%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEV668+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 : Tue May 5 06:56:04 PM UTC 2026
% Result : Theorem 1.44s 1.61s
% Output : Proof 1.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV668+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.15/0.33 % Computer : n009.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 08:04:12 EDT 2026
% 0.15/0.33 % CPUTime :
% 1.44/1.61 % SZS status Theorem
% 1.44/1.61 % SZS output start Proof
% 1.44/1.61 tff(cRedblack_2eTREES_2eT___24a5_type, type, (
% 1.44/1.61 cRedblack_2eTREES_2eT___24a5: ( $i * $i * $i * $i * $i ) > $i)).
% 1.44/1.61 tff(tptp_fun_V4__r_1463_type, type, (
% 1.44/1.61 tptp_fun_V4__r_1463: $i)).
% 1.44/1.61 tff(tptp_fun_V3__v_1462_type, type, (
% 1.44/1.61 tptp_fun_V3__v_1462: $i)).
% 1.44/1.61 tff(tptp_fun_V2__k_1461_type, type, (
% 1.44/1.61 tptp_fun_V2__k_1461: $i)).
% 1.44/1.61 tff(tptp_fun_V1__l_1460_type, type, (
% 1.44/1.61 tptp_fun_V1__l_1460: $i)).
% 1.44/1.61 tff(tptp_fun_V0__c_1459_type, type, (
% 1.44/1.61 tptp_fun_V0__c_1459: $i)).
% 1.44/1.61 tff(cRedblack_2eTREES_2eE_type, type, (
% 1.44/1.61 cRedblack_2eTREES_2eE: $i)).
% 1.44/1.61 tff(cRedblack_2eTREES_2etree___24t_type, type, (
% 1.44/1.61 cRedblack_2eTREES_2etree___24t: $i > $o)).
% 1.44/1.61 tff(cV___24t_type, type, (
% 1.44/1.61 cV___24t: $i > $o)).
% 1.44/1.61 tff(cRedblack_2ekey___24t_type, type, (
% 1.44/1.61 cRedblack_2ekey___24t: $i > $o)).
% 1.44/1.61 tff(cRedblack_2ecolor___24t_type, type, (
% 1.44/1.61 cRedblack_2ecolor___24t: $i > $o)).
% 1.44/1.61 tff(1,plain,
% 1.44/1.61 ((cRedblack_2ecolor___24t(V0__c!1459) & (cRedblack_2eTREES_2etree___24t(V1__l!1460) & cRedblack_2ekey___24t(V2__k!1461) & cV___24t(V3__v!1462) & (~((~cRedblack_2eTREES_2etree___24t(V4__r!1463)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c!1459, V1__l!1460, V2__k!1461, V3__v!1462, V4__r!1463) = cRedblack_2eTREES_2eE)))))) <=> (cRedblack_2ecolor___24t(V0__c!1459) & cRedblack_2eTREES_2etree___24t(V1__l!1460) & cRedblack_2ekey___24t(V2__k!1461) & cV___24t(V3__v!1462) & (~((~cRedblack_2eTREES_2etree___24t(V4__r!1463)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c!1459, V1__l!1460, V2__k!1461, V3__v!1462, V4__r!1463) = cRedblack_2eTREES_2eE)))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2,plain,
% 1.44/1.61 ((cRedblack_2eTREES_2etree___24t(V1__l!1460) & (cRedblack_2ekey___24t(V2__k!1461) & cV___24t(V3__v!1462) & (~((~cRedblack_2eTREES_2etree___24t(V4__r!1463)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c!1459, V1__l!1460, V2__k!1461, V3__v!1462, V4__r!1463) = cRedblack_2eTREES_2eE)))))) <=> (cRedblack_2eTREES_2etree___24t(V1__l!1460) & cRedblack_2ekey___24t(V2__k!1461) & cV___24t(V3__v!1462) & (~((~cRedblack_2eTREES_2etree___24t(V4__r!1463)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c!1459, V1__l!1460, V2__k!1461, V3__v!1462, V4__r!1463) = cRedblack_2eTREES_2eE)))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(3,plain,
% 1.44/1.61 ((cRedblack_2ekey___24t(V2__k!1461) & (cV___24t(V3__v!1462) & (~((~cRedblack_2eTREES_2etree___24t(V4__r!1463)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c!1459, V1__l!1460, V2__k!1461, V3__v!1462, V4__r!1463) = cRedblack_2eTREES_2eE)))))) <=> (cRedblack_2ekey___24t(V2__k!1461) & cV___24t(V3__v!1462) & (~((~cRedblack_2eTREES_2etree___24t(V4__r!1463)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c!1459, V1__l!1460, V2__k!1461, V3__v!1462, V4__r!1463) = cRedblack_2eTREES_2eE)))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(4,plain,
% 1.44/1.61 ((cRedblack_2eTREES_2etree___24t(V1__l!1460) & (cRedblack_2ekey___24t(V2__k!1461) & (cV___24t(V3__v!1462) & (~((~cRedblack_2eTREES_2etree___24t(V4__r!1463)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c!1459, V1__l!1460, V2__k!1461, V3__v!1462, V4__r!1463) = cRedblack_2eTREES_2eE))))))) <=> (cRedblack_2eTREES_2etree___24t(V1__l!1460) & (cRedblack_2ekey___24t(V2__k!1461) & cV___24t(V3__v!1462) & (~((~cRedblack_2eTREES_2etree___24t(V4__r!1463)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c!1459, V1__l!1460, V2__k!1461, V3__v!1462, V4__r!1463) = cRedblack_2eTREES_2eE))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3])).
