%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP004^4 : TPTP v9.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n022.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 : Thu Oct 9 01:46:22 PM UTC 2025
% Result : Theorem 165.62s 164.44s
% Output : Proof 165.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : ITP004^4 : TPTP v9.2.0. Bugfixed v7.5.0.
% 0.13/0.15 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.37 % Computer : n022.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Wed Oct 8 17:58:38 EDT 2025
% 0.14/0.37 % CPUTime :
% 165.62/164.44 % SZS status Theorem
% 165.62/164.44 % Mode: mode500:USE_SINE=true:SINE_TOLERANCE=1.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 165.62/164.44 % Inferences: 0
% 165.62/164.44 % SZS output start Proof
% 165.62/164.44 thf(thm_2Epred__set_2EREST__SUBSET,conjecture,(![X1:d]:(![X2:u]:(j_mono_2Etyop_2Emin_2Ebool @ ((s @ tyop_2Emin_2Ebool) @ ((c_2Epred__set_2ESUBSET_2E2 @ ((s @ ((tyop_2Emin_2Efun @ X1) @ tyop_2Emin_2Ebool)) @ (c_2Epred__set_2EREST_2E1 @ ((s @ ((tyop_2Emin_2Efun @ X1) @ tyop_2Emin_2Ebool)) @ X2)))) @ ((s @ ((tyop_2Emin_2Efun @ X1) @ tyop_2Emin_2Ebool)) @ X2))))))).
% 165.62/164.44 thf(h0,negated_conjecture,(~((![X1:d]:(![X2:u]:(j_mono_2Etyop_2Emin_2Ebool @ ((s @ tyop_2Emin_2Ebool) @ ((c_2Epred__set_2ESUBSET_2E2 @ ((s @ ((tyop_2Emin_2Efun @ X1) @ tyop_2Emin_2Ebool)) @ (c_2Epred__set_2EREST_2E1 @ ((s @ ((tyop_2Emin_2Efun @ X1) @ tyop_2Emin_2Ebool)) @ X2)))) @ ((s @ ((tyop_2Emin_2Efun @ X1) @ tyop_2Emin_2Ebool)) @ X2)))))))),inference(assume_negation,[status(cth)],[thm_2Epred__set_2EREST__SUBSET])).
% 165.62/164.44 thf(pax13, axiom, (p13=>![X1:d, X2:u, X8:u]:fj_mono_2Etyop_2Emin_2Ebool @ (fs @ ftyop_2Emin_2Ebool @ (fc_2Epred__set_2ESUBSET_2E2 @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ (fc_2Epred__set_2EDELETE_2E2 @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ X8) @ (fs @ X1 @ X2))) @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ X8)))), file('<stdin>', pax13)).
% 165.62/164.44 thf(pax53, axiom, (p53=>![X1:d, X2:u]:(fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ (fc_2Epred__set_2EREST_2E1 @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ X2)))=(fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ (fc_2Epred__set_2EDELETE_2E2 @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ X2) @ (fs @ X1 @ (fc_2Epred__set_2ECHOICE_2E1 @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ X2)))))), file('<stdin>', pax53)).
% 165.62/164.44 thf(nax1, axiom, (p1<=![X1:d, X2:u]:fj_mono_2Etyop_2Emin_2Ebool @ (fs @ ftyop_2Emin_2Ebool @ (fc_2Epred__set_2ESUBSET_2E2 @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ (fc_2Epred__set_2EREST_2E1 @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ X2))) @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ X2)))), file('<stdin>', nax1)).
% 165.62/164.44 thf(ax52, axiom, ~(p1), file('<stdin>', ax52)).
% 165.62/164.44 thf(ax40, axiom, p13, file('<stdin>', ax40)).
% 165.62/164.44 thf(ax0, axiom, p53, file('<stdin>', ax0)).
% 165.62/164.44 thf(c_0_6, plain, ![X144:d, X145:u, X146:u]:(~p13|fj_mono_2Etyop_2Emin_2Ebool @ (fs @ ftyop_2Emin_2Ebool @ (fc_2Epred__set_2ESUBSET_2E2 @ (fs @ (ftyop_2Emin_2Efun @ X144 @ ftyop_2Emin_2Ebool) @ (fc_2Epred__set_2EDELETE_2E2 @ (fs @ (ftyop_2Emin_2Efun @ X144 @ ftyop_2Emin_2Ebool) @ X146) @ (fs @ X144 @ X145))) @ (fs @ (ftyop_2Emin_2Efun @ X144 @ ftyop_2Emin_2Ebool) @ X146)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax13])])])).
% 165.62/164.44 thf(c_0_7, plain, ![X14:d, X15:u]:(~p53|(fs @ (ftyop_2Emin_2Efun @ X14 @ ftyop_2Emin_2Ebool) @ (fc_2Epred__set_2EREST_2E1 @ (fs @ (ftyop_2Emin_2Efun @ X14 @ ftyop_2Emin_2Ebool) @ X15)))=(fs @ (ftyop_2Emin_2Efun @ X14 @ ftyop_2Emin_2Ebool) @ (fc_2Epred__set_2EDELETE_2E2 @ (fs @ (ftyop_2Emin_2Efun @ X14 @ ftyop_2Emin_2Ebool) @ X15) @ (fs @ X14 @ (fc_2Epred__set_2ECHOICE_2E1 @ (fs @ (ftyop_2Emin_2Efun @ X14 @ ftyop_2Emin_2Ebool) @ X15)))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax53])])])).
