%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP113^1 : 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 : n011.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 01:47:00 PM UTC 2025
% Result : Theorem 78.93s 79.08s
% Output : Proof 78.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ITP113^1 : TPTP v9.2.0. Released v7.5.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 18:03:38 EDT 2025
% 0.14/0.35 % CPUTime :
% 78.93/79.08 % SZS status Theorem
% 78.93/79.08 % Mode: mode500:USE_SINE=true:SINE_TOLERANCE=1.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 78.93/79.08 % Inferences: 10
% 78.93/79.08 % SZS output start Proof
% 78.93/79.08 thf(conj_1,conjecture,thesis).
% 78.93/79.08 thf(h0,negated_conjecture,(~(thesis)),inference(assume_negation,[status(cth)],[conj_1])).
% 78.93/79.08 thf(nax1, axiom, (p1<=fthesis), file('<stdin>', nax1)).
% 78.93/79.08 thf(ax63, axiom, ~(p1), file('<stdin>', ax63)).
% 78.93/79.08 thf(pax2, axiom, (p2=>![X82:a, X83:real]:(~((fmember1103263856a_real @ (fproduct_Pair_a_real @ X82 @ X83) @ (flower_930854854raph_a @ ftop_top_set_a @ ff)=>~(ford_less_real @ (freal_V404783528a_real @ (fproduct_Pair_a_real @ X82 @ X83) @ (fproduct_Pair_a_real @ fx @ fy)) @ fe)))=>fthesis)), file('<stdin>', pax2)).
% 78.93/79.08 thf(pax7, axiom, (p7=>![X77:product_prod_a_real]:~(![X78:a, X79:real]:~((X77)=(fproduct_Pair_a_real @ X78 @ X79)))), file('<stdin>', pax7)).
% 78.93/79.08 thf(ax62, axiom, p2, file('<stdin>', ax62)).
% 78.93/79.08 thf(ax57, axiom, p7, file('<stdin>', ax57)).
% 78.93/79.08 thf(nax59, axiom, (p59<=![X1:product_prod_a_real]:(fmember1103263856a_real @ X1 @ (flower_930854854raph_a @ ftop_top_set_a @ ff)=>~(ford_less_real @ (freal_V404783528a_real @ X1 @ (fproduct_Pair_a_real @ fx @ fy)) @ fe))), file('<stdin>', nax59)).
% 78.93/79.08 thf(ax5, axiom, ~(p59), file('<stdin>', ax5)).
% 78.93/79.08 thf(c_0_8, plain, (~fthesis|p1), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])).
% 78.93/79.08 thf(c_0_9, plain, ~p1, inference(fof_simplification,[status(thm)],[ax63])).
% 78.93/79.08 thf(c_0_10, plain, ![X368:a, X369:real]:(~p2|(~fmember1103263856a_real @ (fproduct_Pair_a_real @ X368 @ X369) @ (flower_930854854raph_a @ ftop_top_set_a @ ff)|~ford_less_real @ (freal_V404783528a_real @ (fproduct_Pair_a_real @ X368 @ X369) @ (fproduct_Pair_a_real @ fx @ fy)) @ fe|fthesis)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax2])])])])).
% 78.93/79.08 thf(c_0_11, plain, (p1|~fthesis), inference(split_conjunct,[status(thm)],[c_0_8])).
% 78.93/79.08 thf(c_0_12, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_9])).
% 78.93/79.08 thf(c_0_13, plain, ![X356:product_prod_a_real]:(~p7|(X356)=(fproduct_Pair_a_real @ (esk137_1 @ X356) @ (esk138_1 @ X356))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax7])])])])])).
% 78.93/79.08 thf(c_0_14, plain, ![X4:a, X3:real]:(fthesis|~p2|~fmember1103263856a_real @ (fproduct_Pair_a_real @ X4 @ X3) @ (flower_930854854raph_a @ ftop_top_set_a @ ff)|~ford_less_real @ (freal_V404783528a_real @ (fproduct_Pair_a_real @ X4 @ X3) @ (fproduct_Pair_a_real @ fx @ fy)) @ fe), inference(split_conjunct,[status(thm)],[c_0_10])).
