TSTP Solution File: KRS003_1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : KRS003_1 : TPTP v8.2.0. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n024.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 May 29 17:17:10 EDT 2024
% Result : Theorem 0.16s 0.52s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : KRS003_1 : TPTP v8.2.0. Released v5.0.0.
% 0.10/0.12 % Command : do_cvc5 %s %d
% 0.11/0.32 % Computer : n024.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sun May 26 08:49:39 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.16/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.16/0.52 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.16/0.52 % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.S0R3GuT1rn/cvc5---1.0.5_21603.smt2
% 0.16/0.52 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.S0R3GuT1rn/cvc5---1.0.5_21603.smt2
% 0.16/0.52 (assume a0 (forall ((X1 tptp.unreal)) (=> (tptp.c X1) (tptp.s2least X1))))
% 0.16/0.52 (assume a1 (forall ((X1 tptp.unreal)) (=> (tptp.s2least X1) (tptp.c X1))))
% 0.16/0.52 (assume a2 (forall ((X1 tptp.unreal)) (not (and (tptp.s2least X1) (tptp.equalish (tptp.u1r2 X1) (tptp.u1r1 X1))))))
% 0.16/0.52 (assume a3 (forall ((X1 tptp.unreal)) (=> (tptp.s2least X1) (tptp.s X1 (tptp.u1r1 X1)))))
% 0.16/0.52 (assume a4 (forall ((X1 tptp.unreal)) (=> (tptp.s2least X1) (tptp.s X1 (tptp.u1r2 X1)))))
% 0.16/0.52 (assume a5 (forall ((X2 tptp.real) (X3 tptp.real) (X1 tptp.unreal)) (=> (and (tptp.s X1 X3) (tptp.s X1 X2)) (or (tptp.s2least X1) (tptp.equalish X3 X2)))))
% 0.16/0.52 (assume a6 (forall ((X1 tptp.unreal)) (=> (tptp.d X1) (tptp.s1most X1))))
% 0.16/0.52 (assume a7 (forall ((X1 tptp.unreal)) (=> (tptp.s1most X1) (tptp.d X1))))
% 0.16/0.52 (assume a8 (forall ((X2 tptp.real) (X3 tptp.real) (X1 tptp.unreal)) (=> (and (tptp.s1most X1) (tptp.s X1 X3) (tptp.s X1 X2)) (tptp.equalish X3 X2))))
% 0.16/0.52 (assume a9 (forall ((X1 tptp.unreal)) (=> (tptp.equalish (tptp.u3r2 X1) (tptp.u3r1 X1)) (tptp.s1most X1))))
% 0.16/0.52 (assume a10 (forall ((X1 tptp.unreal)) (or (tptp.s1most X1) (tptp.s X1 (tptp.u3r1 X1)))))
% 0.16/0.52 (assume a11 (forall ((X1 tptp.unreal)) (or (tptp.s1most X1) (tptp.s X1 (tptp.u3r2 X1)))))
% 0.16/0.52 (assume a12 (forall ((X1 tptp.unreal)) (=> (tptp.e X1) (tptp.c X1))))
% 0.16/0.52 (assume a13 (forall ((X1 tptp.unreal)) (=> (tptp.f X1) (tptp.d X1))))
% 0.16/0.52 (assume a14 (not (or (not (tptp.e tptp.exist)) (not (tptp.f tptp.exist)))))
% 0.16/0.52 (assume a15 true)
% 0.16/0.52 (step t1 (cl (=> (forall ((X2 tptp.real) (X3 tptp.real) (X1 tptp.unreal)) (or (not (tptp.s1most X1)) (not (tptp.s X1 X3)) (not (tptp.s X1 X2)) (tptp.equalish X3 X2))) (or (not (tptp.s1most tptp.exist)) (not (tptp.s tptp.exist (tptp.u1r2 tptp.exist))) (not (tptp.s tptp.exist (tptp.u1r1 tptp.exist))) (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist)))) (forall ((X2 tptp.real) (X3 tptp.real) (X1 tptp.unreal)) (or (not (tptp.s1most X1)) (not (tptp.s X1 X3)) (not (tptp.s X1 X2)) (tptp.equalish X3 X2)))) :rule implies_neg1)
% 0.16/0.52 (anchor :step t2)
% 0.16/0.52 (assume t2.a0 (forall ((X2 tptp.real) (X3 tptp.real) (X1 tptp.unreal)) (or (not (tptp.s1most X1)) (not (tptp.s X1 X3)) (not (tptp.s X1 X2)) (tptp.equalish X3 X2))))
% 0.16/0.52 (step t2.t1 (cl (or (not (forall ((X2 tptp.real) (X3 tptp.real) (X1 tptp.unreal)) (or (not (tptp.s1most X1)) (not (tptp.s X1 X3)) (not (tptp.s X1 X2)) (tptp.equalish X3 X2)))) (or (not (tptp.s1most tptp.exist)) (not (tptp.s tptp.exist (tptp.u1r2 tptp.exist))) (not (tptp.s tptp.exist (tptp.u1r1 tptp.exist))) (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist))))) :rule forall_inst :args ((:= X2 (tptp.u1r1 tptp.exist)) (:= X3 (tptp.u1r2 tptp.exist)) (:= X1 tptp.exist)))
% 0.16/0.52 (step t2.t2 (cl (not (forall ((X2 tptp.real) (X3 tptp.real) (X1 tptp.unreal)) (or (not (tptp.s1most X1)) (not (tptp.s X1 X3)) (not (tptp.s X1 X2)) (tptp.equalish X3 X2)))) (or (not (tptp.s1most tptp.exist)) (not (tptp.s tptp.exist (tptp.u1r2 tptp.exist))) (not (tptp.s tptp.exist (tptp.u1r1 tptp.exist))) (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist)))) :rule or :premises (t2.t1))
% 0.16/0.52 (step t2.t3 (cl (or (not (tptp.s1most tptp.exist)) (not (tptp.s tptp.exist (tptp.u1r2 tptp.exist))) (not (tptp.s tptp.exist (tptp.u1r1 tptp.exist))) (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist)))) :rule resolution :premises (t2.t2 t2.a0))
