%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GRP660+2 : TPTP v9.2.1. Released v4.0.0. % 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 08:21:14 AM UTC 2026 % Result : Theorem 2.43s 2.69s % Output : Proof 0.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GRP660+2 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n022.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 01:44:38 EDT 2026 % 0.15/0.34 % CPUTime : % 0.29/0.49 %----Proving TF0_NAR, FOF, or CNF % 2.43/2.69 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 2.43/2.69 % SZS status Theorem % 2.43/2.69 % SZS output start Proof % 2.43/2.69 ( % 2.43/2.69 (declare-sort $$unsorted 0) % 2.43/2.69 (declare-const tptp.rd (-> $$unsorted $$unsorted $$unsorted)) % 2.43/2.69 (declare-const tptp.mult (-> $$unsorted $$unsorted $$unsorted)) % 2.43/2.69 (declare-const tptp.ld (-> $$unsorted $$unsorted $$unsorted)) % 2.43/2.69 (define @t1 () (@var "B" $$unsorted)) % 2.43/2.69 (define @t2 () (@var "A" $$unsorted)) % 2.43/2.69 (define @t3 () (@list @t1 @t2)) % 2.43/2.69 (define @t4 () (tptp.mult @t2 @t1)) % 2.43/2.69 (define @t5 () (tptp.ld @t2 @t4)) % 2.43/2.69 (define @t6 () (forall @t3 (= @t5 @t1))) % 2.43/2.69 (define @t7 () (tptp.mult (tptp.rd @t2 @t1) @t1)) % 2.43/2.69 (define @t8 () (forall @t3 (= @t7 @t2))) % 2.43/2.69 (define @t9 () (tptp.rd @t4 @t1)) % 2.43/2.69 (define @t10 () (forall @t3 (= @t9 @t2))) % 2.43/2.69 (define @t11 () (@var "C" $$unsorted)) % 2.43/2.69 (define @t12 () (@var "X0" $$unsorted)) % 2.43/2.69 (define @t13 () (@var "X1" $$unsorted)) % 2.43/2.69 (define @t14 () (tptp.rd @t13 @t13)) % 2.43/2.69 (define @t15 () (tptp.mult @t14 @t12)) % 2.43/2.69 (define @t16 () (tptp.mult @t12 @t14)) % 2.43/2.69 (define @t17 () (and (= @t16 @t12) (= @t15 @t12))) % 2.43/2.69 (define @t18 () (@list @t12 @t13)) % 2.43/2.69 (define @t19 () (forall @t18 @t17)) % 2.43/2.69 (define @t20 () (not @t19)) % 2.43/2.69 (define @t21 () (@var "BOUND_VARIABLE_7467" $$unsorted)) % 2.43/2.69 (define @t22 () (@var "BOUND_VARIABLE_7465" $$unsorted)) % 2.43/2.69 (define @t23 () (forall (@list @t22 @t21) (= @t22 (tptp.mult @t22 (tptp.rd @t21 @t21))))) % 2.43/2.69 (define @t24 () (@quantifiers_skolemize @t23 1)) % 2.43/2.69 (define @t25 () (tptp.rd @t24 @t24)) % 2.43/2.69 (define @t26 () (tptp.mult @t25 @t25)) % 2.43/2.69 (define @t27 () (tptp.mult @t24 @t26)) % 2.43/2.69 (define @t28 () (tptp.mult @t24 @t25)) % 2.43/2.69 (define @t29 () (tptp.mult @t28 @t25)) % 2.43/2.69 (define @t30 () (tptp.mult @t25 @t24)) % 2.43/2.69 (define @t31 () (tptp.mult @t25 @t30)) % 2.43/2.69 (define @t32 () (@list @t31 @t24)) % 2.43/2.69 (define @t33 () (tptp.mult @t27 @t26)) % 2.43/2.69 (define @t34 () (tptp.mult @t26 (tptp.mult @t26 @t24))) % 2.43/2.69 (define @t35 () (tptp.mult @t25 @t27)) % 2.43/2.69 (define @t36 () (tptp.mult @t26 @t35)) % 2.43/2.69 (define @t37 () (tptp.mult @t26 @t27)) % 2.43/2.69 (define @t38 () (tptp.mult @t26 @t26)) % 2.43/2.69 (define @t39 () (tptp.mult @t38 @t24)) % 2.43/2.69 (define @t40 () (@quantifiers_skolemize @t23 0)) % 2.43/2.69 (define @t41 () (tptp.mult @t40 @t38)) % 2.43/2.69 (define @t42 () (tptp.mult @t26 @t40)) % 2.43/2.69 (define @t43 () (tptp.mult @t25 @t28)) % 2.43/2.69 (define @t44 () (tptp.mult @t25 @t43)) % 2.43/2.69 (define @t45 () (tptp.mult @t25 @t29)) % 2.43/2.69 (define @t46 () (tptp.mult @t26 @t28)) % 2.43/2.69 (define @t47 () (tptp.mult @t25 @t46)) % 2.43/2.69 (define @t48 () (tptp.mult @t25 @t47)) % 2.43/2.69 (define @t49 () (tptp.mult @t29 @t25)) % 2.43/2.69 (define @t50 () (tptp.mult @t49 @t28)) % 2.43/2.69 (define @t51 () (tptp.mult @t25 @t26)) % 2.43/2.69 (define @t52 () (tptp.mult @t51 @t40)) % 2.43/2.69 (define @t53 () (tptp.mult @t26 @t41)) % 2.43/2.69 (define @t54 () (tptp.mult @t42 @t26)) % 2.43/2.69 (define @t55 () (tptp.mult @t54 @t26)) % 2.43/2.69 (define @t56 () (tptp.mult @t25 @t55)) % 2.43/2.69 (define @t57 () (tptp.mult @t25 @t54)) % 2.43/2.69 (define @t58 () (tptp.mult @t57 @t25)) % 2.43/2.69 (define @t59 () (tptp.mult @t57 @t26)) % 2.43/2.69 (define @t60 () (tptp.mult @t26 @t54)) % 2.43/2.69 (define @t61 () (tptp.mult @t25 @t53)) % 2.43/2.69 (define @t62 () (tptp.mult @t61 @t25)) % 2.43/2.69 (define @t63 () (= @t40 (tptp.mult @t40 @t25))) % 2.43/2.69 (define @t64 () (not @t63)) % 2.43/2.69 (define @t65 () (not @t23)) % 2.43/2.69 (define @t66 () (@list false)) % 2.43/2.69 (define @t67 () (@var "BOUND_VARIABLE_7474" $$unsorted)) % 2.43/2.69 (define @t68 () (@var "BOUND_VARIABLE_7476" $$unsorted)) % 2.43/2.69 (define @t69 () (forall (@list @t67 @t68) (= @t67 (tptp.mult (tptp.rd @t68 @t68) @t67)))) % 2.43/2.69 (define @t70 () (@quantifiers_skolemize @t69 0)) % 2.43/2.69 (define @t71 () (@quantifiers_skolemize @t69 1)) % 2.43/2.69 (define @t72 () (tptp.rd @t71 @t71)) % 2.43/2.69 (define @t73 () (tptp.mult @t72 @t72)) % 2.43/2.69 (define @t74 () (tptp.mult @t71 @t73)) % 2.43/2.69 (define @t75 () (tptp.mult @t71 @t72)) % 2.43/2.69 (define @t76 () (tptp.mult @t75 @t72)) % 2.43/2.69 (define @t77 () (tptp.mult @t72 @t71)) % 2.43/2.69 (define @t78 () (tptp.mult @t72 @t77)) % 2.43/2.69 (define @t79 () (@list @t78 @t71)) % 2.43/2.69 (define @t80 () (tptp.mult @t74 @t73)) % 2.43/2.69 (define @t81 () (tptp.mult @t73 (tptp.mult @t73 @t71))) % 2.43/2.69 (define @t82 () (tptp.mult @t72 @t74)) % 2.43/2.69 (define @t83 () (tptp.mult @t73 @t82)) % 2.43/2.69 (define @t84 () (tptp.mult @t73 @t74)) % 2.43/2.69 (define @t85 () (tptp.mult @t73 @t84)) % 2.43/2.69 (define @t86 () (tptp.mult @t73 @t73)) % 2.43/2.69 (define @t87 () (tptp.mult @t86 @t71)) % 2.43/2.69 (define @t88 () (tptp.mult @t86 @t70)) % 2.43/2.69 (define @t89 () (tptp.mult @t72 @t76)) % 2.43/2.69 (define @t90 () (tptp.mult @t73 @t75)) % 2.43/2.69 (define @t91 () (tptp.mult @t90 @t72)) % 2.43/2.69 (define @t92 () (tptp.mult @t91 @t72)) % 2.43/2.69 (define @t93 () (tptp.mult @t72 @t75)) % 2.43/2.69 (define @t94 () (tptp.mult @t82 @t72)) % 2.43/2.69 (define @t95 () (tptp.mult @t72 @t94)) % 2.43/2.69 (define @t96 () (tptp.mult @t72 @t93)) % 2.43/2.69 (define @t97 () (tptp.mult @t75 @t96)) % 2.43/2.69 (define @t98 () (tptp.mult @t70 @t73)) % 2.43/2.69 (define @t99 () (tptp.mult @t86 @t72)) % 2.43/2.69 (define @t100 () (tptp.mult @t73 @t72)) % 2.43/2.69 (define @t101 () (tptp.mult @t70 @t100)) % 2.43/2.69 (define @t102 () (tptp.mult @t72 @t70)) % 2.43/2.69 (define @t103 () (tptp.mult @t88 @t73)) % 2.43/2.69 (define @t104 () (tptp.mult @t73 @t98)) % 2.43/2.69 (define @t105 () (tptp.mult @t73 @t104)) % 2.43/2.69 (define @t106 () (tptp.mult @t104 @t72)) % 2.43/2.69 (define @t107 () (tptp.mult @t72 @t106)) % 2.43/2.69 (define @t108 () (tptp.mult @t98 @t73)) % 2.43/2.69 (define @t109 () (tptp.mult @t106 @t72)) % 2.43/2.69 (define @t110 () (tptp.mult @t72 @t109)) % 2.43/2.69 (define @t111 () (tptp.mult @t98 @t72)) % 2.43/2.69 (define @t112 () (tptp.mult @t88 @t72)) % 2.43/2.69 (define @t113 () (tptp.mult @t72 @t112)) % 2.43/2.69 (define @t114 () (tptp.mult @t72 @t88)) % 2.43/2.69 (define @t115 () (tptp.mult @t114 @t72)) % 2.43/2.69 (define @t116 () (= @t70 @t102)) % 2.43/2.69 (define @t117 () (not @t116)) % 2.43/2.69 (define @t118 () (not @t69)) % 2.43/2.69 (define @t119 () (= @t12 @t15)) % 2.43/2.69 (define @t120 () (forall @t18 @t119)) % 2.43/2.69 (define @t121 () (@list @t12 @t13)) % 2.43/2.69 (define @t122 () (= @t12 @t16)) % 2.43/2.69 (define @t123 () (forall @t18 @t122)) % 2.43/2.69 (define @t124 () (and @t123 @t120)) % 2.43/2.69 (assume @p1 (forall @t3 (= (tptp.mult @t2 (tptp.ld @t2 @t1)) @t1))) % 2.43/2.69 (assume @p2 @t6) % 2.43/2.69 (assume @p3 @t8) % 2.43/2.69 (assume @p4 @t10) % 2.43/2.69 (assume @p5 (forall (@list @t11 @t1 @t2) (= (tptp.mult (tptp.mult @t4 @t11) @t2) (tptp.mult @t2 (tptp.mult @t1 (tptp.mult @t11 @t2)))))) % 2.43/2.69 (assume @p6 @t20) % 2.43/2.69 (assume @p7 true) % 2.43/2.69 (step @p8 :rule refl :args (@t24)) % 2.43/2.69 (step @p9 :rule eq-symm :args (@t9 @t2)) % 2.43/2.69 (step @p10 :rule cong :premises (@p9) :args (@t10)) % 2.43/2.69 (step @p11 :rule eq_resolve :premises (@p4 @p10)) % 2.43/2.69 (step @p12 :rule instantiate :premises (@p11) :args ((@list @t26 @t24))) % 2.43/2.69 (step @p13 :rule