TSTP Solution File: ITP078^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP078^1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n023.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 : 600s
% DateTime : Sun Jul 17 00:29:01 EDT 2022
% Result : Theorem 25.39s 25.57s
% Output : Proof 25.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP078^1 : TPTP v8.1.0. Released v7.5.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jun 3 22:15:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.42/0.59 slave returned with unknown status
% 25.39/25.57 % SZS status Theorem
% 25.39/25.57 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 25.39/25.57 % Inferences: 304
% 25.39/25.57 % SZS output start Proof
% 25.39/25.57 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)))))).
% 25.39/25.57 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])).
% 25.39/25.57 thf(ax1320, axiom, (~(p3)|p1|~(p3)|~(p193)), file('<stdin>', ax1320)).
% 25.39/25.57 thf(ax1516, axiom, ~(p1), file('<stdin>', ax1516)).
% 25.39/25.57 thf(pax3, axiom, (p3=>(fmset_a @ fxs)=(fimage_mset_nat_a @ (fnth_a @ fys) @ (fimage_mset_nat_nat @ ff @ (fmset_set_nat @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs)))))), file('<stdin>', pax3)).
% 25.39/25.57 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)).
% 25.39/25.57 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)).
% 25.39/25.57 thf(pax2, axiom, (p2=>finj_on_nat_nat @ ff @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs))), file('<stdin>', pax2)).
% 25.39/25.57 thf(nax193, axiom, (p193<=(fmset_a @ fxs)=(fimage_mset_nat_a @ (fnth_a @ fys) @ (fmset_set_nat @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fys))))), file('<stdin>', nax193)).
% 25.39/25.57 thf(ax1514, axiom, p3, file('<stdin>', ax1514)).
% 25.39/25.57 thf(ax1472, axiom, p45, file('<stdin>', ax1472)).
% 25.39/25.58 thf(ax1512, axiom, p5, file('<stdin>', ax1512)).
% 25.39/25.58 thf(ax1515, axiom, p2, file('<stdin>', ax1515)).
% 25.39/25.58 thf(c_0_11, plain, (~p3|p1|~p3|~p193), inference(fof_simplification,[status(thm)],[ax1320])).
% 25.39/25.58 thf(c_0_12, plain, (p1|~p3|~p3|~p193), inference(split_conjunct,[status(thm)],[c_0_11])).
% 25.39/25.58 thf(c_0_13, plain, ~p1, inference(fof_simplification,[status(thm)],[ax1516])).
% 25.39/25.58 thf(c_0_14, plain, (~p3|(fmset_a @ fxs)=(fimage_mset_nat_a @ (fnth_a @ fys) @ (fimage_mset_nat_nat @ ff @ (fmset_set_nat @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs)))))), inference(fof_nnf,[status(thm)],[pax3])).
% 25.39/25.58 thf(c_0_15, 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])])])).
% 25.39/25.58 thf(c_0_16, 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])).
% 25.39/25.58 thf(c_0_17, plain, (~p2|finj_on_nat_nat @ ff @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs))), inference(fof_nnf,[status(thm)],[pax2])).
% 25.39/25.58 thf(c_0_18, plain, ((fmset_a @ fxs)!=(fimage_mset_nat_a @ (fnth_a @ fys) @ (fmset_set_nat @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fys))))|p193), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax193])])).
% 25.39/25.58 thf(c_0_19, plain, (p1|~p3|~p193), inference(cn,[status(thm)],[c_0_12])).
% 25.39/25.58 thf(c_0_20, plain, p3, inference(split_conjunct,[status(thm)],[ax1514])).
% 25.39/25.58 thf(c_0_21, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_13])).
% 25.39/25.58 thf(c_0_22, plain, ((fmset_a @ fxs)=(fimage_mset_nat_a @ (fnth_a @ fys) @ (fimage_mset_nat_nat @ ff @ (fmset_set_nat @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs)))))|~p3), inference(split_conjunct,[status(thm)],[c_0_14])).
% 25.39/25.58 thf(c_0_23, 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_15])).
% 25.39/25.58 thf(c_0_24, plain, p45, inference(split_conjunct,[status(thm)],[ax1472])).
% 25.39/25.58 thf(c_0_25, 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_16])).
% 25.39/25.58 thf(c_0_26, plain, p5, inference(split_conjunct,[status(thm)],[ax1512])).
% 25.39/25.58 thf(c_0_27, 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_17])).
% 25.39/25.58 thf(c_0_28, plain, p2, inference(split_conjunct,[status(thm)],[ax1515])).
% 25.39/25.58 thf(c_0_29, plain, (p193|(fmset_a @ fxs)!=(fimage_mset_nat_a @ (fnth_a @ fys) @ (fmset_set_nat @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fys))))), inference(split_conjunct,[status(thm)],[c_0_18])).
% 25.39/25.58 thf(c_0_30, plain, ~p193, inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_20])]), c_0_21])).
% 25.39/25.58 thf(c_0_31, plain, (fimage_mset_nat_a @ (fnth_a @ fys) @ (fimage_mset_nat_nat @ ff @ (fmset_set_nat @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fxs)))))=(fmset_a @ fxs), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22, c_0_20])])).
% 25.39/25.58 thf(c_0_32, 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_23, c_0_24])])).
% 25.39/25.58 thf(c_0_33, 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_25, c_0_26])])).
% 25.39/25.58 thf(c_0_34, 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_27, c_0_28])])).
% 25.39/25.58 thf(c_0_35, plain, (fimage_mset_nat_a @ (fnth_a @ fys) @ (fmset_set_nat @ (fset_or562006527an_nat @ fzero_zero_nat @ (fsize_size_list_a @ fys))))!=(fmset_a @ fxs), inference(sr,[status(thm)],[c_0_29, c_0_30])).
% 25.39/25.58 thf(c_0_36, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_32]), c_0_33]), c_0_34])]), c_0_35]), ['proof']).
% 25.39/25.58 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 25.39/25.58 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])).
% 25.39/25.58 % SZS output end Proof
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