% 1.44/1.61 tff(5,plain,
% 1.44/1.61 ((cRedblack_2eTREES_2etree___24t(V1__l!1460) & (cRedblack_2ekey___24t(V2__k!1461) & (cV___24t(V3__v!1462) & (~((~cRedblack_2eTREES_2etree___24t(V4__r!1463)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c!1459, V1__l!1460, V2__k!1461, V3__v!1462, V4__r!1463) = cRedblack_2eTREES_2eE))))))) <=> (cRedblack_2eTREES_2etree___24t(V1__l!1460) & cRedblack_2ekey___24t(V2__k!1461) & cV___24t(V3__v!1462) & (~((~cRedblack_2eTREES_2etree___24t(V4__r!1463)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c!1459, V1__l!1460, V2__k!1461, V3__v!1462, V4__r!1463) = cRedblack_2eTREES_2eE)))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[4, 2])).
% 1.44/1.61 tff(6,plain,
% 1.44/1.61 ((cRedblack_2ecolor___24t(V0__c!1459) & (cRedblack_2eTREES_2etree___24t(V1__l!1460) & (cRedblack_2ekey___24t(V2__k!1461) & (cV___24t(V3__v!1462) & (~((~cRedblack_2eTREES_2etree___24t(V4__r!1463)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c!1459, V1__l!1460, V2__k!1461, V3__v!1462, V4__r!1463) = cRedblack_2eTREES_2eE)))))))) <=> (cRedblack_2ecolor___24t(V0__c!1459) & (cRedblack_2eTREES_2etree___24t(V1__l!1460) & cRedblack_2ekey___24t(V2__k!1461) & cV___24t(V3__v!1462) & (~((~cRedblack_2eTREES_2etree___24t(V4__r!1463)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c!1459, V1__l!1460, V2__k!1461, V3__v!1462, V4__r!1463) = cRedblack_2eTREES_2eE))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[5])).
% 1.44/1.61 tff(7,plain,
% 1.44/1.61 ((cRedblack_2ecolor___24t(V0__c!1459) & (cRedblack_2eTREES_2etree___24t(V1__l!1460) & (cRedblack_2ekey___24t(V2__k!1461) & (cV___24t(V3__v!1462) & (~((~cRedblack_2eTREES_2etree___24t(V4__r!1463)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c!1459, V1__l!1460, V2__k!1461, V3__v!1462, V4__r!1463) = cRedblack_2eTREES_2eE)))))))) <=> (cRedblack_2ecolor___24t(V0__c!1459) & cRedblack_2eTREES_2etree___24t(V1__l!1460) & cRedblack_2ekey___24t(V2__k!1461) & cV___24t(V3__v!1462) & (~((~cRedblack_2eTREES_2etree___24t(V4__r!1463)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c!1459, V1__l!1460, V2__k!1461, V3__v!1462, V4__r!1463) = cRedblack_2eTREES_2eE)))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[6, 1])).
