%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : KRS260+1 : TPTP v9.2.1. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n004.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 08:29:11 AM UTC 2026 % Result : Theorem 202.99s 203.29s % Output : Proof 202.99s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KRS260+1 : TPTP v9.2.1. Bugfixed v5.4.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n004.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 05:36:07 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 202.99/203.29 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 202.99/203.29 --- Run --no-e-matching --full-saturate-quant at 6... % 202.99/203.29 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 202.99/203.29 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 202.99/203.29 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 202.99/203.29 --- Run --trigger-sel=max --full-saturate-quant at 15... % 202.99/203.29 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 33... % 202.99/203.29 --- Run --multi-trigger-cache --full-saturate-quant at 15... % 202.99/203.29 --- Run --prenex-quant=none --full-saturate-quant at 30... % 202.99/203.29 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 15... % 202.99/203.29 --- Run --relevant-triggers --full-saturate-quant at 30... % 202.99/203.29 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 15... % 202.99/203.29 % SZS status Theorem % 202.99/203.29 % SZS output start Proof % 202.99/203.29 ( % 202.99/203.29 (declare-sort $$unsorted 0) % 202.99/203.29 (declare-const tptp.xora (-> $$unsorted $$unsorted Bool)) % 202.99/203.29 (declare-const tptp.nevera (-> $$unsorted $$unsorted Bool)) % 202.99/203.29 (declare-const tptp.nota (-> $$unsorted $$unsorted Bool)) % 202.99/203.29 (declare-const tptp.mighta (-> $$unsorted $$unsorted Bool)) % 202.99/203.29 (declare-const tptp.noc $$unsorted) % 202.99/203.29 (declare-const tptp.uns $$unsorted) % 202.99/203.29 (declare-const tptp.not (-> $$unsorted $$unsorted)) % 202.99/203.29 (declare-const tptp.tca $$unsorted) % 202.99/203.29 (declare-const tptp.sca $$unsorted) % 202.99/203.29 (declare-const tptp.wth $$unsorted) % 202.99/203.29 (declare-const tptp.unp $$unsorted) % 202.99/203.29 (declare-const tptp.wca $$unsorted) % 202.99/203.29 (declare-const tptp.wec $$unsorted) % 202.99/203.29 (declare-const tptp.sap $$unsorted) % 202.99/203.29 (declare-const tptp.wtc $$unsorted) % 202.99/203.29 (declare-const tptp.model (-> $$unsorted $$unsorted Bool)) % 202.99/203.29 (declare-const tptp.sat $$unsorted) % 202.99/203.29 (declare-const tptp.cax $$unsorted) % 202.99/203.29 (declare-const tptp.eqv $$unsorted) % 202.99/203.29 (declare-const tptp.esa $$unsorted) % 202.99/203.29 (declare-const tptp.csa $$unsorted) % 202.99/203.29 (declare-const tptp.status (-> $$unsorted $$unsorted $$unsorted Bool)) % 202.99/203.29 (declare-const tptp.thm $$unsorted) % 202.99/203.29 (declare-const tptp.isa (-> $$unsorted $$unsorted Bool)) % 202.99/203.29 (declare-const tptp.eth $$unsorted) % 202.99/203.29 (declare-const tptp.tac $$unsorted) % 202.99/203.29 (declare-const tptp.tau $$unsorted) % 202.99/203.29 (define @t1 () (@var "C" $$unsorted)) % 202.99/203.29 (define @t2 () (@var "Ax" $$unsorted)) % 202.99/203.29 (define @t3 () (@var "I2" $$unsorted)) % 202.99/203.29 (define @t4 () (tptp.model @t3 @t1)) % 202.99/203.29 (define @t5 () (@list @t3)) % 202.99/203.29 (define @t6 () (exists @t5 @t4)) % 202.99/203.29 (define @t7 () (@var "I1" $$unsorted)) % 202.99/203.29 (define @t8 () (tptp.model @t7 @t2)) % 202.99/203.29 (define @t9 () (@list @t7)) % 202.99/203.29 (define @t10 () (exists @t9 @t8)) % 202.99/203.29 (define @t11 () (not @t10)) % 202.99/203.29 (define @t12 () (@list @t2 @t1)) % 202.99/203.29 (define @t13 () (tptp.model @t7 @t1)) % 202.99/203.29 (define @t14 () (and @t8 @t13)) % 202.99/203.29 (define @t15 () (exists @t9 @t14)) % 202.99/203.29 (define @t16 () (tptp.status @t2 @t1 tptp.thm)) % 202.99/203.29 (define @t17 () (forall @t9 (=> @t8 @t13))) % 202.99/203.29 (define @t18 () (= @t17 @t16)) % 202.99/203.29 (define @t19 () (forall @t12 @t18)) % 202.99/203.29 (define @t20 () (tptp.model @t3 @t2)) % 202.99/203.29 (define @t21 () (forall @t5 @t4)) % 202.99/203.29 (define @t22 () (tptp.status @t2 @t1 tptp.wec)) % 202.99/203.29 (define @t23 () (@var "I3" $$unsorted)) % 202.99/203.29 (define @t24 () (tptp.model @t23 @t2)) % 202.99/203.29 (define @t25 () (not @t24)) % 202.99/203.29 (define @t26 () (tptp.model @t23 @t1)) % 202.99/203.29 (define @t27 () (and @t26 @t25)) % 202.99/203.29 (define @t28 () (@list @t23)) % 202.99/203.29 (define @t29 () (exists @t28 @t27)) % 202.99/203.29 (define @t30 () (forall @t5 (=> @t20 @t4))) % 202.99/203.29 (define @t31 () (and @t10 @t30 @t29)) % 202.99/203.29 (define @t32 () (= @t31 @t22)) % 202.99/203.29 (define @t33 () (forall @t12 @t32)) % 202.99/203.29 (define @t34 () (not @t20)) % 202.99/203.29 (define @t35 () (exists @t5 @t34)) % 202.99/203.29 (define @t36 () (@var "I4" $$unsorted)) % 202.99/203.29 (define @t37 () (exists (@list @t36) (not (tptp.model @t36 @t1)))) % 202.99/203.29 (define @t38 () (not @t26)) % 202.99/203.29 (define @t39 () (tptp.not @t1)) % 202.99/203.29 (define @t40 () (tptp.model @t3 @t39)) % 202.99/203.29 (define @t41 () (@var "S2" $$unsorted)) % 202.99/203.29 (define @t42 () (@var "S1" $$unsorted)) % 202.99/203.29 (define @t43 () (tptp.mighta @t42 @t41)) % 202.99/203.29 (define @t44 () (tptp.status @t2 @t1 @t41)) % 202.99/203.29 (define @t45 () (tptp.status @t2 @t1 @t42)) % 202.99/203.29 (define @t46 () (and @t45 @t44)) % 202.99/203.29 (define @t47 () (exists @t12 @t46)) % 202.99/203.29 (define @t48 () (= @t47 @t43)) % 202.99/203.29 (define @t49 () (@list @t42 @t41)) % 202.99/203.29 (define @t50 () (forall @t49 @t48)) % 202.99/203.29 (define @t51 () (not @t44)) % 202.99/203.29 (define @t52 () (@var "F" $$unsorted)) % 202.99/203.29 (define @t53 () (@var "I" $$unsorted)) % 202.99/203.29 (define @t54 () (tptp.model @t53 (tptp.not @t52))) % 202.99/203.29 (define @t55 () (tptp.model @t53 @t52)) % 202.99/203.29 (define @t56 () (@list @t53 @t52)) % 202.99/203.29 (define @t57 () (@list @t53)) % 202.99/203.29 (define @t58 () (forall @t57 @t55)) % 202.99/203.29 (define @t59 () (@list @t52)) % 202.99/203.29 (define @t60 () (exists @t59 @t58)) % 202.99/203.29 (define @t61 () (tptp.model @t3 @t52)) % 202.99/203.29 (define @t62 () (not @t61)) % 202.99/203.29 (define @t63 () (exists @t5 @t62)) % 202.99/203.29 (define @t64 () (tptp.model @t7 @t52)) % 202.99/203.29 (define @t65 () (exists @t9 @t64)) % 202.99/203.29 (define @t66 () (and @t65 @t63)) % 202.99/203.29 (define @t67 () (exists @t59 @t66)) % 202.99/203.29 (define @t68 () (not (tptp.mighta tptp.wec tptp.thm))) % 202.99/203.29 (define @t69 () (@var "b_I" it_8_$$unsorted)) % 202.99/203.29 (define @t70 () (@const 0 (-> it_8_$$unsorted $$unsorted Bool))) % 202.99/203.29 (define @t71 () (@list @t69)) % 202.99/203.29 (define @t72 () (forall @t59 (not (forall @t71 (_ @t70 @t69 @t52))))) % 202.99/203.29 (define @t73 () (not @t72)) % 202.99/203.29 (define @t74 () (not (forall @t59 (not @t58)))) % 202.99/203.29 (define @t75 () (@quantifiers_skolemize @t72 0)) % 202.99/203.29 (define @t76 () (forall @t71 (_ @t70 @t69 @t75))) % 202.99/203.29 (define @t77 () (not (not @t76))) % 202.99/203.29 (define @t78 () (@list true)) % 202.99/203.29 (define @t79 () (@var "b_I1" it_8_$$unsorted)) % 202.99/203.29 (define @t80 () (_ @t70 @t79 @t75)) % 202.99/203.29 (define @t81 () (@var "b_BOUND_VARIABLE_7854" it_8_$$unsorted)) % 202.99/203.29 (define @t82 () (@var "b_BOUND_VARIABLE_7850" it_8_$$unsorted)) % 202.99/203.29 (define @t83 () (forall (@list @t52 @t82 @t81) (or (not (_ @t70 @t82 @t52)) (_ @t70 @t81 @t52)))) % 202.99/203.29 (define @t84 () (@quantifiers_skolemize @t83 0)) % 202.99/203.29 (define @t85 () (_ @t70 @t79 @t84)) % 202.99/203.29 (define @t86 () (@list @t79)) % 202.99/203.29 (define @t87 () (forall @t86 (or (not @t85) @t80))) % 202.99/203.29 (define @t88 () (@quantifiers_skolemize @t87 0)) % 202.99/203.29 (define @t89 () (_ @t70 @t88 @t75)) % 202.99/203.29 (define @t90 () (or (not (_ @t70 @t88 @t84)) @t89)) % 202.99/203.29 (define @t91 () (@list false)) % 202.99/203.29 (define @t92 () (not @t90)) % 202.99/203.29 (define @t93 () (not @t87)) % 202.99/203.29 (define @t94 () (@list @t79)) % 202.99/203.29 (define @t95 () (@var "b_I2" it_8_$$unsorted)) % 202.99/203.29 (define @t96 () (@list @t95)) % 202.99/203.29 (define @t97 () (forall @t96 (or (not (_ @t70 @t95 @t84)) (_ @t70 @t95 @t75)))) % 202.99/203.29 (define @t98 () (@var "b_I3" it_8_$$unsorted)) % 202.99/203.29 (define @t99 () (@list @t98)) % 202.99/203.29 (define @t100 () (@var "b_I1" it_8_$$unsorted)) % 202.99/203.29 (define @t101 () (@list @t100)) % 202.99/203.29 (define @t102 () (@const 1 it_7_$$unsorted)) % 202.99/203.29 (define @t103 () (@const 2 (-> $$unsorted $$unsorted it_7_$$unsorted Bool))) % 202.99/203.29 (define @t104 () (_ @t103 @t2 @t1 @t102)) % 202.99/203.29 (define @t105 () (not @t8)) % 202.99/203.29 (define @t106 () (not (forall @t9 @t105))) % 202.99/203.29 (define @t107 () (and @t106 (forall @t5 (or @t34 @t4)) (not (forall @t28 (or @t38 @t24))))) % 202.99/203.29 (define @t108 () (forall @t28 (not @t27))) % 202.99/203.29 (define @t109 () (not @t108)) % 202.99/203.29 (define @t110 () (@list @t84 @t75)) % 202.99/203.29 (define @t111 () (forall @t99 (or (not (_ @t70 @t98 @t75)) (_ @t70 @t98 @t84)))) % 202.99/203.29 (define @t112 () (not @t111)) % 202.99/203.29 (define @t113 () (forall @t101 (not (_ @t70 @t100 @t84)))) % 202.99/203.29 (define @t114 () (not @t113)) % 202.99/203.29 (define @t115 () (and @t114 @t97 @t112)) % 202.99/203.29 (define @t116 () (_ @t103 @t84 @t75 @t102)) % 202.99/203.29 (define @t117 () (= @t116 @t115)) % 202.99/203.29 (define @t118 () (not @t117)) % 202.99/203.29 (define @t119 () (not @t116)) % 202.99/203.29 (define @t120 () (@var "b_S2" it_7_$$unsorted)) % 202.99/203.29 (define @t121 () (@var "b_S1" it_7_$$unsorted)) % 202.99/203.29 (define @t122 () (@const 3 (-> it_7_$$unsorted it_7_$$unsorted Bool))) % 202.99/203.29 (define @t123 () (not (forall @t12 (or (not @t45) @t51)))) % 202.99/203.29 (define @t124 () (forall @t12 (not @t46))) % 202.99/203.29 (define @t125 () (not @t124)) % 202.99/203.29 (define @t126 () (@const 4 it_7_$$unsorted)) % 202.99/203.29 (define @t127 () (_ @t122 @t102 @t126)) % 202.99/203.29 (define @t128 () (_ @t103 @t2 @t1 @t126)) % 202.99/203.29 (define @t129 () (forall @t12 (or (not @t104) (not @t128)))) % 202.99/203.29 (define @t130 () (not @t129)) % 202.99/203.29 (define @t131 () (= @t127 @t130)) % 202.99/203.29 (define @t132 () (not @t131)) % 202.99/203.29 (define @t133 () (@list true false)) % 202.99/203.29 (define @t134 () (_ @t103 @t84 @t75 @t126)) % 202.99/203.29 (define @t135 () (not @t134)) % 202.99/203.29 (define @t136 () (or @t119 @t135)) % 202.99/203.29 (define @t137 () (not @t115)) % 202.99/203.29 (define @t138 () (forall @t9 (or @t105 @t13))) % 202.99/203.29 (define @t139 () (= @t134 @t87)) % 202.99/203.29 (define @t140 () (@var "BOUND_VARIABLE_7854" $$unsorted)) % 202.99/203.29 (define @t141 () (tptp.model @t140 @t52)) % 202.99/203.29 (define @t142 () (@var "BOUND_VARIABLE_7850" $$unsorted)) % 202.99/203.29 (define @t143 () (not (tptp.model @t142 @t52))) % 202.99/203.29 (define @t144 () (or @t143 @t141)) % 202.99/203.29 (define @t145 () (forall (@list @t52 @t142 @t140) @t144)) % 202.99/203.29 (define @t146 () (forall (@list @t142 @t140) @t144)) % 202.99/203.29 (define @t147 () (forall (@list @t140) @t141)) % 202.99/203.29 (define @t148 () (forall (@list @t142) @t143)) % 202.99/203.29 (define @t149 () (or @t148 @t147)) % 202.99/203.29 (define @t150 () (forall @t5 @t61)) % 202.99/203.29 (define @t151 () (forall @t9 (not @t64))) % 202.99/203.29 (define @t152 () (not @t150)) % 202.99/203.29 (define @t153 () (not @t151)) % 202.99/203.29 (define @t154 () (and @t153 @t152)) % 202.99/203.29 (define @t155 () (forall @t59 (not @t154))) % 202.99/203.29 (define @t156 () (not @t155)) % 202.99/203.29 (define @t157 () (forall @t5 (not @t62))) % 202.99/203.29 (define @t158 () (not @t157)) % 202.99/203.29 (define @t159 () (@quantifiers_skolemize @t83 1)) % 202.99/203.29 (define @t160 () (_ @t70 @t159 @t84)) % 202.99/203.29 (define @t161 () (@quantifiers_skolemize @t83 2)) % 202.99/203.29 (define @t162 () (_ @t70 @t161 @t84)) % 202.99/203.29 (define @t163 () (not @t160)) % 202.99/203.29 (define @t164 () (or @t163 @t162)) % 202.99/203.29 (define @t165 () (@list @t164)) % 202.99/203.29 (define @t166 () (@var "b_I1" it_8_$$unsorted)) % 202.99/203.29 (define @t167 () (forall (@list @t166) (not (_ @t70 @t166 @t84)))) % 202.99/203.29 (define @t168 () (not @t167)) % 202.99/203.29 (define @t169 () (not @t97)) % 202.99/203.29 (define @t170 () (forall @t86 (or (not @t80) @t85))) % 202.99/203.29 (define @t171 () (@list @t161)) % 202.99/203.29 (define @t172 () (_ @t70 @t161 @t75)) % 202.99/203.29 (define @t173 () (not @t172)) % 202.99/203.29 (define @t174 () (or @t173 @t162)) % 202.99/203.29 (define @t175 () (not @t174)) % 202.99/203.29 (assume @p1 (forall @t12 (= (=> @t11 (not @t6)) (tptp.status @t2 @t1 tptp.unp)))) % 202.99/203.29 (assume @p2 (forall @t12 (= (=> @t10 @t6) (tptp.status @t2 @t1 tptp.sap)))) % 202.99/203.29 (assume @p3 (forall @t12 (= (= @t10 @t6) (tptp.status @t2 @t1 tptp.esa)))) % 202.99/203.29 (assume @p4 (forall @t12 (= @t15 (tptp.status @t2 @t1 tptp.sat)))) % 202.99/203.29 (assume @p5 @t19) % 202.99/203.29 (assume @p6 (forall @t12 (= (and @t10 (forall @t5 (= @t20 @t4))) (tptp.status @t2 @t1 tptp.eqv)))) % 202.99/203.29 (assume @p7 (forall @t12 (= (and @t10 @t21) (tptp.status @t2 @t1 tptp.tac)))) % 202.99/203.29 (assume @p8 @t33) % 202.99/203.29 (assume @p9 (forall @t12 (= (and @t10 @t35 (forall @t28 (= @t24 @t26))) (tptp.status @t2 @t1 tptp.eth)))) % 202.99/203.29 (assume @p10 (forall @t12 (= (forall @t9 @t14) (tptp.status @t2 @t1 tptp.tau)))) % 202.99/203.29 (assume @p11 (forall @t12 (= (and @t10 @t35 (forall @t28 @t26)) (tptp.status @t2 @t1 tptp.wtc)))) % 202.99/203.29 (assume @p12 (forall @t12 (= (and @t10 @t30 @t29 @t37) (tptp.status @t2 @t1 tptp.wth)))) % 202.99/203.29 (assume @p13 (forall @t12 (= @t11 (tptp.status @t2 @t1 tptp.cax)))) % 202.99/203.29 (assume @p14 (forall @t12 (= (and @t11 @t6) (tptp.status @t2 @t1 tptp.sca)))) % 202.99/203.29 (assume @p15 (forall @t12 (= (and @t11 @t21) (tptp.status @t2 @t1 tptp.tca)))) % 202.99/203.29 (assume @p16 (forall @t12 (= (and @t11 @t6 (exists @t28 @t38)) (tptp.status @t2 @t1 tptp.wca)))) % 202.99/203.29 (assume @p17 (forall @t12 (= (exists @t9 (and @t8 (tptp.model @t7 @t39))) (tptp.status @t2 @t1 tptp.csa)))) % 202.99/203.29 (assume @p18 (forall @t12 (= (and (forall @t9 @t8) (forall @t5 @t40)) (tptp.status @t2 @t1 tptp.uns)))) % 202.99/203.29 (assume @p19 (forall @t12 (= (and @t15 (exists @t5 (and @t20 @t40))) (tptp.status @t2 @t1 tptp.noc)))) % 202.99/203.29 (assume @p20 @t50) % 202.99/203.29 (assume @p21 (forall @t49 (= (forall @t12 (=> @t45 @t44)) (tptp.isa @t42 @t41)))) % 202.99/203.29 (assume @p22 (forall @t49 (= (exists @t12 (and @t45 @t51)) (tptp.nota @t42 @t41)))) % 202.99/203.29 (assume @p23 (forall @t49 (= (forall @t12 (=> @t45 @t51)) (tptp.nevera @t42 @t41)))) % 202.99/203.29 (assume @p24 (forall @t49 (= (forall @t12 (xor @t45 @t44)) (tptp.xora @t42 @t41)))) % 202.99/203.29 (assume @p25 (forall @t56 (xor @t55 @t54))) % 202.99/203.29 (assume @p26 (forall @t56 (= @t55 (not @t54)))) % 202.99/203.29 (assume @p27 @t60) % 202.99/203.29 (assume @p28 @t67) % 202.99/203.29 (assume @p29 (exists @t59 (forall @t57 (not @t55)))) % 202.99/203.29 (assume @p30 (exists @t12 (and @t15 (exists @t5 (or @t34 (not @t4)))))) % 202.99/203.29 (assume @p31 (exists @t12 (and @t10 @t30 (exists @t28 (and @t25 @t26)) @t37))) % 202.99/203.29 (assume @p32 (exists (@list @t7 @t2 @t1) (and @t8 (not @t13) @t6))) % 202.99/203.29 (assume @p33 @t68) % 202.99/203.29 (assume @p34 true) % 202.99/203.29 ; WARNING: add trust step for TRUST % 202.99/203.29 ; trust TRUST PREPROCESS_SORT_INFER % 202.99/203.29 (step @p35 :rule trust :premises () :args ((= @t74 @t73))) % 202.99/203.29 (step @p36 :rule exists-elim :args ((= @t60 @t74))) % 202.99/203.29 (step @p37 :rule trans :premises (@p36 @p35)) % 202.99/203.29 (step @p38 :rule eq_resolve :premises (@p27 @p37)) % 202.99/203.29 (step @p39 :rule refl :args (@t76)) % 202.99/203.29 (step @p40 :rule bool-double-not-elim :args (@t72)) % 202.99/203.29 (step @p41 :rule nary_cong :premises (@p40 @p39) :args ((or (not @t73) @t76))) % 202.99/203.29 (step @p42 :rule bool-double-not-elim :args (@t76)) % 202.99/203.29 (step @p43 :rule refl :args (@t73)) % 202.99/203.29 (step @p44 :rule cong :premises (@p43 @p42) :args ((=> @t73 @t77))) % 202.99/203.29 (assume-push @p214 @t73) % 202.99/203.29 (step @p46 :rule skolemize :premises (@p38)) % 202.99/203.29 (step-pop @p215 :rule scope :premises (@p46)) % 202.99/203.29 (step @p47 :rule process_scope :premises (@p215) :args (@t77)) % 202.99/203.29 (step @p49 :rule eq_resolve :premises (@p47 @p44)) % 202.99/203.29 (step @p50 :rule implies_elim :premises (@p49)) % 202.99/203.29 (step @p51 :rule eq_resolve :premises (@p50 @p41)) % 202.99/203.29 (step @p52 :rule chain_m_resolution :premises (@p51 @p38) :args (@t76 @t78 (@list @t72))) % 202.99/203.29 (step @p53 :rule instantiate :premises (@p52) :args ((@list @t88))) % 202.99/203.29 (step @p54 :rule cnf_or_neg :args (@t90 1)) % 202.99/203.29 (step @p55 :rule chain_m_resolution :premises (@p54 @p53) :args (@t90 @t91 (@list @t89))) % 202.99/203.29 (step @p56 :rule refl :args (@t92)) % 202.99/203.29 (step @p57 :rule bool-double-not-elim :args (@t87)) % 202.99/203.29 (step @p58 :rule nary_cong :premises (@p57 @p56) :args ((or (not @t93) @t92))) % 202.99/203.29 (assume-push @p216 @t93) % 202.99/203.29 (step @p60 :rule skolemize :premises (@p216)) % 202.99/203.29 (step-pop @p217 :rule scope :premises (@p60)) % 202.99/203.29 (step @p61 :rule process_scope :premises (@p217) :args (@t92)) % 202.99/203.29 (step @p63 :rule implies_elim :premises (@p61)) % 202.99/203.29 (step @p64 :rule eq_resolve :premises (@p63 @p58)) % 202.99/203.29 (step @p65 :rule chain_m_resolution :premises (@p64 @p55) :args (@t87 @t91 (@list @t90))) % 202.99/203.29 (step @p66 :rule alpha_equiv :args (@t87 @t94 (@list @t95))) % 202.99/203.29 (step @p67 :rule equiv_elim1 :premises (@p66)) % 202.99/203.29 (step @p68 :rule reordering :premises (@p67) :args ((or @t97 @t93))) % 202.99/203.29 (step @p69 :rule chain_m_resolution :premises (@p68 @p65) :args (@t97 @t91 (@list @t87))) % 202.99/203.29 ; trust TRUST PREPROCESS_SORT_INFER % 202.99/203.29 (step @p70 :rule trust :premises () :args ((= (forall @t12 (= @t22 @t107)) (forall @t12 (= @t104 (and (not (forall @t101 (not (_ @t70 @t100 @t2)))) (forall @t96 (or (not (_ @t70 @t95 @t2)) (_ @t70 @t95 @t1))) (not (forall @t99 (or (not (_ @t70 @t98 @t1)) (_ @t70 @t98 @t2)))))))))) % 202.99/203.29 (step @p71 :rule eq-symm :args (@t107 @t22)) % 202.99/203.29 (step @p72 :rule refl :args (@t22)) % 202.99/203.29 (step @p73 :rule bool-double-not-elim :args (@t24)) % 