%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC255+1 : TPTP v9.2.1. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n011.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 08:58:37 AM UTC 2026 % Result : Theorem 0.36s 0.65s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC255+1 : TPTP v9.2.1. Released v2.4.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.33 % Computer : n011.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.33 % CPULimit : 300 % 0.15/0.33 % WCLimit : 300 % 0.15/0.33 % DateTime : Tue Jun 2 19:33:20 EDT 2026 % 0.15/0.34 % CPUTime : % 0.29/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.65 % SZS status Theorem % 0.36/0.65 % SZS output start Proof % 0.36/0.65 ( % 0.36/0.65 (declare-sort $$unsorted 0) % 0.36/0.65 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.65 (declare-const tptp.nil $$unsorted) % 0.36/0.65 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.36/0.65 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.36/0.65 (define @t1 () (@var "V" $$unsorted)) % 0.36/0.65 (define @t2 () (@var "U" $$unsorted)) % 0.36/0.65 (define @t3 () (= @t2 @t1)) % 0.36/0.65 (define @t4 () (not @t3)) % 0.36/0.65 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.36/0.65 (define @t6 () (tptp.ssItem @t1)) % 0.36/0.65 (define @t7 () (@list @t1)) % 0.36/0.65 (define @t8 () (tptp.ssItem @t2)) % 0.36/0.65 (define @t9 () (@list @t2)) % 0.36/0.65 (define @t10 () (@var "X" $$unsorted)) % 0.36/0.65 (define @t11 () (tptp.cons @t1 @t10)) % 0.36/0.65 (define @t12 () (@var "W" $$unsorted)) % 0.36/0.65 (define @t13 () (tptp.ssList @t10)) % 0.36/0.65 (define @t14 () (@list @t10)) % 0.36/0.65 (define @t15 () (tptp.ssList @t12)) % 0.36/0.65 (define @t16 () (@list @t12)) % 0.36/0.65 (define @t17 () (tptp.ssList @t2)) % 0.36/0.65 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.36/0.65 (define @t19 () (tptp.singletonP @t2)) % 0.36/0.65 (define @t20 () (tptp.app @t1 @t12)) % 0.36/0.65 (define @t21 () (tptp.frontsegP @t2 @t1)) % 0.36/0.65 (define @t22 () (tptp.ssList @t1)) % 0.36/0.65 (define @t23 () (tptp.app @t12 @t1)) % 0.36/0.65 (define @t24 () (tptp.rearsegP @t2 @t1)) % 0.36/0.65 (define @t25 () (tptp.segmentP @t2 @t1)) % 0.36/0.65 (define @t26 () (tptp.leq @t12 @t1)) % 0.36/0.65 (define @t27 () (tptp.leq @t1 @t12)) % 0.36/0.65 (define @t28 () (@var "Z" $$unsorted)) % 0.36/0.65 (define @t29 () (@var "Y" $$unsorted)) % 0.36/0.65 (define @t30 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t29)) (tptp.cons @t12 @t28)) @t2)) % 0.36/0.65 (define @t31 () (tptp.ssList @t28)) % 0.36/0.65 (define @t32 () (@list @t28)) % 0.36/0.65 (define @t33 () (tptp.ssList @t29)) % 0.36/0.65 (define @t34 () (@list @t29)) % 0.36/0.65 (define @t35 () (tptp.ssItem @t12)) % 0.36/0.65 (define @t36 () (tptp.lt @t1 @t12)) % 0.36/0.65 (define @t37 () (= @t1 @t12)) % 0.36/0.65 (define @t38 () (tptp.cons @t1 @t2)) % 0.36/0.65 (define @t39 () (= @t1 @t2)) % 0.36/0.65 (define @t40 () (tptp.cons @t12 @t1)) % 0.36/0.65 (define @t41 () (= tptp.nil @t2)) % 0.36/0.65 (define @t42 () (tptp.hd @t2)) % 0.36/0.65 (define @t43 () (not @t41)) % 0.36/0.65 (define @t44 () (tptp.tl @t2)) % 0.36/0.65 (define @t45 () (tptp.app @t2 @t1)) % 0.36/0.65 (define @t46 () (tptp.app @t1 @t2)) % 0.36/0.65 (define @t47 () (tptp.leq @t1 @t2)) % 0.36/0.65 (define @t48 () (tptp.leq @t2 @t1)) % 0.36/0.65 (define @t49 () (tptp.geq @t2 @t1)) % 0.36/0.65 (define @t50 () (tptp.lt @t1 @t2)) % 0.36/0.65 (define @t51 () (tptp.lt @t2 @t1)) % 0.36/0.65 (define @t52 () (tptp.lt @t2 @t12)) % 0.36/0.65 (define @t53 () (tptp.gt @t2 @t1)) % 0.36/0.65 (define @t54 () (tptp.memberP @t12 @t2)) % 0.36/0.65 (define @t55 () (tptp.app @t12 @t2)) % 0.36/0.65 (define @t56 () (tptp.cons @t2 tptp.nil)) % 0.36/0.65 (define @t57 () (tptp.hd @t1)) % 0.36/0.65 (define @t58 () (= tptp.nil @t1)) % 0.36/0.65 (define @t59 () (not @t58)) % 0.36/0.65 (define @t60 () (tptp.cons @t2 @t1)) % 0.36/0.65 (define @t61 () (= @t12 @t2)) % 0.36/0.65 (define @t62 () (tptp.neq @t1 tptp.nil)) % 0.36/0.65 (define @t63 () (not @t62)) % 0.36/0.65 (define @t64 () (not (tptp.singletonP @t12))) % 0.36/0.65 (define @t65 () (or @t63 @t64 @t19)) % 0.36/0.65 (define @t66 () (and @t65 (or @t63 (tptp.neq @t10 tptp.nil)))) % 0.36/0.65 (define @t67 () (not (= @t2 @t12))) % 0.36/0.65 (define @t68 () (not (= @t1 @t10))) % 0.36/0.65 (define @t69 () (or @t68 @t67 @t66)) % 0.36/0.65 (define @t70 () (forall @t14 (=> @t13 @t69))) % 0.36/0.65 (define @t71 () (=> @t15 @t70)) % 0.36/0.65 (define @t72 () (forall @t16 @t71)) % 0.36/0.65 (define @t73 () (=> @t22 @t72)) % 0.36/0.65 (define @t74 () (forall @t7 @t73)) % 0.36/0.65 (define @t75 () (=> @t17 @t74)) % 0.36/0.65 (define @t76 () (forall @t9 @t75)) % 0.36/0.65 (define @t77 () (not @t76)) % 0.36/0.65 (define @t78 () (not @t22)) % 0.36/0.65 (define @t79 () (or @t78 true)) % 0.36/0.65 (define @t80 () (not @t17)) % 0.36/0.65 (define @t81 () (not @t19)) % 0.36/0.65 (define @t82 () (or @t78 @t63 @t19 @t80 @t81)) % 0.36/0.65 (define @t83 () (or @t80 @t81)) % 0.36/0.65 (define @t84 () (not (= @t2 @t2))) % 0.36/0.65 (define @t85 () (or @t80 @t84 @t81)) % 0.36/0.65 (define @t86 () (not @t15)) % 0.36/0.65 (define @t87 () (or @t67 @t86 @t67 @t64)) % 0.36/0.65 (define @t88 () (or @t86 @t67 @t64)) % 0.36/0.65 (define @t89 () (forall @t16 @t88)) % 0.36/0.65 (define @t90 () (or @t78 @t63 @t19 @t89)) % 0.36/0.65 (define @t91 () (or @t78 @t63 @t19 @t88)) % 0.36/0.65 (define @t92 () (or @t86 @t67 @t78 @t63 @t64 @t19)) % 0.36/0.65 (define @t93 () (and @t65 true)) % 0.36/0.65 (define @t94 () (or @t86 @t67 @t78 @t93)) % 0.36/0.65 (define @t95 () (and @t65 (or @t63 @t62))) % 0.36/0.65 (define @t96 () (or @t67 @t78 @t95)) % 0.36/0.65 (define @t97 () (or @t78 @t95)) % 0.36/0.65 (define @t98 () (not (= @t1 @t1))) % 0.36/0.65 (define @t99 () (or @t78 @t98 @t95)) % 0.36/0.65 (define @t100 () (not @t13)) % 0.36/0.65 (define @t101 () (or @t68 @t100 @t68 @t66)) % 0.36/0.65 (define @t102 () (or @t100 @t68 @t66)) % 0.36/0.65 (define @t103 () (forall @t14 @t102)) % 0.36/0.65 (define @t104 () (or @t67 @t103)) % 0.36/0.65 (define @t105 () (or @t67 @t102)) % 0.36/0.65 (define @t106 () (or @t100 @t68 @t67 @t66)) % 0.36/0.65 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.36/0.65 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.36/0.65 (assume @p3 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.memberP @t2 @t1) (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t12 @t11) @t2))))))))))) % 0.36/0.65 (assume @p4 (forall @t9 (=> @t17 (= @t19 (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.36/0.65 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (= @t21 (exists @t16 (and @t15 (= @t20 @t2))))))))) % 0.36/0.65 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (= @t24 (exists @t16 (and @t15 (= @t23 @t2))))))))) % 0.36/0.65 