% 1.44/1.61 tff(8,plain,
% 1.44/1.61 ((~![V0__c: $i] : ((~cRedblack_2ecolor___24t(V0__c)) | ![V1__l: $i] : ((~cRedblack_2eTREES_2etree___24t(V1__l)) | ![V2__k: $i] : ((~cRedblack_2ekey___24t(V2__k)) | ![V3__v: $i] : ((~cV___24t(V3__v)) | ![V4__r: $i] : ((~cRedblack_2eTREES_2etree___24t(V4__r)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c, V1__l, V2__k, V3__v, V4__r) = cRedblack_2eTREES_2eE)))))))) <=> (~![V0__c: $i] : ((~cRedblack_2ecolor___24t(V0__c)) | ![V1__l: $i] : ((~cRedblack_2eTREES_2etree___24t(V1__l)) | ![V2__k: $i] : ((~cRedblack_2ekey___24t(V2__k)) | ![V3__v: $i] : ((~cV___24t(V3__v)) | ![V4__r: $i] : ((~cRedblack_2eTREES_2etree___24t(V4__r)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c, V1__l, V2__k, V3__v, V4__r) = cRedblack_2eTREES_2eE))))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(9,plain,
% 1.44/1.61 ((~![V0__c: $i] : (cRedblack_2ecolor___24t(V0__c) => ![V1__l: $i] : (cRedblack_2eTREES_2etree___24t(V1__l) => ![V2__k: $i] : (cRedblack_2ekey___24t(V2__k) => ![V3__v: $i] : (cV___24t(V3__v) => ![V4__r: $i] : (cRedblack_2eTREES_2etree___24t(V4__r) => (~(cRedblack_2eTREES_2eT___24a5(V0__c, V1__l, V2__k, V3__v, V4__r) = cRedblack_2eTREES_2eE)))))))) <=> (~![V0__c: $i] : ((~cRedblack_2ecolor___24t(V0__c)) | ![V1__l: $i] : ((~cRedblack_2eTREES_2etree___24t(V1__l)) | ![V2__k: $i] : ((~cRedblack_2ekey___24t(V2__k)) | ![V3__v: $i] : ((~cV___24t(V3__v)) | ![V4__r: $i] : ((~cRedblack_2eTREES_2etree___24t(V4__r)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c, V1__l, V2__k, V3__v, V4__r) = cRedblack_2eTREES_2eE))))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(10,axiom,(~![V0__c: $i] : (cRedblack_2ecolor___24t(V0__c) => ![V1__l: $i] : (cRedblack_2eTREES_2etree___24t(V1__l) => ![V2__k: $i] : (cRedblack_2ekey___24t(V2__k) => ![V3__v: $i] : (cV___24t(V3__v) => ![V4__r: $i] : (cRedblack_2eTREES_2etree___24t(V4__r) => (~(cRedblack_2eTREES_2eT___24a5(V0__c, V1__l, V2__k, V3__v, V4__r) = cRedblack_2eTREES_2eE)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''_HAMMER_GOAL'')).
% 1.44/1.61 tff(11,plain,
% 1.44/1.61 (~![V0__c: $i] : ((~cRedblack_2ecolor___24t(V0__c)) | ![V1__l: $i] : ((~cRedblack_2eTREES_2etree___24t(V1__l)) | ![V2__k: $i] : ((~cRedblack_2ekey___24t(V2__k)) | ![V3__v: $i] : ((~cV___24t(V3__v)) | ![V4__r: $i] : ((~cRedblack_2eTREES_2etree___24t(V4__r)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c, V1__l, V2__k, V3__v, V4__r) = cRedblack_2eTREES_2eE)))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[10, 9])).
% 1.44/1.61 tff(12,plain,
% 1.44/1.61 (~![V0__c: $i] : ((~cRedblack_2ecolor___24t(V0__c)) | ![V1__l: $i] : ((~cRedblack_2eTREES_2etree___24t(V1__l)) | ![V2__k: $i] : ((~cRedblack_2ekey___24t(V2__k)) | ![V3__v: $i] : ((~cV___24t(V3__v)) | ![V4__r: $i] : ((~cRedblack_2eTREES_2etree___24t(V4__r)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c, V1__l, V2__k, V3__v, V4__r) = cRedblack_2eTREES_2eE)))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[11, 8])).
% 1.44/1.61 tff(13,plain,
% 1.44/1.61 (~![V0__c: $i] : ((~cRedblack_2ecolor___24t(V0__c)) | ![V1__l: $i] : ((~cRedblack_2eTREES_2etree___24t(V1__l)) | ![V2__k: $i] : ((~cRedblack_2ekey___24t(V2__k)) | ![V3__v: $i] : ((~cV___24t(V3__v)) | ![V4__r: $i] : ((~cRedblack_2eTREES_2etree___24t(V4__r)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c, V1__l, V2__k, V3__v, V4__r) = cRedblack_2eTREES_2eE)))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[12, 8])).
