%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : KRS268+1 : TPTP v9.2.1. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n002.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 08:29:12 AM UTC 2026 % Result : Theorem 203.09s 203.30s % Output : Proof 203.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KRS268+1 : TPTP v9.2.1. Bugfixed v5.4.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n002.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 05:37:18 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 203.09/203.30 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 203.09/203.30 --- Run --no-e-matching --full-saturate-quant at 6... % 203.09/203.30 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 203.09/203.30 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 203.09/203.30 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 203.09/203.30 --- Run --trigger-sel=max --full-saturate-quant at 15... % 203.09/203.30 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 33... % 203.09/203.30 --- Run --multi-trigger-cache --full-saturate-quant at 15... % 203.09/203.30 --- Run --prenex-quant=none --full-saturate-quant at 30... % 203.09/203.30 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 15... % 203.09/203.30 --- Run --relevant-triggers --full-saturate-quant at 30... % 203.09/203.30 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 15... % 203.09/203.30 % SZS status Theorem % 203.09/203.30 % SZS output start Proof % 203.09/203.30 ( % 203.09/203.30 (declare-sort $$unsorted 0) % 203.09/203.30 (declare-const tptp.xora (-> $$unsorted $$unsorted Bool)) % 203.09/203.30 (declare-const tptp.nevera (-> $$unsorted $$unsorted Bool)) % 203.09/203.30 (declare-const tptp.nota (-> $$unsorted $$unsorted Bool)) % 203.09/203.30 (declare-const tptp.mighta (-> $$unsorted $$unsorted Bool)) % 203.09/203.30 (declare-const tptp.noc $$unsorted) % 203.09/203.30 (declare-const tptp.uns $$unsorted) % 203.09/203.30 (declare-const tptp.not (-> $$unsorted $$unsorted)) % 203.09/203.30 (declare-const tptp.tca $$unsorted) % 203.09/203.30 (declare-const tptp.sca $$unsorted) % 203.09/203.30 (declare-const tptp.wth $$unsorted) % 203.09/203.30 (declare-const tptp.unp $$unsorted) % 203.09/203.30 (declare-const tptp.wca $$unsorted) % 203.09/203.30 (declare-const tptp.wec $$unsorted) % 203.09/203.30 (declare-const tptp.sap $$unsorted) % 203.09/203.30 (declare-const tptp.wtc $$unsorted) % 203.09/203.30 (declare-const tptp.model (-> $$unsorted $$unsorted Bool)) % 203.09/203.30 (declare-const tptp.sat $$unsorted) % 203.09/203.30 (declare-const tptp.cax $$unsorted) % 203.09/203.30 (declare-const tptp.eqv $$unsorted) % 203.09/203.30 (declare-const tptp.esa $$unsorted) % 203.09/203.30 (declare-const tptp.csa $$unsorted) % 203.09/203.30 (declare-const tptp.status (-> $$unsorted $$unsorted $$unsorted Bool)) % 203.09/203.30 (declare-const tptp.thm $$unsorted) % 203.09/203.30 (declare-const tptp.isa (-> $$unsorted $$unsorted Bool)) % 203.09/203.30 (declare-const tptp.eth $$unsorted) % 203.09/203.30 (declare-const tptp.tac $$unsorted) % 203.09/203.30 (declare-const tptp.tau $$unsorted) % 203.09/203.30 (define @t1 () (@var "C" $$unsorted)) % 203.09/203.30 (define @t2 () (@var "Ax" $$unsorted)) % 203.09/203.30 (define @t3 () (@var "I2" $$unsorted)) % 203.09/203.30 (define @t4 () (tptp.model @t3 @t1)) % 203.09/203.30 (define @t5 () (@list @t3)) % 203.09/203.30 (define @t6 () (exists @t5 @t4)) % 203.09/203.30 (define @t7 () (@var "I1" $$unsorted)) % 203.09/203.30 (define @t8 () (tptp.model @t7 @t2)) % 203.09/203.30 (define @t9 () (@list @t7)) % 203.09/203.30 (define @t10 () (exists @t9 @t8)) % 203.09/203.30 (define @t11 () (not @t10)) % 203.09/203.30 (define @t12 () (@list @t2 @t1)) % 203.09/203.30 (define @t13 () (tptp.model @t7 @t1)) % 203.09/203.30 (define @t14 () (and @t8 @t13)) % 203.09/203.30 (define @t15 () (exists @t9 @t14)) % 203.09/203.30 (define @t16 () (tptp.status @t2 @t1 tptp.thm)) % 203.09/203.30 (define @t17 () (forall @t9 (=> @t8 @t13))) % 203.09/203.30 (define @t18 () (= @t17 @t16)) % 203.09/203.30 (define @t19 () (forall @t12 @t18)) % 203.09/203.30 (define @t20 () (tptp.model @t3 @t2)) % 203.09/203.30 (define @t21 () (forall @t5 @t4)) % 203.09/203.30 (define @t22 () (@var "I3" $$unsorted)) % 203.09/203.30 (define @t23 () (tptp.model @t22 @t2)) % 203.09/203.30 (define @t24 () (not @t23)) % 203.09/203.30 (define @t25 () (tptp.model @t22 @t1)) % 203.09/203.30 (define @t26 () (@list @t22)) % 203.09/203.30 (define @t27 () (exists @t26 (and @t25 @t24))) % 203.09/203.30 (define @t28 () (forall @t5 (=> @t20 @t4))) % 203.09/203.30 (define @t29 () (not @t20)) % 203.09/203.30 (define @t30 () (exists @t5 @t29)) % 203.09/203.30 (define @t31 () (forall @t26 @t25)) % 203.09/203.30 (define @t32 () (@var "I4" $$unsorted)) % 203.09/203.30 (define @t33 () (exists (@list @t32) (not (tptp.model @t32 @t1)))) % 203.09/203.30 (define @t34 () (tptp.status @t2 @t1 tptp.wca)) % 203.09/203.30 (define @t35 () (not @t25)) % 203.09/203.30 (define @t36 () (exists @t26 @t35)) % 203.09/203.30 (define @t37 () (and @t11 @t6 @t36)) % 203.09/203.30 (define @t38 () (= @t37 @t34)) % 203.09/203.30 (define @t39 () (forall @t12 @t38)) % 203.09/203.30 (define @t40 () (tptp.not @t1)) % 203.09/203.30 (define @t41 () (tptp.model @t3 @t40)) % 203.09/203.30 (define @t42 () (@var "S2" $$unsorted)) % 203.09/203.30 (define @t43 () (@var "S1" $$unsorted)) % 203.09/203.30 (define @t44 () (tptp.mighta @t43 @t42)) % 203.09/203.30 (define @t45 () (tptp.status @t2 @t1 @t42)) % 203.09/203.30 (define @t46 () (tptp.status @t2 @t1 @t43)) % 203.09/203.30 (define @t47 () (and @t46 @t45)) % 203.09/203.30 (define @t48 () (exists @t12 @t47)) % 203.09/203.30 (define @t49 () (= @t48 @t44)) % 203.09/203.30 (define @t50 () (@list @t43 @t42)) % 203.09/203.30 (define @t51 () (forall @t50 @t49)) % 203.09/203.30 (define @t52 () (not @t45)) % 203.09/203.30 (define @t53 () (@var "F" $$unsorted)) % 203.09/203.30 (define @t54 () (@var "I" $$unsorted)) % 203.09/203.30 (define @t55 () (tptp.model @t54 (tptp.not @t53))) % 203.09/203.30 (define @t56 () (tptp.model @t54 @t53)) % 203.09/203.30 (define @t57 () (@list @t54 @t53)) % 203.09/203.30 (define @t58 () (@list @t54)) % 203.09/203.30 (define @t59 () (@list @t53)) % 203.09/203.30 (define @t60 () (tptp.model @t3 @t53)) % 203.09/203.30 (define @t61 () (not @t60)) % 203.09/203.30 (define @t62 () (exists @t5 @t61)) % 203.09/203.30 (define @t63 () (tptp.model @t7 @t53)) % 203.09/203.30 (define @t64 () (exists @t9 @t63)) % 203.09/203.30 (define @t65 () (and @t64 @t62)) % 203.09/203.30 (define @t66 () (exists @t59 @t65)) % 203.09/203.30 (define @t67 () (forall @t58 (not @t56))) % 203.09/203.30 (define @t68 () (exists @t59 @t67)) % 203.09/203.30 (define @t69 () (not @t4)) % 203.09/203.30 (define @t70 () (not (tptp.mighta tptp.wca tptp.thm))) % 203.09/203.30 (define @t71 () (@var "b_I" it_8_$$unsorted)) % 203.09/203.30 (define @t72 () (@const 0 (-> it_8_$$unsorted $$unsorted Bool))) % 203.09/203.30 (define @t73 () (@list @t71)) % 203.09/203.30 (define @t74 () (forall @t59 (not (forall @t73 (not (_ @t72 @t71 @t53)))))) % 203.09/203.30 (define @t75 () (not @t74)) % 203.09/203.30 (define @t76 () (not (forall @t59 (not @t67)))) % 203.09/203.30 (define @t77 () (@quantifiers_skolemize @t74 0)) % 203.09/203.30 (define @t78 () (forall @t73 (not (_ @t72 @t71 @t77)))) % 203.09/203.30 (define @t79 () (not (not @t78))) % 203.09/203.30 (define @t80 () (@list true)) % 203.09/203.30 (define @t81 () (@var "b_I1" it_8_$$unsorted)) % 203.09/203.30 (define @t82 () (@list @t81)) % 203.09/203.30 (define @t83 () (@const 1 it_7_$$unsorted)) % 203.09/203.30 (define @t84 () (@const 2 (-> $$unsorted $$unsorted it_7_$$unsorted Bool))) % 203.09/203.30 (define @t85 () (_ @t84 @t2 @t1 @t83)) % 203.09/203.30 (define @t86 () (not @t8)) % 203.09/203.30 (define @t87 () (forall @t9 (or @t86 @t13))) % 203.09/203.30 (define @t88 () (@var "b_BOUND_VARIABLE_7854" it_8_$$unsorted)) % 203.09/203.30 (define @t89 () (@var "b_BOUND_VARIABLE_7850" it_8_$$unsorted)) % 203.09/203.30 (define @t90 () (forall (@list @t53 @t89 @t88) (or (not (_ @t72 @t89 @t53)) (_ @t72 @t88 @t53)))) % 203.09/203.30 (define @t91 () (@quantifiers_skolemize @t90 0)) % 203.09/203.30 (define @t92 () (@list @t77 @t91)) % 203.09/203.30 (define @t93 () (@var "b_S2" it_7_$$unsorted)) % 203.09/203.30 (define @t94 () (@var "b_S1" it_7_$$unsorted)) % 203.09/203.30 (define @t95 () (@const 3 (-> it_7_$$unsorted it_7_$$unsorted Bool))) % 203.09/203.30 (define @t96 () (not (forall @t12 (or (not @t46) @t52)))) % 203.09/203.30 (define @t97 () (forall @t12 (not @t47))) % 203.09/203.30 (define @t98 () (not @t97)) % 203.09/203.30 (define @t99 () (@const 4 it_7_$$unsorted)) % 203.09/203.30 (define @t100 () (_ @t95 @t99 @t83)) % 203.09/203.30 (define @t101 () (_ @t84 @t2 @t1 @t99)) % 203.09/203.30 (define @t102 () (forall @t12 (or (not @t101) (not @t85)))) % 203.09/203.30 (define @t103 () (not @t102)) % 203.09/203.30 (define @t104 () (= @t100 @t103)) % 203.09/203.30 (define @t105 () (not @t104)) % 203.09/203.30 (define @t106 () (@list true false)) % 203.09/203.30 (define @t107 () (@var "b_I3" it_8_$$unsorted)) % 203.09/203.30 (define @t108 () (@list @t107)) % 203.09/203.30 (define @t109 () (@var "b_I2" it_8_$$unsorted)) % 203.09/203.30 (define @t110 () (@list @t109)) % 203.09/203.30 (define @t111 () (@var "b_I1" it_8_$$unsorted)) % 203.09/203.30 (define @t112 () (@list @t111)) % 203.09/203.30 (define @t113 () (not (forall @t5 @t69))) % 203.09/203.30 (define @t114 () (forall @t9 @t86)) % 203.09/203.30 (define @t115 () (and @t114 @t113 (not @t31))) % 203.09/203.30 (define @t116 () (forall @t26 (not @t35))) % 203.09/203.30 (define @t117 () (not @t116)) % 203.09/203.30 (define @t118 () (forall @t112 (not (_ @t72 @t111 @t77)))) % 203.09/203.30 (define @t119 () (@list false)) % 203.09/203.30 (define @t120 () (@var "BOUND_VARIABLE_7854" $$unsorted)) % 203.09/203.30 (define @t121 () (tptp.model @t120 @t53)) % 203.09/203.30 (define @t122 () (@var "BOUND_VARIABLE_7850" $$unsorted)) % 203.09/203.30 (define @t123 () (not (tptp.model @t122 @t53))) % 203.09/203.30 (define @t124 () (or @t123 @t121)) % 203.09/203.30 (define @t125 () (forall (@list @t53 @t122 @t120) @t124)) % 203.09/203.30 (define @t126 () (forall (@list @t122 @t120) @t124)) % 203.09/203.30 (define @t127 () (forall (@list @t120) @t121)) % 203.09/203.30 (define @t128 () (forall (@list @t122) @t123)) % 203.09/203.30 (define @t129 () (or @t128 @t127)) % 203.09/203.30 (define @t130 () (forall @t5 @t60)) % 203.09/203.30 (define @t131 () (forall @t9 (not @t63))) % 203.09/203.30 (define @t132 () (not @t130)) % 203.09/203.30 (define @t133 () (not @t131)) % 203.09/203.30 (define @t134 () (and @t133 @t132)) % 203.09/203.30 (define @t135 () (forall @t59 (not @t134))) % 203.09/203.30 (define @t136 () (not @t135)) % 203.09/203.30 (define @t137 () (forall @t5 (not @t61))) % 203.09/203.30 (define @t138 () (not @t137)) % 203.09/203.30 (define @t139 () (@quantifiers_skolemize @t90 2)) % 203.09/203.30 (define @t140 () (_ @t72 @t139 @t91)) % 203.09/203.30 (define @t141 () (@quantifiers_skolemize @t90 1)) % 203.09/203.30 (define @t142 () (_ @t72 @t141 @t91)) % 203.09/203.30 (define @t143 () (not @t142)) % 203.09/203.30 (define @t144 () (or @t143 @t140)) % 203.09/203.30 (define @t145 () (@list @t144)) % 203.09/203.30 (define @t146 () (@var "b_I2" it_8_$$unsorted)) % 203.09/203.30 (define @t147 () (forall (@list @t146) (_ @t72 @t146 @t91))) % 203.09/203.30 (define @t148 () (not @t147)) % 203.09/203.30 (define @t149 () (forall @t108 (_ @t72 @t107 @t91))) % 203.09/203.30 (define @t150 () (not @t149)) % 203.09/203.30 (define @t151 () (@var "b_I1" it_8_$$unsorted)) % 203.09/203.30 (define @t152 () (forall (@list @t151) (not (_ @t72 @t151 @t91)))) % 203.09/203.30 (define @t153 () (not @t152)) % 203.09/203.30 (define @t154 () (forall @t110 (not (_ @t72 @t109 @t91)))) % 203.09/203.30 (define @t155 () (not @t154)) % 203.09/203.30 (define @t156 () (not @t118)) % 203.09/203.30 (define @t157 () (and @t118 @t155 @t150)) % 203.09/203.30 (define @t158 () (_ @t84 @t77 @t91 @t99)) % 203.09/203.30 (define @t159 () (= @t158 @t157)) % 203.09/203.30 (define @t160 () (@list false false)) % 203.09/203.30 (define @t161 () (_ @t84 @t77 @t91 @t83)) % 203.09/203.30 (define @t162 () (not @t161)) % 203.09/203.30 (define @t163 () (not @t158)) % 203.09/203.30 (define @t164 () (or @t163 @t162)) % 203.09/203.30 (define @t165 () (forall @t82 (or (not (_ @t72 @t81 @t77)) (_ @t72 @t81 @t91)))) % 203.09/203.30 (define @t166 () (= @t161 @t165)) % 203.09/203.30 (define @t167 () (not @t165)) % 203.09/203.30 (define @t168 () (@quantifiers_skolemize @t165 0)) % 203.09/203.30 (define @t169 () (_ @t72 @t168 @t77)) % 203.09/203.30 (define @t170 () (not @t169)) % 203.09/203.30 (define @t171 () (or @t170 (_ @t72 @t168 @t91))) % 203.09/203.30 (define @t172 () (not @t171)) % 203.09/203.30 (assume @p1 (forall @t12 (= (=> @t11 (not @t6)) (tptp.status @t2 @t1 tptp.unp)))) % 203.09/203.30 (assume @p2 (forall @t12 (= (=> @t10 @t6) (tptp.status @t2 @t1 tptp.sap)))) % 203.09/203.30 (assume @p3 (forall @t12 (= (= @t10 @t6) (tptp.status @t2 @t1 tptp.esa)))) % 203.09/203.30 (assume @p4 (forall @t12 (= @t15 (tptp.status @t2 @t1 tptp.sat)))) % 203.09/203.30 (assume @p5 @t19) % 203.09/203.30 (assume @p6 (forall @t12 (= (and @t10 (forall @t5 (= @t20 @t4))) (tptp.status @t2 @t1 tptp.eqv)))) % 203.09/203.30 (assume @p7 (forall @t12 (= (and @t10 @t21) (tptp.status @t2 @t1 tptp.tac)))) % 203.09/203.30 (assume @p8 (forall @t12 (= (and @t10 @t28 @t27) (tptp.status @t2 @t1 tptp.wec)))) % 203.09/203.30 (assume @p9 (forall @t12 (= (and @t10 @t30 (forall @t26 (= @t23 @t25))) (tptp.status @t2 @t1 tptp.eth)))) % 203.09/203.30 (assume @p10 (forall @t12 (= (forall @t9 @t14) (tptp.status @t2 @t1 tptp.tau)))) % 203.09/203.30 (assume @p11 (forall @t12 (= (and @t10 @t30 @t31) (tptp.status @t2 @t1 tptp.wtc)))) % 203.09/203.30 (assume @p12 (forall @t12 (= (and @t10 @t28 @t27 @t33) (tptp.status @t2 @t1 tptp.wth)))) % 203.09/203.30 (assume @p13 (forall @t12 (= @t11 (tptp.status @t2 @t1 tptp.cax)))) % 203.09/203.30 (assume @p14 (forall @t12 (= (and @t11 @t6) (tptp.status @t2 @t1 tptp.sca)))) % 203.09/203.30 (assume @p15 (forall @t12 (= (and @t11 @t21) (tptp.status @t2 @t1 tptp.tca)))) % 203.09/203.30 (assume @p16 @t39) % 203.09/203.30 (assume @p17 (forall @t12 (= (exists @t9 (and @t8 (tptp.model @t7 @t40))) (tptp.status @t2 @t1 tptp.csa)))) % 203.09/203.30 (assume @p18 (forall @t12 (= (and (forall @t9 @t8) (forall @t5 @t41)) (tptp.status @t2 @t1 tptp.uns)))) % 203.09/203.30 (assume @p19 (forall @t12 (= (and @t15 (exists @t5 (and @t20 @t41))) (tptp.status @t2 @t1 tptp.noc)))) % 203.09/203.30 (assume @p20 @t51) % 203.09/203.30 (assume @p21 (forall @t50 (= (forall @t12 (=> @t46 @t45)) (tptp.isa @t43 @t42)))) % 203.09/203.30 (assume @p22 (forall @t50 (= (exists @t12 (and @t46 @t52)) (tptp.nota @t43 @t42)))) % 203.09/203.30 (assume @p23 (forall @t50 (= (forall @t12 (=> @t46 @t52)) (tptp.nevera @t43 @t42)))) % 203.09/203.30 (assume @p24 (forall @t50 (= (forall @t12 (xor @t46 @t45)) (tptp.xora @t43 @t42)))) % 203.09/203.30 (assume @p25 (forall @t57 (xor @t56 @t55))) % 203.09/203.30 (assume @p26 (forall @t57 (= @t56 (not @t55)))) % 203.09/203.30 (assume @p27 (exists @t59 (forall @t58 @t56))) % 203.09/203.30 (assume @p28 @t66) % 203.09/203.30 (assume @p29 @t68) % 203.09/203.30 (assume @p30 (exists @t12 (and @t15 (exists @t5 (or @t29 @t69))))) % 203.09/203.30 (assume @p31 (exists @t12 (and @t10 @t28 (exists @t26 (and @t24 @t25)) @t33))) % 203.09/203.30 (assume @p32 (exists (@list @t7 @t2 @t1) (and @t8 (not @t13) @t6))) % 203.09/203.30 (assume @p33 @t70) % 203.09/203.30 (assume @p34 true) % 203.09/203.30 ; WARNING: add trust step for TRUST % 203.09/203.30 ; trust TRUST PREPROCESS_SORT_INFER % 203.09/203.30 (step @p35 :rule trust :premises () :args ((= @t76 @t75))) % 203.09/203.30 (step @p36 :rule exists-elim :args ((= @t68 @t76))) % 203.09/203.30 (step @p37 :rule trans :premises (@p36 @p35)) % 203.09/203.30 (step @p38 :rule eq_resolve :premises (@p29 @p37)) % 203.09/203.30 (step @p39 :rule refl :args (@t78)) % 203.09/203.30 (step @p40 :rule bool-double-not-elim :args (@t74)) % 203.09/203.30 (step @p41 :rule nary_cong :premises (@p40 @p39) :args ((or (not @t75) @t78))) % 203.09/203.30 (step @p42 :rule bool-double-not-elim :args (@t78)) % 203.09/203.30 (step @p43 :rule refl :args (@t75)) % 203.09/203.30 (step @p44 :rule cong :premises (@p43 @p42) :args ((=> @t75 @t79))) % 203.09/203.30 (assume-push @p214 @t75) % 203.09/203.30 (step @p46 :rule skolemize :premises (@p38)) % 203.09/203.30 (step-pop @p215 :rule scope :premises (@p46)) % 203.09/203.30 (step @p47 :rule process_scope :premises (@p215) :args (@t79)) % 203.09/203.30 (step @p49 :rule eq_resolve :premises (@p47 @p44)) % 203.09/203.30 (step @p50 :rule implies_elim :premises (@p49)) % 203.09/203.30 (step @p51 :rule eq_resolve :premises (@p50 @p41)) % 203.09/203.30 (step @p52 :rule chain_m_resolution :premises (@p51 @p38) :args (@t78 @t80 (@list @t74))) % 203.09/203.30 ; trust TRUST PREPROCESS_SORT_INFER % 203.09/203.30 (step @p53 :rule trust :premises () :args ((= (forall @t12 (= @t16 @t87)) (forall @t12 (= @t85 (forall @t82 (or (not (_ @t72 @t81 @t2)) (_ @t72 @t81 @t1)))))))) % 203.09/203.30 (step @p54 :rule eq-symm :args (@t87 @t16)) % 203.09/203.30 (step @p55 :rule refl :args (@t16)) % 203.09/203.30 (step @p56 :rule bool-impl-elim :args (@t8 @t13)) % 203.09/203.30 (step @p57 :rule cong :premises (@p56) :args (@t17)) % 203.09/203.30 (step @p58 :rule cong :premises (@p57 @p55) :args (@t18)) % 203.09/203.30 (step @p59 :rule trans :premises (@p58 @p54)) % 203.09/203.30 (step @p60 :rule cong :premises (@p59) :args (@t19)) % 203.09/203.30 (step @p61 :rule trans :premises (@p60 @p53)) % 203.09/203.30 (step @p62 :rule eq_resolve :premises (@p5 @p61)) % 203.09/203.30 (step @p63 :rule instantiate :premises (@p62) :args (@t92)) % 203.09/203.30 ; trust TRUST PREPROCESS_SORT_INFER % 203.09/203.30 (step @p64 :rule trust :premises () :args ((= (forall @t50 (= @t44 @t96)) (forall (@list @t94 @t93) (= (_ @t95 @t94 @t93) (not (forall @t12 (or (not (_ @t84 @t2 @t1 @t94)) (not (_ @t84 @t2 @t1 @t93)))))))))) % 203.09/203.30 (step @p65 :rule eq-symm :args (@t96 @t44)) % 203.09/203.30 (step @p66 :rule refl :args (@t44)) % 203.09/203.30 (step @p67 :rule bool-and-de-morgan :args (@t46 @t45 true)) % 203.09/203.30 (step @p68 :rule cong :premises (@p67) :args (@t97)) % 203.09/203.30 (step @p69 :rule cong :premises (@p68) :args (@t98)) % 203.09/203.30 (step @p70 :rule exists-elim :args ((= @t48 @t98))) % 203.09/203.30 (step @p71 :rule trans :premises (@p70 @p69)) % 203.09/203.30 (step @p72 :rule cong :premises (@p71 @p66) :args (@t49)) % 203.09/203.30 (step @p73 :rule trans :premises (@p72 @p65)) % 203.09/203.30 (step @p74 :rule cong :premises (@p73) :args (@t51)) % 203.09/203.30 (step @p75 :rule trans :premises (@p74 @p64)) % 203.09/203.30 (step @p76 :rule eq_resolve :premises (@p20 @p75)) % 203.09/203.30 (step @p77 :rule instantiate :premises (@p76) :args ((@list @t99 @t83))) % 203.09/203.30 ; trust TRUST PREPROCESS_SORT_INFER % 203.09/203.30 (step @p78 :rule trust :premises () :args ((= @t70 (not @t100)))) % 203.09/203.30 (step @p79 :rule eq_resolve :premises (@p33 @p78)) % 203.09/203.30 (step @p80 :rule bool-double-not-elim :args (@t102)) % 203.09/203.30 (step @p81 :rule refl :args (@t100)) % 203.09/203.30 (step @p82 :rule refl :args (@t105)) % 203.09/203.30 (step @p83 :rule nary_cong :premises (@p82 @p81 @p80) :args ((or @t105 @t100 (not @t103)))) % 203.09/203.30 (step @p84 :rule cnf_equiv_pos2 :args (@t104)) % 203.09/203.30 (step @p85 :rule eq_resolve :premises (@p84 @p83)) % 203.09/203.30 (step @p86 :rule reordering :premises (@p85) :args ((or @t100 @t102 @t105))) % 203.09/203.30 (step @p87 :rule chain_m_resolution :premises (@p86 @p79 @p77) :args (@t102 @t106 (@list @t100 @t104))) % 203.09/203.30 (step @p88 :rule instantiate :premises (@p87) :args (@t92)) % 203.09/203.30 ; trust TRUST PREPROCESS_SORT_INFER % 203.09/203.30 (step @p89 :rule trust :premises () :args ((= (forall @t12 (= @t34 @t115)) (forall @t12 (= @t101 (and (forall @t112 (not (_ @t72 @t111 @t2))) (not (forall @t110 (not (_ @t72 @t109 @t1)))) (not (forall @t108 (_ @t72 @t107 @t1))))))))) % 203.09/203.30 (step @p90 :rule eq-symm :args (@t115 @t34)) % 203.09/203.30 (step @p91 :rule refl :args (@t34)) % 203.09/203.30 (step @p92 :rule bool-double-not-elim :args (@t25)) % 203.09/203.30 (step @p93 :rule cong :premises (@p92) :args (@t116)) % 203.09/203.30 (step @p94 :rule cong :premises (@p93) :args (@t117)) % 203.09/203.30 (step @p95 :rule exists-elim :args ((= @t36 @t117))) % 203.09/203.30 (step @p96 :rule trans :premises (@p95 @p94)) % 203.09/203.30 (step @p97 :rule exists-elim :args ((= @t6 @t113))) % 203.09/203.30 (step @p98 :rule bool-double-not-elim :args (@t114)) % 203.09/203.30 (step @p99 :rule exists-elim :args ((= @t10 (not @t114)))) % 203.09/203.30 (step @p100 :rule cong :premises (@p99) :args (@t11)) % 203.09/203.30 (step @p101 :rule trans :premises (@p100 @p98)) % 203.09/203.30 (step @p102 :rule nary_cong :premises (@p101 @p97 @p96) :args (@t37)) % 203.09/203.30 (step @p103 :rule cong :premises (@p102 @p91) :args (@t38)) % 203.09/203.30 (step @p104 :rule trans :premises (@p103 @p90)) % 203.09/203.30 (step @p105 :rule cong :premises (@p104) :args (@t39)) % 203.09/203.30 (step @p106 :rule trans :premises (@p105 @p89)) % 203.09/203.30 (step @p107 :rule eq_resolve :premises (@p16 @p106)) % 203.09/203.30 (step @p108 :rule instantiate :premises (@p107) :args (@t92)) % 203.09/203.30 (step @p109 :rule alpha_equiv :args (@t78 (@list @t71) (@list @t111))) % 203.09/203.30 (step @p110 :rule equiv_elim1 :premises (@p109)) % 203.09/203.30 (step @p111 :rule chain_m_resolution :premises (@p110 @p52) :args (@t118 @t119 (@list @t78))) % 203.09/203.30 ; trust TRUST PREPROCESS_SORT_INFER % 203.09/203.30 (step @p112 :rule trust :premises () :args ((= (not @t125) (not @t90)))) % 203.09/203.30 (step @p113 :rule quant-merge-prenex :args ((= (forall @t59 @t126) @t125))) % 203.09/203.30 (step @p114 :rule alpha_equiv :args (@t127 (@list @t120) (@list @t3))) % 203.09/203.30 (step @p115 :rule alpha_equiv :args (@t128 (@list @t122) (@list @t7))) % 203.09/203.30 (step @p116 :rule nary_cong :premises (@p115 @p114) :args (@t129)) % 203.09/203.30 (step @p117 :rule quant-miniscope-or :args ((= @t126 @t129))) % 203.09/203.30 (step @p118 :rule trans :premises (@p117 @p116)) % 203.09/203.30 (step @p119 :rule symm :premises (@p118)) % 203.09/203.30 (step @p120 :rule cong :premises (@p119) :args ((forall @t59 (or @t131 @t130)))) % 203.09/203.30 (step @p121 :rule trans :premises (@p120 @p113)) % 203.09/203.30 (step @p122 :rule bool-double-not-elim :args (@t130)) % 203.09/203.30 (step @p123 :rule bool-double-not-elim :args (@t131)) % 203.09/203.30 (step @p124 :rule nary_cong :premises (@p123 @p122) :args ((or (not @t133) (not @t132)))) % 203.09/203.30 (step @p125 :rule bool-and-de-morgan :args (@t133 @t132 true)) % 203.09/203.30 (step @p126 :rule trans :premises (@p125 @p124)) % 203.09/203.30 (step @p127 :rule cong :premises (@p126) :args (@t135)) % 203.09/203.30 (step @p128 :rule trans :premises (@p127 @p121)) % 203.09/203.30 (step @p129 :rule cong :premises (@p128) :args (@t136)) % 203.09/203.30 (step @p130 :rule exists-elim :args ((= (exists @t59 @t134) @t136))) % 203.09/203.30 (step @p131 :rule trans :premises (@p130 @p129)) % 203.09/203.30 (step @p132 :rule bool-double-not-elim :args (@t60)) % 203.09/203.30 (step @p133 :rule cong :premises (@p132) :args (@t137)) % 203.09/203.30 (step @p134 :rule cong :premises (@p133) :args (@t138)) % 203.09/203.30 (step @p135 :rule exists-elim :args ((= @t62 @t138))) % 203.09/203.30 (step @p136 :rule trans :premises (@p135 @p134)) % 203.09/203.30 (step @p137 :rule exists-elim :args ((= @t64 @t133))) % 203.09/203.30 (step @p138 :rule nary_cong :premises (@p137 @p136) :args (@t65)) % 203.09/203.30 (step @p139 :rule cong :premises (@p138) :args (@t66)) % 203.09/203.30 (step @p140 :rule trans :premises (@p139 @p131)) % 203.09/203.30 (step @p141 :rule trans :premises (@p140 @p112)) % 203.09/203.30 (step @p142 :rule eq_resolve :premises (@p28 @p141)) % 203.09/203.30 (step @p143 :rule skolemize :premises (@p142)) % 203.09/203.30 (step @p144 :rule cnf_or_neg :args (@t144 1)) % 203.09/203.30 (step @p145 :rule chain_m_resolution :premises (@p144 @p143) :args ((not @t140) @t80 @t145)) % 203.09/203.30 (assume-push @p216 @t147) % 203.09/203.30 (step @p147 :rule instantiate :premises (@p216) :args ((@list @t139))) % 203.09/203.30 (step-pop @p217 :rule scope :premises (@p147)) % 203.09/203.30 (step @p148 :rule process_scope :premises (@p217) :args (@t140)) % 203.09/203.30 (step @p150 :rule implies_elim :premises (@p148)) % 203.09/203.30 (step @p151 :rule reordering :premises (@p150) :args ((or @t140 @t148))) % 203.09/203.30 (step @p152 :rule chain_m_resolution :premises (@p151 @p145) :args (@t148 @t80 (@list @t140))) % 203.09/203.30 (step @p153 :rule alpha_equiv :args (@t147 (@list @t146) (@list @t107))) % 203.09/203.30 (step @p154 :rule equiv_elim2 :premises (@p153)) % 203.09/203.30 (step @p155 :rule chain_m_resolution :premises (@p154 @p152) :args (@t150 @t80 (@list @t147))) % 203.09/203.30 (step @p156 :rule bool-double-not-elim :args (@t142)) % 203.09/203.30 (step @p157 :rule refl :args (@t144)) % 203.09/203.30 (step @p158 :rule nary_cong :premises (@p157 @p156) :args ((or @t144 (not @t143)))) % 203.09/203.30 (step @p159 :rule cnf_or_neg :args (@t144 0)) % 203.09/203.30 (step @p160 :rule eq_resolve :premises (@p159 @p158)) % 203.09/203.30 (step @p161 :rule reordering :premises (@p160) :args ((or @t142 @t144))) % 203.09/203.30 (step @p162 :rule chain_m_resolution :premises (@p161 @p143) :args (@t142 @t80 @t145)) % 203.09/203.30 (assume-push @p218 @t152) % 203.09/203.30 (step @p164 :rule instantiate :premises (@p218) :args ((@list @t141))) % 203.09/203.30 (step-pop @p219 :rule scope :premises (@p164)) % 203.09/203.30 (step @p165 :rule process_scope :premises (@p219) :args (@t143)) % 203.09/203.30 (step @p167 :rule implies_elim :premises (@p165)) % 203.09/203.30 (step @p168 :rule reordering :premises (@p167) :args ((or @t143 @t153))) % 203.09/203.30 (step @p169 :rule chain_m_resolution :premises (@p168 @p162) :args (@t153 @t119 (@list @t142))) % 203.09/203.30 (step @p170 :rule