%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP101^1 : 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 : n021.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 01:46:58 PM UTC 2025
% Result : Theorem 0.94s 1.14s
% Output : Proof 0.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : ITP101^1 : TPTP v9.2.0. Released v7.5.0.
% 0.03/0.15 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.37 % Computer : n021.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 18:38:38 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.94/1.14 % SZS status Theorem
% 0.94/1.14 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 0.94/1.14 % Inferences: 1
% 0.94/1.14 % SZS output start Proof
% 0.94/1.14 thf(conj_3,conjecture,(((nth_a @ xs) @ x) = ((nth_a @ ys) @ x))).
% 0.94/1.14 thf(h0,negated_conjecture,(~((((nth_a @ xs) @ x) = ((nth_a @ ys) @ x)))),inference(assume_negation,[status(cth)],[conj_3])).
% 0.94/1.14 thf(pax21, axiom, (p21=>![X3:nat]:~(((ford_less_nat @ X3 @ (fsize_size_list_a @ fys)=>~(((ford_less_nat @ X3 @ (fsize_size_list_a @ fys)=>(fnth_a @ fxs @ X3)=(fnth_a @ fys @ X3))=>~((~(ford_less_nat @ X3 @ (fsize_size_list_a @ fys))=>(ff @ (fminus_minus_nat @ X3 @ (fsize_size_list_a @ fxs)))=(fnth_a @ fys @ X3))))))=>~((~(ford_less_nat @ X3 @ (fsize_size_list_a @ fys))=>~(((ford_less_nat @ X3 @ (fsize_size_list_a @ fys)=>(fnth_a @ fxs @ X3)=(fg @ (fminus_minus_nat @ X3 @ (fsize_size_list_a @ fys))))=>~((~(ford_less_nat @ X3 @ (fsize_size_list_a @ fys))=>(ff @ (fminus_minus_nat @ X3 @ (fsize_size_list_a @ fxs)))=(fg @ (fminus_minus_nat @ X3 @ (fsize_size_list_a @ fys)))))))))))), file('<stdin>', pax21)).
% 0.94/1.14 thf(ax2, axiom, p21, file('<stdin>', ax2)).
% 0.94/1.14 thf(pax22, axiom, (p22=>ford_less_nat @ fx @ (fsize_size_list_a @ fys)), file('<stdin>', pax22)).
% 0.94/1.14 thf(nax23, axiom, (p23<=(fnth_a @ fxs @ fx)=(fnth_a @ fys @ fx)), file('<stdin>', nax23)).
% 0.94/1.14 thf(ax0, axiom, ~(p23), file('<stdin>', ax0)).
% 0.94/1.14 thf(ax1, axiom, p22, file('<stdin>', ax1)).
% 0.94/1.14 thf(c_0_6, plain, (epred1_0<=>![X3:nat]:~(((ford_less_nat @ X3 @ (fsize_size_list_a @ fys)=>~(((ford_less_nat @ X3 @ (fsize_size_list_a @ fys)=>(fnth_a @ fxs @ X3)=(fnth_a @ fys @ X3))=>~((~(ford_less_nat @ X3 @ (fsize_size_list_a @ fys))=>(ff @ (fminus_minus_nat @ X3 @ (fsize_size_list_a @ fxs)))=(fnth_a @ fys @ X3))))))=>~((~(ford_less_nat @ X3 @ (fsize_size_list_a @ fys))=>~(((ford_less_nat @ X3 @ (fsize_size_list_a @ fys)=>(fnth_a @ fxs @ X3)=(fg @ (fminus_minus_nat @ X3 @ (fsize_size_list_a @ fys))))=>~((~(ford_less_nat @ X3 @ (fsize_size_list_a @ fys))=>(ff @ (fminus_minus_nat @ X3 @ (fsize_size_list_a @ fxs)))=(fg @ (fminus_minus_nat @ X3 @ (fsize_size_list_a @ fys)))))))))))), introduced(definition)).
% 0.94/1.14 thf(c_0_7, plain, (epred1_0=>![X3:nat]:~(((ford_less_nat @ X3 @ (fsize_size_list_a @ fys)=>~(((ford_less_nat @ X3 @ (fsize_size_list_a @ fys)=>(fnth_a @ fxs @ X3)=(fnth_a @ fys @ X3))=>~((~(ford_less_nat @ X3 @ (fsize_size_list_a @ fys))=>(ff @ (fminus_minus_nat @ X3 @ (fsize_size_list_a @ fxs)))=(fnth_a @ fys @ X3))))))=>~((~(ford_less_nat @ X3 @ (fsize_size_list_a @ fys))=>~(((ford_less_nat @ X3 @ (fsize_size_list_a @ fys)=>(fnth_a @ fxs @ X3)=(fg @ (fminus_minus_nat @ X3 @ (fsize_size_list_a @ fys))))=>~((~(ford_less_nat @ X3 @ (fsize_size_list_a @ fys))=>(ff @ (fminus_minus_nat @ X3 @ (fsize_size_list_a @ fxs)))=(fg @ (fminus_minus_nat @ X3 @ (fsize_size_list_a @ fys)))))))))))), inference(split_equiv,[status(thm)],[c_0_6])).
