%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU764^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n006.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 02:48:21 PM UTC 2025
% Result : Theorem 19.59s 19.73s
% Output : Proof 19.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU764^2 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 8 21:09:08 EDT 2025
% 0.14/0.35 % CPUTime :
% 19.59/19.73 % SZS status Theorem
% 19.59/19.73 % Mode: mode485
% 19.59/19.73 % Inferences: 213
% 19.59/19.73 % SZS output start Proof
% 19.59/19.73 thf(def_binunionT_lem,definition,(binunionT_lem = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binunion @ X2) @ X3)) @ (powerset @ X1))))))))).
% 19.59/19.73 thf(def_demorgan1,definition,(demorgan1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))))).
% 19.59/19.73 thf(def_demorgan2,definition,(demorgan2 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))))).
% 19.59/19.73 thf(woz1_2,conjecture,((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binunion @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))))))).
% 19.59/19.73 thf(h0,negated_conjecture,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binunion @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5)))))))))))))))))),inference(assume_negation,[status(cth)],[woz1_2])).
% 19.59/19.73 thf(ax1027, axiom, (p1|~(p3)), file('<stdin>', ax1027)).
% 19.59/19.73 thf(ax1029, axiom, ~(p1), file('<stdin>', ax1029)).
% 19.59/19.73 thf(ax1025, axiom, (p3|~(p5)), file('<stdin>', ax1025)).
% 19.59/19.73 thf(nax1, axiom, (p1<=(![X1:$i, X2:$i]:(fin @ X2 @ (fpowerset @ X1)=>![X3:$i]:(fin @ X3 @ (fpowerset @ X1)=>fin @ (fbinunion @ X2 @ X3) @ (fpowerset @ X1)))=>(![X1:$i, X2:$i]:(fin @ X2 @ (fpowerset @ X1)=>![X3:$i]:(fin @ X3 @ (fpowerset @ X1)=>(fsetminus @ X1 @ (fbinintersect @ X2 @ X3))=(fbinunion @ (fsetminus @ X1 @ X2) @ (fsetminus @ X1 @ X3))))=>(![X1:$i, X2:$i]:(fin @ X2 @ (fpowerset @ X1)=>![X3:$i]:(fin @ X3 @ (fpowerset @ X1)=>(fsetminus @ X1 @ (fbinunion @ X2 @ X3))=(fbinintersect @ (fsetminus @ X1 @ X2) @ (fsetminus @ X1 @ X3))))=>![X1:$i, X2:$i]:(fin @ X2 @ (fpowerset @ X1)=>![X3:$i]:(fin @ X3 @ (fpowerset @ X1)=>![X4:$i]:(fin @ X4 @ (fpowerset @ X1)=>![X5:$i]:(fin @ X5 @ (fpowerset @ X1)=>(fsetminus @ X1 @ (fbinintersect @ (fbinunion @ X2 @ X3) @ (fbinunion @ X4 @ X5)))=(fbinunion @ (fbinintersect @ (fsetminus @ X1 @ X2) @ (fsetminus @ X1 @ X3)) @ (fbinintersect @ (fsetminus @ X1 @ X4) @ (fsetminus @ X1 @ X5))))))))))), file('<stdin>', nax1)).
% 19.59/19.73 thf(pax8, axiom, (p8=>![X1:$i, X2:$i]:(fin @ X2 @ (fpowerset @ X1)=>![X3:$i]:(fin @ X3 @ (fpowerset @ X1)=>(fsetminus @ X1 @ (fbinunion @ X2 @ X3))=(fbinintersect @ (fsetminus @ X1 @ X2) @ (fsetminus @ X1 @ X3))))), file('<stdin>', pax8)).
% 19.59/19.73 thf(ax1022, axiom, (p5|p8), file('<stdin>', ax1022)).
% 19.59/19.73 thf(pax4, axiom, (p4=>![X1:$i, X2:$i]:(fin @ X2 @ (fpowerset @ X1)=>![X3:$i]:(fin @ X3 @ (fpowerset @ X1)=>(fsetminus @ X1 @ (fbinintersect @ X2 @ X3))=(fbinunion @ (fsetminus @ X1 @ X2) @ (fsetminus @ X1 @ X3))))), file('<stdin>', pax4)).
