%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP078^1 : 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 : n009.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 01:46:54 PM UTC 2025
% Result : Theorem 13.57s 13.76s
% Output : Proof 13.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ITP078^1 : TPTP v9.2.0. Released v7.5.0.
% 0.12/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 8 18:02:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.46/0.62 slave returned with unknown status
% 13.57/13.76 % SZS status Theorem
% 13.57/13.76 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 13.57/13.76 % Inferences: 304
% 13.57/13.76 % SZS output start Proof
% 13.57/13.76 thf(conj_0,conjecture,(((image_mset_nat_a @ (nth_a @ ys)) @ ((image_mset_nat_nat @ f) @ (mset_set_nat @ ((set_or562006527an_nat @ zero_zero_nat) @ (size_size_list_a @ xs))))) = ((image_mset_nat_a @ (nth_a @ ys)) @ (mset_set_nat @ ((set_or562006527an_nat @ zero_zero_nat) @ (size_size_list_a @ ys)))))).
% 13.57/13.76 thf(h0,negated_conjecture,(~((((image_mset_nat_a @ (nth_a @ ys)) @ ((image_mset_nat_nat @ f) @ (mset_set_nat @ ((set_or562006527an_nat @ zero_zero_nat) @ (size_size_list_a @ xs))))) = ((image_mset_nat_a @ (nth_a @ ys)) @ (mset_set_nat @ ((set_or562006527an_nat @ zero_zero_nat) @ (size_size_list_a @ ys))))))),inference(assume_negation,[status(cth)],[conj_0])).
% 13.57/13.76 thf(ax1333, axiom, (~(p180)|p183), file('<stdin>', ax1333)).
% 13.57/13.76 thf(ax1332, axiom, (~(p183)|p184), file('<stdin>', ax1332)).
% 13.57/13.76 thf(ax1337, axiom, p180, file('<stdin>', ax1337)).
% 13.57/13.76 thf(ax1340, axiom, (p1|~(p176)|~(p177)), file('<stdin>', ax1340)).
% 13.57/13.76 thf(ax1516, axiom, ~(p1), file('<stdin>', ax1516)).
% 13.57/13.76 thf(ax1331, axiom, (~(p184)|~(p179)|p177), file('<stdin>', ax1331)).
% 13.57/13.76 thf(ax1339, axiom, p176, file('<stdin>', ax1339)).
% 13.57/13.76 thf(nax179, axiom, (p179<=(fmset_set_nat @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fys)))=(fimage_mset_nat_nat @ ff @ (fmset_set_nat @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs))))), file('<stdin>', nax179)).
% 13.57/13.76 thf(pax45, axiom, (p45=>![X125:nat > nat, X128:set_nat]:(finj_on_nat_nat @ X125 @ X128=>(fimage_mset_nat_nat @ X125 @ (fmset_set_nat @ X128))=(fmset_set_nat @ (fimage_nat_nat @ X125 @ X128)))), file('<stdin>', pax45)).
% 13.57/13.76 thf(pax5, axiom, (p5=>(fimage_nat_nat @ ff @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs)))=(fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fys))), file('<stdin>', pax5)).
% 13.57/13.76 thf(pax2, axiom, (p2=>finj_on_nat_nat @ ff @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs))), file('<stdin>', pax2)).
% 13.57/13.76 thf(ax1472, axiom, p45, file('<stdin>', ax1472)).
% 13.57/13.76 thf(ax1512, axiom, p5, file('<stdin>', ax1512)).
% 13.57/13.76 thf(ax1515, axiom, p2, file('<stdin>', ax1515)).
% 13.57/13.76 thf(c_0_14, plain, (~p180|p183), inference(fof_simplification,[status(thm)],[ax1333])).
% 13.57/13.76 thf(c_0_15, plain, (~p183|p184), inference(fof_simplification,[status(thm)],[ax1332])).
% 13.57/13.76 thf(c_0_16, plain, (p183|~p180), inference(split_conjunct,[status(thm)],[c_0_14])).
% 13.57/13.76 thf(c_0_17, plain, p180, inference(split_conjunct,[status(thm)],[ax1337])).
% 13.57/13.76 thf(c_0_18, plain, (p1|~p176|~p177), inference(fof_simplification,[status(thm)],[ax1340])).
% 13.57/13.76 thf(c_0_19, plain, ~p1, inference(fof_simplification,[status(thm)],[ax1516])).
% 13.57/13.76 thf(c_0_20, plain, (~p184|~p179|p177), inference(fof_simplification,[status(thm)],[ax1331])).
% 13.57/13.76 thf(c_0_21, plain, (p184|~p183), inference(split_conjunct,[status(thm)],[c_0_15])).
% 13.57/13.76 thf(c_0_22, plain, p183, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16, c_0_17])])).
