38/0.58 (step @p29 :rule quant-unused-vars :args ((= (forall @t41 true) true))) % 0.38/0.58 (step @p30 :rule beta-reduce :args ((= @t66 true))) % 0.38/0.58 (step @p31 :rule cong :premises (@p30) :args (@t67)) % 0.38/0.58 (step @p32 :rule trans :premises (@p31 @p29)) % 0.38/0.58 (step @p33 :rule beta-reduce :args ((= (_ @t69 @t65) @t67))) % 0.38/0.58 (step @p34 :rule trans :premises (@p33 @p32)) % 0.38/0.58 (step @p35 :rule refl :args (@t65)) % 0.38/0.58 (step @p36 :rule symm :premises (@p35)) % 0.38/0.58 (step @p37 :rule alpha_equiv :args ((lambda @t70 true) (@list @t16) (@list @t64))) % 0.38/0.58 (step @p38 :rule trans :premises (@p37 @p36)) % 0.38/0.58 (step @p39 :rule quant-unused-vars :args ((= (forall @t27 true) true))) % 0.38/0.58 (step @p40 :rule bool-or-taut2 :args ((or @t71) @t72 false false)) % 0.38/0.58 (step @p41 :rule cong :premises (@p40) :args ((forall @t27 (or @t71 @t73 @t72)))) % 0.38/0.58 (step @p42 :rule trans :premises (@p41 @p39)) % 0.38/0.58 (step @p43 :rule refl :args (@t72)) % 0.38/0.58 (step @p44 :rule refl :args (@t74)) % 0.38/0.58 (step @p45 :rule cong :premises (@p44 @p43) :args ((= @t74 @t72))) % 0.38/0.58 (step @p46 :rule symm :premises (@p45)) % 0.38/0.58 (step @p47 :rule eq_resolve :premises (@p44 @p46)) % 0.38/0.58 (step @p48 :rule refl :args (@t73)) % 0.38/0.58 (step @p49 :rule refl :args (@t71)) % 0.38/0.58 (step @p50 :rule nary_cong :premises (@p49 @p48 @p47) :args (@t75)) % 0.38/0.58 (step @p51 :rule cong :premises (@p50) :args ((forall @t27 @t75))) % 0.38/0.58 (step @p52 :rule trans :premises (@p51 @p42)) % 0.38/0.58 (step @p53 :rule beta-reduce :args ((= @t77 @t74))) % 0.38/0.58 (step @p54 :rule refl :args (@t73)) % 0.38/0.58 (step @p55 :rule refl :args (@t71)) % 0.38/0.58 (step @p56 :rule nary_cong :premises (@p55 @p54 @p53) :args (@t78)) % 0.38/0.58 (step @p57 :rule cong :premises (@p56) :args (@t79)) % 0.38/0.58 (step @p58 :rule trans :premises (@p57 @p52)) % 0.38/0.58 (step @p59 :rule cong :premises (@p58) :args (@t80)) % 0.38/0.58 (step @p60 :rule trans :premises (@p59 @p38)) % 0.38/0.58 (step @p61 :rule beta-reduce :args ((= (_ (lambda @t82 (forall @t27 (or @t71 @t73 @t81))) @t76) @t80))) % 0.38/0.58 (step @p62 :rule trans :premises (@p61 @p60)) % 0.38/0.58 (step @p63 :rule beta-reduce :args ((= @t83 @t76))) % 0.38/0.58 (step @p64 :rule refl :args (@t81)) % 0.38/0.58 (step @p65 :rule cong :premises (@p47) :args (@t84)) % 0.38/0.58 (step @p66 :rule nary_cong :premises (@p49 @p65 @p64) :args (@t85)) % 0.38/0.58 (step @p67 :rule cong :premises (@p66) :args ((forall @t27 @t85))) % 0.38/0.58 (step @p68 :rule refl :args (@t81)) % 0.38/0.58 (step @p69 :rule cong :premises (@p53) :args (@t86)) % 0.38/0.58 (step @p70 :rule nary_cong :premises (@p55 @p69 @p68) :args (@t87)) % 0.38/0.58 (step @p71 :rule cong :premises (@p70) :args (@t88)) % 0.38/0.58 (step @p72 :rule trans :premises (@p71 @p67)) % 0.38/0.58 (step @p73 :rule cong :premises (@p72) :args (@t89)) % 0.38/0.58 (step @p74 :rule beta-reduce :args ((= (_ @t93 @t76) @t89))) % 0.38/0.58 (step @p75 :rule trans :premises (@p74 @p73)) % 0.38/0.58 (step @p76 :rule refl :args (@t93)) % 0.38/0.58 (step @p77 :rule ho_cong :premises (@p76 @p63)) % 0.38/0.58 (step @p78 :rule trans :premises (@p77 @p75)) % 0.38/0.58 (step @p79 :rule ho_cong :premises (@p78 @p63)) % 0.38/0.58 (step @p80 :rule trans :premises (@p79 @p62)) % 0.38/0.58 (step @p81 :rule refl :args (@t69)) % 0.38/0.58 (step @p82 :rule ho_cong :premises (@p81 @p80)) % 0.38/0.58 (step @p83 :rule trans :premises (@p82 @p34)) % 0.38/0.58 (step @p84 :rule cong :premises (@p83) :args ((not (_ @t69 (_ (_ @t93 @t83) @t83))))) % 0.38/0.58 (step @p85 :rule trans :premises (@p84 @p28)) % 0.38/0.58 (step @p86 :rule refl :args (tptp.a)) % 0.38/0.58 (step @p87 :rule ho_cong :premises (@p21 @p86)) % 0.38/0.58 (step @p88 :rule beta-reduce :args ((= (_ (lambda @t4 (forall @t27 (or @t94 @t91 @t81))) @t16) @t92))) % 0.38/0.58 (step @p89 :rule refl :args (@t16)) % 0.38/0.58 (step @p90 :rule refl :args (@t81)) % 0.38/0.58 (step @p91 :rule refl :args (@t95)) % 0.38/0.58 (step @p92 :rule cong :premises (@p91 @p90) :args ((= @t95 @t81))) % 0.38/0.58 (step @p93 :rule symm :premises (@p92)) % 0.38/0.58 (step @p94 :rule eq_resolve :premises (@p91 @p93)) % 0.38/0.58 (step @p95 :rule refl :args (@t90)) % 0.38/0.58 (step @p96 :rule refl :args (@t96)) % 0.38/0.58 (step @p97 :rule cong :premises (@p96 @p95) :args ((= @t96 @t90))) % 0.38/0.58 (step @p98 :rule symm :premises (@p97)) % 0.38/0.58 (step @p99 :rule eq_resolve :premises (@p96 @p98)) % 0.38/0.58 (step @p100 :rule cong :premises (@p99) :args (@t97)) % 0.38/0.58 (step @p101 :rule refl :args (@t94)) % 0.38/0.58 (step @p102 :rule nary_cong :premises (@p101 @p100 @p94) :args (@t98)) % 0.38/0.58 (step @p103 :rule cong :premises (@p102) :args ((forall @t27 @t98))) % 0.38/0.58 (step @p104 :rule aci_norm :args ((= (or @t94 @t99) @t98))) % 0.38/0.58 (step @p105 :rule beta-reduce :args ((= @t102 @t99))) % 0.38/0.58 (step @p106 :rule refl :args (@t94)) % 0.38/0.58 (step @p107 :rule nary_cong :premises (@p106 @p105) :args (@t103)) % 0.38/0.58 (step @p108 :rule trans :premises (@p107 @p104)) % 0.38/0.58 (step @p109 :rule cong :premises (@p108) :args (@t104)) % 0.38/0.58 (step @p110 :rule trans :premises (@p109 @p103)) % 0.38/0.58 (step @p111 :rule cong :premises (@p110) :args (@t105)) % 0.38/0.58 (step @p112 :rule beta-reduce :args ((= (_ @t107 @t101) @t105))) % 0.38/0.58 (step @p113 :rule trans :premises (@p112 @p111)) % 0.38/0.58 (step @p114 :rule beta-reduce :args ((= (_ @t109 @t53) @t101))) % 0.38/0.58 (step @p115 :rule refl :args (@t53)) % 0.38/0.58 (step @p116 :rule beta-reduce :args ((= (_ (lambda @t19 @t110) @t54) @t109))) % 0.38/0.58 (step @p117 :rule ho_cong :premises (@p116 @p115)) % 0.38/0.58 (step @p118 :rule trans :premises (@p117 @p114)) % 0.38/0.58 (step @p119 :rule beta-reduce :args ((= (_ (lambda @t29 (forall @t27 (or (not @t111) @t106))) tptp.rel) @t107))) % 0.38/0.58 (step @p120 :rule ho_cong :premises (@p119 @p118)) % 0.38/0.58 (step @p121 :rule trans :premises (@p120 @p113)) % 0.38/0.58 (step @p122 :rule ho_cong :premises (@p121 @p89)) % 0.38/0.58 (step @p123 :rule trans :premises (@p122 @p88)) % 0.38/0.58 (step @p124 :rule refl :args (@t54)) % 0.38/0.58 (step @p125 :rule beta-reduce :args ((= (_ @t114 @t16) @t110))) % 0.38/0.58 (step @p126 :rule beta-reduce :args ((= (_ (lambda @t115 (or @t112 @t12)) @t17) @t114))) % 0.38/0.58 (step @p127 :rule refl :args (@t17)) % 0.38/0.58 (step @p128 :rule refl :args (@t12)) % 0.38/0.58 (step @p129 :rule beta-reduce :args ((= @t117 @t112))) % 0.38/0.58 (step @p130 :rule nary_cong :premises (@p129 @p128) :args (@t118)) % 0.38/0.58 (step @p131 :rule cong :premises (@p130) :args (@t119)) % 0.38/0.58 (step @p132 :rule beta-reduce :args ((= (_ @t14 @t116) @t119))) % 0.38/0.58 (step @p133 :rule trans :premises (@p132 @p131)) % 0.38/0.58 (step @p134 :rule beta-reduce :args ((= (_ @t10 @t18) @t116))) % 0.38/0.58 (step @p135 :rule refl :args (@t14)) % 0.38/0.58 (step @p136 :rule ho_cong :premises (@p135 @p134)) % 0.38/0.58 (step @p137 :rule trans :premises (@p136 @p133)) % 0.38/0.58 (step @p138 :rule ho_cong :premises (@p137 @p127)) % 0.38/0.58 (step @p139 :rule trans :premises (@p138 @p126)) % 0.38/0.58 (step @p140 :rule ho_cong :premises (@p139 @p89)) % 0.38/0.58 (step @p141 :rule trans :premises (@p140 @p125)) % 0.38/0.58 (step @p142 :rule refl :args (@t18)) % 0.38/0.58 (step @p143 :rule ho_cong :premises (@p7 @p142)) % 0.38/0.58 (step @p144 :rule ho_cong :premises (@p8 @p143)) % 0.38/0.58 (step @p145 :rule ho_cong :premises (@p144 @p127)) % 0.38/0.58 (step @p146 :rule ho_cong :premises (@p145 @p89)) % 0.38/0.58 (step @p147 :rule trans :premises (@p146 @p141)) % 0.38/0.58 (step @p148 :rule cong :premises (@p147) :args (@t20)) % 0.38/0.58 (step @p149 :rule trans :premises (@p10 @p148)) % 0.38/0.58 (step @p150 :rule ho_cong :premises (@p149 @p124)) % 0.38/0.58 (step @p151 :rule ho_cong :premises (@p150 @p115)) % 0.38/0.58 (step @p152 :rule refl :args (tptp.rel)) % 0.38/0.58 (step @p153 :rule refl :args (@t106)) % 0.38/0.58 (step @p154 :rule refl :args (@t24)) % 0.38/0.58 (step @p155 :rule cong :premises (@p154 @p153) :args ((= @t24 @t106))) % 0.38/0.58 (step @p156 :rule symm :premises (@p155)) % 0.38/0.58 (step @p157 :rule eq_resolve :premises (@p154 @p156)) % 0.38/0.58 (step @p158 :rule refl :args (@t111)) % 0.38/0.58 (step @p159 :rule refl :args (@t26)) % 0.38/0.58 (step @p160 :rule cong :premises (@p159 @p158) :args ((= @t26 @t111))) % 0.38/0.58 (step @p161 :rule symm :premises (@p160)) % 0.38/0.58 (step @p162 :rule eq_resolve :premises (@p159 @p161)) % 0.38/0.58 (step @p163 :rule cong :premises (@p162) :args (@t120)) % 0.38/0.58 (step @p164 :rule nary_cong :premises (@p163 @p157) :args (@t121)) % 0.38/0.58 (step @p165 :rule cong :premises (@p164) :args ((forall @t27 @t121))) % 0.38/0.58 (step @p166 :rule bool-impl-elim :args (@t26 @t24)) % 0.38/0.58 (step @p167 :rule cong :premises (@p166) :args (@t28)) % 0.38/0.58 (step @p168 :rule trans :premises (@p167 @p165)) % 0.38/0.58 (step @p169 :rule cong :premises (@p168) :args (@t30)) % 0.38/0.58 (step @p170 :rule trans :premises (@p12 @p169)) % 0.38/0.58 (step @p171 :rule ho_cong :premises (@p170 @p152)) % 0.38/0.58 (step @p172 :rule ho_cong :premises (@p171 @p151)) % 0.38/0.58 (step @p173 :rule ho_cong :premises (@p172 @p89)) % 0.38/0.58 (step @p174 :rule trans :premises (@p173 @p123)) % 0.38/0.58 (step @p175 :rule cong :premises (@p174) :args (@t59)) % 0.38/0.58 (step @p176 :rule trans :premises (@p27 @p175)) % 0.38/0.58 (step @p177 :rule ho_cong :premises (@p176 @p87)) % 0.38/0.58 (step @p178 :rule ho_cong :premises (@p177 @p87)) % 0.38/0.58 (step @p179 :rule beta-reduce :args ((= (_ (lambda @t43 (forall @t41 @t122)) @t8) @t68))) % 0.38/0.58 (step @p180 :rule refl :args (@t8)) % 0.38/0.58 (step @p181 :rule refl :args (@t122)) % 0.38/0.58 (step @p182 :rule refl :args (@t40)) % 0.38/0.58 (step @p183 :rule cong :premises (@p182 @p181) :args ((= @t40 @t122))) % 0.38/0.58 (step @p184 :rule symm :premises (@p183)) % 0.38/0.58 (step @p185 :rule eq_resolve :premises (@p182 @p184)) % 0.38/0.58 (step @p186 :rule cong :premises (@p185) :args (@t42)) % 0.38/0.58 (step @p187 :rule cong :premises (@p186) :args (@t44)) % 0.38/0.58 (step @p188 :rule trans :premises (@p16 @p187)) % 0.38/0.58 (step @p189 :rule ho_cong :premises (@p188 @p180)) % 0.38/0.58 (step @p190 :rule trans :premises (@p189 @p179)) % 0.38/0.58 (step @p191 :rule cong :premises (@p190) :args (@t63)) % 0.38/0.58 (step @p192 :rule trans :premises (@p26 @p191)) % 0.38/0.58 (step @p193 :rule ho_cong :premises (@p192 @p178)) % 0.38/0.58 (step @p194 :rule cong :premises (@p193) :args (@t2)) % 0.38/0.58 (step @p195 :rule trans :premises (@p194 @p85)) % 0.38/0.58 (step @p196 false :rule eq_resolve :premises (@p3 @p195)) % 0.38/0.58 ) % 0.38/0.58 % SZS output end Proof % 0.38/0.58 % cvc5 exiting %------------------------------------------------------------------------------