% 0.16/0.52 (step t2 (cl (not (forall ((X2 tptp.real) (X3 tptp.real) (X1 tptp.unreal)) (or (not (tptp.s1most X1)) (not (tptp.s X1 X3)) (not (tptp.s X1 X2)) (tptp.equalish X3 X2)))) (or (not (tptp.s1most tptp.exist)) (not (tptp.s tptp.exist (tptp.u1r2 tptp.exist))) (not (tptp.s tptp.exist (tptp.u1r1 tptp.exist))) (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist)))) :rule subproof :discharge (t2.a0))
% 0.16/0.52 (step t3 (cl (=> (forall ((X2 tptp.real) (X3 tptp.real) (X1 tptp.unreal)) (or (not (tptp.s1most X1)) (not (tptp.s X1 X3)) (not (tptp.s X1 X2)) (tptp.equalish X3 X2))) (or (not (tptp.s1most tptp.exist)) (not (tptp.s tptp.exist (tptp.u1r2 tptp.exist))) (not (tptp.s tptp.exist (tptp.u1r1 tptp.exist))) (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist)))) (or (not (tptp.s1most tptp.exist)) (not (tptp.s tptp.exist (tptp.u1r2 tptp.exist))) (not (tptp.s tptp.exist (tptp.u1r1 tptp.exist))) (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist)))) :rule resolution :premises (t1 t2))
% 0.16/0.52 (step t4 (cl (=> (forall ((X2 tptp.real) (X3 tptp.real) (X1 tptp.unreal)) (or (not (tptp.s1most X1)) (not (tptp.s X1 X3)) (not (tptp.s X1 X2)) (tptp.equalish X3 X2))) (or (not (tptp.s1most tptp.exist)) (not (tptp.s tptp.exist (tptp.u1r2 tptp.exist))) (not (tptp.s tptp.exist (tptp.u1r1 tptp.exist))) (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist)))) (not (or (not (tptp.s1most tptp.exist)) (not (tptp.s tptp.exist (tptp.u1r2 tptp.exist))) (not (tptp.s tptp.exist (tptp.u1r1 tptp.exist))) (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist))))) :rule implies_neg2)
% 0.16/0.52 (step t5 (cl (=> (forall ((X2 tptp.real) (X3 tptp.real) (X1 tptp.unreal)) (or (not (tptp.s1most X1)) (not (tptp.s X1 X3)) (not (tptp.s X1 X2)) (tptp.equalish X3 X2))) (or (not (tptp.s1most tptp.exist)) (not (tptp.s tptp.exist (tptp.u1r2 tptp.exist))) (not (tptp.s tptp.exist (tptp.u1r1 tptp.exist))) (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist)))) (=> (forall ((X2 tptp.real) (X3 tptp.real) (X1 tptp.unreal)) (or (not (tptp.s1most X1)) (not (tptp.s X1 X3)) (not (tptp.s X1 X2)) (tptp.equalish X3 X2))) (or (not (tptp.s1most tptp.exist)) (not (tptp.s tptp.exist (tptp.u1r2 tptp.exist))) (not (tptp.s tptp.exist (tptp.u1r1 tptp.exist))) (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist))))) :rule resolution :premises (t3 t4))
% 0.16/0.52 (step t6 (cl (=> (forall ((X2 tptp.real) (X3 tptp.real) (X1 tptp.unreal)) (or (not (tptp.s1most X1)) (not (tptp.s X1 X3)) (not (tptp.s X1 X2)) (tptp.equalish X3 X2))) (or (not (tptp.s1most tptp.exist)) (not (tptp.s tptp.exist (tptp.u1r2 tptp.exist))) (not (tptp.s tptp.exist (tptp.u1r1 tptp.exist))) (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist))))) :rule contraction :premises (t5))
% 0.16/0.52 (step t7 (cl (not (forall ((X2 tptp.real) (X3 tptp.real) (X1 tptp.unreal)) (or (not (tptp.s1most X1)) (not (tptp.s X1 X3)) (not (tptp.s X1 X2)) (tptp.equalish X3 X2)))) (or (not (tptp.s1most tptp.exist)) (not (tptp.s tptp.exist (tptp.u1r2 tptp.exist))) (not (tptp.s tptp.exist (tptp.u1r1 tptp.exist))) (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist)))) :rule implies :premises (t6))
% 0.16/0.52 (step t8 (cl (not (or (not (tptp.s1most tptp.exist)) (not (tptp.s tptp.exist (tptp.u1r2 tptp.exist))) (not (tptp.s tptp.exist (tptp.u1r1 tptp.exist))) (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist)))) (not (tptp.s1most tptp.exist)) (not (tptp.s tptp.exist (tptp.u1r2 tptp.exist))) (not (tptp.s tptp.exist (tptp.u1r1 tptp.exist))) (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist))) :rule or_pos)
% 0.16/0.52 (step t9 (cl (not (tptp.s1most tptp.exist)) (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist)) (not (tptp.s tptp.exist (tptp.u1r1 tptp.exist))) (not (tptp.s tptp.exist (tptp.u1r2 tptp.exist))) (not (or (not (tptp.s1most tptp.exist)) (not (tptp.s tptp.exist (tptp.u1r2 tptp.exist))) (not (tptp.s tptp.exist (tptp.u1r1 tptp.exist))) (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist))))) :rule reordering :premises (t8))
% 0.16/0.52 (step t10 (cl (not (or (not (tptp.d tptp.exist)) (tptp.s1most tptp.exist))) (not (tptp.d tptp.exist)) (tptp.s1most tptp.exist)) :rule or_pos)
% 0.16/0.52 (step t11 (cl (not (tptp.d tptp.exist)) (tptp.s1most tptp.exist) (not (or (not (tptp.d tptp.exist)) (tptp.s1most tptp.exist)))) :rule reordering :premises (t10))
% 0.16/0.52 (step t12 (cl (not (or (not (tptp.f tptp.exist)) (tptp.d tptp.exist))) (not (tptp.f tptp.exist)) (tptp.d tptp.exist)) :rule or_pos)
% 0.16/0.52 (step t13 (cl (not (tptp.f tptp.exist)) (tptp.d tptp.exist) (not (or (not (tptp.f tptp.exist)) (tptp.d tptp.exist)))) :rule reordering :premises (t12))
% 0.16/0.52 (step t14 (cl (not (not (not (tptp.f tptp.exist)))) (tptp.f tptp.exist)) :rule not_not)
