%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM547+1 : 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 : n025.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 08:39:47 AM UTC 2026 % Result : Theorem 15.89s 16.31s % Output : Proof 15.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM547+1 : TPTP v9.2.1. Released v4.0.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n025.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 11:29:01 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.49 %----Proving TF0_NAR, FOF, or CNF % 15.89/16.31 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.89/16.31 --- Run --no-e-matching --full-saturate-quant at 6... % 15.89/16.31 % SZS status Theorem % 15.89/16.31 % SZS output start Proof % 15.89/16.31 ( % 15.89/16.31 (declare-sort $$unsorted 0) % 15.89/16.31 (declare-const tptp.xT $$unsorted) % 15.89/16.31 (declare-const tptp.slbdtsldtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 15.89/16.31 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 15.89/16.31 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 15.89/16.31 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 15.89/16.31 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 15.89/16.31 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 15.89/16.31 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 15.89/16.31 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 15.89/16.31 (declare-const tptp.xS $$unsorted) % 15.89/16.31 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 15.89/16.31 (declare-const tptp.xx $$unsorted) % 15.89/16.31 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 15.89/16.31 (declare-const tptp.slcrc0 $$unsorted) % 15.89/16.31 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 15.89/16.31 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 15.89/16.31 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 15.89/16.31 (declare-const tptp.xk $$unsorted) % 15.89/16.31 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 15.89/16.31 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 15.89/16.31 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 15.89/16.31 (declare-const tptp.szNzAzT0 $$unsorted) % 15.89/16.31 (declare-const tptp.sz00 $$unsorted) % 15.89/16.31 (define @t1 () (@var "W0" $$unsorted)) % 15.89/16.31 (define @t2 () (tptp.aSet0 @t1)) % 15.89/16.31 (define @t3 () (@list @t1)) % 15.89/16.31 (define @t4 () (tptp.aElement0 @t1)) % 15.89/16.31 (define @t5 () (@var "W1" $$unsorted)) % 15.89/16.31 (define @t6 () (tptp.aElement0 @t5)) % 15.89/16.31 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 15.89/16.31 (define @t8 () (@list @t5)) % 15.89/16.31 (define @t9 () (tptp.isFinite0 @t1)) % 15.89/16.31 (define @t10 () (exists @t8 @t7)) % 15.89/16.31 (define @t11 () (not @t10)) % 15.89/16.31 (define @t12 () (and @t2 @t11)) % 15.89/16.31 (define @t13 () (= @t1 tptp.slcrc0)) % 15.89/16.31 (define @t14 () (= @t13 @t12)) % 15.89/16.31 (define @t15 () (forall @t3 @t14)) % 15.89/16.31 (define @t16 () (tptp.isCountable0 @t1)) % 15.89/16.31 (define @t17 () (not @t9)) % 15.89/16.31 (define @t18 () (and @t2 @t16)) % 15.89/16.31 (define @t19 () (not @t13)) % 15.89/16.31 (define @t20 () (@var "W2" $$unsorted)) % 15.89/16.31 (define @t21 () (tptp.aElementOf0 @t20 @t1)) % 15.89/16.31 (define @t22 () (tptp.aElementOf0 @t20 @t5)) % 15.89/16.31 (define @t23 () (@list @t20)) % 15.89/16.31 (define @t24 () (tptp.aSet0 @t5)) % 15.89/16.31 (define @t25 () (tptp.aSubsetOf0 @t5 @t1)) % 15.89/16.31 (define @t26 () (tptp.isFinite0 @t5)) % 15.89/16.31 (define @t27 () (and @t2 @t9)) % 15.89/16.31 (define @t28 () (= @t1 @t5)) % 15.89/16.31 (define @t29 () (tptp.aSubsetOf0 @t1 @t5)) % 15.89/16.31 (define @t30 () (@list @t1 @t5)) % 15.89/16.31 (define @t31 () (tptp.aSet0 @t20)) % 15.89/16.31 (define @t32 () (@list @t1 @t5 @t20)) % 15.89/16.31 (define @t33 () (@var "W3" $$unsorted)) % 15.89/16.31 (define @t34 () (= @t33 @t5)) % 15.89/16.31 (define @t35 () (tptp.aElementOf0 @t33 @t1)) % 15.89/16.31 (define @t36 () (tptp.aElement0 @t33)) % 15.89/16.31 (define @t37 () (tptp.aElementOf0 @t33 @t20)) % 15.89/16.31 (define @t38 () (@list @t33)) % 15.89/16.31 (define @t39 () (tptp.sdtpldt0 @t1 @t5)) % 15.89/16.31 (define @t40 () (and @t2 @t6)) % 15.89/16.31 (define @t41 () (tptp.sdtmndt0 @t1 @t5)) % 15.89/16.31 (define @t42 () (tptp.sdtpldt0 @t5 @t1)) % 15.89/16.31 (define @t43 () (and @t24 (tptp.isCountable0 @t5))) % 15.89/16.31 (define @t44 () (tptp.sdtmndt0 @t5 @t1)) % 15.89/16.31 (define @t45 () (and @t24 @t26)) % 15.89/16.31 (define @t46 () (tptp.szszuzczcdt0 @t1)) % 15.89/16.31 (define @t47 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 15.89/16.31 (define @t48 () (tptp.szszuzczcdt0 @t5)) % 15.89/16.31 (define @t49 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 15.89/16.31 (define @t50 () (and @t47 @t49)) % 15.89/16.31 (define @t51 () (tptp.sdtlseqdt0 @t1 @t5)) % 15.89/16.31 (define @t52 () (tptp.sdtlseqdt0 @t5 @t20)) % 15.89/16.31 (define @t53 () (tptp.aElementOf0 @t20 tptp.szNzAzT0)) % 15.89/16.31 (define @t54 () (tptp.sbrdtbr0 @t1)) % 15.89/16.31 (define @t55 () (not @t7)) % 15.89/16.31 (define @t56 () (and @t2 @t49)) % 15.89/16.31 (define @t57 () (tptp.szmzizndt0 @t1)) % 15.89/16.31 (define @t58 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 15.89/16.31 (define @t59 () (tptp.szmzizndt0 @t5)) % 15.89/16.31 (define @t60 () (tptp.slbdtrb0 @t1)) % 15.89/16.31 (define @t61 () (tptp.slbdtrb0 tptp.sz00)) % 15.89/16.31 (define @t62 () (tptp.slbdtrb0 @t5)) % 15.89/16.31 (define @t63 () (tptp.sbrdtbr0 @t33)) % 15.89/16.31 (define @t64 () (tptp.aSubsetOf0 @t33 @t1)) % 15.89/16.31 (define @t65 () (and @t64 (= @t63 @t5))) % 15.89/16.31 (define @t66 () (= @t37 @t65)) % 15.89/16.31 (define @t67 () (forall @t38 @t66)) % 15.89/16.31 (define @t68 () (and @t31 @t67)) % 15.89/16.31 (define @t69 () (tptp.slbdtsldtrb0 @t1 @t5)) % 15.89/16.31 (define @t70 () (= @t20 @t69)) % 15.89/16.31 (define @t71 () (= @t70 @t68)) % 15.89/16.31 (define @t72 () (forall @t23 @t71)) % 15.89/16.31 (define @t73 () (=> @t56 @t72)) % 15.89/16.31 (define @t74 () (forall @t30 @t73)) % 15.89/16.31 (define @t75 () (tptp.aElementOf0 tptp.xk tptp.szNzAzT0)) % 15.89/16.31 (define @t76 () (tptp.aSet0 tptp.xS)) % 