%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GRP660+3 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n027.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 08:21:14 AM UTC 2026 % Result : Theorem 2.61s 2.83s % Output : Proof 2.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : GRP660+3 : TPTP v9.2.1. Released v4.0.0. % 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n027.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.36 % CPULimit : 300 % 0.16/0.36 % WCLimit : 300 % 0.16/0.36 % DateTime : Tue Jun 2 01:44:51 EDT 2026 % 0.16/0.36 % CPUTime : % 0.27/0.51 %----Proving TF0_NAR, FOF, or CNF % 2.61/2.83 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 2.61/2.83 % SZS status Theorem % 2.61/2.83 % SZS output start Proof % 2.61/2.83 ( % 2.61/2.83 (declare-sort $$unsorted 0) % 2.61/2.83 (declare-const tptp.rd (-> $$unsorted $$unsorted $$unsorted)) % 2.61/2.83 (declare-const tptp.mult (-> $$unsorted $$unsorted $$unsorted)) % 2.61/2.83 (declare-const tptp.ld (-> $$unsorted $$unsorted $$unsorted)) % 2.61/2.83 (define @t1 () (@var "B" $$unsorted)) % 2.61/2.83 (define @t2 () (@var "A" $$unsorted)) % 2.61/2.83 (define @t3 () (tptp.mult @t2 (tptp.ld @t2 @t1))) % 2.61/2.83 (define @t4 () (@list @t1 @t2)) % 2.61/2.83 (define @t5 () (forall @t4 (= @t3 @t1))) % 2.61/2.83 (define @t6 () (tptp.mult @t2 @t1)) % 2.61/2.83 (define @t7 () (tptp.ld @t2 @t6)) % 2.61/2.83 (define @t8 () (forall @t4 (= @t7 @t1))) % 2.61/2.83 (define @t9 () (tptp.rd @t6 @t1)) % 2.61/2.83 (define @t10 () (forall @t4 (= @t9 @t2))) % 2.61/2.83 (define @t11 () (@var "C" $$unsorted)) % 2.61/2.83 (define @t12 () (@var "X0" $$unsorted)) % 2.61/2.83 (define @t13 () (@var "X1" $$unsorted)) % 2.61/2.83 (define @t14 () (tptp.ld @t13 @t13)) % 2.61/2.83 (define @t15 () (tptp.mult @t14 @t12)) % 2.61/2.83 (define @t16 () (tptp.mult @t12 @t14)) % 2.61/2.83 (define @t17 () (and (= @t16 @t12) (= @t15 @t12))) % 2.61/2.83 (define @t18 () (@list @t12 @t13)) % 2.61/2.83 (define @t19 () (forall @t18 @t17)) % 2.61/2.83 (define @t20 () (not @t19)) % 2.61/2.83 (define @t21 () (@var "BOUND_VARIABLE_7467" $$unsorted)) % 2.61/2.83 (define @t22 () (@var "BOUND_VARIABLE_7465" $$unsorted)) % 2.61/2.83 (define @t23 () (forall (@list @t22 @t21) (= @t22 (tptp.mult @t22 (tptp.ld @t21 @t21))))) % 2.61/2.83 (define @t24 () (@quantifiers_skolemize @t23 1)) % 2.61/2.83 (define @t25 () (tptp.ld @t24 @t24)) % 2.61/2.83 (define @t26 () (tptp.mult @t25 @t25)) % 2.61/2.83 (define @t27 () (tptp.mult @t26 @t24)) % 2.61/2.83 (define @t28 () (tptp.mult @t25 @t24)) % 2.61/2.83 (define @t29 () (tptp.mult @t25 @t28)) % 2.61/2.83 (define @t30 () (tptp.mult @t24 @t25)) % 2.61/2.83 (define @t31 () (tptp.mult @t30 @t25)) % 2.61/2.83 (define @t32 () (@list @t24 @t31)) % 2.61/2.83 (define @t33 () (tptp.mult @t27 @t25)) % 2.61/2.83 (define @t34 () (tptp.mult @t26 @t27)) % 2.61/2.83 (define @t35 () (tptp.mult (tptp.mult @t24 @t26) @t26)) % 2.61/2.83 (define @t36 () (tptp.mult @t33 @t26)) % 2.61/2.83 (define @t37 () (tptp.mult @t27 @t26)) % 2.61/2.83 (define @t38 () (tptp.mult @t26 @t26)) % 2.61/2.83 (define @t39 () (tptp.mult @t24 @t38)) % 