alpha_equiv :args (@t152 (@list @t151) (@list @t109))) % 203.09/203.30 (step @p171 :rule equiv_elim2 :premises (@p170)) % 203.09/203.30 (step @p172 :rule chain_m_resolution :premises (@p171 @p169) :args (@t155 @t80 (@list @t152))) % 203.09/203.30 (step @p173 :rule bool-double-not-elim :args (@t149)) % 203.09/203.30 (step @p174 :rule bool-double-not-elim :args (@t154)) % 203.09/203.30 (step @p175 :rule refl :args (@t156)) % 203.09/203.30 (step @p176 :rule refl :args (@t157)) % 203.09/203.30 (step @p177 :rule nary_cong :premises (@p176 @p175 @p174 @p173) :args ((or @t157 @t156 (not @t155) (not @t150)))) % 203.09/203.30 (step @p178 :rule cnf_and_neg :args (@t157)) % 203.09/203.30 (step @p179 :rule eq_resolve :premises (@p178 @p177)) % 203.09/203.30 (step @p180 :rule reordering :premises (@p179) :args ((or @t154 @t149 @t157 @t156))) % 203.09/203.30 (step @p181 :rule chain_m_resolution :premises (@p180 @p172 @p155 @p111) :args (@t157 (@list true true false) (@list @t154 @t149 @t118))) % 203.09/203.30 (step @p182 :rule cnf_equiv_pos2 :args (@t159)) % 203.09/203.30 (step @p183 :rule reordering :premises (@p182) :args ((or @t158 (not @t157) (not @t159)))) % 203.09/203.30 (step @p184 :rule chain_m_resolution :premises (@p183 @p181 @p108) :args (@t158 @t160 (@list @t157 @t159))) % 203.09/203.30 (step @p185 :rule cnf_or_pos :args (@t164)) % 203.09/203.30 (step @p186 :rule reordering :premises (@p185) :args ((or @t163 @t162 (not @t164)))) % 203.09/203.30 (step @p187 :rule chain_m_resolution :premises (@p186 @p184 @p88) :args (@t162 @t160 (@list @t158 @t164))) % 203.09/203.30 (step @p188 :rule cnf_equiv_pos2 :args (@t166)) % 203.09/203.30 (step @p189 :rule reordering :premises (@p188) :args ((or @t161 @t167 (not @t166)))) % 203.09/203.30 (step @p190 :rule chain_m_resolution :premises (@p189 @p187 @p63) :args (@t167 @t106 (@list @t161 @t166))) % 203.09/203.30 (step @p191 :rule refl :args (@t172)) % 203.09/203.30 (step @p192 :rule bool-double-not-elim :args (@t165)) % 203.09/203.30 (step @p193 :rule nary_cong :premises (@p192 @p191) :args ((or (not @t167) @t172))) % 203.09/203.30 (assume-push @p220 @t167) % 203.09/203.30 (step @p195 :rule skolemize :premises (@p220)) % 203.09/203.30 (step-pop @p221 :rule scope :premises (@p195)) % 203.09/203.30 (step @p196 :rule process_scope :premises (@p221) :args (@t172)) % 203.09/203.30 (step @p198 :rule implies_elim :premises (@p196)) % 203.09/203.30 (step @p199 :rule eq_resolve :premises (@p198 @p193)) % 203.09/203.30 (step @p200 :rule chain_m_resolution :premises (@p199 @p190) :args (@t172 @t80 (@list @t165))) % 203.09/203.30 (step @p201 :rule bool-double-not-elim :args (@t169)) % 203.09/203.30 (step @p202 :rule refl :args (@t171)) % 203.09/203.30 (step @p203 :rule nary_cong :premises (@p202 @p201) :args ((or @t171 (not @t170)))) % 203.09/203.30 (step @p204 :rule cnf_or_neg :args (@t171 0)) % 203.09/203.30 (step @p205 :rule eq_resolve :premises (@p204 @p203)) % 203.09/203.30 (step @p206 :rule reordering :premises (@p205) :args ((or @t169 @t171))) % 203.09/203.30 (step @p207 :rule chain_m_resolution :premises (@p206 @p200) :args (@t169 @t80 (@list @t171))) % 203.09/203.30 (assume-push @p222 @t78) % 203.09/203.30 (step @p209 :rule instantiate :premises (@p52) :args ((@list @t168))) % 203.09/203.30 (step-pop @p223 :rule scope :premises (@p209)) % 203.09/203.30 (step @p210 :rule process_scope :premises (@p223) :args (@t170)) % 203.09/203.30 (step @p212 :rule implies_elim :premises (@p210)) % 203.09/203.30 (step @p213 false :rule chain_m_resolution :premises (@p212 @p207 @p52) :args (false @t160 (@list @t169 @t78))) % 203.09/203.30 ) % 203.09/203.30 % SZS output end Proof % 203.09/203.30 % cvc5 exiting %------------------------------------------------------------------------------