%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB002+4 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 : Sat Jun 21 05:29:28 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWB002+4 : TPTP v9.0.0. Released v5.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 07:46:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(iext_type, type, (
% 0.20/0.38 iext: ( $i * $i * $i ) > $o)).
% 0.20/0.38 tff(uri_ex_s_type, type, (
% 0.20/0.38 uri_ex_s: $i)).
% 0.20/0.38 tff(tptp_fun_BNODE_o_0_type, type, (
% 0.20/0.38 tptp_fun_BNODE_o_0: $i)).
% 0.20/0.38 tff(uri_ex_q_type, type, (
% 0.20/0.38 uri_ex_q: $i)).
% 0.20/0.38 tff(uri_ex_p_type, type, (
% 0.20/0.38 uri_ex_p: $i)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (?[BNODE_o: $i] : (iext(uri_ex_p, uri_ex_s, BNODE_o) & iext(uri_ex_q, BNODE_o, uri_ex_s)) <=> ?[BNODE_o: $i] : (iext(uri_ex_p, uri_ex_s, BNODE_o) & iext(uri_ex_q, BNODE_o, uri_ex_s))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(2,axiom,(?[BNODE_o: $i] : (iext(uri_ex_p, uri_ex_s, BNODE_o) & iext(uri_ex_q, BNODE_o, uri_ex_s))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_premise_fullish_002_Existential_Blank_Nodes')).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (?[BNODE_o: $i] : (iext(uri_ex_p, uri_ex_s, BNODE_o) & iext(uri_ex_q, BNODE_o, uri_ex_s))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.20/0.38 tff(4,plain,(
% 0.20/0.38 iext(uri_ex_p, uri_ex_s, BNODE_o!0) & iext(uri_ex_q, BNODE_o!0, uri_ex_s)),
% 0.20/0.38 inference(skolemize,[status(sab)],[3])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (iext(uri_ex_q, BNODE_o!0, uri_ex_s)),
% 0.20/0.38 inference(and_elim,[status(thm)],[4])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (iext(uri_ex_p, uri_ex_s, BNODE_o!0)),
% 0.20/0.38 inference(and_elim,[status(thm)],[4])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (^[BNODE_x: $i, BNODE_y: $i] : refl(((~iext(uri_ex_p, BNODE_x, BNODE_y)) | (~iext(uri_ex_q, BNODE_y, BNODE_x))) <=> ((~iext(uri_ex_p, BNODE_x, BNODE_y)) | (~iext(uri_ex_q, BNODE_y, BNODE_x))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![BNODE_x: $i, BNODE_y: $i] : ((~iext(uri_ex_p, BNODE_x, BNODE_y)) | (~iext(uri_ex_q, BNODE_y, BNODE_x))) <=> ![BNODE_x: $i, BNODE_y: $i] : ((~iext(uri_ex_p, BNODE_x, BNODE_y)) | (~iext(uri_ex_q, BNODE_y, BNODE_x)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (^[BNODE_x: $i, BNODE_y: $i] : trans(monotonicity(rewrite((iext(uri_ex_p, BNODE_x, BNODE_y) & iext(uri_ex_q, BNODE_y, BNODE_x)) <=> (~((~iext(uri_ex_p, BNODE_x, BNODE_y)) | (~iext(uri_ex_q, BNODE_y, BNODE_x))))), ((~(iext(uri_ex_p, BNODE_x, BNODE_y) & iext(uri_ex_q, BNODE_y, BNODE_x))) <=> (~(~((~iext(uri_ex_p, BNODE_x, BNODE_y)) | (~iext(uri_ex_q, BNODE_y, BNODE_x))))))), rewrite((~(~((~iext(uri_ex_p, BNODE_x, BNODE_y)) | (~iext(uri_ex_q, BNODE_y, BNODE_x))))) <=> ((~iext(uri_ex_p, BNODE_x, BNODE_y)) | (~iext(uri_ex_q, BNODE_y, BNODE_x)))), ((~(iext(uri_ex_p, BNODE_x, BNODE_y) & iext(uri_ex_q, BNODE_y, BNODE_x))) <=> ((~iext(uri_ex_p, BNODE_x, BNODE_y)) | (~iext(uri_ex_q, BNODE_y, BNODE_x)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (![BNODE_x: $i, BNODE_y: $i] : (~(iext(uri_ex_p, BNODE_x, BNODE_y) & iext(uri_ex_q, BNODE_y, BNODE_x))) <=> ![BNODE_x: $i, BNODE_y: $i] : ((~iext(uri_ex_p, BNODE_x, BNODE_y)) | (~iext(uri_ex_q, BNODE_y, BNODE_x)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 ((~?