% 0.16/0.52 (step t15 (cl (not (not (tptp.f tptp.exist)))) :rule not_or :premises (a14))
% 0.16/0.52 (step t16 (cl (tptp.f tptp.exist)) :rule resolution :premises (t14 t15))
% 0.16/0.52 (step t17 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.f X1)) (tptp.d X1))) (or (not (tptp.f tptp.exist)) (tptp.d tptp.exist))) (forall ((X1 tptp.unreal)) (or (not (tptp.f X1)) (tptp.d X1)))) :rule implies_neg1)
% 0.16/0.52 (anchor :step t18)
% 0.16/0.52 (assume t18.a0 (forall ((X1 tptp.unreal)) (or (not (tptp.f X1)) (tptp.d X1))))
% 0.16/0.52 (step t18.t1 (cl (or (not (forall ((X1 tptp.unreal)) (or (not (tptp.f X1)) (tptp.d X1)))) (or (not (tptp.f tptp.exist)) (tptp.d tptp.exist)))) :rule forall_inst :args ((:= X1 tptp.exist)))
% 0.16/0.52 (step t18.t2 (cl (not (forall ((X1 tptp.unreal)) (or (not (tptp.f X1)) (tptp.d X1)))) (or (not (tptp.f tptp.exist)) (tptp.d tptp.exist))) :rule or :premises (t18.t1))
% 0.16/0.52 (step t18.t3 (cl (or (not (tptp.f tptp.exist)) (tptp.d tptp.exist))) :rule resolution :premises (t18.t2 t18.a0))
% 0.16/0.52 (step t18 (cl (not (forall ((X1 tptp.unreal)) (or (not (tptp.f X1)) (tptp.d X1)))) (or (not (tptp.f tptp.exist)) (tptp.d tptp.exist))) :rule subproof :discharge (t18.a0))
% 0.16/0.52 (step t19 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.f X1)) (tptp.d X1))) (or (not (tptp.f tptp.exist)) (tptp.d tptp.exist))) (or (not (tptp.f tptp.exist)) (tptp.d tptp.exist))) :rule resolution :premises (t17 t18))
% 0.16/0.52 (step t20 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.f X1)) (tptp.d X1))) (or (not (tptp.f tptp.exist)) (tptp.d tptp.exist))) (not (or (not (tptp.f tptp.exist)) (tptp.d tptp.exist)))) :rule implies_neg2)
% 0.16/0.52 (step t21 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.f X1)) (tptp.d X1))) (or (not (tptp.f tptp.exist)) (tptp.d tptp.exist))) (=> (forall ((X1 tptp.unreal)) (or (not (tptp.f X1)) (tptp.d X1))) (or (not (tptp.f tptp.exist)) (tptp.d tptp.exist)))) :rule resolution :premises (t19 t20))
% 0.16/0.52 (step t22 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.f X1)) (tptp.d X1))) (or (not (tptp.f tptp.exist)) (tptp.d tptp.exist)))) :rule contraction :premises (t21))
% 0.16/0.52 (step t23 (cl (not (forall ((X1 tptp.unreal)) (or (not (tptp.f X1)) (tptp.d X1)))) (or (not (tptp.f tptp.exist)) (tptp.d tptp.exist))) :rule implies :premises (t22))
% 0.16/0.52 (step t24 (cl (not (= (forall ((X1 tptp.unreal)) (=> (tptp.f X1) (tptp.d X1))) (forall ((X1 tptp.unreal)) (or (not (tptp.f X1)) (tptp.d X1))))) (not (forall ((X1 tptp.unreal)) (=> (tptp.f X1) (tptp.d X1)))) (forall ((X1 tptp.unreal)) (or (not (tptp.f X1)) (tptp.d X1)))) :rule equiv_pos2)
% 0.16/0.52 (step t25 (cl (= (forall ((X1 tptp.unreal)) (=> (tptp.f X1) (tptp.d X1))) (forall ((X1 tptp.unreal)) (or (not (tptp.f X1)) (tptp.d X1))))) :rule all_simplify)
% 0.16/0.52 (step t26 (cl (forall ((X1 tptp.unreal)) (or (not (tptp.f X1)) (tptp.d X1)))) :rule resolution :premises (t24 t25 a13))
% 0.16/0.52 (step t27 (cl (or (not (tptp.f tptp.exist)) (tptp.d tptp.exist))) :rule resolution :premises (t23 t26))
% 0.16/0.52 (step t28 (cl (tptp.d tptp.exist)) :rule resolution :premises (t13 t16 t27))
% 0.16/0.52 (step t29 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.d X1)) (tptp.s1most X1))) (or (not (tptp.d tptp.exist)) (tptp.s1most tptp.exist))) (forall ((X1 tptp.unreal)) (or (not (tptp.d X1)) (tptp.s1most X1)))) :rule implies_neg1)
% 0.16/0.52 (anchor :step t30)
% 0.16/0.52 (assume t30.a0 (forall ((X1 tptp.unreal)) (or (not (tptp.d X1)) (tptp.s1most X1))))
% 0.16/0.52 (step t30.t1 (cl (or (not (forall ((X1 tptp.unreal)) (or (not (tptp.d X1)) (tptp.s1most X1)))) (or (not (tptp.d tptp.exist)) (tptp.s1most tptp.exist)))) :rule forall_inst :args ((:= X1 tptp.exist)))
% 0.16/0.52 (step t30.t2 (cl (not (forall ((X1 tptp.unreal)) (or (not (tptp.d X1)) (tptp.s1most X1)))) (or (not (tptp.d tptp.exist)) (tptp.s1most tptp.exist))) :rule or :premises (t30.t1))
% 0.16/0.52 (step t30.t3 (cl (or (not (tptp.d tptp.exist)) (tptp.s1most tptp.exist))) :rule resolution :premises (t30.t2 t30.a0))
% 0.16/0.52 (step t30 (cl (not (forall ((X1 tptp.unreal)) (or (not (tptp.d X1)) (tptp.s1most X1)))) (or (not (tptp.d tptp.exist)) (tptp.s1most tptp.exist))) :rule subproof :discharge (t30.a0))
% 0.16/0.52 (step t31 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.d X1)) (tptp.s1most X1))) (or (not (tptp.d tptp.exist)) (tptp.s1most tptp.exist))) (or (not (tptp.d tptp.exist)) (tptp.s1most tptp.exist))) :rule resolution :premises (t29 t30))