% 19.59/19.73 thf(ax1026, axiom, (p3|p4), file('<stdin>', ax1026)).
% 19.59/19.73 thf(pax2, axiom, (p2=>![X1:$i, X2:$i]:(fin @ X2 @ (fpowerset @ X1)=>![X3:$i]:(fin @ X3 @ (fpowerset @ X1)=>fin @ (fbinunion @ X2 @ X3) @ (fpowerset @ X1)))), file('<stdin>', pax2)).
% 19.59/19.73 thf(ax1028, axiom, (p1|p2), file('<stdin>', ax1028)).
% 19.59/19.73 thf(c_0_10, plain, (p1|~p3), inference(fof_simplification,[status(thm)],[ax1027])).
% 19.59/19.73 thf(c_0_11, plain, ~p1, inference(fof_simplification,[status(thm)],[ax1029])).
% 19.59/19.73 thf(c_0_12, plain, (p3|~p5), inference(fof_simplification,[status(thm)],[ax1025])).
% 19.59/19.73 thf(c_0_13, plain, (p1|~p3), inference(split_conjunct,[status(thm)],[c_0_10])).
% 19.59/19.73 thf(c_0_14, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_11])).
% 19.59/19.73 thf(c_0_15, plain, (p3|~p5), inference(split_conjunct,[status(thm)],[c_0_12])).
% 19.59/19.73 thf(c_0_16, plain, ~p3, inference(sr,[status(thm)],[c_0_13, c_0_14])).
% 19.59/19.73 thf(c_0_17, plain, ![X1434:$i, X1435:$i, X1436:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i]:((~fin @ X1435 @ (fpowerset @ X1434)|(~fin @ X1436 @ (fpowerset @ X1434)|fin @ (fbinunion @ X1435 @ X1436) @ (fpowerset @ X1434))|p1)&((~fin @ X1438 @ (fpowerset @ X1437)|(~fin @ X1439 @ (fpowerset @ X1437)|(fsetminus @ X1437 @ (fbinintersect @ X1438 @ X1439))=(fbinunion @ (fsetminus @ X1437 @ X1438) @ (fsetminus @ X1437 @ X1439)))|p1)&((~fin @ X1441 @ (fpowerset @ X1440)|(~fin @ X1442 @ (fpowerset @ X1440)|(fsetminus @ X1440 @ (fbinunion @ X1441 @ X1442))=(fbinintersect @ (fsetminus @ X1440 @ X1441) @ (fsetminus @ X1440 @ X1442)))|p1)&((fin @ esk718_0 @ (fpowerset @ esk717_0)|p1)&((fin @ esk719_0 @ (fpowerset @ esk717_0)|p1)&((fin @ esk720_0 @ (fpowerset @ esk717_0)|p1)&((fin @ esk721_0 @ (fpowerset @ esk717_0)|p1)&((fsetminus @ esk717_0 @ (fbinintersect @ (fbinunion @ esk718_0 @ esk719_0) @ (fbinunion @ esk720_0 @ esk721_0)))!=(fbinunion @ (fbinintersect @ (fsetminus @ esk717_0 @ esk718_0) @ (fsetminus @ esk717_0 @ esk719_0)) @ (fbinintersect @ (fsetminus @ esk717_0 @ esk720_0) @ (fsetminus @ esk717_0 @ esk721_0)))|p1)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])])])])])).
% 19.59/19.73 thf(c_0_18, plain, ![X1356:$i, X1357:$i, X1358:$i]:(~p8|(~fin @ X1357 @ (fpowerset @ X1356)|(~fin @ X1358 @ (fpowerset @ X1356)|(fsetminus @ X1356 @ (fbinunion @ X1357 @ X1358))=(fbinintersect @ (fsetminus @ X1356 @ X1357) @ (fsetminus @ X1356 @ X1358))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax8])])])).
% 19.59/19.73 thf(c_0_19, plain, (p5|p8), inference(split_conjunct,[status(thm)],[ax1022])).
% 19.59/19.73 thf(c_0_20, plain, ~p5, inference(sr,[status(thm)],[c_0_15, c_0_16])).
