%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWX197+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n018.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 09:07:20 AM UTC 2026 % Result : Theorem 158.65s 158.91s % Output : Proof 158.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX197+1 : TPTP v9.3.0. Released v9.3.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n018.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 23:05:50 EDT 2026 % 0.18/0.35 % CPUTime : % 0.28/0.51 %----Proving TF0_NAR, FOF, or CNF % 158.65/158.91 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 158.65/158.91 --- Run --no-e-matching --full-saturate-quant at 6... % 158.65/158.91 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 158.65/158.91 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 158.65/158.91 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 158.65/158.91 --- Run --trigger-sel=max --full-saturate-quant at 15... % 158.65/158.91 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 33... % 158.65/158.91 --- Run --multi-trigger-cache --full-saturate-quant at 15... % 158.65/158.91 --- Run --prenex-quant=none --full-saturate-quant at 30... % 158.65/158.91 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 15... % 158.65/158.91 % SZS status Theorem % 158.65/158.91 % SZS output start Proof % 158.65/158.91 ( % 158.65/158.91 (declare-sort $$unsorted 0) % 158.65/158.91 (declare-const tptp.apply1 (-> $$unsorted $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.append (-> $$unsorted $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.eval (-> $$unsorted $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.mulNat (-> $$unsorted $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.fetch (-> $$unsorted $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.map (-> $$unsorted $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.opti2 (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.store (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.nil2 $$unsorted) % 158.65/158.91 (declare-const tptp.cons2 (-> $$unsorted $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.proj1Eq (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.addNat (-> $$unsorted $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.eq (-> $$unsorted $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.n (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.proj2Mul (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.proj2Add (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.while (-> $$unsorted $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.proj1Add (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.proj1Mul (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.add (-> $$unsorted $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.proj3If (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.proj1Print (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.proj1Suc (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.mul (-> $$unsorted $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.head (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.proj2Eq (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.proj1 (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.run (-> $$unsorted $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.tail (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.proj1V (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.v (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.proj2 (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.suc (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.print (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.x (-> $$unsorted $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.nil $$unsorted) % 158.65/158.91 (declare-const tptp.proj1While (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.lam $$unsorted) % 158.65/158.91 (declare-const tptp.head2 (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.proj2While (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.tail2 (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.if (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.zero $$unsorted) % 158.65/158.91 (declare-const tptp.proj1If (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.proj1N (-> $$unsorted $$unsorted)) % 158.65/158.91 (declare-const tptp.proj2If (-> $$unsorted $$unsorted)) % 158.65/158.91 (define @t1 () (@var "X" $$unsorted)) % 158.65/158.91 (define @t2 () (tptp.suc @t1)) % 158.65/158.91 (define @t3 () (@list @t1)) % 158.65/158.91 (define @t4 () (tptp.n @t1)) % 158.65/158.91 (define @t5 () (@var "X2" $$unsorted)) % 158.65/158.91 (define @t6 () (tptp.add @t1 @t5)) % 158.65/158.91 (define @t7 () (@list @t1 @t5)) % 158.65/158.91 (define @t8 () (tptp.mul @t1 @t5)) % 158.65/158.91 (define @t9 () (tptp.eq @t1 @t5)) % 158.65/158.91 (define @t10 () (@var "X3" $$unsorted)) % 158.65/158.91 (define @t11 () (@list @t1 @t5 @t10)) % 158.65/158.91 (define @t12 () (@var "X4" $$unsorted)) % 158.65/158.91 (define @t13 () (@list @t1 @t5 @t10 @t12)) % 158.65/158.91 (define @t14 () (tptp.eq @t10 @t12)) % 158.65/158.91 (define @t15 () (tptp.v @t10)) % 158.65/158.91 (define @t16 () (tptp.print @t1)) % 158.65/158.91 (define @t17 () (tptp.x @t1 @t5)) % 158.65/158.91 (define @t18 () (tptp.while @t1 @t5)) % 158.65/158.91 (define @t19 () (tptp.if @t1 @t5 @t10)) % 158.65/158.91 (define @t20 () (@var "X5" $$unsorted)) % 158.65/158.91 (define @t21 () (tptp.if @t10 @t12 @t20)) % 158.65/158.91 (define @t22 () (@list @t1 @t5 @t10 @t12 @t20)) % 158.65/158.91 (define @t23 () (tptp.cons @t1 @t5)) % 158.65/158.91 (define @t24 () (not (= tptp.nil @t23))) % 158.65/158.91 (define @t25 () (forall @t7 @t24)) % 158.65/158.91 (define @t26 () (tptp.cons2 @t1 @t5)) % 158.65/158.91 (define @t27 () (@var "Z" $$unsorted)) % 158.65/158.91 (define @t28 () (@list @t27)) % 158.65/158.91 (define @t29 () (tptp.suc @t5)) % 158.65/158.91 (define @t30 () (@list @t27 @t5)) % 158.65/158.91 (define @t31 () (@var "St" $$unsorted)) % 158.65/158.91 (define @t32 () (@var "N" $$unsorted)) % 158.65/158.91 (define @t33 () (tptp.cons @t32 @t31)) % 158.65/158.91 (define @t34 () (tptp.suc @t10)) % 158.65/158.91 (define @t35 () (@var "P" $$unsorted)) % 158.65/158.91 (define @t36 () (@var "E" $$unsorted)) % 158.65/158.91 (define @t37 () (@var "Q" $$unsorted)) % 158.65/158.91 (define @t38 () (@var "R" $$unsorted)) % 158.65/158.91 (define @t39 () (@var "C" $$unsorted)) % 158.65/158.91 (define @t40 () (tptp.suc tptp.zero)) % 158.65/158.91 (define @t41 () (tptp.n @t40)) % 158.65/158.91 (define @t42 () (@var "Y" $$unsorted)) % 158.65/158.91 (define @t43 () (@list @t42)) % 158.65/158.91 (define @t44 () (tptp.suc @t27)) % 158.65/158.91 (define @t45 () (tptp.eval @t1 (tptp.n @t32))) % 158.65/158.91 (define @t46 () (forall (@list @t1 @t32) (= @t45 @t32))) % 158.65/158.91 (define @t47 () (@var "B" $$unsorted)) % 158.65/158.91 (define @t48 () (@var "A" $$unsorted)) % 158.65/158.91 (define @t49 () (@var "B2" $$unsorted)) % 158.65/158.91 (define @t50 () (@var "B3" $$unsorted)) % 158.65/158.91 (define @t51 () (@var "A2" $$unsorted)) % 158.65/158.91 (define @t52 () (tptp.eval @t1 (tptp.eq @t51 @t50))) % 158.65/158.91 (define @t53 () (= (tptp.eval @t1 @t51) (tptp.eval @t1 @t50))) % 158.65/158.91 (define @t54 () (@list @t1 @t51 @t50)) % 158.65/158.91 (define @t55 () (tptp.run @t1 tptp.nil2)) % 158.65/158.91 (define @t56 () (forall @t3 (= @t55 tptp.nil))) % 158.65/158.91 (define @t57 () (@var "E2" $$unsorted)) % 158.65/158.91 (define @t58 () (@var "E3" $$unsorted)) % 158.65/158.91 (define @t59 () (tptp.while @t58 @t35)) % 158.65/158.91 (define @t60 () (@var "Q2" $$unsorted)) % 158.65/158.91 (define @t61 () (@var "E4" $$unsorted)) % 158.65/158.91 (define @t62 () (tptp.run @t1 (tptp.cons2 (tptp.if @t61 @t37 @t60) @t38))) % 158.65/158.91 (define @t63 () (tptp.eval @t1 @t61)) % 158.65/158.91 (define @t64 () (= @t62 (tptp.run @t1 (tptp.append @t37 @t38)))) % 158.65/158.91 (define @t65 () (=> (= @t63 @t34) @t64)) % 158.65/158.91 (define @t66 () (@list @t1 @t38 @t61 @t37 @t60 @t10)) % 158.65/158.91 (define @t67 () (forall @t66 @t65)) % 158.65/158.91 (define @t68 () (@var "F" $$unsorted)) % 158.65/158.91 (define @t69 () (@var "Xs" $$unsorted)) % 158.65/158.91 (define @t70 () (tptp.append tptp.nil2 @t42)) % 158.65/158.91 (define @t71 () (forall @t43 (= @t70 @t42))) % 158.65/158.91 (define @t72 () (= (tptp.run tptp.nil (tptp.cons2 @t35 tptp.nil2)) (tptp.run tptp.nil (tptp.cons2 (tptp.opti2 @t35) tptp.nil2)))) % 158.65/158.91 (define @t73 () (not @t72)) % 158.65/158.91 (define @t74 () (@list @t35)) % 158.65/158.91 (define @t75 () (exists @t74 @t73)) % 158.65/158.91 (define @t76 () (not @t75)) % 158.65/158.91 (define @t77 () (= @t34 @t63)) % 158.65/158.91 (define @t78 () (tptp.print @t41)) % 158.65/158.91 (define @t79 () (tptp.cons2 @t78 tptp.nil2)) % 158.65/158.91 (define @t80 () (tptp.add @t41 @t41)) % 158.65/158.91 (define @t81 () (tptp.cons2 (tptp.if @t80 @t79 tptp.nil2) tptp.nil2)) % 158.65/158.91 (define @t82 () (tptp.run tptp.nil @t81)) % 158.65/158.91 (define @t83 () (tptp.run tptp.nil (tptp.append @t79 tptp.nil2))) % 158.65/158.91 (define @t84 () (tptp.addNat tptp.zero @t40)) % 158.65/158.91 (define @t85 () (= (tptp.suc @t84) (tptp.eval tptp.nil @t80))) % 158.65/158.91 (define @t86 () (not @t85)) % 158.65/158.91 (define @t87 () (= @t82 @t83)) % 158.65/158.91 (define @t88 () (or @t86 @t87)) % 158.65/158.91 (define @t89 () (forall @t66 (or (not @t77) @t64))) % 158.65/158.91 (define @t90 () (= @t83 @t82)) % 158.65/158.91 (define @t91 () (or @t86 @t90)) % 