[BNODE_x: $i, BNODE_y: $i] : (iext(uri_ex_p, BNODE_x, BNODE_y) & iext(uri_ex_q, BNODE_y, BNODE_x))) <=> (~?[BNODE_x: $i, BNODE_y: $i] : (iext(uri_ex_p, BNODE_x, BNODE_y) & iext(uri_ex_q, BNODE_y, BNODE_x)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(12,axiom,(~?[BNODE_x: $i, BNODE_y: $i] : (iext(uri_ex_p, BNODE_x, BNODE_y) & iext(uri_ex_q, BNODE_y, BNODE_x))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_conclusion_fullish_002_Existential_Blank_Nodes')).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (~?[BNODE_x: $i, BNODE_y: $i] : (iext(uri_ex_p, BNODE_x, BNODE_y) & iext(uri_ex_q, BNODE_y, BNODE_x))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (~?[BNODE_x: $i, BNODE_y: $i] : (iext(uri_ex_p, BNODE_x, BNODE_y) & iext(uri_ex_q, BNODE_y, BNODE_x))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[13, 11])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (~?[BNODE_x: $i, BNODE_y: $i] : (iext(uri_ex_p, BNODE_x, BNODE_y) & iext(uri_ex_q, BNODE_y, BNODE_x))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (~?[BNODE_x: $i, BNODE_y: $i] : (iext(uri_ex_p, BNODE_x, BNODE_y) & iext(uri_ex_q, BNODE_y, BNODE_x))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (^[BNODE_x: $i, BNODE_y: $i] : refl($oeq((~(iext(uri_ex_p, BNODE_x, BNODE_y) & iext(uri_ex_q, BNODE_y, BNODE_x))), (~(iext(uri_ex_p, BNODE_x, BNODE_y) & iext(uri_ex_q, BNODE_y, BNODE_x)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(18,plain,(
% 0.20/0.38 ![BNODE_x: $i, BNODE_y: $i] : (~(iext(uri_ex_p, BNODE_x, BNODE_y) & iext(uri_ex_q, BNODE_y, BNODE_x)))),
% 0.20/0.38 inference(nnf-neg,[status(sab)],[16, 17])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (![BNODE_x: $i, BNODE_y: $i] : ((~iext(uri_ex_p, BNODE_x, BNODE_y)) | (~iext(uri_ex_q, BNODE_y, BNODE_x)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (![BNODE_x: $i, BNODE_y: $i] : ((~iext(uri_ex_p, BNODE_x, BNODE_y)) | (~iext(uri_ex_q, BNODE_y, BNODE_x)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[19, 8])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (((~![BNODE_x: $i, BNODE_y: $i] : ((~iext(uri_ex_p, BNODE_x, BNODE_y)) | (~iext(uri_ex_q, BNODE_y, BNODE_x)))) | ((~iext(uri_ex_p, uri_ex_s, BNODE_o!0)) | (~iext(uri_ex_q, BNODE_o!0, uri_ex_s)))) <=> ((~![BNODE_x: $i, BNODE_y: $i] : ((~iext(uri_ex_p, BNODE_x, BNODE_y)) | (~iext(uri_ex_q, BNODE_y, BNODE_x)))) | (~iext(uri_ex_p, uri_ex_s, BNODE_o!0)) | (~iext(uri_ex_q, BNODE_o!0, uri_ex_s)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 ((~![BNODE_x: $i, BNODE_y: $i] : ((~iext(uri_ex_p, BNODE_x, BNODE_y)) | (~iext(uri_ex_q, BNODE_y, BNODE_x)))) | ((~iext(uri_ex_p, uri_ex_s, BNODE_o!0)) | (~iext(uri_ex_q, BNODE_o!0, uri_ex_s)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 ((~![BNODE_x: $i, BNODE_y: $i] : ((~iext(uri_ex_p, BNODE_x, BNODE_y)) | (~iext(uri_ex_q, BNODE_y, BNODE_x)))) | (~iext(uri_ex_p, uri_ex_s, BNODE_o!0)) | (~iext(uri_ex_q, BNODE_o!0, uri_ex_s))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[23, 20, 6, 5])).
% 0.20/0.38 % SZS output end Proof
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------