% 1.44/1.61 tff(14,plain,
% 1.44/1.61 (~![V0__c: $i] : ((~cRedblack_2ecolor___24t(V0__c)) | ![V1__l: $i] : ((~cRedblack_2eTREES_2etree___24t(V1__l)) | ![V2__k: $i] : ((~cRedblack_2ekey___24t(V2__k)) | ![V3__v: $i] : ((~cV___24t(V3__v)) | ![V4__r: $i] : ((~cRedblack_2eTREES_2etree___24t(V4__r)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c, V1__l, V2__k, V3__v, V4__r) = cRedblack_2eTREES_2eE)))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[13, 8])).
% 1.44/1.61 tff(15,plain,
% 1.44/1.61 (cRedblack_2ecolor___24t(V0__c!1459) & cRedblack_2eTREES_2etree___24t(V1__l!1460) & cRedblack_2ekey___24t(V2__k!1461) & cV___24t(V3__v!1462) & (~((~cRedblack_2eTREES_2etree___24t(V4__r!1463)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c!1459, V1__l!1460, V2__k!1461, V3__v!1462, V4__r!1463) = cRedblack_2eTREES_2eE))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[14, 7])).
% 1.44/1.61 tff(16,plain,
% 1.44/1.61 (~((~cRedblack_2eTREES_2etree___24t(V4__r!1463)) | (~(cRedblack_2eTREES_2eT___24a5(V0__c!1459, V1__l!1460, V2__k!1461, V3__v!1462, V4__r!1463) = cRedblack_2eTREES_2eE)))),
% 1.44/1.61 inference(and_elim,[status(thm)],[15])).
% 1.44/1.61 tff(17,plain,
% 1.44/1.61 (cRedblack_2eTREES_2eT___24a5(V0__c!1459, V1__l!1460, V2__k!1461, V3__v!1462, V4__r!1463) = cRedblack_2eTREES_2eE),
% 1.44/1.61 inference(or_elim,[status(thm)],[16])).
% 1.44/1.61 tff(18,plain,
% 1.44/1.61 (cRedblack_2eTREES_2eE = cRedblack_2eTREES_2eT___24a5(V0__c!1459, V1__l!1460, V2__k!1461, V3__v!1462, V4__r!1463)),
% 1.44/1.61 inference(symmetry,[status(thm)],[17])).
% 1.44/1.61 tff(19,plain,
% 1.44/1.61 (^[Vvar__0___24Anonymous__3183: $i, Vvar__1___24Anonymous__3184: $i, Vvar__2___24Anonymous__3185: $i, Vvar__3___24Anonymous__3186: $i, Vvar__4___24Anonymous__3187: $i] : refl((~(cRedblack_2eTREES_2eE = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__3183, Vvar__1___24Anonymous__3184, Vvar__2___24Anonymous__3185, Vvar__3___24Anonymous__3186, Vvar__4___24Anonymous__3187))) <=> (~(cRedblack_2eTREES_2eE = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__3183, Vvar__1___24Anonymous__3184, Vvar__2___24Anonymous__3185, Vvar__3___24Anonymous__3186, Vvar__4___24Anonymous__3187))))),
% 1.44/1.61 inference(bind,[status(th)],[])).
% 1.44/1.61 tff(20,plain,
% 1.44/1.61 (![Vvar__0___24Anonymous__3183: $i, Vvar__1___24Anonymous__3184: $i, Vvar__2___24Anonymous__3185: $i, Vvar__3___24Anonymous__3186: $i, Vvar__4___24Anonymous__3187: $i] : (~(cRedblack_2eTREES_2eE = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__3183, Vvar__1___24Anonymous__3184, Vvar__2___24Anonymous__3185, Vvar__3___24Anonymous__3186, Vvar__4___24Anonymous__3187))) <=> ![Vvar__0___24Anonymous__3183: $i, Vvar__1___24Anonymous__3184: $i, Vvar__2___24Anonymous__3185: $i, Vvar__3___24Anonymous__3186: $i, Vvar__4___24Anonymous__3187: $i] : (~(cRedblack_2eTREES_2eE = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__3183, Vvar__1___24Anonymous__3184, Vvar__2___24Anonymous__3185, Vvar__3___24Anonymous__3186, Vvar__4___24Anonymous__3187)))),
% 1.44/1.61 inference(quant_intro,[status(thm)],[19])).