15.89/16.31 (define @t77 () (tptp.slbdtsldtrb0 tptp.xS tptp.xk)) % 15.89/16.31 (define @t78 () (not (= @t77 tptp.slcrc0))) % 15.89/16.31 (define @t79 () (tptp.aElementOf0 @t1 @t77)) % 15.89/16.31 (define @t80 () (exists @t3 @t79)) % 15.89/16.31 (define @t81 () (not @t80)) % 15.89/16.31 (define @t82 () (forall @t3 (not @t79))) % 15.89/16.31 (define @t83 () (forall @t8 (not (tptp.aElementOf0 @t5 @t77)))) % 15.89/16.31 (define @t84 () (@list false)) % 15.89/16.31 (define @t85 () (= @t1 @t61)) % 15.89/16.31 (define @t86 () (forall @t8 @t55)) % 15.89/16.31 (define @t87 () (and @t2 @t86)) % 15.89/16.31 (define @t88 () (= @t13 @t87)) % 15.89/16.31 (define @t89 () (tptp.aSet0 @t77)) % 15.89/16.31 (define @t90 () (and @t89 @t83)) % 15.89/16.31 (define @t91 () (= @t77 @t61)) % 15.89/16.31 (define @t92 () (forall @t3 (= @t87 @t85))) % 15.89/16.31 (define @t93 () (= @t90 @t91)) % 15.89/16.31 (define @t94 () (= @t61 @t77)) % 15.89/16.31 (define @t95 () (= @t94 @t90)) % 15.89/16.31 (define @t96 () (= tptp.slcrc0 @t77)) % 15.89/16.31 (define @t97 () (not @t90)) % 15.89/16.31 (define @t98 () (@list true false)) % 15.89/16.31 (define @t99 () (tptp.aSubsetOf0 @t33 tptp.xS)) % 15.89/16.31 (define @t100 () (and @t99 (= @t63 tptp.xk))) % 15.89/16.31 (define @t101 () (tptp.aElementOf0 @t33 @t77)) % 15.89/16.31 (define @t102 () (and @t89 (forall @t38 (= @t101 @t100)))) % 15.89/16.31 (define @t103 () (not @t102)) % 15.89/16.31 (define @t104 () (@var "BOUND_VARIABLE_8462" $$unsorted)) % 15.89/16.31 (define @t105 () (tptp.aElementOf0 @t33 @t104)) % 15.89/16.31 (define @t106 () (and @t64 (= @t5 @t63))) % 15.89/16.31 (define @t107 () (forall @t38 (= @t105 @t106))) % 15.89/16.31 (define @t108 () (tptp.aSet0 @t104)) % 15.89/16.31 (define @t109 () (and @t108 @t107)) % 15.89/16.31 (define @t110 () (= (= @t104 @t69) @t109)) % 15.89/16.31 (define @t111 () (not @t49)) % 15.89/16.31 (define @t112 () (not @t2)) % 15.89/16.31 (define @t113 () (or @t112 @t111 @t110)) % 15.89/16.31 (define @t114 () (@list @t1 @t5 @t104)) % 15.89/16.31 (define @t115 () (forall @t114 @t113)) % 15.89/16.31 (define @t116 () (@list @t104)) % 15.89/16.31 (define @t117 () (forall @t116 @t113)) % 15.89/16.31 (define @t118 () (forall @t116 @t110)) % 15.89/16.31 (define @t119 () (or @t112 @t111 @t118)) % 15.89/16.31 (define @t120 () (forall @t23 (= @t70 (and @t31 (forall @t38 (= @t37 @t106)))))) % 15.89/16.31 (define @t121 () (or @t112 @t111 @t120)) % 15.89/16.31 (define @t122 () (and @t99 (= tptp.xk @t63))) % 15.89/16.31 (define @t123 () (= @t122 @t101)) % 15.89/16.31 (define @t124 () (forall @t38 @t123)) % 15.89/16.31 (define @t125 () (and @t89 @t124)) % 15.89/16.31 (define @t126 () (= (= @t77 @t77) @t125)) % 15.89/16.31 (define @t127 () (not @t75)) % 15.89/16.31 (define @t128 () (not @t76)) % 15.89/16.31 (define @t129 () (or @t128 @t127 @t126)) % 15.89/16.31 (define @t130 () (forall @t114 (or @t112 @t111 (= (= @t69 @t104) (and @t108 (forall @t38 (= @t106 @t105))))))) % 15.89/16.31 (define @t131 () (or @t128 @t127 @t102)) % 15.89/16.31 (assume @p1 (forall @t3 (=> @t2 true))) % 15.89/16.31 (assume @p2 (forall @t3 (=> @t4 true))) % 15.89/16.31 