%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP069^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 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 : Thu Oct 9 01:46:52 PM UTC 2025
% Result : Theorem 0.88s 1.13s
% Output : Proof 0.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ITP069^1 : TPTP v9.2.0. Released v7.5.0.
% 0.03/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.35 % Computer : n005.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Wed Oct 8 18:39:23 EDT 2025
% 0.12/0.35 % CPUTime :
% 0.88/1.13 % SZS status Theorem
% 0.88/1.13 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 0.88/1.13 % Inferences: 2
% 0.88/1.13 % SZS output start Proof
% 0.88/1.13 thf(ty_a, type, a : $tType).
% 0.88/1.13 thf(ty_tree_a, type, tree_a : $tType).
% 0.88/1.13 thf(ty_t_a, type, t_a : (a>tree_a>tree_a>tree_a)).
% 0.88/1.13 thf(ty_v, type, v : a).
% 0.88/1.13 thf(ty_heapIm1091024090Down_a, type, heapIm1091024090Down_a : (tree_a>tree_a)).
% 0.88/1.13 thf(ty_r, type, r : tree_a).
% 0.88/1.13 thf(ty_is_heap_a, type, is_heap_a : (tree_a>$o)).
% 0.88/1.13 thf(ty_heapIm970322378pify_a, type, heapIm970322378pify_a : (tree_a>tree_a)).
% 0.88/1.13 thf(ty_l, type, l : tree_a).
% 0.88/1.13 thf(sP1,plain,sP1 <=> (is_heap_a @ (heapIm970322378pify_a @ l)),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.88/1.13 thf(sP2,plain,sP2 <=> (is_heap_a @ (heapIm970322378pify_a @ r)),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.88/1.13 thf(conj_0,conjecture,(is_heap_a @ (heapIm970322378pify_a @ (((t_a @ v) @ l) @ r)))).
% 0.88/1.13 thf(h0,negated_conjecture,(~((is_heap_a @ (heapIm970322378pify_a @ (((t_a @ v) @ l) @ r))))),inference(assume_negation,[status(cth)],[conj_0])).
% 0.88/1.13 thf(h1,assumption,(~(sP1)),introduced(assumption,[])).
% 0.88/1.13 thf(h2,assumption,(sP2 => (((((t_a @ v) @ (heapIm970322378pify_a @ l)) @ (heapIm970322378pify_a @ r)) = (((t_a @ v) @ (heapIm970322378pify_a @ l)) @ (heapIm970322378pify_a @ r))) => (is_heap_a @ (heapIm1091024090Down_a @ (((t_a @ v) @ (heapIm970322378pify_a @ l)) @ (heapIm970322378pify_a @ r)))))),introduced(assumption,[])).
% 0.88/1.13 thf(fact_1_T_Ohyps_I1_J,axiom,sP1).
% 0.88/1.13 thf(1,plain,$false,inference(tab_conflict,[status(thm),assumptions([h1,h0])],[fact_1_T_Ohyps_I1_J,h1])).
% 0.88/1.13 thf(h3,assumption,(~(sP2)),introduced(assumption,[])).
% 0.88/1.13 thf(h4,assumption,(((((t_a @ v) @ (heapIm970322378pify_a @ l)) @ (heapIm970322378pify_a @ r)) = (((t_a @ v) @ (heapIm970322378pify_a @ l)) @ (heapIm970322378pify_a @ r))) => (is_heap_a @ (heapIm1091024090Down_a @ (((t_a @ v) @ (heapIm970322378pify_a @ l)) @ (heapIm970322378pify_a @ r))))),introduced(assumption,[])).
% 0.88/1.13 thf(fact_0_T_Ohyps_I2_J,axiom,sP2).
% 0.88/1.13 thf(2,plain,$false,inference(tab_conflict,[status(thm),assumptions([h3,h2,h0])],[fact_0_T_Ohyps_I2_J,h3])).
% 0.88/1.13 thf(h5,assumption,(~(((((t_a @ v) @ (heapIm970322378pify_a @ l)) @ (heapIm970322378pify_a @ r)) = (((t_a @ v) @ (heapIm970322378pify_a @ l)) @ (heapIm970322378pify_a @ r))))),introduced(assumption,[])).
% 0.88/1.13 thf(h6,assumption,(is_heap_a @ (heapIm1091024090Down_a @ (((t_a @ v) @ (heapIm970322378pify_a @ l)) @ (heapIm970322378pify_a @ r)))),introduced(assumption,[])).
% 0.88/1.13 thf(3,plain,$false,inference(tab_negrefl,[status(thm),assumptions([h5,h4,h2,h0])],[h5])).
% 0.88/1.13 thf(pax3, axiom, (p3=>fis_heap_a @ (fheapIm1091024090Down_a @ (ft_a @ fv @ (fheapIm970322378pify_a @ fl) @ (fheapIm970322378pify_a @ fr)))), file('<stdin>', pax3)).
% 0.88/1.13 thf(pax4, axiom, (p4=>![X30:a, X27:tree_a, X28:tree_a]:(fheapIm970322378pify_a @ (ft_a @ X30 @ X27 @ X28))=(fheapIm1091024090Down_a @ (ft_a @ X30 @ (fheapIm970322378pify_a @ X27) @ (fheapIm970322378pify_a @ X28)))), file('<stdin>', pax4)).
% 0.88/1.13 thf(nax27, axiom, (p27<=fis_heap_a @ (fheapIm970322378pify_a @ (ft_a @ fv @ fl @ fr))), file('<stdin>', nax27)).