% 19.59/19.73 thf(c_0_21, plain, (p1|(fsetminus @ esk717_0 @ (fbinintersect @ (fbinunion @ esk718_0 @ esk719_0) @ (fbinunion @ esk720_0 @ esk721_0)))!=(fbinunion @ (fbinintersect @ (fsetminus @ esk717_0 @ esk718_0) @ (fsetminus @ esk717_0 @ esk719_0)) @ (fbinintersect @ (fsetminus @ esk717_0 @ esk720_0) @ (fsetminus @ esk717_0 @ esk721_0)))), inference(split_conjunct,[status(thm)],[c_0_17])).
% 19.59/19.73 thf(c_0_22, plain, ![X1:$i, X3:$i, X2:$i]:((fsetminus @ X2 @ (fbinunion @ X1 @ X3))=(fbinintersect @ (fsetminus @ X2 @ X1) @ (fsetminus @ X2 @ X3))|~p8|~fin @ X1 @ (fpowerset @ X2)|~fin @ X3 @ (fpowerset @ X2)), inference(split_conjunct,[status(thm)],[c_0_18])).
% 19.59/19.73 thf(c_0_23, plain, p8, inference(sr,[status(thm)],[c_0_19, c_0_20])).
% 19.59/19.73 thf(c_0_24, plain, (fin @ esk721_0 @ (fpowerset @ esk717_0)|p1), inference(split_conjunct,[status(thm)],[c_0_17])).
% 19.59/19.73 thf(c_0_25, plain, (fin @ esk720_0 @ (fpowerset @ esk717_0)|p1), inference(split_conjunct,[status(thm)],[c_0_17])).
% 19.59/19.73 thf(c_0_26, plain, (fbinunion @ (fbinintersect @ (fsetminus @ esk717_0 @ esk718_0) @ (fsetminus @ esk717_0 @ esk719_0)) @ (fbinintersect @ (fsetminus @ esk717_0 @ esk720_0) @ (fsetminus @ esk717_0 @ esk721_0)))!=(fsetminus @ esk717_0 @ (fbinintersect @ (fbinunion @ esk718_0 @ esk719_0) @ (fbinunion @ esk720_0 @ esk721_0))), inference(sr,[status(thm)],[c_0_21, c_0_14])).
% 19.59/19.73 thf(c_0_27, plain, ![X3:$i, X2:$i, X1:$i]:((fbinintersect @ (fsetminus @ X1 @ X2) @ (fsetminus @ X1 @ X3))=(fsetminus @ X1 @ (fbinunion @ X2 @ X3))|~fin @ X3 @ (fpowerset @ X1)|~fin @ X2 @ (fpowerset @ X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22, c_0_23])])).
% 19.59/19.73 thf(c_0_28, plain, fin @ esk721_0 @ (fpowerset @ esk717_0), inference(sr,[status(thm)],[c_0_24, c_0_14])).
% 19.59/19.73 thf(c_0_29, plain, fin @ esk720_0 @ (fpowerset @ esk717_0), inference(sr,[status(thm)],[c_0_25, c_0_14])).
% 19.59/19.73 thf(c_0_30, plain, (fin @ esk719_0 @ (fpowerset @ esk717_0)|p1), inference(split_conjunct,[status(thm)],[c_0_17])).
% 19.59/19.73 thf(c_0_31, plain, (fin @ esk718_0 @ (fpowerset @ esk717_0)|p1), inference(split_conjunct,[status(thm)],[c_0_17])).
% 19.59/19.73 thf(c_0_32, plain, ![X1386:$i, X1387:$i, X1388:$i]:(~p4|(~fin @ X1387 @ (fpowerset @ X1386)|(~fin @ X1388 @ (fpowerset @ X1386)|(fsetminus @ X1386 @ (fbinintersect @ X1387 @ X1388))=(fbinunion @ (fsetminus @ X1386 @ X1387) @ (fsetminus @ X1386 @ X1388))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax4])])])).
% 19.59/19.73 thf(c_0_33, plain, (p3|p4), inference(split_conjunct,[status(thm)],[ax1026])).
% 19.59/19.73 thf(c_0_34, plain, (fbinunion @ (fbinintersect @ (fsetminus @ esk717_0 @ esk718_0) @ (fsetminus @ esk717_0 @ esk719_0)) @ (fsetminus @ esk717_0 @ (fbinunion @ esk720_0 @ esk721_0)))!=(fsetminus @ esk717_0 @ (fbinintersect @ (fbinunion @ esk718_0 @ esk719_0) @ (fbinunion @ esk720_0 @ esk721_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26, c_0_27]), c_0_28]), c_0_29])])).
