%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU632^2 : 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 : 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 : 300s
% DateTime : Thu Oct 9 02:44:19 PM UTC 2025
% Result : Theorem 23.85s 23.97s
% Output : Proof 23.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU632^2 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n023.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 21:55:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 23.85/23.97 % SZS status Theorem
% 23.85/23.97 % Mode: mode371
% 23.85/23.97 % Inferences: 4100
% 23.85/23.97 % SZS output start Proof
% 23.85/23.97 thf(def_iskpair,definition,(iskpair = (^[X1:$i]:(~((![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (![X3:$i]:(((in @ X3) @ (setunion @ X1)) => (~((X1 = ((setadjoin @ ((setadjoin @ X2) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X2) @ ((setadjoin @ X3) @ emptyset))) @ emptyset)))))))))))))).
% 23.85/23.97 thf(def_kpair,definition,(kpair = (^[X1:$i]:(^[X2:$i]:((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))).
% 23.85/23.97 thf(def_kpairp,definition,(kpairp = (![X1:$i]:(![X2:$i]:(iskpair @ ((kpair @ X1) @ X2)))))).
% 23.85/23.97 thf(def_cartprodmempair1,definition,(cartprodmempair1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))))).
% 23.85/23.97 thf(cartprodmempair,conjecture,(kpairp => (cartprodmempair1 => (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3)))))))).
% 23.85/23.97 thf(h0,negated_conjecture,(~((kpairp => (cartprodmempair1 => (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))))))),inference(assume_negation,[status(cth)],[cartprodmempair])).
% 23.85/23.97 thf(ax102, axiom, (p1|~(p7)), file('<stdin>', ax102)).
% 23.85/23.97 thf(ax108, axiom, ~(p1), file('<stdin>', ax108)).
% 23.85/23.97 thf(nax1, axiom, (p1<=(fkpairp=>(fcartprodmempair1=>![X8:$i, X9:$i, X3:$i]:(fin @ X3 @ (fcartprod @ X8 @ X9)=>fiskpair @ X3)))), file('<stdin>', nax1)).
% 23.85/23.97 thf(nax6, axiom, (p6<=fkpairp), file('<stdin>', nax6)).
% 23.85/23.97 thf(ax0, axiom, (~(p5)|~(p8)|p85), file('<stdin>', ax0)).
% 23.85/23.97 thf(ax101, axiom, (p7|p8), file('<stdin>', ax101)).
% 23.85/23.97 thf(ax9, axiom, (~(p4)|~(p6)|p78), file('<stdin>', ax9)).
% 23.85/23.97 thf(pax85, axiom, (p85=>![X1:$i, X2:$i, X3:$i]:(fin @ X3 @ (fcartprod @ X1 @ X2)=>~(![X4:$i]:(fin @ X4 @ X1=>![X5:$i]:(fin @ X5 @ X2=>~((X3)=(fkpair @ X4 @ X5))))))), file('<stdin>', pax85)).
% 23.85/23.97 thf(ax104, axiom, p5, file('<stdin>', ax104)).
% 23.85/23.97 thf(pax78, axiom, (p78=>![X1:$i, X2:$i]:fiskpair @ (fkpair @ X1 @ X2)), file('<stdin>', pax78)).
% 23.85/23.97 thf(ax105, axiom, p4, file('<stdin>', ax105)).
% 23.85/23.97 thf(c_0_11, plain, (p1|~p7), inference(fof_simplification,[status(thm)],[ax102])).
% 23.85/23.97 thf(c_0_12, plain, ~p1, inference(fof_simplification,[status(thm)],[ax108])).
% 23.85/23.97 thf(c_0_13, plain, ((fkpairp|p1)&((fcartprodmempair1|p1)&((fin @ esk32_0 @ (fcartprod @ esk30_0 @ esk31_0)|p1)&(~fiskpair @ esk32_0|p1)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])])])])).
% 23.85/23.97 thf(c_0_14, plain, (p1|~p7), inference(split_conjunct,[status(thm)],[c_0_11])).
% 23.85/23.97 thf(c_0_15, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_12])).
% 23.85/23.97 thf(c_0_16, plain, (~fkpairp|p6), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax6])])).
% 23.85/23.97 thf(c_0_17, plain, (fkpairp|p1), inference(split_conjunct,[status(thm)],[c_0_13])).
% 23.85/23.97 thf(c_0_18, plain, (~p5|~p8|p85), inference(fof_simplification,[status(thm)],[ax0])).
% 23.85/23.97 thf(c_0_19, plain, (p7|p8), inference(split_conjunct,[status(thm)],[ax101])).
% 23.85/23.97 thf(c_0_20, plain, ~p7, inference(sr,[status(thm)],[c_0_14, c_0_15])).