% 0.88/1.13 thf(ax9, axiom, ~(p27), file('<stdin>', ax9)).
% 0.88/1.13 thf(ax33, axiom, p3, file('<stdin>', ax33)).
% 0.88/1.13 thf(ax32, axiom, p4, file('<stdin>', ax32)).
% 0.88/1.13 thf(c_0_6, plain, (~p3|fis_heap_a @ (fheapIm1091024090Down_a @ (ft_a @ fv @ (fheapIm970322378pify_a @ fl) @ (fheapIm970322378pify_a @ fr)))), inference(fof_nnf,[status(thm)],[pax3])).
% 0.88/1.13 thf(c_0_7, plain, ![X171:a, X172:tree_a, X173:tree_a]:(~p4|(fheapIm970322378pify_a @ (ft_a @ X171 @ X172 @ X173))=(fheapIm1091024090Down_a @ (ft_a @ X171 @ (fheapIm970322378pify_a @ X172) @ (fheapIm970322378pify_a @ X173)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax4])])])).
% 0.88/1.13 thf(c_0_8, plain, (~fis_heap_a @ (fheapIm970322378pify_a @ (ft_a @ fv @ fl @ fr))|p27), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax27])])).
% 0.88/1.13 thf(c_0_9, plain, ~p27, inference(fof_simplification,[status(thm)],[ax9])).
% 0.88/1.13 thf(c_0_10, plain, (fis_heap_a @ (fheapIm1091024090Down_a @ (ft_a @ fv @ (fheapIm970322378pify_a @ fl) @ (fheapIm970322378pify_a @ fr)))|~p3), inference(split_conjunct,[status(thm)],[c_0_6])).
% 0.88/1.13 thf(c_0_11, plain, p3, inference(split_conjunct,[status(thm)],[ax33])).
% 0.88/1.13 thf(c_0_12, plain, ![X1:tree_a, X2:a, X3:tree_a]:((fheapIm970322378pify_a @ (ft_a @ X2 @ X1 @ X3))=(fheapIm1091024090Down_a @ (ft_a @ X2 @ (fheapIm970322378pify_a @ X1) @ (fheapIm970322378pify_a @ X3)))|~p4), inference(split_conjunct,[status(thm)],[c_0_7])).
% 0.88/1.13 thf(c_0_13, plain, p4, inference(split_conjunct,[status(thm)],[ax32])).
% 0.88/1.13 thf(c_0_14, plain, (p27|~fis_heap_a @ (fheapIm970322378pify_a @ (ft_a @ fv @ fl @ fr))), inference(split_conjunct,[status(thm)],[c_0_8])).
% 0.88/1.13 thf(c_0_15, plain, ~p27, inference(split_conjunct,[status(thm)],[c_0_9])).
% 0.88/1.13 thf(c_0_16, plain, fis_heap_a @ (fheapIm1091024090Down_a @ (ft_a @ fv @ (fheapIm970322378pify_a @ fl) @ (fheapIm970322378pify_a @ fr))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10, c_0_11])])).
% 0.88/1.13 thf(c_0_17, plain, ![X1:tree_a, X2:a, X3:tree_a]:(fheapIm1091024090Down_a @ (ft_a @ X2 @ (fheapIm970322378pify_a @ X1) @ (fheapIm970322378pify_a @ X3)))=(fheapIm970322378pify_a @ (ft_a @ X2 @ X1 @ X3)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13])])).
% 0.88/1.13 thf(c_0_18, plain, ~fis_heap_a @ (fheapIm970322378pify_a @ (ft_a @ fv @ fl @ fr)), inference(sr,[status(thm)],[c_0_14, c_0_15])).
% 0.88/1.13 thf(c_0_19, plain, ($false), inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_16, c_0_17]), c_0_18]), ['proof']).
% 0.88/1.13 thf(4,plain,$false,inference(eprover,[status(thm),assumptions([h6,h4,h2,h0])],[])).
% 0.88/1.13 thf(5,plain,$false,inference(tab_imp,[status(thm),assumptions([h4,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[h4,3,4,h5,h6])).
% 0.88/1.13 thf(6,plain,$false,inference(tab_imp,[status(thm),assumptions([h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[h2,2,5,h3,h4])).
% 0.88/1.13 thf(fact_2__092_060open_062_092_060lbrakk_062is__heap_A_Iheapify_Al_J_059_Ais__heap_A_Iheapify_Ar_J_059_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_A_061_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Ais__heap_A_IsiftDown_A_IT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_J_J_092_060close_062,axiom,(sP1 => (sP2 => (((((t_a @ v) @ (heapIm970322378pify_a @ l)) @ (heapIm970322378pify_a @ r)) = (((t_a @ v) @ (heapIm970322378pify_a @ l)) @ (heapIm970322378pify_a @ r))) => (is_heap_a @ (heapIm1091024090Down_a @ (((t_a @ v) @ (heapIm970322378pify_a @ l)) @ (heapIm970322378pify_a @ r)))))))).
% 0.88/1.13 thf(7,plain,$false,inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_2__092_060open_062_092_060lbrakk_062is__heap_A_Iheapify_Al_J_059_Ais__heap_A_Iheapify_Ar_J_059_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_A_061_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Ais__heap_A_IsiftDown_A_IT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_J_J_092_060close_062,1,6,h1,h2])).
% 0.88/1.13 thf(0,theorem,(is_heap_a @ (heapIm970322378pify_a @ (((t_a @ v) @ l) @ r))),inference(contra,[status(thm),contra(discharge,[h0])],[7,h0])).
% 0.88/1.13 % SZS output end Proof
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