% 0.16/0.52 (step t32 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.d X1)) (tptp.s1most X1))) (or (not (tptp.d tptp.exist)) (tptp.s1most tptp.exist))) (not (or (not (tptp.d tptp.exist)) (tptp.s1most tptp.exist)))) :rule implies_neg2)
% 0.16/0.52 (step t33 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.d X1)) (tptp.s1most X1))) (or (not (tptp.d tptp.exist)) (tptp.s1most tptp.exist))) (=> (forall ((X1 tptp.unreal)) (or (not (tptp.d X1)) (tptp.s1most X1))) (or (not (tptp.d tptp.exist)) (tptp.s1most tptp.exist)))) :rule resolution :premises (t31 t32))
% 0.16/0.52 (step t34 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.d X1)) (tptp.s1most X1))) (or (not (tptp.d tptp.exist)) (tptp.s1most tptp.exist)))) :rule contraction :premises (t33))
% 0.16/0.52 (step t35 (cl (not (forall ((X1 tptp.unreal)) (or (not (tptp.d X1)) (tptp.s1most X1)))) (or (not (tptp.d tptp.exist)) (tptp.s1most tptp.exist))) :rule implies :premises (t34))
% 0.16/0.52 (step t36 (cl (not (= (forall ((X1 tptp.unreal)) (=> (tptp.d X1) (tptp.s1most X1))) (forall ((X1 tptp.unreal)) (or (not (tptp.d X1)) (tptp.s1most X1))))) (not (forall ((X1 tptp.unreal)) (=> (tptp.d X1) (tptp.s1most X1)))) (forall ((X1 tptp.unreal)) (or (not (tptp.d X1)) (tptp.s1most X1)))) :rule equiv_pos2)
% 0.16/0.52 (step t37 (cl (= (forall ((X1 tptp.unreal)) (=> (tptp.d X1) (tptp.s1most X1))) (forall ((X1 tptp.unreal)) (or (not (tptp.d X1)) (tptp.s1most X1))))) :rule all_simplify)
% 0.16/0.52 (step t38 (cl (forall ((X1 tptp.unreal)) (or (not (tptp.d X1)) (tptp.s1most X1)))) :rule resolution :premises (t36 t37 a6))
% 0.16/0.52 (step t39 (cl (or (not (tptp.d tptp.exist)) (tptp.s1most tptp.exist))) :rule resolution :premises (t35 t38))
% 0.16/0.52 (step t40 (cl (tptp.s1most tptp.exist)) :rule resolution :premises (t11 t28 t39))
% 0.16/0.52 (step t41 (cl (not (or (not (tptp.s2least tptp.exist)) (not (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist))))) (not (tptp.s2least tptp.exist)) (not (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist)))) :rule or_pos)
% 0.16/0.52 (step t42 (cl (not (tptp.s2least tptp.exist)) (not (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist))) (not (or (not (tptp.s2least tptp.exist)) (not (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist)))))) :rule reordering :premises (t41))
% 0.16/0.52 (step t43 (cl (not (or (not (tptp.c tptp.exist)) (tptp.s2least tptp.exist))) (not (tptp.c tptp.exist)) (tptp.s2least tptp.exist)) :rule or_pos)
% 0.16/0.52 (step t44 (cl (not (tptp.c tptp.exist)) (tptp.s2least tptp.exist) (not (or (not (tptp.c tptp.exist)) (tptp.s2least tptp.exist)))) :rule reordering :premises (t43))
% 0.16/0.52 (step t45 (cl (not (or (not (tptp.e tptp.exist)) (tptp.c tptp.exist))) (not (tptp.e tptp.exist)) (tptp.c tptp.exist)) :rule or_pos)
% 0.16/0.52 (step t46 (cl (not (tptp.e tptp.exist)) (tptp.c tptp.exist) (not (or (not (tptp.e tptp.exist)) (tptp.c tptp.exist)))) :rule reordering :premises (t45))
% 0.16/0.52 (step t47 (cl (not (not (not (tptp.e tptp.exist)))) (tptp.e tptp.exist)) :rule not_not)
% 0.16/0.52 (step t48 (cl (not (not (tptp.e tptp.exist)))) :rule not_or :premises (a14))
% 0.16/0.52 (step t49 (cl (tptp.e tptp.exist)) :rule resolution :premises (t47 t48))
% 0.16/0.52 (step t50 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.e X1)) (tptp.c X1))) (or (not (tptp.e tptp.exist)) (tptp.c tptp.exist))) (forall ((X1 tptp.unreal)) (or (not (tptp.e X1)) (tptp.c X1)))) :rule implies_neg1)
% 0.16/0.52 (anchor :step t51)
% 0.16/0.52 (assume t51.a0 (forall ((X1 tptp.unreal)) (or (not (tptp.e X1)) (tptp.c X1))))
% 0.16/0.52 (step t51.t1 (cl (or (not (forall ((X1 tptp.unreal)) (or (not (tptp.e X1)) (tptp.c X1)))) (or (not (tptp.e tptp.exist)) (tptp.c tptp.exist)))) :rule forall_inst :args ((:= X1 tptp.exist)))
% 0.16/0.52 (step t51.t2 (cl (not (forall ((X1 tptp.unreal)) (or (not (tptp.e X1)) (tptp.c X1)))) (or (not (tptp.e tptp.exist)) (tptp.c tptp.exist))) :rule or :premises (t51.t1))
% 0.16/0.52 (step t51.t3 (cl (or (not (tptp.e tptp.exist)) (tptp.c tptp.exist))) :rule resolution :premises (t51.t2 t51.a0))
% 0.16/0.52 (step t51 (cl (not (forall ((X1 tptp.unreal)) (or (not (tptp.e X1)) (tptp.c X1)))) (or (not (tptp.e tptp.exist)) (tptp.c tptp.exist))) :rule subproof :discharge (t51.a0))
% 0.16/0.52 (step t52 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.e X1)) (tptp.c X1))) (or (not (tptp.e tptp.exist)) (tptp.c tptp.exist))) (or (not (tptp.e tptp.exist)) (tptp.c tptp.exist))) :rule resolution :premises (t50 t51))
% 0.16/0.52 (step t53 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.e X1)) (tptp.c X1))) (or (not (tptp.e tptp.exist)) (tptp.c tptp.exist))) (not (or (not (tptp.e tptp.exist)) (tptp.c tptp.exist)))) :rule implies_neg2)