202.99/203.29 (step @p74 :rule refl :args (@t38)) % 202.99/203.29 (step @p75 :rule nary_cong :premises (@p74 @p73) :args ((or @t38 (not @t25)))) % 202.99/203.29 (step @p76 :rule bool-and-de-morgan :args (@t26 @t25 true)) % 202.99/203.29 (step @p77 :rule trans :premises (@p76 @p75)) % 202.99/203.29 (step @p78 :rule cong :premises (@p77) :args (@t108)) % 202.99/203.29 (step @p79 :rule cong :premises (@p78) :args (@t109)) % 202.99/203.29 (step @p80 :rule exists-elim :args ((= @t29 @t109))) % 202.99/203.29 (step @p81 :rule trans :premises (@p80 @p79)) % 202.99/203.29 (step @p82 :rule bool-impl-elim :args (@t20 @t4)) % 202.99/203.29 (step @p83 :rule cong :premises (@p82) :args (@t30)) % 202.99/203.29 (step @p84 :rule exists-elim :args ((= @t10 @t106))) % 202.99/203.29 (step @p85 :rule nary_cong :premises (@p84 @p83 @p81) :args (@t31)) % 202.99/203.29 (step @p86 :rule cong :premises (@p85 @p72) :args (@t32)) % 202.99/203.29 (step @p87 :rule trans :premises (@p86 @p71)) % 202.99/203.29 (step @p88 :rule cong :premises (@p87) :args (@t33)) % 202.99/203.29 (step @p89 :rule trans :premises (@p88 @p70)) % 202.99/203.29 (step @p90 :rule eq_resolve :premises (@p8 @p89)) % 202.99/203.29 (step @p91 :rule instantiate :premises (@p90) :args (@t110)) % 202.99/203.29 (step @p92 :rule cnf_equiv_pos1 :args (@t117)) % 202.99/203.29 (step @p93 :rule reordering :premises (@p92) :args ((or @t115 @t119 @t118))) % 202.99/203.29 ; trust TRUST PREPROCESS_SORT_INFER % 202.99/203.29 (step @p94 :rule trust :premises () :args ((= (forall @t49 (= @t43 @t123)) (forall (@list @t121 @t120) (= (_ @t122 @t121 @t120) (not (forall @t12 (or (not (_ @t103 @t2 @t1 @t121)) (not (_ @t103 @t2 @t1 @t120)))))))))) % 202.99/203.29 (step @p95 :rule eq-symm :args (@t123 @t43)) % 202.99/203.29 (step @p96 :rule refl :args (@t43)) % 202.99/203.29 (step @p97 :rule bool-and-de-morgan :args (@t45 @t44 true)) % 202.99/203.29 (step @p98 :rule cong :premises (@p97) :args (@t124)) % 202.99/203.29 (step @p99 :rule cong :premises (@p98) :args (@t125)) % 202.99/203.29 (step @p100 :rule exists-elim :args ((= @t47 @t125))) % 202.99/203.29 (step @p101 :rule trans :premises (@p100 @p99)) % 202.99/203.29 (step @p102 :rule cong :premises (@p101 @p96) :args (@t48)) % 202.99/203.29 (step @p103 :rule trans :premises (@p102 @p95)) % 202.99/203.29 (step @p104 :rule cong :premises (@p103) :args (@t50)) % 202.99/203.29 (step @p105 :rule trans :premises (@p104 @p94)) % 202.99/203.29 (step @p106 :rule eq_resolve :premises (@p20 @p105)) % 202.99/203.29 (step @p107 :rule instantiate :premises (@p106) :args ((@list @t102 @t126))) % 202.99/203.29 ; trust TRUST PREPROCESS_SORT_INFER % 202.99/203.29 (step @p108 :rule trust :premises () :args ((= @t68 (not @t127)))) % 202.99/203.29 (step @p109 :rule eq_resolve :premises (@p33 @p108)) % 202.99/203.29 (step @p110 :rule bool-double-not-elim :args (@t129)) % 202.99/203.29 (step @p111 :rule refl :args (@t127)) % 202.99/203.29 (step @p112 :rule refl :args (@t132)) % 202.99/203.29 (step @p113 :rule nary_cong :premises (@p112 @p111 @p110) :args ((or @t132 @t127 (not @t130)))) % 202.99/203.29 (step @p114 :rule cnf_equiv_pos2 :args (@t131)) % 202.99/203.29 (step @p115 :rule eq_resolve :premises (@p114 @p113)) % 202.99/203.29 (step @p116 :rule reordering :premises (@p115) :args ((or @t127 @t129 @t132))) % 202.99/203.29 (step @p117 :rule chain_m_resolution :premises (@p116 @p109 @p107) :args (@t129 @t133 (@list @t127 @t131))) % 202.99/203.29 (step @p118 :rule instantiate :premises (@p117) :args (@t110)) % 202.99/203.29 (step @p119 :rule cnf_or_pos :args (@t136)) % 202.99/203.29 (step @p120 :rule reordering :premises (@p119) :args ((or @t119 @t135 (not @t136)))) % 202.99/203.29 (step @p121 :rule cnf_and_pos :args (@t115 1)) % 202.99/203.29 (step @p122 :rule reordering :premises (@p121) :args ((or @t97 @t137))) % 202.99/203.29 ; trust TRUST PREPROCESS_SORT_INFER % 202.99/203.29 (step @p123 :rule trust :premises () :args ((= (forall @t12 (= @t16 @t138)) (forall @t12 (= @t128 (forall @t86 (or (not (_ @t70 @t79 @t2)) (_ @t70 @t79 @t1)))))))) % 202.99/203.29 (step @p124 :rule eq-symm :args (@t138 @t16)) % 202.99/203.29 (step @p125 :rule refl :args (@t16)) % 202.99/203.29 (step @p126 :rule bool-impl-elim :args (@t8 @t13)) % 202.99/203.29 (step @p127 :rule cong :premises (@p126) :args (@t17)) % 202.99/203.29 (step @p128 :rule cong :premises (@p127 @p125) :args (@t18)) % 202.99/203.29 (step @p129 :rule trans :premises (@p128 @p124)) % 202.99/203.29 (step @p130 :rule cong :premises (@p129) :args (@t19)) % 202.99/203.29 (step @p131 :rule trans :premises (@p130 @p123)) % 202.99/203.29 (step @p132 :rule eq_resolve :premises (@p5 @p131)) % 202.99/203.29 (step @p133 :rule instantiate :premises (@p132) :args (@t110)) % 202.99/203.29 (step @p134 :rule cnf_equiv_pos2 :args (@t139)) % 202.99/203.29 (step @p135 :rule reordering :premises (@p134) :args ((or @t134 @t93 (not @t139)))) % 202.99/203.29 (step @p136 :rule equiv_elim2 :premises (@p66)) % 202.99/203.29 (step @p137 :rule chain_m_resolution :premises (@p136 @p135 @p133 @p122 @p120 @p118 @p93 @p91) :args (@t119 (@list true false false true false false false) (@list @t87 @t139 @t97 @t134 @t136 @t115 @t117))) % 202.99/203.29 (step @p138 :rule cnf_equiv_pos2 :args (@t117)) % 202.99/203.29 (step @p139 :rule reordering :premises (@p138) :args ((or @t116 @t137 @t118))) % 202.99/203.29 (step @p140 :rule chain_m_resolution :premises (@p139 @p137 @p91) :args (@t137 @t133 (@list @t116 @t117))) % 202.99/203.29 ; trust TRUST PREPROCESS_SORT_INFER % 202.99/203.29 (step @p141 :rule trust :premises () :args ((= (not @t145) (not @t83)))) % 202.99/203.29 (step @p142 :rule quant-merge-prenex :args ((= (forall @t59 @t146) @t145))) % 202.99/203.29 (step @p143 :rule alpha_equiv :args (@t147 (@list @t140) (@list @t3))) % 202.99/203.29 (step @p144 :rule alpha_equiv :args (@t148 (@list @t142) (@list @t7))) % 202.99/203.29 (step @p145 :rule nary_cong :premises (@p144 @p143) :args (@t149)) % 202.99/203.29 (step @p146 :rule quant-miniscope-or :args ((= @t146 @t149))) % 202.99/203.29 (step @p147 :rule trans :premises (@p146 @p145)) % 202.99/203.29 (step @p148 :rule symm :premises (@p147)) % 202.99/203.29 (step @p149 :rule cong :premises (@p148) :args ((forall @t59 (or @t151 @t150)))) % 202.99/203.29 (step @p150 :rule trans :premises (@p149 @p142)) % 202.99/203.29 (step @p151 :rule bool-double-not-elim :args (@t150)) % 202.99/203.29 (step @p152 :rule bool-double-not-elim :args (@t151)) % 202.99/203.29 (step @p153 :rule nary_cong :premises (@p152 @p151) :args ((or (not @t153) (not @t152)))) % 202.99/203.29 (step @p154 :rule bool-and-de-morgan :args (@t153 @t152 true)) % 202.99/203.29 (step @p155 :rule trans :premises (@p154 @p153)) % 202.99/203.29 (step @p156 :rule cong :premises (@p155) :args (@t155)) % 202.99/203.29 (step @p157 :rule trans :premises (@p156 @p150)) % 202.99/203.29 (step @p158 :rule cong :premises (@p157) :args (@t156)) % 202.99/203.29 (step @p159 :rule exists-elim :args ((= (exists @t59 @t154) @t156))) % 202.99/203.29 (step @p160 :rule trans :premises (@p159 @p158)) % 202.99/203.29 (step @p161 :rule bool-double-not-elim :args (@t61)) % 202.99/203.29 (step @p162 :rule cong :premises (@p161) :args (@t157)) % 202.99/203.29 (step @p163 :rule cong :premises (@p162) :args (@t158)) % 202.99/203.29 (step @p164 :rule exists-elim :args ((= @t63 @t158))) % 202.99/203.29 (step @p165 :rule trans :premises (@p164 @p163)) % 202.99/203.29 (step @p166 :rule exists-elim :args ((= @t65 @t153))) % 202.99/203.29 (step @p167 :rule nary_cong :premises (@p166 @p165) :args (@t66)) % 202.99/203.29 (step @p168 :rule cong :premises (@p167) :args (@t67)) % 202.99/203.29 (step @p169 :rule trans :premises (@p168 @p160)) % 202.99/203.29 (step @p170 :rule trans :premises (@p169 @p141)) % 202.99/203.29 (step @p171 :rule eq_resolve :premises (@p28 @p170)) % 202.99/203.29 (step @p172 :rule skolemize :premises (@p171)) % 202.99/203.29 (step @p173 :rule bool-double-not-elim :args (@t160)) % 202.99/203.29 (step @p174 :rule refl :args (@t164)) % 202.99/203.29 (step @p175 :rule nary_cong :premises (@p174 @p173) :args ((or @t164 (not @t163)))) % 202.99/203.29 (step @p176 :rule cnf_or_neg :args (@t164 0)) % 202.99/203.29 (step @p177 :rule eq_resolve :premises (@p176 @p175)) % 202.99/203.29 (step @p178 :rule reordering :premises (@p177) :args ((or @t160 @t164))) % 202.99/203.29 (step @p179 :rule chain_m_resolution :premises (@p178 @p172) :args (@t160 @t78 @t165)) % 202.99/203.29 (assume-push @p218 @t167) % 202.99/203.29 (step @p181 :rule instantiate :premises (@p218) :args ((@list @t159))) % 202.99/203.29 (step-pop @p219 :rule scope :premises (@p181)) % 202.99/203.29 (step @p182 :rule process_scope :premises (@p219) :args (@t163)) % 202.99/203.29 (step @p184 :rule implies_elim :premises (@p182)) % 202.99/203.29 (step @p185 :rule reordering :premises (@p184) :args ((or @t163 @t168))) % 202.99/203.29 (step @p186 :rule chain_m_resolution :premises (@p185 @p179) :args (@t168 @t91 (@list @t160))) % 202.99/203.29 (step @p187 :rule alpha_equiv :args (@t167 (@list @t166) (@list @t100))) % 202.99/203.29 (step @p188 :rule equiv_elim2 :premises (@p187)) % 202.99/203.29 (step @p189 :rule chain_m_resolution :premises (@p188 @p186) :args (@t114 @t78 (@list @t167))) % 202.99/203.29 (step @p190 :rule bool-double-not-elim :args (@t111)) % 202.99/203.29 (step @p191 :rule refl :args (@t169)) % 202.99/203.29 (step @p192 :rule bool-double-not-elim :args (@t113)) % 202.99/203.29 (step @p193 :rule refl :args (@t115)) % 202.99/203.29 (step @p194 :rule nary_cong :premises (@p193 @p192 @p191 @p190) :args ((or @t115 (not @t114) @t169 (not @t112)))) % 202.99/203.29 (step @p195 :rule cnf_and_neg :args (@t115)) % 202.99/203.29 (step @p196 :rule eq_resolve :premises (@p195 @p194)) % 202.99/203.29 (step @p197 :rule reordering :premises (@p196) :args ((or @t113 @t111 @t115 @t169))) % 202.99/203.29 (step @p198 :rule chain_m_resolution :premises (@p197 @p189 @p140 @p69) :args (@t111 (@list true true false) (@list @t113 @t115 @t97))) % 202.99/203.29 (step @p199 :rule alpha_equiv :args (@t170 @t94 (@list @t98))) % 202.99/203.29 (step @p200 :rule equiv_elim2 :premises (@p199)) % 202.99/203.29 (step @p201 :rule chain_m_resolution :premises (@p200 @p198) :args (@t170 @t91 (@list @t111))) % 202.99/203.29 (step @p202 :rule instantiate :premises (@p52) :args (@t171)) % 202.99/203.29 (step @p203 :rule cnf_or_neg :args (@t164 1)) % 202.99/203.29 (step @p204 :rule chain_m_resolution :premises (@p203 @p172) :args ((not @t162) @t78 @t165)) % 202.99/203.29 (step @p205 :rule cnf_or_pos :args (@t174)) % 202.99/203.29 (step @p206 :rule reordering :premises (@p205) :args ((or @t162 @t173 @t175))) % 202.99/203.29 (step @p207 :rule chain_m_resolution :premises (@p206 @p204 @p202) :args (@t175 @t133 (@list @t162 @t172))) % 202.99/203.29 (assume-push @p220 @t170) % 202.99/203.29 (step @p209 :rule instantiate :premises (@p220) :args (@t171)) % 202.99/203.29 (step-pop @p221 :rule scope :premises (@p209)) % 202.99/203.29 (step @p210 :rule process_scope :premises (@p221) :args (@t174)) % 202.99/203.29 (step @p212 :rule implies_elim :premises (@p210)) % 202.99/203.29 (step @p213 false :rule chain_m_resolution :premises (@p212 @p207 @p201) :args (false @t133 (@list @t174 @t170))) % 202.99/203.29 ) % 202.99/203.29 % SZS output end Proof % 202.99/203.29 % cvc5 exiting %------------------------------------------------------------------------------