% 0.94/1.14 thf(c_0_8, axiom, (p21=>epred1_0), inference(apply_def,[status(thm)],[pax21, c_0_6])).
% 0.94/1.14 thf(c_0_9, plain, ![X95:nat]:(((~ford_less_nat @ X95 @ (fsize_size_list_a @ fys)|(fnth_a @ fxs @ X95)=(fnth_a @ fys @ X95)|~ford_less_nat @ X95 @ (fsize_size_list_a @ fys)|~epred1_0)&(ford_less_nat @ X95 @ (fsize_size_list_a @ fys)|(ff @ (fminus_minus_nat @ X95 @ (fsize_size_list_a @ fxs)))=(fnth_a @ fys @ X95)|~ford_less_nat @ X95 @ (fsize_size_list_a @ fys)|~epred1_0))&((~ford_less_nat @ X95 @ (fsize_size_list_a @ fys)|(fnth_a @ fxs @ X95)=(fg @ (fminus_minus_nat @ X95 @ (fsize_size_list_a @ fys)))|ford_less_nat @ X95 @ (fsize_size_list_a @ fys)|~epred1_0)&(ford_less_nat @ X95 @ (fsize_size_list_a @ fys)|(ff @ (fminus_minus_nat @ X95 @ (fsize_size_list_a @ fxs)))=(fg @ (fminus_minus_nat @ X95 @ (fsize_size_list_a @ fys)))|ford_less_nat @ X95 @ (fsize_size_list_a @ fys)|~epred1_0))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_7])])])])])).
% 0.94/1.14 thf(c_0_10, plain, (~p21|epred1_0), inference(fof_nnf,[status(thm)],[c_0_8])).
% 0.94/1.14 thf(c_0_11, plain, ![X3:nat]:((fnth_a @ fxs @ X3)=(fnth_a @ fys @ X3)|~ford_less_nat @ X3 @ (fsize_size_list_a @ fys)|~ford_less_nat @ X3 @ (fsize_size_list_a @ fys)|~epred1_0), inference(split_conjunct,[status(thm)],[c_0_9])).
% 0.94/1.14 thf(c_0_12, plain, (epred1_0|~p21), inference(split_conjunct,[status(thm)],[c_0_10])).
% 0.94/1.14 thf(c_0_13, plain, p21, inference(split_conjunct,[status(thm)],[ax2])).
% 0.94/1.14 thf(c_0_14, plain, (~p22|ford_less_nat @ fx @ (fsize_size_list_a @ fys)), inference(fof_nnf,[status(thm)],[pax22])).
% 0.94/1.14 thf(c_0_15, plain, ((fnth_a @ fxs @ fx)!=(fnth_a @ fys @ fx)|p23), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax23])])).
% 0.94/1.14 thf(c_0_16, plain, ~p23, inference(fof_simplification,[status(thm)],[ax0])).
% 0.94/1.14 thf(c_0_17, plain, ![X3:nat]:((fnth_a @ fxs @ X3)=(fnth_a @ fys @ X3)|~epred1_0|~ford_less_nat @ X3 @ (fsize_size_list_a @ fys)), inference(cn,[status(thm)],[c_0_11])).
% 0.94/1.14 thf(c_0_18, plain, epred1_0, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13])])).
% 0.94/1.14 thf(c_0_19, plain, (ford_less_nat @ fx @ (fsize_size_list_a @ fys)|~p22), inference(split_conjunct,[status(thm)],[c_0_14])).
% 0.94/1.14 thf(c_0_20, plain, p22, inference(split_conjunct,[status(thm)],[ax1])).
% 0.94/1.14 thf(c_0_21, plain, (p23|(fnth_a @ fxs @ fx)!=(fnth_a @ fys @ fx)), inference(split_conjunct,[status(thm)],[c_0_15])).
% 0.94/1.14 thf(c_0_22, plain, ~p23, inference(split_conjunct,[status(thm)],[c_0_16])).
% 0.94/1.14 thf(c_0_23, plain, ![X3:nat]:((fnth_a @ fxs @ X3)=(fnth_a @ fys @ X3)|~ford_less_nat @ X3 @ (fsize_size_list_a @ fys)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17, c_0_18])])).
% 0.94/1.14 thf(c_0_24, plain, ford_less_nat @ fx @ (fsize_size_list_a @ fys), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_20])])).
% 0.94/1.14 thf(c_0_25, plain, (fnth_a @ fxs @ fx)!=(fnth_a @ fys @ fx), inference(sr,[status(thm)],[c_0_21, c_0_22])).
% 0.94/1.14 thf(c_0_26, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_24]), c_0_25]), ['proof']).
% 0.94/1.14 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 0.94/1.14 thf(0,theorem,(((nth_a @ xs) @ x) = ((nth_a @ ys) @ x)),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 0.94/1.14 % SZS output end Proof
%------------------------------------------------------------------------------