symm :premises (@p12)) % 2.43/2.69 (step @p14 :rule refl :args (@t26)) % 2.43/2.69 (step @p15 :rule eq-symm :args (@t5 @t1)) % 2.43/2.69 (step @p16 :rule cong :premises (@p15) :args (@t6)) % 2.43/2.69 (step @p17 :rule eq_resolve :premises (@p2 @p16)) % 2.43/2.69 (step @p18 :rule instantiate :premises (@p17) :args ((@list @t27 @t25))) % 2.43/2.69 (step @p19 :rule symm :premises (@p18)) % 2.43/2.69 (step @p20 :rule instantiate :premises (@p5) :args ((@list @t25 @t24 @t25))) % 2.43/2.69 (step @p21 :rule refl :args (@t25)) % 2.43/2.69 (step @p22 :rule eq-symm :args (@t7 @t2)) % 2.43/2.69 (step @p23 :rule cong :premises (@p22) :args (@t8)) % 2.43/2.69 (step @p24 :rule eq_resolve :premises (@p3 @p23)) % 2.43/2.69 (step @p25 :rule instantiate :premises (@p24) :args ((@list @t24 @t24))) % 2.43/2.69 (step @p26 :rule cong :premises (@p25 @p21) :args (@t28)) % 2.43/2.69 (step @p27 :rule cong :premises (@p26 @p21) :args (@t29)) % 2.43/2.69 (step @p28 :rule instantiate :premises (@p11) :args ((@list @t24 @t29))) % 2.43/2.69 (step @p29 :rule symm :premises (@p28)) % 2.43/2.69 (step @p30 :rule symm :premises (@p25)) % 2.43/2.69 (step @p31 :rule cong :premises (@p21 @p30) :args (@t31)) % 2.43/2.69 (step @p32 :rule trans :premises (@p31 @p30)) % 2.43/2.69 (step @p33 :rule instantiate :premises (@p5) :args ((@list @t25 @t25 @t24))) % 2.43/2.69 (step @p34 :rule symm :premises (@p33)) % 2.43/2.69 (step @p35 :rule cong :premises (@p34 @p32) :args ((tptp.rd (tptp.mult @t24 @t31) @t31))) % 2.43/2.69 (step @p36 :rule instantiate :premises (@p11) :args (@t32)) % 2.43/2.69 (step @p37 :rule trans :premises (@p30 @p36 @p35 @p29 @p27 @p20)) % 2.43/2.69 (step @p38 :rule cong :premises (@p21 @p37) :args ((tptp.ld @t25 @t30))) % 2.43/2.69 (step @p39 :rule instantiate :premises (@p17) :args ((@list @t24 @t25))) % 2.43/2.69 (step @p40 :rule trans :premises (@p39 @p38 @p19)) % 2.43/2.69 (step @p41 :rule instantiate :premises (@p17) :args (@t32)) % 2.43/2.69 (step @p42 :rule symm :premises (@p41)) % 2.43/2.69 (step @p43 :rule symm :premises (@p32)) % 2.43/2.69 (step @p44 :rule symm :premises (@p39)) % 2.43/2.69 (step @p45 :rule symm :premises (@p38)) % 2.43/2.69 (step @p46 :rule symm :premises (@p40)) % 2.43/2.69 (step @p47 :rule cong :premises (@p46 @p14) :args (@t33)) % 2.43/2.69 (step @p48 :rule trans :premises (@p47 @p18 @p45 @p44)) % 2.43/2.69 (step @p49 :rule cong :premises (@p48 @p43) :args ((tptp.mult @t33 @t24))) % 2.43/2.69 (step @p50 :rule instantiate :premises (@p5) :args ((@list @t26 @t26 @t24))) % 2.43/2.69 (step @p51 :rule symm :premises (@p50)) % 2.43/2.69 (step @p52 :rule trans :premises (@p51 @p49)) % 2.43/2.69 (step @p53 :rule cong :premises (@p8 @p52) :args ((tptp.ld @t24 (tptp.mult @t24 @t34)))) % 2.43/2.69 (step @p54 :rule instantiate :premises (@p17) :args ((@list @t34 @t24))) % 2.43/2.69 (step @p55 :rule symm :premises (@p36)) % 2.43/2.69 (step @p56 :rule symm :premises (@p35)) % 2.43/2.69 (step @p57 :rule symm :premises (@p27)) % 2.43/2.69 (step @p58 :rule symm :premises (@p20)) % 2.43/2.69 (step @p59 :rule trans :premises (@p58 @p57 @p28 @p56 @p55)) % 2.43/2.69 (step @p60 :rule cong :premises (@p14 @p59) :args (@t36)) % 2.43/2.69 (step @p61 :rule trans :premises (@p18 @p45 @p44 @p36 @p35 @p29 @p27 @p20)) % 2.43/2.69 (step @p62 :rule cong :premises (@p14 @p61) :args (@t37)) % 2.43/2.69 (step @p63 :rule trans :premises (@p62 @p60)) % 2.43/2.69 (step @p64 :rule cong :premises (@p14 @p63) :args ((tptp.mult @t26 @t37))) % 2.43/2.69 (step @p65 :rule instantiate :premises (@p5) :args ((@list @t24 @t26 @t26))) % 2.43/2.69 (step @p66 :rule trans :premises (@p65 @p64 @p54 @p53 @p42 @p31 @p30)) % 2.43/2.69 (step @p67 :rule trans :premises (@p66 @p40)) % 2.43/2.69 (step @p68 :rule cong :premises (@p67 @p14) :args ((tptp.rd (tptp.mult @t39 @t26) @t26))) % 2.43/2.69 (step @p69 :rule instantiate :premises (@p11) :args ((@list @t26 @t39))) % 2.43/2.69 (step @p70 :rule trans :premises (@p69 @p68 @p13)) % 2.43/2.69 (step @p71 :rule cong :premises (@p70 @p8) :args ((tptp.rd @t39 @t24))) % 2.43/2.69 (step @p72 :rule instantiate :premises (@p11) :args ((@list @t24 @t38))) % 2.43/2.69 (step @p73 :rule trans :premises (@p72 @p71)) % 2.43/2.69 (step @p74 :rule refl :args (@t40)) % 2.43/2.69 (step @p75 :rule cong :premises (@p74 @p73) :args (@t41)) % 2.43/2.69 (step @p76 :rule symm :premises (@p73)) % 2.43/2.69 (step @p77 :rule instantiate :premises (@p17) :args ((@list @t40 @t26))) % 2.43/2.69 (step @p78 :rule symm :premises (@p77)) % 2.43/2.69 (step @p79 :rule instantiate :premises (@p11) :args ((@list @t26 @t42))) % 2.43/2.69 (step @p80 :rule symm :premises (@p79)) % 2.43/2.69 (step @p81 :rule instantiate :premises (@p11) :args ((@list @t37 @t26))) % 2.43/2.69 (step @p82 :rule symm :premises (@p81)) % 2.43/2.69 (step @p83 :rule symm :premises (@p62)) % 2.43/2.69 (step @p84 :rule instantiate :premises (@p11) :args ((@list @t25 @t36))) % 2.43/2.69 (step @p85 :rule symm :premises (@p84)) % 2.43/2.69 (step @p86 :rule instantiate :premises (@p5) :args ((@list @t35 @t25 @t25))) % 2.43/2.69 (step @p87 :rule symm :premises (@p86)) % 2.43/2.69 (step @p88 :rule symm :premises (@p59)) % 2.43/2.69 (step @p89 :rule cong :premises (@p88 @p21) :args (@t28)) % 2.43/2.69 (step @p90 :rule cong :premises (@p21 @p89) :args (@t43)) % 2.43/2.69 (step @p91 :rule cong :premises (@p21 @p90) :args (@t44)) % 2.43/2.69 (step @p92 :rule instantiate :premises (@p17) :args ((@list @t44 @t28))) % 2.43/2.69 (step @p93 :rule symm :premises (@p92)) % 2.43/2.69 (step @p94 :rule symm :premises (@p91)) % 2.43/2.69 (step @p95 :rule instantiate :premises (@p11) :args ((@list @t25 @t28))) % 2.43/2.69 (step @p96 :rule symm :premises (@p95)) % 2.43/2.69 (step @p97 :rule trans :premises (@p36 @p35 @p29)) % 2.43/2.69 (step @p98 :rule trans :premises (@p28 @p56 @p55 @p25)) % 2.43/2.69 (step @p99 :rule cong :premises (@p21 @p98) :args (@t45)) % 2.43/2.69 (step @p100 :rule trans :premises (@p99 @p31)) % 2.43/2.69 (step @p101 :rule cong :premises (@p21 @p100) :args ((tptp.mult @t25 @t45))) % 2.43/2.69 (step @p102 :rule instantiate :premises (@p5) :args ((@list @t28 @t25 @t25))) % 2.43/2.69 (step @p103 :rule trans :premises (@p102 @p101 @p31 @p30)) % 2.43/2.69 (step @p104 :rule trans :premises (@p103 @p97)) % 2.43/2.69 (step @p105 :rule cong :premises (@p104 @p21) :args ((tptp.rd (tptp.mult @t46 @t25) @t25))) % 2.43/2.69 (step @p106 :rule instantiate :premises (@p11) :args ((@list @t25 @t46))) % 2.43/2.69 (step @p107 :rule trans :premises (@p106 @p105 @p96)) % 2.43/2.69 (step @p108 :rule cong :premises (@p21 @p107) :args (@t47)) % 2.43/2.69 (step @p109 :rule trans :premises (@p108 @p90)) % 2.43/2.69 (step @p110 :rule cong :premises (@p21 @p109) :args (@t48)) % 2.43/2.69 (step @p111 :rule trans :premises (@p110 @p94)) % 2.43/2.69 (step @p112 :rule cong :premises (@p107 @p111) :args ((tptp.mult @t46 @t48))) % 2.43/2.69 (step @p113 :rule instantiate :premises (@p5) :args ((@list @t25 @t25 @t46))) % 2.43/2.69 (step @p114 :rule symm :premises (@p107)) % 2.43/2.69 (step @p115 :rule symm :premises (@p103)) % 2.43/2.69 (step @p116 :rule cong :premises (@p115 @p21) :args (@t28)) % 2.43/2.69 (step @p117 :rule symm :premises (@p97)) % 2.43/2.69 (step @p118 :rule cong :premises (@p117 @p21) :args (@t49)) % 2.43/2.69 (step @p119 :rule trans :premises (@p118 @p116)) % 2.43/2.69 (step @p120 :rule cong :premises (@p119 @p114) :args (@t50)) % 2.43/2.69 (step @p121 :rule trans :premises (@p120 @p113 @p112)) % 2.43/2.69 (step @p122 :rule cong :premises (@p118 @p121) :args ((tptp.ld @t49 @t50))) % 2.43/2.69 (step @p123 :rule instantiate :premises (@p17) :args ((@list @t28 @t49))) % 2.43/2.69 (step @p124 :rule trans :premises (@p123 @p122 @p93 @p91 @p87)) % 2.43/2.69 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:args (@t104)) % 2.43/2.69 (step @p347 :rule cong :premises (@p346 @p318) :args (@t106)) % 2.43/2.69 (step @p348 :rule trans :premises (@p347 @p345)) % 2.43/2.69 (step @p349 :rule cong :premises (@p348 @p209) :args (@t109)) % 2.43/2.69 (step @p350 :rule trans :premises (@p349 @p343 @p342)) % 2.43/2.69 (step @p351 :rule cong :premises (@p209 @p350) :args (@t110)) % 2.43/2.69 (step @p352 :rule trans :premises (@p351 @p339)) % 2.43/2.69 (step @p353 :rule cong :premises (@p209 @p352) :args ((tptp.mult @t72 @t110))) % 2.43/2.69 (step @p354 :rule instantiate :premises (@p5) :args ((@list @t106 @t72 @t72))) % 2.43/2.69 (step @p355 :rule refl :args (@t106)) % 2.43/2.69 (step @p356 :rule cong :premises (@p318 @p355) :args (@t107)) % 2.43/2.69 (step @p357 :rule symm :premises (@p337)) % 2.43/2.69 (step @p358 :rule symm :premises (@p336)) % 2.43/2.69 (step @p359 :rule trans :premises (@p312 @p358 @p357 @p356)) % 2.43/2.69 (step @p360 :rule cong :premises (@p359 @p307) :args (@t108)) % 2.43/2.69 (step @p361 :rule trans :premises (@p360 @p354 @p353 @p337 @p336 @p313)) % 2.43/2.69 (step @p362 :rule cong :premises (@p361 @p205) :args ((tptp.rd @t108 @t73))) % 2.43/2.69 (step @p363 :rule instantiate :premises (@p11) :args ((@list @t73 @t98))) % 2.43/2.69 (step @p364 :rule trans :premises (@p363 @p362 @p311)) % 2.43/2.69 (step @p365 :rule cong :premises (@p205 @p364) :args (@t104)) % 2.43/2.69 (step @p366 :rule symm :premises (@p356)) % 2.43/2.69 (step @p367 :rule symm :premises (@p349)) % 2.43/2.69 (step @p368 :rule symm :premises (@p343)) % 2.43/2.69 (step @p369 :rule symm :premises (@p342)) % 2.43/2.69 (step @p370 :rule refl :args (@t111)) % 2.43/2.69 (step @p371 :rule cong :premises (@p307 @p370) :args ((tptp.mult @t73 @t111))) % 2.43/2.69 (step @p372 :rule symm :premises (@p360)) % 2.43/2.69 (step @p373 :rule symm :premises (@p354)) % 2.43/2.69 (step @p374 :rule symm :premises (@p353)) % 2.43/2.69 (step @p375 :rule trans :premises (@p312 @p358 @p357 @p374 @p373 @p372 @p341)) % 2.43/2.69 (step @p376 :rule cong :premises (@p205 @p375) :args (@t104)) % 2.43/2.69 (step @p377 :rule trans :premises (@p376 @p371 @p369 @p368 @p367)) % 2.43/2.69 (step @p378 :rule cong :premises (@p307 @p377) :args (@t105)) % 2.43/2.69 (step @p379 :rule trans :premises (@p328 @p378 @p351 @p339)) % 2.43/2.69 (step @p380 :rule cong :premises (@p318 @p379) :args ((tptp.mult @t72 @t103))) % 2.43/2.69 (step @p381 :rule symm :premises (@p327)) % 2.43/2.69 (step @p382 :rule cong :premises (@p259 @p209) :args (@t112)) % 2.43/2.69 (step @p383 :rule trans :premises (@p382 @p381)) % 2.43/2.69 (step @p384 :rule cong :premises (@p209 @p383) :args (@t113)) % 2.43/2.69 (step @p385 :rule trans :premises (@p384 @p380 @p366 @p337 @p336 @p313)) % 2.43/2.69 (step @p386 :rule cong :premises (@p318 @p385) :args ((tptp.mult @t72 @t113))) % 2.43/2.69 (step @p387 :rule instantiate :premises (@p5) :args ((@list @t88 @t72 @t72))) % 2.43/2.69 (step @p388 :rule refl :args (@t88)) % 2.43/2.69 (step @p389 :rule cong :premises (@p318 @p388) :args (@t114)) % 2.43/2.69 (step @p390 :rule cong :premises (@p389 @p307) :args ((tptp.mult @t114 @t73))) % 2.43/2.69 (step @p391 :rule refl :args (@t114)) % 2.43/2.69 (step @p392 :rule cong :premises (@p391 @p318) :args (@t115)) % 2.43/2.69 (step @p393 :rule instantiate :premises (@p11) :args ((@list @t72 @t115))) % 2.43/2.69 (step @p394 :rule symm :premises (@p393)) % 2.43/2.69 (step @p395 :rule instantiate :premises (@p5) :args ((@list @t72 @t88 @t72))) % 2.43/2.69 (step @p396 :rule symm :premises (@p395)) % 2.43/2.69 (step @p397 :rule symm :premises (@p380)) % 2.43/2.69 (step @p398 :rule trans :premises (@p312 @p358 @p357 @p356 @p397 @p396)) % 0.34/2.70 (step @p399 :rule cong :premises (@p398 @p307) :args ((tptp.rd @t98 @t73))) % 0.34/2.70 (step @p400 :rule trans :premises (@p310 @p399 @p394 @p392 @p390 @p387 @p386 @p365 @p309 @p259)) % 0.34/2.70 (step @p401 :rule refl :args (@t117)) % 0.34/2.70 (step @p402 :rule bool-double-not-elim :args (@t69)) % 0.34/2.70 (step @p403 :rule nary_cong :premises (@p402 @p401) :args ((or (not @t118) @t117))) % 0.34/2.70 (assume-push @p427 @t118) % 0.34/2.70 (step @p405 :rule skolemize :premises (@p427)) % 0.34/2.70 (step-pop @p428 :rule scope :premises (@p405)) % 0.34/2.70 (step @p406 :rule process_scope :premises (@p428) :args (@t117)) % 0.34/2.70 (step @p408 :rule implies_elim :premises (@p406)) % 0.34/2.70 (step @p409 :rule eq_resolve :premises (@p408 @p403)) % 0.34/2.70 (step @p410 :rule chain_m_resolution :premises (@p409 @p400) :args (@t69 @t66 (@list @t116))) % 0.34/2.70 (step @p411 :rule alpha_equiv :args (@t120 @t121 (@list @t67 @t68))) % 0.34/2.70 (step @p412 :rule alpha_equiv :args (@t123 @t121 (@list @t22 @t21))) % 0.34/2.70 (step @p413 :rule nary_cong :premises (@p412 @p411) :args (@t124)) % 0.34/2.70 (step @p414 :rule quant-miniscope-and :args ((= (forall @t18 (and @t122 @t119)) @t124))) % 0.34/2.70 (step @p415 :rule trans :premises (@p414 @p413)) % 0.34/2.70 (step @p416 :rule eq-symm :args (@t15 @t12)) % 0.34/2.70 (step @p417 :rule eq-symm :args (@t16 @t12)) % 0.34/2.70 (step @p418 :rule nary_cong :premises (@p417 @p416) :args (@t17)) % 0.34/2.70 (step @p419 :rule cong :premises (@p418) :args (@t19)) % 0.34/2.70 (step @p420 :rule trans :premises (@p419 @p415)) % 0.34/2.70 (step @p421 :rule cong :premises (@p420) :args (@t20)) % 0.34/2.70 (step @p422 :rule eq_resolve :premises (@p6 @p421)) % 0.34/2.70 (step @p423 :rule not_and :premises (@p422)) % 0.34/2.70 (step @p424 false :rule chain_m_resolution :premises (@p423 @p410 @p200) :args (false (@list false false) (@list @t69 @t23))) % 0.34/2.70 ) % 0.34/2.70 % SZS output end Proof % 0.34/2.70 % cvc5 exiting %------------------------------------------------------------------------------