% 23.85/23.97 thf(c_0_21, plain, (~p4|~p6|p78), inference(fof_simplification,[status(thm)],[ax9])).
% 23.85/23.97 thf(c_0_22, plain, (p6|~fkpairp), inference(split_conjunct,[status(thm)],[c_0_16])).
% 23.85/23.97 thf(c_0_23, plain, fkpairp, inference(sr,[status(thm)],[c_0_17, c_0_15])).
% 23.85/23.97 thf(c_0_24, plain, ![X18:$i, X19:$i, X20:$i]:((fin @ (esk5_3 @ X18 @ X19 @ X20) @ X18|~fin @ X20 @ (fcartprod @ X18 @ X19)|~p85)&((fin @ (esk6_3 @ X18 @ X19 @ X20) @ X19|~fin @ X20 @ (fcartprod @ X18 @ X19)|~p85)&((X20)=(fkpair @ (esk5_3 @ X18 @ X19 @ X20) @ (esk6_3 @ X18 @ X19 @ X20))|~fin @ X20 @ (fcartprod @ X18 @ X19)|~p85))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax85])])])])])])).
% 23.85/23.97 thf(c_0_25, plain, (p85|~p5|~p8), inference(split_conjunct,[status(thm)],[c_0_18])).
% 23.85/23.97 thf(c_0_26, plain, p5, inference(split_conjunct,[status(thm)],[ax104])).
% 23.85/23.97 thf(c_0_27, plain, p8, inference(sr,[status(thm)],[c_0_19, c_0_20])).
% 23.85/23.97 thf(c_0_28, plain, ![X30:$i, X31:$i]:(~p78|fiskpair @ (fkpair @ X30 @ X31)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax78])])])).
% 23.85/23.97 thf(c_0_29, plain, (p78|~p4|~p6), inference(split_conjunct,[status(thm)],[c_0_21])).
% 23.85/23.97 thf(c_0_30, plain, p4, inference(split_conjunct,[status(thm)],[ax105])).
% 23.85/23.97 thf(c_0_31, plain, p6, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22, c_0_23])])).
% 23.85/23.97 thf(c_0_32, plain, ![X1:$i, X2:$i, X3:$i]:((X1)=(fkpair @ (esk5_3 @ X2 @ X3 @ X1) @ (esk6_3 @ X2 @ X3 @ X1))|~fin @ X1 @ (fcartprod @ X2 @ X3)|~p85), inference(split_conjunct,[status(thm)],[c_0_24])).
% 23.85/23.97 thf(c_0_33, plain, p85, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25, c_0_26]), c_0_27])])).
% 23.85/23.97 thf(c_0_34, plain, (fin @ esk32_0 @ (fcartprod @ esk30_0 @ esk31_0)|p1), inference(split_conjunct,[status(thm)],[c_0_13])).
% 23.85/23.97 thf(c_0_35, plain, ![X1:$i, X2:$i]:(fiskpair @ (fkpair @ X1 @ X2)|~p78), inference(split_conjunct,[status(thm)],[c_0_28])).
% 23.85/23.97 thf(c_0_36, plain, p78, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29, c_0_30]), c_0_31])])).
% 23.85/23.97 thf(c_0_37, plain, ![X1:$i, X3:$i, X2:$i]:((fkpair @ (esk5_3 @ X1 @ X2 @ X3) @ (esk6_3 @ X1 @ X2 @ X3))=(X3)|~fin @ X3 @ (fcartprod @ X1 @ X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32, c_0_33])])).
% 23.85/23.97 thf(c_0_38, plain, fin @ esk32_0 @ (fcartprod @ esk30_0 @ esk31_0), inference(sr,[status(thm)],[c_0_34, c_0_15])).
% 23.85/23.97 thf(c_0_39, plain, (p1|~fiskpair @ esk32_0), inference(split_conjunct,[status(thm)],[c_0_13])).
% 23.85/23.97 thf(c_0_40, plain, ![X1:$i, X2:$i]:fiskpair @ (fkpair @ X1 @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35, c_0_36])])).
% 23.85/23.97 thf(c_0_41, plain, (fkpair @ (esk5_3 @ esk30_0 @ esk31_0 @ esk32_0) @ (esk6_3 @ esk30_0 @ esk31_0 @ esk32_0))=(esk32_0), inference(spm,[status(thm)],[c_0_37, c_0_38])).
% 23.85/23.97 thf(c_0_42, plain, ~fiskpair @ esk32_0, inference(sr,[status(thm)],[c_0_39, c_0_15])).
% 23.85/23.97 thf(c_0_43, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_41]), c_0_42]), ['proof']).
% 23.85/23.97 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 23.85/23.97 thf(0,theorem,(kpairp => (cartprodmempair1 => (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 23.85/23.97 % SZS output end Proof
%------------------------------------------------------------------------------