2.61/2.83 (define @t40 () (@quantifiers_skolemize @t23 0)) % 2.61/2.83 (define @t41 () (tptp.mult @t40 @t38)) % 2.61/2.83 (define @t42 () (tptp.mult @t26 @t40)) % 2.61/2.83 (define @t43 () (tptp.mult @t25 @t26)) % 2.61/2.83 (define @t44 () (tptp.mult @t24 @t43)) % 2.61/2.83 (define @t45 () (tptp.mult @t29 @t25)) % 2.61/2.83 (define @t46 () (tptp.mult @t28 @t26)) % 2.61/2.83 (define @t47 () (tptp.mult (tptp.mult @t25 @t46) @t43)) % 2.61/2.83 (define @t48 () (tptp.mult @t44 @t38)) % 2.61/2.83 (define @t49 () (tptp.mult @t26 @t44)) % 2.61/2.83 (define @t50 () (tptp.mult @t44 @t25)) % 2.61/2.83 (define @t51 () (tptp.mult @t50 @t25)) % 2.61/2.83 (define @t52 () (tptp.mult @t46 (tptp.mult @t43 @t25))) % 2.61/2.83 (define @t53 () (tptp.mult @t25 (tptp.mult @t25 @t50))) % 2.61/2.83 (define @t54 () (tptp.mult @t43 @t40)) % 2.61/2.83 (define @t55 () (tptp.mult @t26 @t41)) % 2.61/2.83 (define @t56 () (tptp.mult @t42 @t26)) % 2.61/2.83 (define @t57 () (tptp.mult @t56 @t26)) % 2.61/2.83 (define @t58 () (tptp.mult @t25 @t57)) % 2.61/2.83 (define @t59 () (tptp.mult @t25 @t56)) % 2.61/2.83 (define @t60 () (tptp.mult @t59 @t25)) % 2.61/2.83 (define @t61 () (tptp.mult @t59 @t26)) % 2.61/2.83 (define @t62 () (tptp.mult @t26 @t56)) % 2.61/2.83 (define @t63 () (tptp.mult @t25 @t55)) % 2.61/2.83 (define @t64 () (tptp.mult @t63 @t25)) % 2.61/2.83 (define @t65 () (= @t40 (tptp.mult @t40 @t25))) % 2.61/2.83 (define @t66 () (not @t65)) % 2.61/2.83 (define @t67 () (not @t23)) % 2.61/2.83 (define @t68 () (@list false)) % 2.61/2.83 (define @t69 () (@var "BOUND_VARIABLE_7474" $$unsorted)) % 2.61/2.83 (define @t70 () (@var "BOUND_VARIABLE_7476" $$unsorted)) % 2.61/2.83 (define @t71 () (forall (@list @t69 @t70) (= @t69 (tptp.mult (tptp.ld @t70 @t70) @t69)))) % 2.61/2.83 (define @t72 () (@quantifiers_skolemize @t71 0)) % 2.61/2.83 (define @t73 () (@quantifiers_skolemize @t71 1)) % 2.61/2.83 (define @t74 () (tptp.ld @t73 @t73)) % 2.61/2.83 (define @t75 () (tptp.mult @t74 @t74)) % 2.61/2.83 (define @t76 () (tptp.mult @t75 @t73)) % 2.61/2.83 (define @t77 () (tptp.mult @t74 @t73)) % 2.61/2.83 (define @t78 () (tptp.mult @t74 @t77)) % 2.61/2.83 (define @t79 () (tptp.mult @t73 @t74)) % 2.61/2.83 (define @t80 () (tptp.mult @t79 @t74)) % 2.61/2.83 (define @t81 () (@list @t73 @t80)) % 2.61/2.83 (define @t82 () (tptp.mult @t76 @t74)) % 2.61/2.83 (define @t83 () (tptp.mult @t75 @t76)) % 2.61/2.83 (define @t84 () (tptp.mult (tptp.mult @t73 @t75) @t75)) % 2.61/2.83 (define @t85 () (tptp.mult @t82 @t75)) % 2.61/2.83 (define @t86 () (tptp.mult @t76 @t75)) % 2.61/2.83 (define @t87 () (tptp.mult @t75 @t75)) % 2.61/2.83 (define @t88 () (tptp.mult @t73 @t87)) % 2.61/2.83 (define @t89 () (tptp.mult @t87 @t72)) % 2.61/2.83 (define @t90 () (tptp.mult @t74 @t75)) % 2.61/2.83 (define @t91 () (tptp.mult @t73 @t90)) % 2.61/2.83 (define @t92 () (tptp.mult @t75 @t91)) % 2.61/2.83 (define @t93 () (tptp.mult @t91 @t74)) % 2.61/2.83 (define @t94 () (tptp.mult @t91 @t87)) % 2.61/2.83 (define @t95 () (tptp.mult @t93 @t74)) % 2.61/2.83 (define @t96 () (tptp.mult @t95 @t74)) % 2.61/2.83 (define @t97 () (tptp.mult @t78 @t74)) % 2.61/2.83 (define @t98 () (tptp.mult @t77 @t75)) % 2.61/2.83 (define @t99 () (tptp.mult (tptp.mult @t74 @t98) @t90)) % 2.61/2.83 (define @t100 () (tptp.mult @t72 @t75)) % 2.61/2.83 (define @t101 () (tptp.mult @t87 @t74)) % 2.61/2.83 (define @t102 () (tptp.mult @t75 @t74)) % 2.61/2.83 (define @t103 () (tptp.mult @t72 @t102)) % 2.61/2.83 (define @t104 () (tptp.mult @t74 @t72)) % 2.61/2.83 (define @t105 () (tptp.mult @t89 @t75)) % 2.61/2.83 (define @t106 () (tptp.mult @t75 @t100)) % 2.61/2.83 (define @t107 () (tptp.mult @t75 @t106)) % 2.61/2.83 (define @t108 () (tptp.mult @t106 @t74)) % 2.61/2.83 (define @t109 () (tptp.mult @t74 @t108)) % 2.61/2.83 (define @t110 () (tptp.mult @t100 @t75)) % 2.61/2.83 (define @t111 () (tptp.mult @t108 @t74)) % 2.61/2.83 (define @t112 () (tptp.mult @t74 @t111)) % 2.61/2.83 (define @t113 () (tptp.mult @t100 @t74)) % 2.61/2.83 (define @t114 () (tptp.mult @t89 @t74)) % 2.61/2.83 (define @t115 () (tptp.mult @t74 @t114)) % 2.61/2.83 (define @t116 () (tptp.mult @t74 @t89)) % 2.61/2.83 (define @t117 () (tptp.mult @t116 @t74)) % 2.61/2.83 (define @t118 () (= @t72 @t104)) % 2.61/2.83 (define @t119 () (not @t118)) % 2.61/2.83 (define @t120 () (not @t71)) % 2.61/2.83 (define @t121 () (= @t12 @t15)) % 2.61/2.83 (define @t122 () (forall @t18 @t121)) % 2.61/2.83 (define @t123 () (@list @t12 @t13)) % 2.61/2.83 (define @t124 () (= @t12 @t16)) % 2.61/2.83 (define @t125 () (forall @t18 @t124)) % 2.61/2.83 (define @t126 () (and @t125 @t122)) % 2.61/2.83 (assume @p1 @t5) % 2.61/2.83 (assume @p2 @t8) % 2.61/2.83 (assume @p3 (forall @t4 (= (tptp.mult (tptp.rd @t2 @t1) @t1) @t2))) % 2.61/2.83 (assume @p4 @t10) % 2.61/2.83 (assume @p5 (forall (@list @t11 @t1 @t2) (= (tptp.mult (tptp.mult @t6 @t11) @t2) (tptp.mult @t2 (tptp.mult @t1 (tptp.mult @t11 @t2)))))) % 2.61/2.83 (assume @p6 @t20) % 2.61/2.83 (assume @p7 true) % 2.61/2.83 (step @p8 :rule eq-symm :args (@t7 @t1)) % 2.61/2.83 (step @p9 :rule cong :premises (@p8) :args (@t8)) % 2.61/2.83 (step @p10 :rule eq_resolve :premises (@p2 @p9)) % 2.61/2.83 (step @p11 :rule instantiate :premises (@p10) :args ((@list @t24 @t26))) % 2.61/2.83 (step @p12 :rule symm :premises (@p11)) % 2.61/2.83 (step @p13 :rule eq-symm :args (@t9 @t2)) % 2.61/2.83 (step @p14 :rule cong :premises (@p13) :args (@t10)) % 2.61/2.83 (step @p15 :rule eq_resolve :premises (@p4 @p14)) % 2.61/2.83 (step @p16 :rule instantiate :premises (@p15) :args ((@list @t25 @t27))) % 2.61/2.83 (step @p17 :rule symm :premises (@p16)) % 2.61/2.83 (step @p18 :rule refl :args (@t25)) % 2.61/2.83 (step @p19 :rule instantiate :premises (@p5) :args ((@list @t24 @t25 @t25))) % 2.61/2.83 (step @p20 :rule symm :premises (@p19)) % 2.61/2.83 (step @p21 :rule eq-symm :args (@t3 @t1)) % 2.61/2.83 (step @p22 :rule cong :premises (@p21) :args (@t5)) % 2.61/2.83 (step @p23 :rule eq_resolve :premises (@p1 @p22)) % 2.61/2.83 (step @p24 :rule instantiate :premises (@p23) :args ((@list @t24 @t24))) % 2.61/2.83 (step @p25 :rule cong :premises (@p18 @p24) :args (@t28)) % 2.61/2.83 (step @p26 :rule cong :premises (@p18 @p25) :args (@t29)) % 2.61/2.83 (step @p27 :rule instantiate :premises (@p10) :args ((@list @t29 @t24))) % 2.61/2.83 (step @p28 :rule symm :premises (@p27)) % 2.61/2.83 (step @p29 :rule instantiate :premises (@p5) :args ((@list @t25 @t25 @t24))) % 2.61/2.83 (step @p30 :rule symm :premises (@p24)) % 2.61/2.83 (step @p31 :rule cong :premises (@p30 @p18) :args (@t31)) % 2.61/2.83 (step @p32 :rule trans :premises (@p31 @p30)) % 2.61/2.83 (step @p33 :rule cong :premises (@p32 @p29) :args ((tptp.ld @t31 (tptp.mult @t31 @t24)))) % 2.61/2.83 (step @p34 :rule instantiate :premises (@p10) :args (@t32)) % 2.61/2.83 (step @p35 :rule trans :premises (@p30 @p34 @p33 @p28 @p26 @p20)) % 2.61/2.83 (step @p36 :rule cong :premises (@p35 @p18) :args ((tptp.rd @t30 @t25))) % 2.61/2.83 (step @p37 :rule instantiate :premises (@p15) :args ((@list @t25 @t24))) % 2.61/2.83 (step @p38 :rule instantiate :premises (@p15) :args (@t32)) % 2.61/2.83 (step @p39 :rule symm :premises (@p38)) % 2.61/2.83 (step @p40 :rule refl :args (@t24)) % 2.61/2.83 (step @p41 :rule symm :premises (@p29)) % 2.61/2.83 (step @p42 :rule symm :premises (@p37)) % 2.61/2.83 (step @p43 :rule symm :premises (@p36)) % 2.61/2.83 (step @p44 :rule symm :premises (@p34)) % 2.61/2.83 (step @p45 :rule symm :premises (@p33)) % 2.61/2.83 (step @p46 :rule symm :premises (@p26)) % 2.61/2.83 (step @p47 :rule trans :premises (@p19 @p46 @p27 @p45 @p44)) % 2.61/2.83 (step @p48 :rule refl :args (@t26)) % 2.61/2.83 (step @p49 :rule cong :premises (@p48 @p47) :args ((tptp.mult @t26 @t33))) % 2.61/2.83 (step @p50 :rule trans :premises (@p16 @p43 @p42 @p34 @p33 @p28 @p26 @p20)) % 2.61/2.83 (step @p51 :rule cong :premises (@p48 @p50) :args (@t34)) % 2.61/2.83 (step @p52 :rule trans :premises (@p51 @p49 @p16 @p43 @p42)) % 2.61/2.83 (step @p53 :rule symm :premises (@p32)) % 2.61/2.83 (step @p54 :rule cong :premises (@p53 @p52) :args ((tptp.mult @t24 @t34))) % 2.61/2.83 (step @p55 :rule instantiate :premises (@p5) :args ((@list @t26 @t26 @t24))) % 2.61/2.83 (step @p56 :rule trans :premises (@p55 @p54 @p29)) % 2.61/2.83 (step @p57 :rule trans :premises (@p56 @p41)) % 2.61/2.83 (step @p58 :rule cong :premises (@p57 @p40) :args ((tptp.rd (tptp.mult @t35 @t24) @t24))) % 2.61/2.83 (step @p59 :rule instantiate :premises (@p15) :args ((@list @t24 @t35))) % 2.61/2.83 (step @p60 :rule cong :premises (@p47 @p48) :args (@t36)) % 2.61/2.83 (step @p61 :rule cong :premises (@p50 @p48) :args (@t37)) % 2.61/2.83 (step @p62 :rule trans :premises (@p61 @p60)) % 2.61/2.83 (step @p63 :rule cong :premises (@p62 @p48) :args ((tptp.mult @t37 @t26))) % 2.61/2.83 (step @p64 :rule instantiate :premises (@p5) :args ((@list @t26 @t24 @t26))) % 2.61/2.83 (step @p65 :rule symm :premises (@p64)) % 2.61/2.83 (step @p66 :rule trans :premises (@p65 @p63 @p59 @p58 @p39 @p31 @p30 @p37 @p36 @p17)) % 2.61/2.83 (step @p67 :rule cong :premises (@p48 @p66) :args ((tptp.ld @t26 (tptp.mult @t26 @t39)))) % 2.61/2.83 (step @p68 :rule instantiate :premises (@p10) :args ((@list @t39 @t26))) % 2.61/2.83 (step @p69 :rule trans :premises (@p68 @p67 @p12)) % 2.61/2.83 (step @p70 :rule cong :premises (@p40 @p69) :args ((tptp.ld @t24 @t39))) % 2.61/2.83 (step @p71 :rule instantiate :premises (@p10) :args ((@list @t38 @t24))) % 2.61/2.83 (step @p72 :rule trans :premises (@p71 @p70)) % 2.61/2.83 (step @p73 :rule refl :args (@t40)) % 2.61/2.83 (step @p74 :rule cong :premises (@p73 @p72) :args (@t41)) % 2.61/2.83 (step @p75 :rule symm :premises (@p72)) % 2.61/2.83 (step @p76 :rule instantiate :premises (@p10) :args ((@list @t40 @t26))) % 2.61/2.83 (step @p77 :rule symm :premises (@p76)) % 2.61/2.83 (step @p78 :rule instantiate :premises (@p15) :args ((@list @t26 @t42))) % 2.61/2.83 (step @p79 :rule symm :premises (@p78)) % 2.61/2.83 (step @p80 :rule instantiate :premises (@p10) :args ((@list @t26 @t25))) % 2.61/2.83 (step @p81 :rule symm :premises (@p80)) % 2.61/2.83 (step @p82 :rule instantiate :premises (@p10) :args ((@list @t43 @t24))) % 2.61/2.83 (step @p83 :rule symm :premises (@p82)) % 2.61/2.83 (step @p84 :rule instantiate :premises (@p15) :args ((@list @t25 @t44))) % 2.61/2.83 (step @p85 :rule symm :premises (@p84)) % 2.61/2.83 (step @p86 :rule refl :args (@t43)) % 2.61/2.83 (step @p87 :rule trans :premises (@p27 @p45 @p44)) % 2.61/2.83 (step @p88 :rule cong :premises (@p87 @p18) :args (@t45)) % 2.61/2.83 (step @p89 :rule trans :premises (@p88 @p30)) % 2.61/2.83 (step @p90 :rule cong :premises (@p89 @p18) :args ((tptp.mult @t45 @t25))) % 2.61/2.83 (step @p91 :rule instantiate :premises (@p5) :args ((@list @t25 @t28 @t25))) % 2.61/2.83 (step @p92 :rule symm :premises (@p91)) % 2.61/2.83 (step @p93 :rule trans :premises (@p92 @p90 @p30)) % 2.61/2.83 (step @p94 :rule cong :premises (@p93 @p86) :args (@t47)) % 2.61/2.83 (step @p95 :rule cong :premises (@p94 @p18) :args ((tptp.mult @t47 @t25))) % 2.61/2.83 (step @p96 :rule instantiate :premises (@p5) :args ((@list @t43 @t46 @t25))) % 2.61/2.83 (step @p97 :rule symm :premises (@p96)) % 2.61/2.83 (step @p98 :rule trans :premises (@p97 @p95)) % 2.61/2.83 (step @p99 :rule symm :premises (@p95)) % 2.61/2.83 (step @p100 :rule refl :args (@t44)) % 2.61/2.83 (step @p101 :rule cong :premises (@p100 @p72) :args (@t48)) % 2.61/2.83 (step @p102 :rule instantiate :premises (@p10) :args ((@list @t48 @t26))) % 2.61/2.83 (step @p103 :rule symm :premises (@p102)) % 2.61/2.83 (step @p104 :rule instantiate :premises (@p5) :args ((@list @t26 @t44 @t26))) % 2.61/2.83 (step @p105 :rule instantiate :premises (@p5) :args ((@list @t25 @t24 @t26))) % 2.61/2.83 (step @p106 :rule symm :premises (@p60)) % 2.61/2.83 (step @p107 :rule trans :premises (@p106 @p105)) % 2.61/2.83 (step @p108 :rule cong :premises (@p107 @p48) :args (@t35)) % 2.61/2.83 (step @p109 :rule symm :premises (@p59)) % 2.61/2.83 (step @p110 :rule symm :premises (@p58)) % 2.61/2.83 (step @p111 :rule symm :premises (@p31)) % 2.61/2.83 (step @p112 :rule trans :premises (@p24 @p111 @p38 @p110 @p109 @p108)) % 2.61/2.83 (step @p113 :rule trans :premises (@p47 @p112)) % 2.61/2.83 (step @p114 :rule cong :premises (@p113 @p48) :args (@t36)) % 2.61/2.83 (step @p115 :rule symm :premises (@p105)) % 2.61/2.83 (step @p116 :rule trans :premises (@p115 @p114 @p104)) % 2.61/2.83 (step @p117 :rule cong :premises (@p48 @p116) :args ((tptp.ld @t26 @t49))) % 2.61/2.83 (step @p118 :rule