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 15.89/16.31 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 15.89/16.31 (assume @p5 @t15) % 15.89/16.31 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 15.89/16.31 (assume @p7 (forall @t3 (=> @t2 (=> @t16 true)))) % 15.89/16.31 (assume @p8 (forall @t3 (=> @t18 @t17))) % 15.89/16.31 (assume @p9 (forall @t3 (=> @t18 @t19))) % 15.89/16.31 (assume @p10 (forall @t3 (=> @t2 (forall @t8 (= @t25 (and @t24 (forall @t23 (=> @t22 @t21)))))))) % 15.89/16.31 (assume @p11 (forall @t3 (=> @t27 (forall @t8 (=> @t25 @t26))))) % 15.89/16.31 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 15.89/16.31 (assume @p13 (forall @t30 (=> (and @t2 @t24) (=> (and @t29 @t25) @t28)))) % 15.89/16.31 (assume @p14 (forall @t32 (=> (and @t2 @t24 @t31) (=> (and @t29 (tptp.aSubsetOf0 @t5 @t20)) (tptp.aSubsetOf0 @t1 @t20))))) % 15.89/16.31 (assume @p15 (forall @t30 (=> @t40 (forall @t23 (= (= @t20 @t39) (and @t31 (forall @t38 (= @t37 (and @t36 (or @t35 @t34)))))))))) % 15.89/16.31 (assume @p16 (forall @t30 (=> @t40 (forall @t23 (= (= @t20 @t41) (and @t31 (forall @t38 (= @t37 (and @t36 @t35 (not @t34)))))))))) % 15.89/16.31 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t41 @t5) @t1)))))) % 15.89/16.31 (assume @p18 (forall @t30 (=> (and @t4 @t24) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t42 @t1) @t5))))) % 15.89/16.31 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t43 (tptp.isCountable0 @t42)))))) % 15.89/16.31 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t43 (tptp.isCountable0 @t44)))))) % 15.89/16.31 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t45 (tptp.isFinite0 @t42)))))) % 15.89/16.31 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t45 (tptp.isFinite0 @t44)))))) % 15.89/16.31 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 15.89/16.31 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 15.89/16.31 (assume @p25 (forall @t3 (=> @t47 (and (tptp.aElementOf0 @t46 tptp.szNzAzT0) (not (= @t46 tptp.sz00)))))) % 15.89/16.31 (assume @p26 (forall @t30 (=> @t50 (=> (= @t46 @t48) @t28)))) % 15.89/16.31 (assume @p27 (forall @t3 (=> @t47 (or (= @t1 tptp.sz00) (exists @t8 (and @t49 (= @t1 @t48))))))) % 15.89/16.31 (assume @p28 (forall @t3 (=> @t47 (not (= @t1 @t46))))) % 15.89/16.31 (assume @p29 (forall @t30 (=> @t50 (=> @t51 true)))) % 15.89/16.31 (assume @p30 (forall @t3 (=> @t47 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 15.89/16.31 (assume @p31 (forall @t3 (=> @t47 (not (tptp.sdtlseqdt0 @t46 tptp.sz00))))) % 15.89/16.31 (assume @p32 (forall @t30 (=> @t50 (= @t51 (tptp.sdtlseqdt0 @t46 @t48))))) % 15.89/16.31 (assume @p33 (forall @t3 (=> @t47 (tptp.sdtlseqdt0 @t1 @t46)))) % 15.89/16.31 (assume @p34 (forall @t3 (=> @t47 (tptp.sdtlseqdt0 @t1 @t1)))) % 15.89/16.31 (assume @p35 (forall @t30 (=> @t50 (=> (and @t51 (tptp.sdtlseqdt0 @t5 @t1)) @t28)))) % 15.89/16.31 (assume @p36 (forall @t32 (=> (and @t47 @t49 @t53) (=> (and @t51 @t52) (tptp.sdtlseqdt0 @t1 @t20))))) % 15.89/16.31 (assume @p37 (forall @t30 (=> @t50 (or @t51 (tptp.sdtlseqdt0 @t48 @t1))))) % 15.89/16.31 (assume @p38 (forall @t30 (=> @t50 (=> (tptp.iLess0 @t1 @t5) true)))) % 15.89/16.31 (assume @p39 (forall @t3 (=> @t47 (tptp.iLess0 @t1 @t46)))) % 15.89/16.31 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t54)))) % 15.89/16.31 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t54 tptp.szNzAzT0) @t9)))) % 15.89/16.31 (assume @p42 (forall @t3 (=> @t2 (= (= @t54 tptp.sz00) @t13)))) % 15.89/16.31 (assume @p43 (forall @t3 (=> @t27 (forall @t8 (=> @t6 (=> @t55 (= (tptp.sbrdtbr0 @t39) (tptp.szszuzczcdt0 @t54)))))))) % 15.89/16.31 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t41)) @t54)))))) % 15.89/16.31 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t25) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t54)))))) % 15.89/16.31 (assume @p46 (forall @t30 (=> @t56 (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t54)) (exists @t23 (and (tptp.aSubsetOf0 @t20 @t1) (= (tptp.sbrdtbr0 @t20) @t5))))))) % 15.89/16.31 (assume @p47 (forall @t3 (=> (and @t58 @t19) (forall @t8 (= (= @t5 @t57) (and @t7 (forall @t23 (=> @t21 @t52)))))))) % 15.89/16.31 (assume @p48 (forall @t3 (=> (and @t58 @t9 @t19) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t23 (=> @t21 (tptp.sdtlseqdt0 @t20 @t5))))))))) % 15.89/16.31 (assume @p49 (forall @t30 (=> (and @t58 (tptp.aSubsetOf0 @t5 tptp.szNzAzT0) @t19 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t57 @t5) (tptp.aElementOf0 @t59 @t1)) (= @t57 @t59))))) % 15.89/16.31 (assume @p50 (forall @t3 (=> @t47 (forall @t8 (= (= @t5 @t60) (and @t24 (forall @t23 (= @t22 (and @t53 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t20) @t1)))))))))) % 15.89/16.31 (assume @p51 (forall @t3 (=> @t47 (tptp.isFinite0 @t60)))) % 15.89/16.31 (assume @p52 (= @t61 tptp.slcrc0)) % 15.89/16.31 (assume @p53 (forall @t30 (=> @t50 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t48)) (or (tptp.aElementOf0 @t1 @t62) @t28))))) % 15.89/16.31 (assume @p54 (forall @t30 (=> @t50 (= @t51 (tptp.aSubsetOf0 @t60 @t62))))) % 15.89/16.31 (assume @p55 (forall @t3 (=> (and @t58 @t9) (exists @t8 (and @t49 (tptp.aSubsetOf0 @t1 @t62)))))) % 15.89/16.31 (assume @p56 (forall @t3 (=> @t47 (= (tptp.sbrdtbr0 @t60) @t1)))) % 15.89/16.31 (assume @p57 @t74) % 15.89/16.31 (assume @p58 (forall @t3 (=> @t27 (forall @t8 (=> @t49 (tptp.isFinite0 @t69)))))) % 15.89/16.31 (assume @p59 (forall @t3 (=> (and @t2 @t17) (forall @t8 (=> @t49 (not (= @t69 tptp.slcrc0))))))) % 15.89/16.31 (assume @p60 (forall @t3 (=> @t18 (forall @t8 (=> (and @t49 (not (= @t5 tptp.sz00))) (tptp.isCountable0 @t69)))))) % 15.89/16.31 (assume @p61 @t75) % 15.89/16.31 (assume @p62 (and @t76 (tptp.aSet0 tptp.xT) (not (= tptp.xk tptp.sz00)))) % 15.89/16.31 (assume @p63 (and (tptp.aSubsetOf0 @t77 (tptp.slbdtsldtrb0 tptp.xT tptp.xk)) @t78)) % 15.89/16.31 (assume @p64 (tptp.aElementOf0 tptp.xx tptp.xS)) % 15.89/16.31 (assume @p65 @t81) % 15.89/16.31 (assume @p66 true) % 15.89/16.31 (step @p67 :rule and_elim :premises (@p62) :args (0)) % 15.89/16.31 (step @p68 :rule bool-double-not-elim :args (@t82)) % 15.89/16.31 (step @p69 :rule exists-elim :args ((= @t80 (not @t82)))) % 15.89/16.31 (step @p70 :rule cong :premises (@p69) :args (@t81)) % 15.89/16.31 (step @p71 :rule trans :premises (@p70 @p68)) % 15.89/16.31 (step @p72 :rule eq_resolve :premises (@p65 @p71)) % 15.89/16.31 (step @p73 :rule alpha_equiv :args (@t82 (@list @t1) (@list @t5))) % 15.89/16.31 (step @p74 :rule equiv_elim1 :premises (@p73)) % 15.89/16.31 (step @p75 :rule chain_m_resolution :premises (@p74 @p72) :args (@t83 @t84 (@list @t82))) % 15.89/16.31 (step @p76 :rule eq-symm :args (@t85 @t87)) % 15.89/16.31 (step @p77 :rule cong :premises (@p76) :args ((forall @t3 (= @t85 @t87)))) % 15.89/16.31 (step @p78 :rule refl :args (@t87)) % 15.89/16.31 (step @p79 :rule symm :premises (@p52)) % 15.89/16.31 (step @p80 :rule refl :args (@t1)) % 15.89/16.31 (step @p81 :rule cong :premises (@p80 @p79) :args (@t13)) % 15.89/16.31 (step @p82 :rule cong :premises (@p81 @p78) :args (@t88)) % 15.89/16.31 (step @p83 :rule cong :premises (@p82) :args ((forall @t3 @t88))) % 15.89/16.31 (step @p84 :rule trans :premises (@p83 @p77)) % 15.89/16.31 (step @p85 :rule bool-double-not-elim :args (@t86)) % 15.89/16.31 (step @p86 :rule exists-elim :args ((= @t10 (not @t86)))) % 15.89/16.31 (step @p87 :rule cong :premises (@p86) :args (@t11)) % 15.89/16.31 (step @p88 :rule trans :premises (@p87 @p85)) % 15.89/16.31 (step @p89 :rule refl :args (@t2)) % 15.89/16.31 (step @p90 :rule nary_cong :premises (@p89 @p88) :args (@t12)) % 15.89/16.31 (step @p91 :rule refl :args (@t13)) % 15.89/16.31 (step @p92 :rule cong :premises (@p91 @p90) :args (@t14)) % 15.89/16.31 (step @p93 :rule cong :premises (@p92) :args (@t15)) % 15.89/16.31 (step @p94 :rule trans :premises (@p93 @p84)) % 15.89/16.31 (step @p95 :rule eq_resolve :premises (@p5 @p94)) % 15.89/16.31 (step @p96 :rule refl :args (@t90)) % 15.89/16.31 (step @p97 :rule eq-symm :args (@t77 @t61)) % 15.89/16.31 (step @p98 :rule cong :premises (@p97 @p96) :args ((= @t91 @t90))) % 15.89/16.31 (step @p99 :rule eq-symm :args (@t90 @t91)) % 15.89/16.31 (step @p100 :rule trans :premises (@p99 @p98)) % 15.89/16.31 (step @p101 :rule refl :args (@t92)) % 15.89/16.31 (step @p102 :rule cong :premises (@p101 @p100) :args ((=> @t92 @t93))) % 15.89/16.31 (assume-push @p203 @t92) % 15.89/16.31 (step @p104 :rule instantiate :premises (@p95) :args ((@list @t77))) % 15.89/16.31 (step-pop @p204 :rule scope :premises (@p104)) % 15.89/16.31 (step @p105 :rule process_scope :premises (@p204) :args (@t93)) % 15.89/16.31 (step @p107 :rule eq_resolve :premises (@p105 @p102)) % 15.89/16.31 (step @p108 :rule implies_elim :premises (@p107)) % 15.89/16.31 (step @p109 :rule chain_m_resolution :premises (@p108 @p95) :args (@t95 @t84 (@list @t92))) % 15.89/16.31 (step @p110 :rule refl :args (@t77)) % 15.89/16.31 (step @p111 :rule cong :premises (@p79 @p110) :args (@t96)) % 15.89/16.31 (step @p112 :rule cong :premises (@p111) :args ((not @t96))) % 15.89/16.31 (step @p113 :rule eq-symm :args (@t77 tptp.slcrc0)) % 15.89/16.31 (step @p114 :rule cong :premises (@p113) :args (@t78)) % 15.89/16.31 (step @p115 :rule trans :premises (@p114 @p112)) % 15.89/16.31 (step @p116 :rule and_elim :premises (@p63) :args (1)) % 15.89/16.31 (step @p117 :rule eq_resolve :premises (@p116 @p115)) % 15.89/16.31 (step @p118 :rule cnf_equiv_pos2 :args (@t95)) % 15.89/16.31 (step @p119 :rule reordering :premises (@p118) :args ((or @t94 @t97 (not @t95)))) % 15.89/16.31 (step @p120 :rule chain_m_resolution :premises (@p119 @p117 @p109) :args (@t97 @t98 (@list @t94 @t95))) % 15.89/16.31 (step @p121 :rule cnf_and_neg :args (@t90)) % 15.89/16.31 (step @p122 :rule chain_m_resolution :premises (@p121 @p120 @p75) :args ((not @t89) @t98 (@list @t90 @t83))) % 15.89/16.31 (step @p123 :rule cnf_and_pos :args (@t102 0)) % 15.89/16.31 (step @p124 :rule reordering :premises (@p123) :args ((or @t89 @t103))) % 15.89/16.31 (step @p125 :rule chain_m_resolution :premises (@p124 @p122) :args (@t103 (@list true) (@list @t89))) % 15.89/16.31 (step @p126 :rule eq-symm :args (@t105 @t106)) % 15.89/16.31 (step @p127 :rule cong :premises (@p126) :args (@t107)) % 15.89/16.31 (step @p128 :rule refl :args (@t108)) % 15.89/16.31 (step @p129 :rule nary_cong :premises (@p128 @p127) :args (@t109)) % 15.89/16.31 (step @p130 :rule eq-symm :args (@t104 @t69)) % 15.89/16.31 (step @p131 :rule cong :premises (@p130 @p129) :args (@t110)) % 15.89/16.31 (step @p132 :rule refl :args (@t111)) % 15.89/16.31 (step @p133 :rule refl :args (@t112)) % 15.89/16.31 (step @p134 :rule nary_cong :premises (@p133 @p132 @p131) :args (@t113)) % 15.89/16.31 (step @p135 :rule cong :premises (@p134) :args (@t115)) % 15.89/16.31 (step @p136 :rule quant-merge-prenex :args ((= (forall @t30 @t117) @t115))) % 15.89/16.31 (step @p137 :rule alpha_equiv :args (@t118 (@list @t104) (@list @t20))) % 15.89/16.31 (step @p138 :rule refl :args (@t111)) % 15.89/16.31 (step @p139 :rule refl :args (@t112)) % 15.89/16.31 (step @p140 :rule nary_cong :premises (@p139 @p138 @p137) :args (@t119)) % 15.89/16.31 (step @p141 :rule quant-miniscope-or :args ((= @t117 @t119))) % 15.89/16.31 (step @p142 :rule trans :premises (@p141 @p140)) % 15.89/16.31 (step @p143 :rule symm :premises (@p142)) % 15.89/16.31 (step @p144 :rule cong :premises (@p143) :args ((forall @t30 @t121))) % 15.89/16.31 (step @p145 :rule trans :premises (@p144 @p136)) % 15.89/16.31 (step @p146 :rule trans :premises (@p145 @p135)) % 15.89/16.31 (step @p147 :rule aci_norm :args ((= (or (or @t112 @t111) @t120) @t121))) % 15.89/16.31 (step @p148 :rule refl :args (@t120)) % 15.89/16.31 (step @p149 :rule bool-and-de-morgan :args (@t2 @t49 true)) % 15.89/16.31 (step @p150 :rule nary_cong :premises (@p149 @p148) :args ((or (not @t56) @t120))) % 15.89/16.31 (step @p151 :rule trans :premises (@p150 @p147)) % 15.89/16.31 (step @p152 :rule bool-impl-elim :args (@t56 @t120)) % 15.89/16.31 (step @p153 :rule trans :premises (@p152 @p151)) % 15.89/16.31 (step @p154 :rule cong :premises (@p153) :args ((forall @t30 (=> @t56 @t120)))) % 15.89/16.31 (step @p155 :rule trans :premises (@p154 @p146)) % 15.89/16.31 (step @p156 :rule eq-symm :args (@t63 @t5)) % 15.89/16.31 (step @p157 :rule refl :args (@t64)) % 15.89/16.31 (step @p158 :rule nary_cong :premises (@p157 @p156) :args (@t65)) % 15.89/16.31 (step @p159 :rule refl :args (@t37)) % 15.89/16.31 (step @p160 :rule cong :premises (@p159 @p158) :args (@t66)) % 15.89/16.31 (step @p161 :rule cong :premises (@p160) :args (@t67)) % 15.89/16.31 (step @p162 :rule refl :args (@t31)) % 15.89/16.31 (step @p163 :rule nary_cong :premises (@p162 @p161) :args (@t68)) % 15.89/16.31 (step @p164 :rule refl :args (@t70)) % 15.89/16.31 (step @p165 :rule cong :premises (@p164 @p163) :args (@t71)) % 15.89/16.31 (step @p166 :rule cong :premises (@p165) :args (@t72)) % 15.89/16.31 (step @p167 :rule refl :args (@t56)) % 15.89/16.31 (step @p168 :rule cong :premises (@p167 @p166) :args (@t73)) % 15.89/16.31 (step @p169 :rule cong :premises (@p168) :args (@t74)) % 15.89/16.31 (step @p170 :rule trans :premises (@p169 @p155)) % 15.89/16.31 (step @p171 :rule eq_resolve :premises (@p57 @p170)) % 15.89/16.31 (step @p172 :rule bool-eq-true :args (@t102)) % 15.89/16.31 (step @p173 :rule eq-symm :args (true @t102)) % 15.89/16.31 (step @p174 :rule trans :premises (@p173 @p172)) % 15.89/16.31 (step @p175 :rule eq-symm :args (@t100 @t101)) % 15.89/16.31 (step @p176 :rule refl :args (@t101)) % 15.89/16.31 (step @p177 :rule eq-symm :args (tptp.xk @t63)) % 15.89/16.31 (step @p178 :rule refl :args (@t99)) % 15.89/16.31 (step @p179 :rule nary_cong :premises (@p178 @p177) :args (@t122)) % 15.89/16.31 (step @p180 :rule cong :premises (@p179 @p176) :args (@t123)) % 15.89/16.31 (step @p181 :rule trans :premises (@p180 @p175)) % 15.89/16.31 (step @p182 :rule cong :premises (@p181) :args (@t124)) % 15.89/16.31 (step @p183 :rule refl :args (@t89)) % 15.89/16.31 (step @p184 :rule nary_cong :premises (@p183 @p182) :args (@t125)) % 15.89/16.31 (step @p185 :rule eq-refl :args (@t77)) % 15.89/16.31 (step @p186 :rule cong :premises (@p185 @p184) :args (@t126)) % 15.89/16.31 (step @p187 :rule trans :premises (@p186 @p174)) % 15.89/16.31 (step @p188 :rule refl :args (@t127)) % 15.89/16.31 (step @p189 :rule refl :args (@t128)) % 15.89/16.31 (step @p190 :rule nary_cong :premises (@p189 @p188 @p187) :args (@t129)) % 15.89/16.31 (step @p191 :rule refl :args (@t130)) % 15.89/16.31 (step @p192 :rule cong :premises (@p191 @p190) :args ((=> @t130 @t129))) % 15.89/16.31 (assume-push @p205 @t130) % 15.89/16.31 (step @p194 :rule instantiate :premises (@p171) :args ((@list tptp.xS tptp.xk @t77))) % 15.89/16.31 (step-pop @p206 :rule scope :premises (@p194)) % 15.89/16.31 (step @p195 :rule process_scope :premises (@p206) :args (@t129)) % 15.89/16.31 (step @p197 :rule eq_resolve :premises (@p195 @p192)) % 15.89/16.31 (step @p198 :rule implies_elim :premises (@p197)) % 15.89/16.31 (step @p199 :rule chain_m_resolution :premises (@p198 @p171) :args (@t131 @t84 (@list @t130))) % 15.89/16.31 (step @p200 :rule cnf_or_pos :args (@t131)) % 15.89/16.31 (step @p201 :rule reordering :premises (@p200) :args ((or @t127 @t128 @t102 (not @t131)))) % 15.89/16.31 (step @p202 false :rule chain_m_resolution :premises (@p201 @p199 @p125 @p67 @p61) :args (false (@list false true false false) (@list @t131 @t102 @t76 @t75))) % 15.89/16.31 ) % 15.89/16.31 % SZS output end Proof % 15.89/16.31 % cvc5 exiting %------------------------------------------------------------------------------