% 165.62/164.44 thf(c_0_8, plain, (~fj_mono_2Etyop_2Emin_2Ebool @ (fs @ ftyop_2Emin_2Ebool @ (fc_2Epred__set_2ESUBSET_2E2 @ (fs @ (ftyop_2Emin_2Efun @ esk89_0 @ ftyop_2Emin_2Ebool) @ (fc_2Epred__set_2EREST_2E1 @ (fs @ (ftyop_2Emin_2Efun @ esk89_0 @ ftyop_2Emin_2Ebool) @ esk90_0))) @ (fs @ (ftyop_2Emin_2Efun @ esk89_0 @ ftyop_2Emin_2Ebool) @ esk90_0)))|p1), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])])])).
% 165.62/164.44 thf(c_0_9, plain, ~p1, inference(fof_simplification,[status(thm)],[ax52])).
% 165.62/164.44 thf(c_0_10, plain, ![X1:d, X3:u, X2:u]:(fj_mono_2Etyop_2Emin_2Ebool @ (fs @ ftyop_2Emin_2Ebool @ (fc_2Epred__set_2ESUBSET_2E2 @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ (fc_2Epred__set_2EDELETE_2E2 @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ X2) @ (fs @ X1 @ X3))) @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ X2)))|~p13), inference(split_conjunct,[status(thm)],[c_0_6])).
% 165.62/164.44 thf(c_0_11, plain, p13, inference(split_conjunct,[status(thm)],[ax40])).
% 165.62/164.44 thf(c_0_12, plain, ![X1:d, X2:u]:((fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ (fc_2Epred__set_2EREST_2E1 @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ X2)))=(fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ (fc_2Epred__set_2EDELETE_2E2 @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ X2) @ (fs @ X1 @ (fc_2Epred__set_2ECHOICE_2E1 @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ X2)))))|~p53), inference(split_conjunct,[status(thm)],[c_0_7])).
% 165.62/164.44 thf(c_0_13, plain, p53, inference(split_conjunct,[status(thm)],[ax0])).
% 165.62/164.44 thf(c_0_14, plain, (p1|~fj_mono_2Etyop_2Emin_2Ebool @ (fs @ ftyop_2Emin_2Ebool @ (fc_2Epred__set_2ESUBSET_2E2 @ (fs @ (ftyop_2Emin_2Efun @ esk89_0 @ ftyop_2Emin_2Ebool) @ (fc_2Epred__set_2EREST_2E1 @ (fs @ (ftyop_2Emin_2Efun @ esk89_0 @ ftyop_2Emin_2Ebool) @ esk90_0))) @ (fs @ (ftyop_2Emin_2Efun @ esk89_0 @ ftyop_2Emin_2Ebool) @ esk90_0)))), inference(split_conjunct,[status(thm)],[c_0_8])).
% 165.62/164.44 thf(c_0_15, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_9])).
% 165.62/164.44 thf(c_0_16, plain, ![X1:d, X3:u, X2:u]:fj_mono_2Etyop_2Emin_2Ebool @ (fs @ ftyop_2Emin_2Ebool @ (fc_2Epred__set_2ESUBSET_2E2 @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ (fc_2Epred__set_2EDELETE_2E2 @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ X2) @ (fs @ X1 @ X3))) @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10, c_0_11])])).
% 165.62/164.44 thf(c_0_17, plain, ![X1:d, X2:u]:(fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ (fc_2Epred__set_2EDELETE_2E2 @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ X2) @ (fs @ X1 @ (fc_2Epred__set_2ECHOICE_2E1 @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ X2)))))=(fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ (fc_2Epred__set_2EREST_2E1 @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13])])).
% 165.62/164.44 thf(c_0_18, plain, ~fj_mono_2Etyop_2Emin_2Ebool @ (fs @ ftyop_2Emin_2Ebool @ (fc_2Epred__set_2ESUBSET_2E2 @ (fs @ (ftyop_2Emin_2Efun @ esk89_0 @ ftyop_2Emin_2Ebool) @ (fc_2Epred__set_2EREST_2E1 @ (fs @ (ftyop_2Emin_2Efun @ esk89_0 @ ftyop_2Emin_2Ebool) @ esk90_0))) @ (fs @ (ftyop_2Emin_2Efun @ esk89_0 @ ftyop_2Emin_2Ebool) @ esk90_0))), inference(sr,[status(thm)],[c_0_14, c_0_15])).
% 165.62/164.44 thf(c_0_19, plain, ![X1:d, X2:u]:fj_mono_2Etyop_2Emin_2Ebool @ (fs @ ftyop_2Emin_2Ebool @ (fc_2Epred__set_2ESUBSET_2E2 @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ (fc_2Epred__set_2EREST_2E1 @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ X2))) @ (fs @ (ftyop_2Emin_2Efun @ X1 @ ftyop_2Emin_2Ebool) @ X2))), inference(spm,[status(thm)],[c_0_16, c_0_17])).
% 165.62/164.44 thf(c_0_20, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18, c_0_19])]), ['proof']).
% 165.62/164.44 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 165.62/164.44 thf(0,theorem,(![X1:d]:(![X2:u]:(j_mono_2Etyop_2Emin_2Ebool @ ((s @ tyop_2Emin_2Ebool) @ ((c_2Epred__set_2ESUBSET_2E2 @ ((s @ ((tyop_2Emin_2Efun @ X1) @ tyop_2Emin_2Ebool)) @ (c_2Epred__set_2EREST_2E1 @ ((s @ ((tyop_2Emin_2Efun @ X1) @ tyop_2Emin_2Ebool)) @ X2)))) @ ((s @ ((tyop_2Emin_2Efun @ X1) @ tyop_2Emin_2Ebool)) @ X2)))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 165.62/164.44 % SZS output end Proof
%------------------------------------------------------------------------------