instantiate :premises (@p10) :args ((@list @t44 @t26))) % 2.61/2.83 (step @p119 :rule trans :premises (@p118 @p117 @p103 @p101 @p99 @p96)) % 2.61/2.83 (step @p120 :rule symm :premises (@p118)) % 2.61/2.83 (step @p121 :rule symm :premises (@p117)) % 2.61/2.83 (step @p122 :rule symm :premises (@p101)) % 2.61/2.83 (step 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2.61/2.83 (step @p343 :rule instantiate :premises (@p10) :args ((@list @t90 @t73))) % 2.61/2.83 (step @p344 :rule trans :premises (@p343 @p342 @p281)) % 2.61/2.83 (step @p345 :rule cong :premises (@p224 @p344) :args ((tptp.ld @t74 @t90))) % 2.61/2.83 (step @p346 :rule instantiate :premises (@p10) :args ((@list @t75 @t74))) % 2.61/2.83 (step @p347 :rule trans :premises (@p346 @p345 @p279)) % 2.61/2.83 (step @p348 :rule trans :premises (@p347 @p277)) % 2.61/2.83 (step @p349 :rule cong :premises (@p348 @p219) :args ((tptp.mult @t75 @t72))) % 2.61/2.83 (step @p350 :rule instantiate :premises (@p15) :args ((@list @t75 @t72))) % 2.61/2.83 (step @p351 :rule symm :premises (@p350)) % 2.61/2.83 (step @p352 :rule instantiate :premises (@p10) :args ((@list @t100 @t75))) % 2.61/2.83 (step @p353 :rule symm :premises (@p352)) % 2.61/2.83 (step @p354 :rule symm :premises (@p346)) % 2.61/2.83 (step @p355 :rule symm :premises (@p345)) % 2.61/2.83 (step @p356 :rule cong :premises (@p275 @p224) :args (@t101)) % 2.61/2.83 (step @p357 :rule cong :premises (@p356 @p251) :args ((tptp.mult @t101 @t75))) % 2.61/2.83 (step @p358 :rule symm :premises (@p347)) % 2.61/2.83 (step @p359 :rule symm :premises (@p356)) % 2.61/2.83 (step @p360 :rule cong :premises (@p359 @p358) :args (@t102)) % 2.61/2.83 (step @p361 :rule trans :premises (@p360 @p357 @p274 @p273 @p278 @p355 @p354)) % 2.61/2.83 (step @p362 :rule cong :premises (@p219 @p361) :args (@t103)) % 2.61/2.83 (step @p363 :rule cong :premises (@p358 @p362) :args ((tptp.mult @t74 @t103))) % 2.61/2.83 (step @p364 :rule instantiate :premises (@p5) :args ((@list @t75 @t72 @t74))) % 2.61/2.83 (step @p365 :rule refl :args (@t104)) % 2.61/2.83 (step @p366 :rule cong :premises (@p365 @p358) :args ((tptp.mult @t104 @t74))) % 2.61/2.83 (step @p367 :rule cong :premises (@p276 @p347) :args (@t105)) % 2.61/2.83 (step @p368 :rule instantiate :premises (@p5) :args ((@list @t72 @t75 @t75))) % 2.61/2.83 (step @p369 :rule symm :premises (@p368)) % 2.61/2.83 (step @p370 :rule trans :premises (@p369 @p367)) % 2.61/2.83 (step @p371 :rule trans :premises (@p370 @p366)) % 2.61/2.83 (step @p372 :rule cong :premises (@p371 @p224) :args ((tptp.mult @t107 @t74))) % 2.61/2.83 (step @p373 :rule instantiate :premises (@p5) :args ((@list @t106 @t74 @t74))) % 2.61/2.83 (step @p374 :rule symm :premises (@p373)) % 2.61/2.83 (step @p375 :rule trans :premises (@p374 @p372 @p364 @p363)) % 2.61/2.83 (step @p376 :rule cong :premises (@p358 @p375) :args ((tptp.ld @t74 (tptp.mult @t74 @t109)))) % 2.61/2.83 (step @p377 :rule instantiate :premises (@p10) :args ((@list @t109 @t74))) % 2.61/2.83 (step @p378 :rule instantiate :premises (@p5) :args ((@list @t100 @t74 @t74))) % 2.61/2.83 (step @p379 :rule symm :premises (@p378)) % 2.61/2.83 (step @p380 :rule refl :args (@t100)) % 2.61/2.83 (step @p381 :rule cong :premises (@p380 @p347) :args (@t110)) % 2.61/2.83 (step @p382 :rule cong :premises (@p224 @p381) :args ((tptp.mult @t74 @t110))) % 2.61/2.83 (step @p383 :rule instantiate :premises (@p5) :args ((@list @t74 @t100 @t74))) % 2.61/2.83 (step @p384 :rule cong :premises (@p347 @p380) :args (@t106)) % 2.61/2.83 (step @p385 :rule cong :premises (@p384 @p347) :args ((tptp.mult @t106 @t75))) % 2.61/2.83 (step @p386 :rule refl :args (@t106)) % 2.61/2.83 (step @p387 :rule cong :premises (@p386 @p358) :args (@t108)) % 2.61/2.83 (step @p388 :rule trans :premises (@p387 @p385)) % 2.61/2.83 (step @p389 :rule cong :premises (@p388 @p224) :args (@t111)) % 2.61/2.83 (step @p390 :rule trans :premises (@p389 @p383 @p382)) % 2.61/2.83 (step @p391 :rule cong :premises (@p224 @p390) :args (@t112)) % 2.61/2.83 (step @p392 :rule trans :premises (@p391 @p379)) % 2.61/2.83 (step @p393 :rule cong :premises (@p224 @p392) :args ((tptp.mult @t74 @t112))) % 2.61/2.83 (step @p394 :rule instantiate :premises (@p5) :args ((@list @t108 @t74 @t74))) % 2.61/2.83 (step @p395 :rule refl :args (@t108)) % 2.61/2.83 (step @p396 :rule cong :premises (@p358 @p395) :args (@t109)) % 2.61/2.83 (step @p397 :rule symm :premises (@p377)) % 2.61/2.83 (step @p398 :rule symm :premises (@p376)) % 2.61/2.83 (step @p399 :rule trans :premises (@p352 @p398 @p397 @p396)) % 2.61/2.83 (step @p400 :rule cong :premises (@p399 @p347) :args (@t110)) % 2.61/2.83 (step @p401 :rule trans :premises (@p400 @p394 @p393 @p377 @p376 @p353)) % 2.61/2.83 (step @p402 :rule cong :premises (@p401 @p251) :args ((tptp.rd @t110 @t75))) % 2.61/2.83 (step @p403 :rule instantiate :premises (@p15) :args ((@list @t75 @t100))) % 2.61/2.83 (step @p404 :rule trans :premises (@p403 @p402 @p351)) % 2.61/2.83 (step @p405 :rule cong :premises (@p251 @p404) :args (@t106)) % 2.61/2.83 (step @p406 :rule symm :premises (@p396)) % 2.61/2.83 (step @p407 :rule symm :premises (@p389)) % 2.61/2.83 (step @p408 :rule symm :premises (@p383)) % 2.61/2.83 (step @p409 :rule symm :premises (@p382)) % 2.61/2.83 (step @p410 :rule refl :args (@t113)) % 2.61/2.83 (step @p411 :rule cong :premises (@p347 @p410) :args ((tptp.mult @t75 @t113))) % 2.61/2.83 (step @p412 :rule symm :premises (@p400)) % 2.61/2.83 (step @p413 :rule symm :premises (@p394)) % 2.61/2.83 (step @p414 :rule symm :premises (@p393)) % 2.61/2.83 (step @p415 :rule trans :premises (@p352 @p398 @p397 @p414 @p413 @p412 @p381)) % 2.61/2.83 (step @p416 :rule cong :premises (@p251 @p415) :args (@t106)) % 2.61/2.83 (step @p417 :rule trans :premises (@p416 @p411 @p409 @p408 @p407)) % 2.61/2.83 (step @p418 :rule cong :premises (@p347 @p417) :args (@t107)) % 2.61/2.83 (step @p419 :rule trans :premises (@p368 @p418 @p391 @p379)) % 2.61/2.83 (step @p420 :rule cong :premises (@p358 @p419) :args ((tptp.mult @t74 @t105))) % 2.61/2.83 (step @p421 :rule symm :premises (@p367)) % 2.61/2.83 (step @p422 :rule cong :premises (@p276 @p224) :args (@t114)) % 2.61/2.83 (step @p423 :rule trans :premises (@p422 @p421)) % 2.61/2.83 (step @p424 :rule cong :premises (@p224 @p423) :args (@t115)) % 2.61/2.83 (step @p425 :rule trans :premises (@p424 @p420 @p406 @p377 @p376 @p353)) % 2.61/2.83 (step @p426 :rule cong :premises (@p358 @p425) :args ((tptp.mult @t74 @t115))) % 2.61/2.83 (step @p427 :rule instantiate :premises (@p5) :args ((@list @t89 @t74 @t74))) % 2.61/2.83 (step @p428 :rule refl :args (@t89)) % 2.61/2.83 (step @p429 :rule cong :premises (@p358 @p428) :args (@t116)) % 2.61/2.83 (step @p430 :rule cong :premises (@p429 @p347) :args ((tptp.mult @t116 @t75))) % 2.61/2.83 (step @p431 :rule refl :args (@t116)) % 2.61/2.83 (step @p432 :rule cong :premises (@p431 @p358) :args (@t117)) % 2.61/2.83 (step @p433 :rule instantiate :premises (@p15) :args ((@list @t74 @t117))) % 2.61/2.83 (step @p434 :rule symm :premises (@p433)) % 2.61/2.83 (step @p435 :rule instantiate :premises (@p5) :args ((@list @t74 @t89 @t74))) % 2.61/2.83 (step @p436 :rule symm :premises (@p435)) % 2.61/2.83 (step @p437 :rule symm :premises (@p420)) % 2.61/2.83 (step @p438 :rule trans :premises (@p352 @p398 @p397 @p396 @p437 @p436)) % 2.61/2.83 (step @p439 :rule cong :premises (@p438 @p347) :args ((tptp.rd @t100 @t75))) % 2.61/2.83 (step @p440 :rule trans :premises (@p350 @p439 @p434 @p432 @p430 @p427 @p426 @p405 @p349 @p276)) % 2.61/2.83 (step @p441 :rule refl :args (@t119)) % 2.61/2.83 (step @p442 :rule bool-double-not-elim :args (@t71)) % 2.61/2.83 (step @p443 :rule nary_cong :premises (@p442 @p441) :args ((or (not @t120) @t119))) % 2.61/2.83 (assume-push @p467 @t120) % 2.61/2.83 (step @p445 :rule skolemize :premises (@p467)) % 2.61/2.83 (step-pop @p468 :rule scope :premises (@p445)) % 2.61/2.83 (step @p446 :rule process_scope :premises (@p468) :args (@t119)) % 2.61/2.83 (step @p448 :rule implies_elim :premises (@p446)) % 2.61/2.83 (step @p449 :rule eq_resolve :premises (@p448 @p443)) % 2.61/2.83 (step @p450 :rule chain_m_resolution :premises (@p449 @p440) :args (@t71 @t68 (@list @t118))) % 2.61/2.83 (step @p451 :rule alpha_equiv :args (@t122 @t123 (@list @t69 @t70))) % 2.61/2.83 (step @p452 :rule alpha_equiv :args (@t125 @t123 (@list @t22 @t21))) % 2.61/2.83 (step @p453 :rule nary_cong :premises (@p452 @p451) :args (@t126)) % 2.61/2.83 (step @p454 :rule quant-miniscope-and :args ((= (forall @t18 (and @t124 @t121)) @t126))) % 2.61/2.83 (step @p455 :rule trans :premises (@p454 @p453)) % 2.61/2.83 (step @p456 :rule eq-symm :args (@t15 @t12)) % 2.61/2.83 (step @p457 :rule eq-symm :args (@t16 @t12)) % 2.61/2.83 (step @p458 :rule nary_cong :premises (@p457 @p456) :args (@t17)) % 2.61/2.83 (step @p459 :rule cong :premises (@p458) :args (@t19)) % 2.61/2.83 (step @p460 :rule trans :premises (@p459 @p455)) % 2.61/2.83 (step @p461 :rule cong :premises (@p460) :args (@t20)) % 2.61/2.85 (step @p462 :rule eq_resolve :premises (@p6 @p461)) % 2.61/2.85 (step @p463 :rule not_and :premises (@p462)) % 2.61/2.85 (step @p464 false :rule chain_m_resolution :premises (@p463 @p450 @p218) :args (false (@list false false) (@list @t71 @t23))) % 2.61/2.85 ) % 2.61/2.85 % SZS output end Proof % 2.61/2.85 % cvc5 exiting %------------------------------------------------------------------------------