% 13.57/13.76 thf(c_0_23, plain, (p1|~p176|~p177), inference(split_conjunct,[status(thm)],[c_0_18])).
% 13.57/13.76 thf(c_0_24, plain, p176, inference(split_conjunct,[status(thm)],[ax1339])).
% 13.57/13.76 thf(c_0_25, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_19])).
% 13.57/13.76 thf(c_0_26, plain, ((fmset_set_nat @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fys)))!=(fimage_mset_nat_nat @ ff @ (fmset_set_nat @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs))))|p179), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax179])])).
% 13.57/13.76 thf(c_0_27, plain, (p177|~p184|~p179), inference(split_conjunct,[status(thm)],[c_0_20])).
% 13.57/13.76 thf(c_0_28, plain, p184, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21, c_0_22])])).
% 13.57/13.76 thf(c_0_29, plain, ~p177, inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23, c_0_24])]), c_0_25])).
% 13.57/13.76 thf(c_0_30, plain, ![X1305:nat > nat, X1306:set_nat]:(~p45|(~finj_on_nat_nat @ X1305 @ X1306|(fimage_mset_nat_nat @ X1305 @ (fmset_set_nat @ X1306))=(fmset_set_nat @ (fimage_nat_nat @ X1305 @ X1306)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax45])])])).
% 13.57/13.76 thf(c_0_31, plain, (~p5|(fimage_nat_nat @ ff @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs)))=(fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fys))), inference(fof_nnf,[status(thm)],[pax5])).
% 13.57/13.76 thf(c_0_32, plain, (~p2|finj_on_nat_nat @ ff @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs))), inference(fof_nnf,[status(thm)],[pax2])).
% 13.57/13.76 thf(c_0_33, plain, (p179|(fmset_set_nat @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fys)))!=(fimage_mset_nat_nat @ ff @ (fmset_set_nat @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs))))), inference(split_conjunct,[status(thm)],[c_0_26])).
% 13.57/13.76 thf(c_0_34, plain, ~p179, inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27, c_0_28])]), c_0_29])).
% 13.57/13.76 thf(c_0_35, plain, ![X32:nat > nat, X26:set_nat]:((fimage_mset_nat_nat @ X32 @ (fmset_set_nat @ X26))=(fmset_set_nat @ (fimage_nat_nat @ X32 @ X26))|~p45|~finj_on_nat_nat @ X32 @ X26), inference(split_conjunct,[status(thm)],[c_0_30])).
% 13.57/13.76 thf(c_0_36, plain, p45, inference(split_conjunct,[status(thm)],[ax1472])).
% 13.57/13.76 thf(c_0_37, plain, ((fimage_nat_nat @ ff @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs)))=(fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fys))|~p5), inference(split_conjunct,[status(thm)],[c_0_31])).
% 13.57/13.76 thf(c_0_38, plain, p5, inference(split_conjunct,[status(thm)],[ax1512])).
% 13.57/13.76 thf(c_0_39, plain, (finj_on_nat_nat @ ff @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs))|~p2), inference(split_conjunct,[status(thm)],[c_0_32])).
% 13.57/13.76 thf(c_0_40, plain, p2, inference(split_conjunct,[status(thm)],[ax1515])).
% 13.57/13.76 thf(c_0_41, plain, (fimage_mset_nat_nat @ ff @ (fmset_set_nat @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs))))!=(fmset_set_nat @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fys))), inference(sr,[status(thm)],[c_0_33, c_0_34])).
% 13.57/13.76 thf(c_0_42, plain, ![X32:nat > nat, X26:set_nat]:((fimage_mset_nat_nat @ X32 @ (fmset_set_nat @ X26))=(fmset_set_nat @ (fimage_nat_nat @ X32 @ X26))|~finj_on_nat_nat @ X32 @ X26), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35, c_0_36])])).
% 13.57/13.76 thf(c_0_43, plain, (fimage_nat_nat @ ff @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs)))=(fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fys)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37, c_0_38])])).
% 13.57/13.76 thf(c_0_44, plain, finj_on_nat_nat @ ff @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39, c_0_40])])).
% 13.57/13.76 thf(c_0_45, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42]), c_0_43]), c_0_44])]), ['proof']).
% 13.57/13.76 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 13.57/13.76 thf(0,theorem,(((image_mset_nat_a @ (nth_a @ ys)) @ ((image_mset_nat_nat @ f) @ (mset_set_nat @ ((set_or562006527an_nat @ zero_zero_nat) @ (size_size_list_a @ xs))))) = ((image_mset_nat_a @ (nth_a @ ys)) @ (mset_set_nat @ ((set_or562006527an_nat @ zero_zero_nat) @ (size_size_list_a @ ys))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 13.57/13.76 % SZS output end Proof
%------------------------------------------------------------------------------