% 0.16/0.52 (step t54 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.e X1)) (tptp.c X1))) (or (not (tptp.e tptp.exist)) (tptp.c tptp.exist))) (=> (forall ((X1 tptp.unreal)) (or (not (tptp.e X1)) (tptp.c X1))) (or (not (tptp.e tptp.exist)) (tptp.c tptp.exist)))) :rule resolution :premises (t52 t53))
% 0.16/0.52 (step t55 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.e X1)) (tptp.c X1))) (or (not (tptp.e tptp.exist)) (tptp.c tptp.exist)))) :rule contraction :premises (t54))
% 0.16/0.52 (step t56 (cl (not (forall ((X1 tptp.unreal)) (or (not (tptp.e X1)) (tptp.c X1)))) (or (not (tptp.e tptp.exist)) (tptp.c tptp.exist))) :rule implies :premises (t55))
% 0.16/0.52 (step t57 (cl (not (= (forall ((X1 tptp.unreal)) (=> (tptp.e X1) (tptp.c X1))) (forall ((X1 tptp.unreal)) (or (not (tptp.e X1)) (tptp.c X1))))) (not (forall ((X1 tptp.unreal)) (=> (tptp.e X1) (tptp.c X1)))) (forall ((X1 tptp.unreal)) (or (not (tptp.e X1)) (tptp.c X1)))) :rule equiv_pos2)
% 0.16/0.52 (step t58 (cl (= (forall ((X1 tptp.unreal)) (=> (tptp.e X1) (tptp.c X1))) (forall ((X1 tptp.unreal)) (or (not (tptp.e X1)) (tptp.c X1))))) :rule all_simplify)
% 0.16/0.52 (step t59 (cl (forall ((X1 tptp.unreal)) (or (not (tptp.e X1)) (tptp.c X1)))) :rule resolution :premises (t57 t58 a12))
% 0.16/0.52 (step t60 (cl (or (not (tptp.e tptp.exist)) (tptp.c tptp.exist))) :rule resolution :premises (t56 t59))
% 0.16/0.52 (step t61 (cl (tptp.c tptp.exist)) :rule resolution :premises (t46 t49 t60))
% 0.16/0.52 (step t62 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.c X1)) (tptp.s2least X1))) (or (not (tptp.c tptp.exist)) (tptp.s2least tptp.exist))) (forall ((X1 tptp.unreal)) (or (not (tptp.c X1)) (tptp.s2least X1)))) :rule implies_neg1)
% 0.16/0.52 (anchor :step t63)
% 0.16/0.52 (assume t63.a0 (forall ((X1 tptp.unreal)) (or (not (tptp.c X1)) (tptp.s2least X1))))
% 0.16/0.52 (step t63.t1 (cl (or (not (forall ((X1 tptp.unreal)) (or (not (tptp.c X1)) (tptp.s2least X1)))) (or (not (tptp.c tptp.exist)) (tptp.s2least tptp.exist)))) :rule forall_inst :args ((:= X1 tptp.exist)))
% 0.16/0.52 (step t63.t2 (cl (not (forall ((X1 tptp.unreal)) (or (not (tptp.c X1)) (tptp.s2least X1)))) (or (not (tptp.c tptp.exist)) (tptp.s2least tptp.exist))) :rule or :premises (t63.t1))
% 0.16/0.52 (step t63.t3 (cl (or (not (tptp.c tptp.exist)) (tptp.s2least tptp.exist))) :rule resolution :premises (t63.t2 t63.a0))
% 0.16/0.52 (step t63 (cl (not (forall ((X1 tptp.unreal)) (or (not (tptp.c X1)) (tptp.s2least X1)))) (or (not (tptp.c tptp.exist)) (tptp.s2least tptp.exist))) :rule subproof :discharge (t63.a0))
% 0.16/0.52 (step t64 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.c X1)) (tptp.s2least X1))) (or (not (tptp.c tptp.exist)) (tptp.s2least tptp.exist))) (or (not (tptp.c tptp.exist)) (tptp.s2least tptp.exist))) :rule resolution :premises (t62 t63))
% 0.16/0.52 (step t65 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.c X1)) (tptp.s2least X1))) (or (not (tptp.c tptp.exist)) (tptp.s2least tptp.exist))) (not (or (not (tptp.c tptp.exist)) (tptp.s2least tptp.exist)))) :rule implies_neg2)
% 0.16/0.52 (step t66 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.c X1)) (tptp.s2least X1))) (or (not (tptp.c tptp.exist)) (tptp.s2least tptp.exist))) (=> (forall ((X1 tptp.unreal)) (or (not (tptp.c X1)) (tptp.s2least X1))) (or (not (tptp.c tptp.exist)) (tptp.s2least tptp.exist)))) :rule resolution :premises (t64 t65))
% 0.16/0.52 (step t67 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.c X1)) (tptp.s2least X1))) (or (not (tptp.c tptp.exist)) (tptp.s2least tptp.exist)))) :rule contraction :premises (t66))
% 0.16/0.52 (step t68 (cl (not (forall ((X1 tptp.unreal)) (or (not (tptp.c X1)) (tptp.s2least X1)))) (or (not (tptp.c tptp.exist)) (tptp.s2least tptp.exist))) :rule implies :premises (t67))
% 0.16/0.52 (step t69 (cl (not (= (forall ((X1 tptp.unreal)) (=> (tptp.c X1) (tptp.s2least X1))) (forall ((X1 tptp.unreal)) (or (not (tptp.c X1)) (tptp.s2least X1))))) (not (forall ((X1 tptp.unreal)) (=> (tptp.c X1) (tptp.s2least X1)))) (forall ((X1 tptp.unreal)) (or (not (tptp.c X1)) (tptp.s2least X1)))) :rule equiv_pos2)
% 0.16/0.52 (step t70 (cl (= (forall ((X1 tptp.unreal)) (=> (tptp.c X1) (tptp.s2least X1))) (forall ((X1 tptp.unreal)) (or (not (tptp.c X1)) (tptp.s2least X1))))) :rule all_simplify)
% 0.16/0.52 (step t71 (cl (forall ((X1 tptp.unreal)) (or (not (tptp.c X1)) (tptp.s2least X1)))) :rule resolution :premises (t69 t70 a0))
% 0.16/0.52 (step t72 (cl (or (not (tptp.c tptp.exist)) (tptp.s2least tptp.exist))) :rule resolution :premises (t68 t71))