158.65/158.91 (define @t92 () (@list false)) % 158.65/158.91 (define @t93 () (@list @t89)) % 158.65/158.91 (define @t94 () (tptp.run tptp.nil tptp.nil2)) % 158.65/158.91 (define @t95 () (tptp.eval tptp.nil @t41)) % 158.65/158.91 (define @t96 () (tptp.cons @t95 @t94)) % 158.65/158.91 (define @t97 () (not (= @t96 tptp.nil))) % 158.65/158.91 (define @t98 () (forall @t7 (not (= @t23 tptp.nil)))) % 158.65/158.91 (define @t99 () (tptp.append tptp.nil2 tptp.nil2)) % 158.65/158.91 (define @t100 () (tptp.run tptp.nil @t99)) % 158.65/158.91 (define @t101 () (tptp.if @t41 tptp.nil2 @t79)) % 158.65/158.91 (define @t102 () (tptp.run tptp.nil (tptp.cons2 @t101 tptp.nil2))) % 158.65/158.91 (define @t103 () (= @t40 @t95)) % 158.65/158.91 (define @t104 () (not @t103)) % 158.65/158.91 (define @t105 () (or @t104 (= @t102 @t100))) % 158.65/158.91 (define @t106 () (= @t100 @t102)) % 158.65/158.91 (define @t107 () (or @t104 @t106)) % 158.65/158.91 (define @t108 () (forall @t74 (not @t73))) % 158.65/158.91 (define @t109 () (not @t108)) % 158.65/158.91 (assume @p1 (forall @t3 (= (tptp.proj1Suc @t2) @t1))) % 158.65/158.91 (assume @p2 (forall @t3 (not (= tptp.zero @t2)))) % 158.65/158.91 (assume @p3 (forall @t3 (= (tptp.proj1N @t4) @t1))) % 158.65/158.91 (assume @p4 (forall @t7 (= (tptp.proj1Add @t6) @t1))) % 158.65/158.91 (assume @p5 (forall @t7 (= (tptp.proj2Add @t6) @t5))) % 158.65/158.91 (assume @p6 (forall @t7 (= (tptp.proj1Mul @t8) @t1))) % 158.65/158.91 (assume @p7 (forall @t7 (= (tptp.proj2Mul @t8) @t5))) % 158.65/158.91 (assume @p8 (forall @t7 (= (tptp.proj1Eq @t9) @t1))) % 158.65/158.91 (assume @p9 (forall @t7 (= (tptp.proj2Eq @t9) @t5))) % 158.65/158.91 (assume @p10 (forall @t3 (= (tptp.proj1V (tptp.v @t1)) @t1))) % 158.65/158.91 (assume @p11 (forall @t11 (not (= @t4 (tptp.add @t5 @t10))))) % 158.65/158.91 (assume @p12 (forall @t11 (not (= @t4 (tptp.mul @t5 @t10))))) % 158.65/158.91 (assume @p13 (forall @t11 (not (= @t4 (tptp.eq @t5 @t10))))) % 158.65/158.91 (assume @p14 (forall @t7 (not (= @t4 (tptp.v @t5))))) % 158.65/158.91 (assume @p15 (forall @t13 (not (= @t6 (tptp.mul @t10 @t12))))) % 158.65/158.91 (assume @p16 (forall @t13 (not (= @t6 @t14)))) % 158.65/158.91 (assume @p17 (forall @t11 (not (= @t6 @t15)))) % 158.65/158.91 (assume @p18 (forall @t13 (not (= @t8 @t14)))) % 158.65/158.91 (assume @p19 (forall @t11 (not (= @t8 @t15)))) % 158.65/158.91 (assume @p20 (forall @t11 (not (= @t9 @t15)))) % 158.65/158.91 (assume @p21 (forall @t3 (= (tptp.proj1Print @t16) @t1))) % 158.65/158.91 (assume @p22 (forall @t7 (= (tptp.proj1 @t17) @t1))) % 158.65/158.91 (assume @p23 (forall @t7 (= (tptp.proj2 @t17) @t5))) % 158.65/158.91 (assume @p24 (forall @t7 (= (tptp.proj1While @t18) @t1))) % 158.65/158.91 (assume @p25 (forall @t7 (= (tptp.proj2While @t18) @t5))) % 158.65/158.91 (assume @p26 (forall @t11 (= (tptp.proj1If @t19) @t1))) % 158.65/158.91 (assume @p27 (forall @t11 (= (tptp.proj2If @t19) @t5))) % 158.65/158.91 (assume @p28 (forall @t11 (= (tptp.proj3If @t19) @t10))) % 158.65/158.91 (assume @p29 (forall @t11 (not (= @t16 (tptp.x @t5 @t10))))) % 158.65/158.91 (assume @p30 (forall @t11 (not (= @t16 (tptp.while @t5 @t10))))) % 158.65/158.91 (assume @p31 (forall @t13 (not (= @t16 (tptp.if @t5 @t10 @t12))))) % 158.65/158.91 (assume @p32 (forall @t13 (not (= @t17 (tptp.while @t10 @t12))))) % 158.65/158.91 (assume @p33 (forall @t22 (not (= @t17 @t21)))) % 158.65/158.91 (assume @p34 (forall @t22 (not (= @t18 @t21)))) % 158.65/158.91 (assume @p35 (forall @t7 (= (tptp.head @t23) @t1))) % 158.65/158.91 (assume @p36 (forall @t7 (= (tptp.tail @t23) @t5))) % 158.65/158.91 (assume @p37 @t25) % 158.65/158.91 (assume @p38 (forall @t7 (= (tptp.head2 @t26) @t1))) % 158.65/158.91 (assume @p39 (forall @t7 (= (tptp.tail2 @t26) @t5))) % 158.65/158.91 (assume @p40 (forall @t7 (not (= tptp.nil2 @t26)))) % 158.65/158.91 (assume @p41 (forall @t28 (= (tptp.store tptp.nil tptp.zero @t27) (tptp.cons @t27 tptp.nil)))) % 158.65/158.91 (assume @p42 (forall @t30 (= (tptp.store tptp.nil @t29 @t27) (tptp.cons tptp.zero (tptp.store tptp.nil @t5 @t27))))) % 158.65/158.91 (assume @p43 (forall (@list @t27 @t32 @t31) (= (tptp.store @t33 tptp.zero @t27) (tptp.cons @t27 @t31)))) % 158.65/158.91 (assume @p44 (forall (@list @t27 @t32 @t31 @t10) (= (tptp.store @t33 @t34 @t27) (tptp.cons @t32 (tptp.store @t31 @t10 @t27))))) % 158.65/158.91 (assume @p45 (forall @t3 (=> (not (= @t1 (tptp.while (tptp.proj1While @t1) (tptp.proj2While @t1)))) (=> (not (= @t1 (tptp.if (tptp.proj1If @t1) (tptp.proj2If @t1) (tptp.proj3If @t1)))) (= (tptp.opti2 @t1) @t1))))) % 158.65/158.91 (assume @p46 (forall (@list @t36 @t35) (= (tptp.opti2 (tptp.while @t36 @t35)) (tptp.while @t36 (tptp.map tptp.lam @t35))))) % 158.65/158.91 (assume @p47 (forall (@list @t39 @t37 @t38) (= (tptp.opti2 (tptp.if @t39 @t37 @t38)) (tptp.if (tptp.add @t41 @t39) @t38 @t37)))) % 158.65/158.91 (assume @p48 (forall @t43 (= (tptp.fetch tptp.nil @t42) tptp.zero))) % 158.65/158.91 (assume @p49 (forall (@list @t32 @t31) (= (tptp.fetch @t33 tptp.zero) @t32))) % 158.65/158.91 (assume @p50 (forall (@list @t32 @t31 @t27) (= (tptp.fetch @t33 @t44) (tptp.fetch @t31 @t27)))) % 158.65/158.91 (assume @p51 (forall @t43 (= (tptp.addNat tptp.zero @t42) @t42))) % 158.65/158.91 (assume @p52 (forall @t28 (= (tptp.addNat @t44 tptp.zero) @t44))) % 158.65/158.91 (assume @p53 (forall @t30 (= (tptp.addNat @t44 @t29) (tptp.suc (tptp.addNat @t27 @t29))))) % 158.65/158.91 (assume @p54 (forall @t43 (= (tptp.mulNat tptp.zero @t42) tptp.zero))) % 158.65/158.91 (assume @p55 (forall @t28 (= (tptp.mulNat @t44 tptp.zero) tptp.zero))) % 158.65/158.91 (assume @p56 (forall @t30 (= (tptp.mulNat @t44 @t29) (tptp.addNat (tptp.mulNat @t27 @t29) @t29)))) % 158.65/158.91 (assume @p57 @t46) % 158.65/158.91 (assume @p58 (forall (@list @t1 @t48 @t47) (= (tptp.eval @t1 (tptp.add @t48 @t47)) (tptp.addNat (tptp.eval @t1 @t48) (tptp.eval @t1 @t47))))) % 158.65/158.91 (assume @p59 (forall (@list @t1 @t39 @t49) (= (tptp.eval @t1 (tptp.mul @t39 @t49)) (tptp.mulNat (tptp.eval @t1 @t39) (tptp.eval @t1 @t49))))) % 158.65/158.91 (assume @p60 (forall @t54 (=> @t53 (= @t52 @t40)))) % 158.65/158.91 (assume @p61 (forall @t54 (=> (not @t53) (= @t52 tptp.zero)))) % 158.65/158.91 (assume @p62 (forall (@list @t1 @t27) (= (tptp.eval @t1 (tptp.v @t27)) (tptp.fetch @t1 @t27)))) % 158.65/158.91 (assume @p63 @t56) % 158.65/158.91 (assume @p64 (forall (@list @t1 @t38 @t36) (= (tptp.run @t1 (tptp.cons2 (tptp.print @t36) @t38)) (tptp.cons (tptp.eval @t1 @t36) (tptp.run @t1 @t38))))) % 158.65/158.91 (assume @p65 (forall (@list @t1 @t38 @t5 @t57) (= (tptp.run @t1 (tptp.cons2 (tptp.x @t5 @t57) @t38)) (tptp.run (tptp.store @t1 @t5 (tptp.eval @t1 @t57)) @t38)))) % 158.65/158.91 (assume @p66 (forall (@list @t1 @t38 @t58 @t35) (= (tptp.run @t1 (tptp.cons2 @t59 @t38)) (tptp.run @t1 (tptp.cons2 (tptp.if @t58 (tptp.append @t35 (tptp.cons2 @t59 tptp.nil2)) tptp.nil2) @t38))))) % 158.65/158.91 (assume @p67 (forall (@list @t1 @t38 @t61 @t37 @t60) (=> (= @t63 tptp.zero) (= @t62 (tptp.run @t1 (tptp.append @t60 @t38)))))) % 158.65/158.91 (assume @p68 @t67) % 158.65/158.91 (assume @p69 (forall (@list @t68) (= (tptp.map @t68 tptp.nil2) tptp.nil2))) % 158.65/158.91 (assume @p70 (forall (@list @t68 @t42 @t69) (= (tptp.map @t68 (tptp.cons2 @t42 @t69)) (tptp.cons2 (tptp.apply1 @t68 @t42) (tptp.map @t68 @t69))))) % 158.65/158.91 (assume @p71 @t71) % 158.65/158.91 (assume @p72 (forall (@list @t42 @t27 @t69) (= (tptp.append (tptp.cons2 @t27 @t69) @t42) (tptp.cons2 @t27 (tptp.append @t69 @t42))))) % 158.65/158.91 (assume @p73 (forall @t43 (= (tptp.apply1 tptp.lam @t42) (tptp.opti2 @t42)))) % 158.65/158.91 (assume @p74 @t76) % 158.65/158.91 (assume @p75 true) % 158.65/158.91 (step @p76 :rule bool-impl-elim :args (@t77 @t64)) % 158.65/158.91 (step @p77 :rule cong :premises (@p76) :args ((forall @t66 (=> @t77 @t64)))) % 158.65/158.91 (step @p78 :rule refl :args (@t64)) % 158.65/158.91 (step @p79 :rule eq-symm :args (@t63 @t34)) % 158.65/158.91 (step @p80 :rule cong :premises (@p79 @p78) :args (@t65)) % 158.65/158.91 (step @p81 :rule cong :premises (@p80) :args (@t67)) % 158.65/158.91 (step @p82 :rule trans :premises (@p81 @p77)) % 158.65/158.91 (step @p83 :rule eq_resolve :premises (@p68 @p82)) % 158.65/158.91 (step @p84 :rule eq-symm :args (@t82 @t83)) % 158.65/158.91 (step @p85 :rule refl :args (@t86)) % 158.65/158.91 (step @p86 :rule nary_cong :premises (@p85 @p84) :args (@t88)) % 158.65/158.91 (step @p87 :rule refl :args (@t89)) % 158.65/158.91 (step @p88 :rule cong :premises (@p87 @p86) :args ((=> @t89 @t88))) % 158.65/158.91 (assume-push @p186 @t89) % 158.65/158.91 (step @p90 :rule instantiate :premises (@p83) :args ((@list tptp.nil tptp.nil2 @t80 @t79 tptp.nil2 @t84))) % 158.65/158.91 (step-pop @p187 :rule scope :premises (@p90)) % 158.65/158.91 (step @p91 :rule process_scope :premises (@p187) :args (@t88)) % 158.65/158.91 (step @p93 :rule eq_resolve :premises (@p91 @p88)) % 158.65/158.91 (step @p94 :rule implies_elim :premises (@p93)) % 158.65/158.91 (step @p95 :rule chain_m_resolution :premises (@p94 @p83) :args (@t91 @t92 @t93)) % 158.65/158.91 (step @p96 :rule bool-eq-false :args (@t90)) % 158.65/158.91 (step @p97 :rule symm :premises (@p96)) % 158.65/158.91 (step @p98 :rule cong :premises (@p84) :args ((not @t87))) % 158.65/158.91 (step @p99 :rule bool-eq-false :args (@t87)) % 158.65/158.91 (step @p100 :rule trans :premises (@p99 @p98)) % 158.65/158.91 (step @p101 :rule trans :premises (@p100 @p97)) % 158.65/158.91 (step @p102 :rule eq-symm :args (tptp.nil @t23)) % 158.65/158.91 (step @p103 :rule cong :premises (@p102) :args (@t24)) % 158.65/158.91 (step @p104 :rule cong :premises (@p103) :args (@t25)) % 158.65/158.91 (step @p105 :rule eq_resolve :premises (@p37 @p104)) % 158.65/158.91 (step @p106 :rule eq-symm :args (@t96 tptp.nil)) % 158.65/158.91 (step @p107 :rule cong :premises (@p106) :args (@t97)) % 158.65/158.91 (step @p108 :rule refl :args (@t98)) % 158.65/158.91 (step @p109 :rule cong :premises (@p108 @p107) :args ((=> @t98 @t97))) % 158.65/158.91 (assume-push @p188 @t98) % 158.65/158.91 (step @p111 :rule instantiate :premises (@p105) :args ((@list @t95 @t94))) % 158.65/158.91 (step-pop @p189 :rule scope :premises (@p111)) % 158.65/158.91 (step @p112 :rule process_scope :premises (@p189) :args (@t97)) % 158.65/158.91 (step @p114 :rule eq_resolve :premises (@p112 @p109)) % 158.65/158.91 (step @p115 :rule implies_elim :premises (@p114)) % 158.65/158.91 (step @p116 :rule chain_m_resolution :premises (@p115 @p105) :args ((not (= tptp.nil @t96)) @t92 (@list @t98))) % 158.65/158.91 (step @p117 :rule false_intro :premises (@p116)) % 158.65/158.91 (step @p118 :rule instantiate :premises (@p64) :args ((@list tptp.nil tptp.nil2 @t41))) % 158.65/158.91 (step @p119 :rule eq-symm :args (@t70 @t42)) % 158.65/158.91 (step @p120 :rule cong :premises (@p119) :args (@t71)) % 158.65/158.91 (step @p121 :rule eq_resolve :premises (@p71 @p120)) % 158.65/158.91 (step @p122 :rule instantiate :premises (@p121) :args ((@list tptp.nil2))) % 158.65/158.91 (step @p123 :rule symm :premises (@p122)) % 158.65/158.91 (step @p124 :rule refl :args (@t78)) % 158.65/158.91 (step @p125 :rule cong :premises (@p124 @p123) :args ((tptp.cons2 @t78 @t99))) % 158.65/158.91 (step @p126 :rule instantiate :premises (@p72) :args ((@list tptp.nil2 @t78 tptp.nil2))) % 158.65/158.91 (step @p127 :rule trans :premises (@p126 @p125)) % 158.65/158.91 (step @p128 :rule refl :args (tptp.nil)) % 158.65/158.91 (step @p129 :rule cong :premises (@p128 @p127) :args (@t83)) % 158.65/158.91 (step @p130 :rule trans :premises (@p129 @p118)) % 158.65/158.91 (step @p131 :rule eq-symm :args (@t55 tptp.nil)) % 158.65/158.91 (step @p132 :rule cong :premises (@p131) :args (@t56)) % 158.65/158.91 (step @p133 :rule eq_resolve :premises (@p63 @p132)) % 158.65/158.91 (step @p134 :rule instantiate :premises (@p133) :args ((@list tptp.nil))) % 158.65/158.91 (step @p135 :rule symm :premises (@p134)) % 158.65/158.91 (step @p136 :rule cong :premises (@p128 @p123) :args (@t100)) % 158.65/158.91 (step @p137 :rule eq-symm :args (@t102 @t100)) % 158.65/158.91 (step @p138 :rule refl :args (@t104)) % 158.65/158.91 (step @p139 :rule nary_cong :premises (@p138 @p137) :args (@t105)) % 158.65/158.91 (step @p140 :rule cong :premises (@p87 @p139) :args ((=> @t89 @t105))) % 158.65/158.91 (assume-push @p190 @t89) % 158.65/158.91 (step @p142 :rule instantiate :premises (@p83) :args ((@list tptp.nil tptp.nil2 @t41 tptp.nil2 @t79 tptp.zero))) % 158.65/158.91 (step-pop @p191 :rule scope :premises (@p142)) % 158.65/158.91 (step @p143 :rule process_scope :premises (@p191) :args (@t105)) % 158.65/158.91 (step @p145 :rule eq_resolve :premises (@p143 @p140)) % 158.65/158.91 (step @p146 :rule implies_elim :premises (@p145)) % 158.65/158.91 (step @p147 :rule chain_m_resolution :premises (@p146 @p83) :args (@t107 @t92 @t93)) % 158.65/158.91 (step @p148 :rule eq-symm :args (@t45 @t32)) % 158.65/158.91 (step @p149 :rule cong :premises (@p148) :args (@t46)) % 158.65/158.91 (step @p150 :rule eq_resolve :premises (@p57 @p149)) % 158.65/158.91 (step @p151 :rule instantiate :premises (@p150) :args ((@list tptp.nil @t40))) % 158.65/158.91 (step @p152 :rule cnf_or_pos :args (@t107)) % 158.65/158.91 (step @p153 :rule reordering :premises (@p152) :args ((or @t104 @t106 (not @t107)))) % 158.65/158.91 (step @p154 :rule chain_m_resolution :premises (@p153 @p151 @p147) :args (@t106 (@list false false) (@list @t103 @t107))) % 158.65/158.91 (step @p155 :rule symm :premises (@p154)) % 158.65/158.91 (step @p156 :rule bool-double-not-elim :args ((forall @t74 @t72))) % 158.65/158.91 (step @p157 :rule bool-double-not-elim :args (@t72)) % 158.65/158.91 (step @p158 :rule cong :premises (@p157) :args (@t108)) % 158.65/158.91 (step @p159 :rule cong :premises (@p158) :args (@t109)) % 158.65/158.91 (step @p160 :rule exists-elim :args ((= @t75 @t109))) % 158.65/158.91 (step @p161 :rule trans :premises (@p160 @p159)) % 158.65/158.91 (step @p162 :rule cong :premises (@p161) :args (@t76)) % 158.65/158.91 (step @p163 :rule trans :premises (@p162 @p156)) % 158.65/158.91 (step @p164 :rule eq_resolve :premises (@p74 @p163)) % 158.65/158.91 (step @p165 :rule instantiate :premises (@p164) :args ((@list @t101))) % 158.65/158.91 (step @p166 :rule symm :premises (@p165)) % 158.65/158.91 (step @p167 :rule refl :args (tptp.nil2)) % 158.65/158.91 (step @p168 :rule instantiate :premises (@p47) :args ((@list @t41 tptp.nil2 @t79))) % 158.65/158.91 (step @p169 :rule symm :premises (@p168)) % 158.65/158.91 (step @p170 :rule cong :premises (@p169 @p167) :args (@t81)) % 158.65/158.91 (step @p171 :rule cong :premises (@p128 @p170) :args (@t82)) % 158.65/158.91 (step @p172 :rule trans :premises (@p171 @p166 @p155 @p136 @p135)) % 158.65/158.91 (step @p173 :rule cong :premises (@p172 @p130) :args (@t87)) % 158.65/158.91 (step @p174 :rule trans :premises (@p173 @p117)) % 158.65/158.91 (step @p175 :rule eq_resolve :premises (@p174 @p101)) % 158.65/158.91 (step @p176 :rule false_elim :premises (@p175)) % 158.65/158.91 (step @p177 :rule instantiate :premises (@p58) :args ((@list tptp.nil @t41 @t41))) % 158.65/158.91 (step @p178 :rule symm :premises (@p177)) % 158.65/158.91 (step @p179 :rule cong :premises (@p151 @p151) :args ((tptp.addNat @t40 @t40))) % 158.65/158.91 (step @p180 :rule instantiate :premises (@p53) :args ((@list tptp.zero tptp.zero))) % 158.65/158.91 (step @p181 :rule symm :premises (@p180)) % 158.65/158.91 (step @p182 :rule trans :premises (@p181 @p179 @p178)) % 158.65/158.91 (step @p183 :rule cnf_or_pos :args (@t91)) % 158.65/158.91 (step @p184 :rule reordering :premises (@p183) :args ((or @t86 @t90 (not @t91)))) % 158.65/158.91 (step @p185 false :rule chain_m_resolution :premises (@p184 @p182 @p176 @p95) :args (false (@list false true false) (@list @t85 @t90 @t91))) % 158.65/158.91 ) % 158.65/158.91 % SZS output end Proof % 158.65/158.91 % cvc5 exiting %------------------------------------------------------------------------------