% 78.93/79.08 thf(c_0_15, plain, p2, inference(split_conjunct,[status(thm)],[ax62])).
% 78.93/79.08 thf(c_0_16, plain, ~fthesis, inference(sr,[status(thm)],[c_0_11, c_0_12])).
% 78.93/79.08 thf(c_0_17, plain, ![X1:product_prod_a_real]:((X1)=(fproduct_Pair_a_real @ (esk137_1 @ X1) @ (esk138_1 @ X1))|~p7), inference(split_conjunct,[status(thm)],[c_0_13])).
% 78.93/79.08 thf(c_0_18, plain, p7, inference(split_conjunct,[status(thm)],[ax57])).
% 78.93/79.08 thf(c_0_19, plain, ((fmember1103263856a_real @ esk1_0 @ (flower_930854854raph_a @ ftop_top_set_a @ ff)|p59)&(ford_less_real @ (freal_V404783528a_real @ esk1_0 @ (fproduct_Pair_a_real @ fx @ fy)) @ fe|p59)), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax59])])])])])).
% 78.93/79.08 thf(c_0_20, plain, ~p59, inference(fof_simplification,[status(thm)],[ax5])).
% 78.93/79.08 thf(c_0_21, plain, ![X4:a, X3:real]:(~ford_less_real @ (freal_V404783528a_real @ (fproduct_Pair_a_real @ X4 @ X3) @ (fproduct_Pair_a_real @ fx @ fy)) @ fe|~fmember1103263856a_real @ (fproduct_Pair_a_real @ X4 @ X3) @ (flower_930854854raph_a @ ftop_top_set_a @ ff)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_15])]), c_0_16])).
% 78.93/79.08 thf(c_0_22, plain, ![X1:product_prod_a_real]:(fproduct_Pair_a_real @ (esk137_1 @ X1) @ (esk138_1 @ X1))=(X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17, c_0_18])])).
% 78.93/79.08 thf(c_0_23, plain, (fmember1103263856a_real @ esk1_0 @ (flower_930854854raph_a @ ftop_top_set_a @ ff)|p59), inference(split_conjunct,[status(thm)],[c_0_19])).
% 78.93/79.08 thf(c_0_24, plain, ~p59, inference(split_conjunct,[status(thm)],[c_0_20])).
% 78.93/79.08 thf(c_0_25, plain, (ford_less_real @ (freal_V404783528a_real @ esk1_0 @ (fproduct_Pair_a_real @ fx @ fy)) @ fe|p59), inference(split_conjunct,[status(thm)],[c_0_19])).
% 78.93/79.08 thf(c_0_26, plain, ![X1:product_prod_a_real]:(~ford_less_real @ (freal_V404783528a_real @ X1 @ (fproduct_Pair_a_real @ fx @ fy)) @ fe|~fmember1103263856a_real @ X1 @ (flower_930854854raph_a @ ftop_top_set_a @ ff)), inference(spm,[status(thm)],[c_0_21, c_0_22])).
% 78.93/79.08 thf(c_0_27, plain, fmember1103263856a_real @ esk1_0 @ (flower_930854854raph_a @ ftop_top_set_a @ ff), inference(sr,[status(thm)],[c_0_23, c_0_24])).
% 78.93/79.08 thf(c_0_28, plain, ford_less_real @ (freal_V404783528a_real @ esk1_0 @ (fproduct_Pair_a_real @ fx @ fy)) @ fe, inference(sr,[status(thm)],[c_0_25, c_0_24])).
% 78.93/79.08 thf(c_0_29, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26, c_0_27]), c_0_28])]), ['proof']).
% 78.93/79.08 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 78.93/79.08 thf(0,theorem,thesis,inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 78.93/79.08 % SZS output end Proof
%------------------------------------------------------------------------------