% 0.16/0.52 (step t73 (cl (tptp.s2least tptp.exist)) :rule resolution :premises (t44 t61 t72))
% 0.16/0.52 (step t74 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (not (tptp.equalish (tptp.u1r2 X1) (tptp.u1r1 X1))))) (or (not (tptp.s2least tptp.exist)) (not (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist))))) (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (not (tptp.equalish (tptp.u1r2 X1) (tptp.u1r1 X1)))))) :rule implies_neg1)
% 0.16/0.52 (anchor :step t75)
% 0.16/0.52 (assume t75.a0 (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (not (tptp.equalish (tptp.u1r2 X1) (tptp.u1r1 X1))))))
% 0.16/0.52 (step t75.t1 (cl (or (not (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (not (tptp.equalish (tptp.u1r2 X1) (tptp.u1r1 X1)))))) (or (not (tptp.s2least tptp.exist)) (not (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist)))))) :rule forall_inst :args ((:= X1 tptp.exist)))
% 0.16/0.52 (step t75.t2 (cl (not (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (not (tptp.equalish (tptp.u1r2 X1) (tptp.u1r1 X1)))))) (or (not (tptp.s2least tptp.exist)) (not (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist))))) :rule or :premises (t75.t1))
% 0.16/0.52 (step t75.t3 (cl (or (not (tptp.s2least tptp.exist)) (not (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist))))) :rule resolution :premises (t75.t2 t75.a0))
% 0.16/0.52 (step t75 (cl (not (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (not (tptp.equalish (tptp.u1r2 X1) (tptp.u1r1 X1)))))) (or (not (tptp.s2least tptp.exist)) (not (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist))))) :rule subproof :discharge (t75.a0))
% 0.16/0.52 (step t76 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (not (tptp.equalish (tptp.u1r2 X1) (tptp.u1r1 X1))))) (or (not (tptp.s2least tptp.exist)) (not (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist))))) (or (not (tptp.s2least tptp.exist)) (not (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist))))) :rule resolution :premises (t74 t75))
% 0.16/0.52 (step t77 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (not (tptp.equalish (tptp.u1r2 X1) (tptp.u1r1 X1))))) (or (not (tptp.s2least tptp.exist)) (not (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist))))) (not (or (not (tptp.s2least tptp.exist)) (not (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist)))))) :rule implies_neg2)
% 0.16/0.52 (step t78 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (not (tptp.equalish (tptp.u1r2 X1) (tptp.u1r1 X1))))) (or (not (tptp.s2least tptp.exist)) (not (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist))))) (=> (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (not (tptp.equalish (tptp.u1r2 X1) (tptp.u1r1 X1))))) (or (not (tptp.s2least tptp.exist)) (not (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist)))))) :rule resolution :premises (t76 t77))
% 0.16/0.52 (step t79 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (not (tptp.equalish (tptp.u1r2 X1) (tptp.u1r1 X1))))) (or (not (tptp.s2least tptp.exist)) (not (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist)))))) :rule contraction :premises (t78))
% 0.16/0.52 (step t80 (cl (not (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (not (tptp.equalish (tptp.u1r2 X1) (tptp.u1r1 X1)))))) (or (not (tptp.s2least tptp.exist)) (not (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist))))) :rule implies :premises (t79))
% 0.16/0.52 (step t81 (cl (not (= (forall ((X1 tptp.unreal)) (not (and (tptp.s2least X1) (tptp.equalish (tptp.u1r2 X1) (tptp.u1r1 X1))))) (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (not (tptp.equalish (tptp.u1r2 X1) (tptp.u1r1 X1))))))) (not (forall ((X1 tptp.unreal)) (not (and (tptp.s2least X1) (tptp.equalish (tptp.u1r2 X1) (tptp.u1r1 X1)))))) (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (not (tptp.equalish (tptp.u1r2 X1) (tptp.u1r1 X1)))))) :rule equiv_pos2)
% 0.16/0.52 (step t82 (cl (= (forall ((X1 tptp.unreal)) (not (and (tptp.s2least X1) (tptp.equalish (tptp.u1r2 X1) (tptp.u1r1 X1))))) (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (not (tptp.equalish (tptp.u1r2 X1) (tptp.u1r1 X1))))))) :rule all_simplify)
% 0.16/0.52 (step t83 (cl (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (not (tptp.equalish (tptp.u1r2 X1) (tptp.u1r1 X1)))))) :rule resolution :premises (t81 t82 a2))
% 0.16/0.52 (step t84 (cl (or (not (tptp.s2least tptp.exist)) (not (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist))))) :rule resolution :premises (t80 t83))
% 0.16/0.52 (step t85 (cl (not (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist)))) :rule resolution :premises (t42 t73 t84))