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (= @t25 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t23 @t10) @t2))))))))))) % 0.36/0.65 (assume @p8 (forall @t9 (=> @t17 (= (tptp.cyclefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t35 (forall @t14 (=> @t13 (forall @t34 (=> @t33 (forall @t32 (=> @t31 (=> @t30 (not (and @t27 @t26))))))))))))))))) % 0.36/0.65 (assume @p9 (forall @t9 (=> @t17 (= (tptp.totalorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t35 (forall @t14 (=> @t13 (forall @t34 (=> @t33 (forall @t32 (=> @t31 (=> @t30 (or @t27 @t26)))))))))))))))) % 0.36/0.65 (assume @p10 (forall @t9 (=> @t17 (= (tptp.strictorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t35 (forall @t14 (=> @t13 (forall @t34 (=> @t33 (forall @t32 (=> @t31 (=> @t30 (or @t36 (tptp.lt @t12 @t1))))))))))))))))) % 0.36/0.65 (assume @p11 (forall @t9 (=> @t17 (= (tptp.totalorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t35 (forall @t14 (=> @t13 (forall @t34 (=> @t33 (forall @t32 (=> @t31 (=> @t30 @t27))))))))))))))) % 0.36/0.65 (assume @p12 (forall @t9 (=> @t17 (= (tptp.strictorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t35 (forall @t14 (=> @t13 (forall @t34 (=> @t33 (forall @t32 (=> @t31 (=> @t30 @t36))))))))))))))) % 0.36/0.65 (assume @p13 (forall @t9 (=> @t17 (= (tptp.duplicatefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t35 (forall @t14 (=> @t13 (forall @t34 (=> @t33 (forall @t32 (=> @t31 (=> @t30 (not @t37)))))))))))))))) % 0.36/0.65 (assume @p14 (forall @t9 (=> @t17 (= (tptp.equalelemsP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t35 (forall @t14 (=> @t13 (forall @t34 (=> @t33 (=> (= (tptp.app @t10 (tptp.cons @t1 (tptp.cons @t12 @t29))) @t2) @t37))))))))))))) % 0.36/0.65 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t22 @t5))))) % 0.36/0.65 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t38)))))) % 0.36/0.65 (assume @p17 (tptp.ssList tptp.nil)) % 0.36/0.65 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t38 @t2))))))) % 0.36/0.65 (assume @p19 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t35 (forall @t14 (=> (tptp.ssItem @t10) (=> (= (tptp.cons @t12 @t2) (tptp.cons @t10 @t1)) (and (= @t12 @t10) @t39))))))))))) % 0.36/0.65 (assume @p20 (forall @t9 (=> @t17 (or @t41 (exists @t7 (and @t22 (exists @t16 (and @t35 (= @t40 @t2))))))))) % 0.36/0.65 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t38))))))) % 0.36/0.65 (assume @p22 (forall @t9 (=> @t17 (=> @t43 (tptp.ssItem @t42))))) % 0.36/0.65 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t38) @t1)))))) % 0.36/0.65 (assume @p24 (forall @t9 (=> @t17 (=> @t43 (tptp.ssList @t44))))) % 0.36/0.65 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t38) @t2)))))) % 0.36/0.65 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (tptp.ssList @t45)))))) % 0.36/0.65 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t35 (= (tptp.cons @t12 @t46) (tptp.app @t40 @t2))))))))) % 0.36/0.65 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.36/0.65 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t48 @t47) @t3)))))) % 0.36/0.65 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t35 (=> (and @t48 @t27) (tptp.leq @t2 @t12))))))))) % 0.36/0.65 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.36/0.65 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t49 @t47)))))) % 0.36/0.65 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t51 (not @t50))))))) % 0.36/0.65 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t35 (=> (and @t51 @t36) @t52)))))))) % 0.36/0.65 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t53 @t50)))))) % 0.36/0.65 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t22 (forall @t16 (=> @t15 (= (tptp.memberP @t20 @t2) (or (tptp.memberP @t1 @t2) @t54))))))))) % 0.36/0.65 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t54))))))))) % 0.36/0.65 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.36/0.65 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.36/0.65 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t15 (=> (and @t21 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 0.36/0.65 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (=> (and @t21 (tptp.frontsegP @t1 @t2)) @t3)))))) % 0.36/0.65 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.36/0.65 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t15 (=> @t21 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 0.36/0.65 (assume @p44 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (= (tptp.frontsegP (tptp.cons @t2 @t12) @t11) (and @t3 (tptp.frontsegP @t12 @t10)))))))))))) % 0.36/0.65 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 0.36/0.65 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t41)))) % 0.36/0.65 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t15 (=> (and @t24 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 0.36/0.65 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (=> (and @t24 (tptp.rearsegP @t1 @t2)) @t3)))))) % 0.36/0.65 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 0.36/0.65 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t15 (=> @t24 (tptp.rearsegP @t55 @t1))))))))) % 0.36/0.65 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.36/0.65 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t41)))) % 0.36/0.65 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t15 (=> (and @t25 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 0.36/0.65 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (=> (and @t25 (tptp.segmentP @t1 @t2)) @t3)))))) % 0.36/0.65 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 0.36/0.65 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t25 (tptp.segmentP (tptp.app @t55 @t10) @t1))))))))))) % 0.36/0.65 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 0.36/0.65 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t41)))) % 0.36/0.65 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t56)))) % 0.36/0.65 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 0.36/0.65 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t56)))) % 0.36/0.65 (assume @p62 (tptp.totalorderP tptp.nil)) % 0.36/0.65 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t56)))) % 0.36/0.65 (assume @p64 (tptp.strictorderP tptp.nil)) % 0.36/0.65 (assume @p65 (forall @t9 (=> @t8 (tptp.totalorderedP @t56)))) % 0.36/0.65 (assume @p66 (tptp.totalorderedP tptp.nil)) % 0.36/0.65 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t22 (= (tptp.totalorderedP @t60) (or @t58 (and @t59 (tptp.totalorderedP @t1) (tptp.leq @t2 @t57))))))))) % 0.36/0.65 (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t56)))) % 0.36/0.65 (assume @p69 (tptp.strictorderedP tptp.nil)) % 0.36/0.65 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t22 (= (tptp.strictorderedP @t60) (or @t58 (and @t59 (tptp.strictorderedP @t1) (tptp.lt @t2 @t57))))))))) % 0.36/0.65 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t56)))) % 0.36/0.65 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 0.36/0.65 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t56)))) % 0.36/0.65 (assume @p74 (tptp.equalelemsP tptp.nil)) % 0.36/0.65 (assume @p75 (forall @t9 (=> @t17 (=> @t43 (exists @t7 (and @t6 (= @t42 @t1))))))) % 0.36/0.65 (assume @p76 (forall @t9 (=> @t17 (=> @t43 (exists @t7 (and @t22 (= @t44 @t1))))))) % 0.36/0.65 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (=> (and @t59 @t43 (= @t57 @t42) (= (tptp.tl @t1) @t44)) @t39)))))) % 0.36/0.65 (assume @p78 (forall @t9 (=> @t17 (=> @t43 (= (tptp.cons @t42 @t44) @t2))))) % 0.36/0.65 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t15 (=> (= @t23 @t45) @t61)))))))) % 0.36/0.65 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t15 (=> (= @t20 @t46) @t61)))))))) % 0.36/0.65 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t38 (tptp.app @t18 @t2))))))) % 0.36/0.65 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t15 (= (tptp.app @t45 @t12) (tptp.app @t2 @t20))))))))) % 0.36/0.65 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (= (= tptp.nil @t45) (and @t58 @t41))))))) % 0.36/0.65 (assume @p84 (forall @t9 (=> @t17 (= (tptp.app @t2 tptp.nil) @t2)))) % 0.36/0.65 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (=> @t43 (= (tptp.hd @t45) @t42))))))) % 0.36/0.65 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (=> @t43 (= (tptp.tl @t45) (tptp.app @t44 @t1)))))))) % 0.36/0.65 (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t49 (tptp.geq @t1 @t2)) @t3)))))) % 0.36/0.65 (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t35 (=> (and @t49 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12))))))))) % 0.36/0.65 (assume @p89 (forall @t9 (=> @t8 (tptp.geq @t2 @t2)))) % 0.36/0.65 (assume @p90 (forall @t9 (=> @t8 (not (tptp.lt @t2 @t2))))) % 0.36/0.65 (assume @p91 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t35 (=> (and @t48 @t36) @t52)))))))) % 0.36/0.65 (assume @p92 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t48 (or @t3 @t51))))))) % 0.36/0.65 (assume @p93 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t51 (and @t4 @t48))))))) % 0.36/0.65 (assume @p94 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t53 (not (tptp.gt @t1 @t2)))))))) % 0.36/0.65 (assume @p95 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t35 (=> (and @t53 (tptp.gt @t1 @t12)) (tptp.gt @t2 @t12))))))))) % 0.36/0.65 (assume @p96 @t77) % 0.36/0.65 (assume @p97 true) % 0.36/0.65 (step @p98 :rule evaluate :args ((not true))) % 0.36/0.65 (step @p99 :rule quant-unused-vars :args ((= (forall @t9 true) true))) % 0.36/0.65 (step @p100 :rule bool-impl-true1 :args (@t17)) % 0.36/0.65 (step @p101 :rule quant-unused-vars :args ((= (forall @t7 true) true))) % 0.36/0.65 (step @p102 :rule absorb :args ((= @t79 true))) % 0.36/0.65 (step @p103 :rule cong :premises (@p102) :args ((forall @t7 @t79))) % 0.36/0.65 (step @p104 :rule trans :premises (@p103 @p101)) % 0.36/0.65 (step @p105 :rule bool-or-taut :args ((or @t78 @t63) @t19 (or @t80) false)) % 0.36/0.65 (step @p106 :rule refl :args (@t78)) % 0.36/0.65 (step @p107 :rule nary_cong :premises (@p106 @p105) :args ((or @t78 @t82))) % 0.36/0.65 (step @p108 :rule bool-impl-elim :args (@t22 @t82)) % 0.36/0.65 (step @p109 :rule trans :premises (@p108 @p107)) % 