% 19.59/19.73 thf(c_0_35, plain, fin @ esk719_0 @ (fpowerset @ esk717_0), inference(sr,[status(thm)],[c_0_30, c_0_14])).
% 19.59/19.73 thf(c_0_36, plain, fin @ esk718_0 @ (fpowerset @ esk717_0), inference(sr,[status(thm)],[c_0_31, c_0_14])).
% 19.59/19.73 thf(c_0_37, plain, ![X1:$i, X3:$i, X2:$i]:((fsetminus @ X2 @ (fbinintersect @ X1 @ X3))=(fbinunion @ (fsetminus @ X2 @ X1) @ (fsetminus @ X2 @ X3))|~p4|~fin @ X1 @ (fpowerset @ X2)|~fin @ X3 @ (fpowerset @ X2)), inference(split_conjunct,[status(thm)],[c_0_32])).
% 19.59/19.73 thf(c_0_38, plain, p4, inference(sr,[status(thm)],[c_0_33, c_0_16])).
% 19.59/19.73 thf(c_0_39, plain, ![X1414:$i, X1415:$i, X1416:$i]:(~p2|(~fin @ X1415 @ (fpowerset @ X1414)|(~fin @ X1416 @ (fpowerset @ X1414)|fin @ (fbinunion @ X1415 @ X1416) @ (fpowerset @ X1414)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax2])])])).
% 19.59/19.73 thf(c_0_40, plain, (p1|p2), inference(split_conjunct,[status(thm)],[ax1028])).
% 19.59/19.73 thf(c_0_41, plain, (fbinunion @ (fsetminus @ esk717_0 @ (fbinunion @ esk718_0 @ esk719_0)) @ (fsetminus @ esk717_0 @ (fbinunion @ esk720_0 @ esk721_0)))!=(fsetminus @ esk717_0 @ (fbinintersect @ (fbinunion @ esk718_0 @ esk719_0) @ (fbinunion @ esk720_0 @ esk721_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34, c_0_27]), c_0_35]), c_0_36])])).
% 19.59/19.73 thf(c_0_42, plain, ![X3:$i, X2:$i, X1:$i]:((fsetminus @ X1 @ (fbinintersect @ X2 @ X3))=(fbinunion @ (fsetminus @ X1 @ X2) @ (fsetminus @ X1 @ X3))|~fin @ X3 @ (fpowerset @ X1)|~fin @ X2 @ (fpowerset @ X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37, c_0_38])])).
% 19.59/19.73 thf(c_0_43, plain, ![X1:$i, X3:$i, X2:$i]:(fin @ (fbinunion @ X1 @ X3) @ (fpowerset @ X2)|~p2|~fin @ X1 @ (fpowerset @ X2)|~fin @ X3 @ (fpowerset @ X2)), inference(split_conjunct,[status(thm)],[c_0_39])).
% 19.59/19.73 thf(c_0_44, plain, p2, inference(sr,[status(thm)],[c_0_40, c_0_14])).
% 19.59/19.73 thf(c_0_45, plain, (~fin @ (fbinunion @ esk720_0 @ esk721_0) @ (fpowerset @ esk717_0)|~fin @ (fbinunion @ esk718_0 @ esk719_0) @ (fpowerset @ esk717_0)), inference(spm,[status(thm)],[c_0_41, c_0_42])).
% 19.59/19.73 thf(c_0_46, plain, ![X1:$i, X2:$i, X3:$i]:(fin @ (fbinunion @ X1 @ X2) @ (fpowerset @ X3)|~fin @ X2 @ (fpowerset @ X3)|~fin @ X1 @ (fpowerset @ X3)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43, c_0_44])])).
% 19.59/19.73 thf(c_0_47, plain, ~fin @ (fbinunion @ esk718_0 @ esk719_0) @ (fpowerset @ esk717_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_46]), c_0_28]), c_0_29])])).
% 19.59/19.73 thf(c_0_48, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_46]), c_0_35]), c_0_36])]), ['proof']).
% 19.59/19.73 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 19.59/19.73 thf(0,theorem,((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binunion @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5)))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 19.59/19.73 % SZS output end Proof
%------------------------------------------------------------------------------