% 0.16/0.52 (step t86 (cl (not (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r1 tptp.exist)))) (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r1 tptp.exist))) :rule or_pos)
% 0.16/0.52 (step t87 (cl (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r1 tptp.exist)) (not (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r1 tptp.exist))))) :rule reordering :premises (t86))
% 0.16/0.52 (step t88 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r1 X1)))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r1 tptp.exist)))) (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r1 X1))))) :rule implies_neg1)
% 0.16/0.52 (anchor :step t89)
% 0.16/0.52 (assume t89.a0 (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r1 X1)))))
% 0.16/0.52 (step t89.t1 (cl (or (not (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r1 X1))))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r1 tptp.exist))))) :rule forall_inst :args ((:= X1 tptp.exist)))
% 0.16/0.52 (step t89.t2 (cl (not (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r1 X1))))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r1 tptp.exist)))) :rule or :premises (t89.t1))
% 0.16/0.52 (step t89.t3 (cl (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r1 tptp.exist)))) :rule resolution :premises (t89.t2 t89.a0))
% 0.16/0.52 (step t89 (cl (not (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r1 X1))))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r1 tptp.exist)))) :rule subproof :discharge (t89.a0))
% 0.16/0.52 (step t90 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r1 X1)))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r1 tptp.exist)))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r1 tptp.exist)))) :rule resolution :premises (t88 t89))
% 0.16/0.52 (step t91 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r1 X1)))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r1 tptp.exist)))) (not (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r1 tptp.exist))))) :rule implies_neg2)
% 0.16/0.52 (step t92 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r1 X1)))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r1 tptp.exist)))) (=> (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r1 X1)))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r1 tptp.exist))))) :rule resolution :premises (t90 t91))
% 0.16/0.52 (step t93 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r1 X1)))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r1 tptp.exist))))) :rule contraction :premises (t92))
% 0.16/0.52 (step t94 (cl (not (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r1 X1))))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r1 tptp.exist)))) :rule implies :premises (t93))
% 0.16/0.52 (step t95 (cl (not (= (forall ((X1 tptp.unreal)) (=> (tptp.s2least X1) (tptp.s X1 (tptp.u1r1 X1)))) (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r1 X1)))))) (not (forall ((X1 tptp.unreal)) (=> (tptp.s2least X1) (tptp.s X1 (tptp.u1r1 X1))))) (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r1 X1))))) :rule equiv_pos2)
% 0.16/0.52 (step t96 (cl (= (forall ((X1 tptp.unreal)) (=> (tptp.s2least X1) (tptp.s X1 (tptp.u1r1 X1)))) (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r1 X1)))))) :rule all_simplify)
% 0.16/0.52 (step t97 (cl (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r1 X1))))) :rule resolution :premises (t95 t96 a3))
% 0.16/0.52 (step t98 (cl (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r1 tptp.exist)))) :rule resolution :premises (t94 t97))
% 0.16/0.52 (step t99 (cl (tptp.s tptp.exist (tptp.u1r1 tptp.exist))) :rule resolution :premises (t87 t73 t98))
% 0.16/0.52 (step t100 (cl (not (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r2 tptp.exist)))) (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r2 tptp.exist))) :rule or_pos)
% 0.16/0.52 (step t101 (cl (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r2 tptp.exist)) (not (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r2 tptp.exist))))) :rule reordering :premises (t100))
% 0.16/0.52 (step t102 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r2 X1)))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r2 tptp.exist)))) (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r2 X1))))) :rule implies_neg1)
% 0.16/0.52 (anchor :step t103)
% 0.16/0.52 (assume t103.a0 (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r2 X1)))))
% 0.16/0.52 (step t103.t1 (cl (or (not (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r2 X1))))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r2 tptp.exist))))) :rule forall_inst :args ((:= X1 tptp.exist)))