0.36/0.65 (step @p110 :rule cong :premises (@p109) :args ((forall @t7 (=> @t22 @t82)))) % 0.36/0.65 (step @p111 :rule trans :premises (@p110 @p104)) % 0.36/0.65 (step @p112 :rule aci_norm :args ((= (or @t78 @t63 @t19 @t83) @t82))) % 0.36/0.65 (step @p113 :rule aci_norm :args ((= (or @t80 false @t81) @t83))) % 0.36/0.65 (step @p114 :rule refl :args (@t81)) % 0.36/0.65 (step @p115 :rule eq-refl :args (@t2)) % 0.36/0.65 (step @p116 :rule cong :premises (@p115) :args (@t84)) % 0.36/0.65 (step @p117 :rule trans :premises (@p116 @p98)) % 0.36/0.65 (step @p118 :rule refl :args (@t80)) % 0.36/0.65 (step @p119 :rule nary_cong :premises (@p118 @p117 @p114) :args (@t85)) % 0.36/0.65 (step @p120 :rule trans :premises (@p119 @p113)) % 0.36/0.65 (step @p121 :rule quant-var-elim-eq :args ((= (forall @t16 (or (not @t61) @t86 @t67 @t64)) @t85))) % 0.36/0.65 (step @p122 :rule refl :args (@t64)) % 0.36/0.65 (step @p123 :rule refl :args (@t67)) % 0.36/0.65 (step @p124 :rule refl :args (@t86)) % 0.36/0.65 (step @p125 :rule eq-symm :args (@t2 @t12)) % 0.36/0.65 (step @p126 :rule cong :premises (@p125) :args (@t67)) % 0.36/0.65 (step @p127 :rule nary_cong :premises (@p126 @p124 @p123 @p122) :args (@t87)) % 0.36/0.65 (step @p128 :rule aci_norm :args ((= @t88 @t87))) % 0.36/0.65 (step @p129 :rule trans :premises (@p128 @p127)) % 0.36/0.65 (step @p130 :rule cong :premises (@p129) :args (@t89)) % 0.36/0.65 (step @p131 :rule trans :premises (@p130 @p121)) % 0.36/0.65 (step @p132 :rule trans :premises (@p131 @p120)) % 0.36/0.65 (step @p133 :rule refl :args (@t19)) % 0.36/0.65 (step @p134 :rule refl :args (@t63)) % 0.36/0.65 (step @p135 :rule refl :args (@t78)) % 0.36/0.65 (step @p136 :rule nary_cong :premises (@p135 @p134 @p133 @p132) :args (@t90)) % 0.36/0.65 (step @p137 :rule trans :premises (@p136 @p112)) % 0.36/0.65 (step @p138 :rule quant-miniscope-or :args ((= (forall @t16 @t91) @t90))) % 0.36/0.65 (step @p139 :rule aci_norm :args ((= @t92 @t91))) % 0.36/0.65 (step @p140 :rule cong :premises (@p139) :args ((forall @t16 @t92))) % 0.36/0.65 (step @p141 :rule trans :premises (@p140 @p138)) % 0.36/0.65 (step @p142 :rule trans :premises (@p141 @p137)) % 0.36/0.65 (step @p143 :rule aci_norm :args ((= (or @t86 @t67 @t78 @t65) @t92))) % 0.36/0.65 (step @p144 :rule aci_norm :args ((= @t93 @t65))) % 0.36/0.65 (step @p145 :rule refl :args (@t67)) % 0.36/0.65 (step @p146 :rule refl :args (@t86)) % 0.36/0.65 (step @p147 :rule nary_cong :premises (@p146 @p145 @p135 @p144) :args (@t94)) % 0.36/0.65 (step @p148 :rule trans :premises (@p147 @p143)) % 0.36/0.65 (step @p149 :rule cong :premises (@p148) :args ((forall @t16 @t94))) % 0.36/0.65 (step @p150 :rule trans :premises (@p149 @p142)) % 0.36/0.65 (step @p151 :rule aci_norm :args ((= (or @t86 (or @t67 @t78 @t93)) @t94))) % 0.36/0.65 (step @p152 :rule bool-or-taut2 :args (false @t62 false false)) % 0.36/0.65 (step @p153 :rule refl :args (@t65)) % 0.36/0.65 (step @p154 :rule nary_cong :premises (@p153 @p152) :args (@t95)) % 0.36/0.65 (step @p155 :rule nary_cong :premises (@p123 @p106 @p154) :args (@t96)) % 0.36/0.65 (step @p156 :rule nary_cong :premises (@p124 @p155) :args ((or @t86 @t96))) % 0.36/0.65 (step @p157 :rule trans :premises (@p156 @p151)) % 0.36/0.65 (step @p158 :rule bool-impl-elim :args (@t15 @t96)) % 0.36/0.65 (step @p159 :rule trans :premises (@p158 @p157)) % 0.36/0.65 (step @p160 :rule cong :premises (@p159) :args ((forall @t16 (=> @t15 @t96)))) % 0.36/0.65 (step @p161 :rule trans :premises (@p160 @p150)) % 0.36/0.65 (step @p162 :rule aci_norm :args ((= (or @t67 @t97) @t96))) % 0.36/0.65 (step @p163 :rule aci_norm :args ((= (or @t78 false @t95) @t97))) % 0.36/0.65 (step @p164 :rule refl :args (@t95)) % 0.36/0.65 (step @p165 :rule eq-refl :args (@t1)) % 0.36/0.65 (step @p166 :rule cong :premises (@p165) :args (@t98)) % 0.36/0.65 (step @p167 :rule trans :premises (@p166 @p98)) % 0.36/0.65 (step @p168 :rule nary_cong :premises (@p135 @p167 @p164) :args (@t99)) % 0.36/0.65 (step @p169 :rule trans :premises (@p168 @p163)) % 0.36/0.65 (step @p170 :rule quant-var-elim-eq :args ((= (forall @t14 (or (not (= @t10 @t1)) @t100 @t68 @t66)) @t99))) % 0.36/0.65 (step @p171 :rule refl :args (@t66)) % 0.36/0.65 (step @p172 :rule refl :args (@t68)) % 0.36/0.65 (step @p173 :rule refl :args (@t100)) % 0.36/0.65 (step @p174 :rule eq-symm :args (@t1 @t10)) % 0.36/0.65 (step @p175 :rule cong :premises (@p174) :args (@t68)) % 0.36/0.65 (step @p176 :rule nary_cong :premises (@p175 @p173 @p172 @p171) :args (@t101)) % 0.36/0.65 (step @p177 :rule aci_norm :args ((= @t102 @t101))) % 0.36/0.65 (step @p178 :rule trans :premises (@p177 @p176)) % 0.36/0.65 (step @p179 :rule cong :premises (@p178) :args (@t103)) % 0.36/0.65 (step @p180 :rule trans :premises (@p179 @p170)) % 0.36/0.65 (step @p181 :rule trans :premises (@p180 @p169)) % 0.36/0.65 (step @p182 :rule nary_cong :premises (@p145 @p181) :args (@t104)) % 0.36/0.65 (step @p183 :rule trans :premises (@p182 @p162)) % 0.36/0.65 (step @p184 :rule quant-miniscope-or :args ((= (forall @t14 @t105) @t104))) % 0.36/0.65 (step @p185 :rule aci_norm :args ((= @t106 @t105))) % 0.36/0.65 (step @p186 :rule cong :premises (@p185) :args ((forall @t14 @t106))) % 0.36/0.65 (step @p187 :rule trans :premises (@p186 @p184)) % 0.36/0.65 (step @p188 :rule trans :premises (@p187 @p183)) % 0.36/0.65 (step @p189 :rule aci_norm :args ((= (or @t100 @t69) @t106))) % 0.36/0.65 (step @p190 :rule bool-impl-elim :args (@t13 @t69)) % 0.36/0.65 (step @p191 :rule trans :premises (@p190 @p189)) % 0.36/0.65 (step @p192 :rule cong :premises (@p191) :args (@t70)) % 0.36/0.65 (step @p193 :rule trans :premises (@p192 @p188)) % 0.36/0.65 (step @p194 :rule refl :args (@t15)) % 0.36/0.65 (step @p195 :rule cong :premises (@p194 @p193) :args (@t71)) % 0.36/0.65 (step @p196 :rule cong :premises (@p195) :args (@t72)) % 0.36/0.65 (step @p197 :rule trans :premises (@p196 @p161)) % 0.36/0.65 (step @p198 :rule refl :args (@t22)) % 0.36/0.65 (step @p199 :rule cong :premises (@p198 @p197) :args (@t73)) % 0.36/0.65 (step @p200 :rule cong :premises (@p199) :args (@t74)) % 0.36/0.65 (step @p201 :rule trans :premises (@p200 @p111)) % 0.36/0.65 (step @p202 :rule refl :args (@t17)) % 0.36/0.65 (step @p203 :rule cong :premises (@p202 @p201) :args (@t75)) % 0.36/0.65 (step @p204 :rule trans :premises (@p203 @p100)) % 0.36/0.65 (step @p205 :rule cong :premises (@p204) :args (@t76)) % 0.36/0.65 (step @p206 :rule trans :premises (@p205 @p99)) % 0.36/0.65 (step @p207 :rule cong :premises (@p206) :args (@t77)) % 0.36/0.65 (step @p208 :rule trans :premises (@p207 @p98)) % 0.36/0.65 (step @p209 false :rule eq_resolve :premises (@p96 @p208)) % 0.36/0.65 ) % 0.36/0.65 % SZS output end Proof % 0.36/0.65 % cvc5 exiting %------------------------------------------------------------------------------