% 1.44/1.61 tff(21,plain,
% 1.44/1.61 (![Vvar__0___24Anonymous__3183: $i, Vvar__1___24Anonymous__3184: $i, Vvar__2___24Anonymous__3185: $i, Vvar__3___24Anonymous__3186: $i, Vvar__4___24Anonymous__3187: $i] : (~(cRedblack_2eTREES_2eE = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__3183, Vvar__1___24Anonymous__3184, Vvar__2___24Anonymous__3185, Vvar__3___24Anonymous__3186, Vvar__4___24Anonymous__3187))) <=> ![Vvar__0___24Anonymous__3183: $i, Vvar__1___24Anonymous__3184: $i, Vvar__2___24Anonymous__3185: $i, Vvar__3___24Anonymous__3186: $i, Vvar__4___24Anonymous__3187: $i] : (~(cRedblack_2eTREES_2eE = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__3183, Vvar__1___24Anonymous__3184, Vvar__2___24Anonymous__3185, Vvar__3___24Anonymous__3186, Vvar__4___24Anonymous__3187)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(22,axiom,(![Vvar__0___24Anonymous__3183: $i, Vvar__1___24Anonymous__3184: $i, Vvar__2___24Anonymous__3185: $i, Vvar__3___24Anonymous__3186: $i, Vvar__4___24Anonymous__3187: $i] : (~(cRedblack_2eTREES_2eE = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__3183, Vvar__1___24Anonymous__3184, Vvar__2___24Anonymous__3185, Vvar__3___24Anonymous__3186, Vvar__4___24Anonymous__3187)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''$_discrim_Redblack.TREES.E$Redblack.TREES.T'')).
% 1.54/1.74 tff(23,plain,
% 1.54/1.74 (![Vvar__0___24Anonymous__3183: $i, Vvar__1___24Anonymous__3184: $i, Vvar__2___24Anonymous__3185: $i, Vvar__3___24Anonymous__3186: $i, Vvar__4___24Anonymous__3187: $i] : (~(cRedblack_2eTREES_2eE = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__3183, Vvar__1___24Anonymous__3184, Vvar__2___24Anonymous__3185, Vvar__3___24Anonymous__3186, Vvar__4___24Anonymous__3187)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[22, 21])).
% 1.54/1.74 tff(24,plain,(
% 1.54/1.74 ![Vvar__0___24Anonymous__3183: $i, Vvar__1___24Anonymous__3184: $i, Vvar__2___24Anonymous__3185: $i, Vvar__3___24Anonymous__3186: $i, Vvar__4___24Anonymous__3187: $i] : (~(cRedblack_2eTREES_2eE = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__3183, Vvar__1___24Anonymous__3184, Vvar__2___24Anonymous__3185, Vvar__3___24Anonymous__3186, Vvar__4___24Anonymous__3187)))),
% 1.54/1.74 inference(skolemize,[status(sab)],[23])).
% 1.54/1.74 tff(25,plain,
% 1.54/1.74 (![Vvar__0___24Anonymous__3183: $i, Vvar__1___24Anonymous__3184: $i, Vvar__2___24Anonymous__3185: $i, Vvar__3___24Anonymous__3186: $i, Vvar__4___24Anonymous__3187: $i] : (~(cRedblack_2eTREES_2eE = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__3183, Vvar__1___24Anonymous__3184, Vvar__2___24Anonymous__3185, Vvar__3___24Anonymous__3186, Vvar__4___24Anonymous__3187)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[24, 20])).
% 1.54/1.74 tff(26,plain,
% 1.54/1.74 ((~![Vvar__0___24Anonymous__3183: $i, Vvar__1___24Anonymous__3184: $i, Vvar__2___24Anonymous__3185: $i, Vvar__3___24Anonymous__3186: $i, Vvar__4___24Anonymous__3187: $i] : (~(cRedblack_2eTREES_2eE = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__3183, Vvar__1___24Anonymous__3184, Vvar__2___24Anonymous__3185, Vvar__3___24Anonymous__3186, Vvar__4___24Anonymous__3187)))) | (~(cRedblack_2eTREES_2eE = cRedblack_2eTREES_2eT___24a5(V0__c!1459, V1__l!1460, V2__k!1461, V3__v!1462, V4__r!1463)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(27,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[26, 25, 18])).
% 1.54/1.74 % SZS output end Proof
% 1.54/1.75 % E exiting
%------------------------------------------------------------------------------