% 0.16/0.52 (step t103.t2 (cl (not (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r2 X1))))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r2 tptp.exist)))) :rule or :premises (t103.t1))
% 0.16/0.52 (step t103.t3 (cl (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r2 tptp.exist)))) :rule resolution :premises (t103.t2 t103.a0))
% 0.16/0.52 (step t103 (cl (not (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r2 X1))))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r2 tptp.exist)))) :rule subproof :discharge (t103.a0))
% 0.16/0.52 (step t104 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r2 X1)))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r2 tptp.exist)))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r2 tptp.exist)))) :rule resolution :premises (t102 t103))
% 0.16/0.52 (step t105 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r2 X1)))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r2 tptp.exist)))) (not (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r2 tptp.exist))))) :rule implies_neg2)
% 0.16/0.52 (step t106 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r2 X1)))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r2 tptp.exist)))) (=> (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r2 X1)))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r2 tptp.exist))))) :rule resolution :premises (t104 t105))
% 0.16/0.52 (step t107 (cl (=> (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r2 X1)))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r2 tptp.exist))))) :rule contraction :premises (t106))
% 0.16/0.52 (step t108 (cl (not (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r2 X1))))) (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r2 tptp.exist)))) :rule implies :premises (t107))
% 0.16/0.52 (step t109 (cl (not (= (forall ((X1 tptp.unreal)) (=> (tptp.s2least X1) (tptp.s X1 (tptp.u1r2 X1)))) (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r2 X1)))))) (not (forall ((X1 tptp.unreal)) (=> (tptp.s2least X1) (tptp.s X1 (tptp.u1r2 X1))))) (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r2 X1))))) :rule equiv_pos2)
% 0.16/0.53 (step t110 (cl (= (forall ((X1 tptp.unreal)) (=> (tptp.s2least X1) (tptp.s X1 (tptp.u1r2 X1)))) (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r2 X1)))))) :rule all_simplify)
% 0.16/0.53 (step t111 (cl (forall ((X1 tptp.unreal)) (or (not (tptp.s2least X1)) (tptp.s X1 (tptp.u1r2 X1))))) :rule resolution :premises (t109 t110 a4))
% 0.16/0.53 (step t112 (cl (or (not (tptp.s2least tptp.exist)) (tptp.s tptp.exist (tptp.u1r2 tptp.exist)))) :rule resolution :premises (t108 t111))
% 0.16/0.53 (step t113 (cl (tptp.s tptp.exist (tptp.u1r2 tptp.exist))) :rule resolution :premises (t101 t73 t112))
% 0.16/0.53 (step t114 (cl (not (or (not (tptp.s1most tptp.exist)) (not (tptp.s tptp.exist (tptp.u1r2 tptp.exist))) (not (tptp.s tptp.exist (tptp.u1r1 tptp.exist))) (tptp.equalish (tptp.u1r2 tptp.exist) (tptp.u1r1 tptp.exist))))) :rule resolution :premises (t9 t40 t85 t99 t113))
% 0.16/0.53 (step t115 (cl (not (= (forall ((X2 tptp.real) (X3 tptp.real) (X1 tptp.unreal)) (=> (and (tptp.s1most X1) (tptp.s X1 X3) (tptp.s X1 X2)) (tptp.equalish X3 X2))) (forall ((X2 tptp.real) (X3 tptp.real) (X1 tptp.unreal)) (or (not (tptp.s1most X1)) (not (tptp.s X1 X3)) (not (tptp.s X1 X2)) (tptp.equalish X3 X2))))) (not (forall ((X2 tptp.real) (X3 tptp.real) (X1 tptp.unreal)) (=> (and (tptp.s1most X1) (tptp.s X1 X3) (tptp.s X1 X2)) (tptp.equalish X3 X2)))) (forall ((X2 tptp.real) (X3 tptp.real) (X1 tptp.unreal)) (or (not (tptp.s1most X1)) (not (tptp.s X1 X3)) (not (tptp.s X1 X2)) (tptp.equalish X3 X2)))) :rule equiv_pos2)
% 0.16/0.53 (step t116 (cl (= (forall ((X2 tptp.real) (X3 tptp.real) (X1 tptp.unreal)) (=> (and (tptp.s1most X1) (tptp.s X1 X3) (tptp.s X1 X2)) (tptp.equalish X3 X2))) (forall ((X2 tptp.real) (X3 tptp.real) (X1 tptp.unreal)) (or (not (tptp.s1most X1)) (not (tptp.s X1 X3)) (not (tptp.s X1 X2)) (tptp.equalish X3 X2))))) :rule all_simplify)
% 0.16/0.53 (step t117 (cl (forall ((X2 tptp.real) (X3 tptp.real) (X1 tptp.unreal)) (or (not (tptp.s1most X1)) (not (tptp.s X1 X3)) (not (tptp.s X1 X2)) (tptp.equalish X3 X2)))) :rule resolution :premises (t115 t116 a8))
% 0.16/0.53 (step t118 (cl) :rule resolution :premises (t7 t114 t117))
% 0.16/0.53
% 0.16/0.53 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.S0R3GuT1rn/cvc5---1.0.5_21603.smt2
% 0.16/0.53 % cvc5---1.0.5 exiting
% 0.16/0.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------