%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU658^2 : 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 : n029.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 02:44:43 PM UTC 2025
% Result : Theorem 1.47s 1.65s
% Output : Proof 1.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU658^2 : TPTP v9.2.0. Released v3.7.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Oct 8 20:40:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.47/1.65 % SZS status Theorem
% 1.47/1.65 % Mode: mode506
% 1.47/1.65 % Inferences: 79
% 1.47/1.65 % SZS output start Proof
% 1.47/1.65 thf(def_cartprodmempair1,definition,(cartprodmempair1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))))).
% 1.47/1.65 thf(def_ksndpairEq,definition,(ksndpairEq = (![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))))).
% 1.47/1.65 thf(cartprodsndin,conjecture,((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2)))))))).
% 1.47/1.65 thf(h0,negated_conjecture,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))))))),inference(assume_negation,[status(cth)],[cartprodsndin])).
% 1.47/1.65 thf(ax1128, axiom, ~(p1), file('<stdin>', ax1128)).
% 1.47/1.65 thf(nax1, axiom, (p1<=(![X1:$i, X2:$i, X3:$i]:(fin @ X3 @ (fcartprod @ X1 @ X2)=>~(![X4:$i]:(fin @ X4 @ X1=>![X5:$i]:(fin @ X5 @ X2=>~((X3)=(fkpair @ X4 @ X5))))))=>(![X1:$i, X2:$i]:(fksnd @ (fkpair @ X1 @ X2))=(X2)=>![X1:$i, X2:$i, X3:$i]:(fin @ X3 @ (fcartprod @ X1 @ X2)=>fin @ (fksnd @ X3) @ X2)))), file('<stdin>', nax1)).
% 1.47/1.65 thf(pax2, axiom, (p2=>![X1:$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>', pax2)).
% 1.47/1.65 thf(ax1127, axiom, (p1|p2), file('<stdin>', ax1127)).
% 1.47/1.65 thf(c_0_4, plain, ~p1, inference(fof_simplification,[status(thm)],[ax1128])).
% 1.47/1.65 thf(c_0_5, plain, ![X1198:$i, X1199:$i, X1200:$i, X1203:$i, X1204:$i]:(((fin @ (esk597_3 @ X1198 @ X1199 @ X1200) @ X1198|~fin @ X1200 @ (fcartprod @ X1198 @ X1199)|p1)&((fin @ (esk598_3 @ X1198 @ X1199 @ X1200) @ X1199|~fin @ X1200 @ (fcartprod @ X1198 @ X1199)|p1)&((X1200)=(fkpair @ (esk597_3 @ X1198 @ X1199 @ X1200) @ (esk598_3 @ X1198 @ X1199 @ X1200))|~fin @ X1200 @ (fcartprod @ X1198 @ X1199)|p1)))&(((fksnd @ (fkpair @ X1203 @ X1204))=(X1204)|p1)&((fin @ esk601_0 @ (fcartprod @ esk599_0 @ esk600_0)|p1)&(~fin @ (fksnd @ esk601_0) @ esk600_0|p1)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])])])])])).
% 1.47/1.65 thf(c_0_6, plain, ![X1178:$i, X1179:$i, X1180:$i]:((fin @ (esk587_3 @ X1178 @ X1179 @ X1180) @ X1178|~fin @ X1180 @ (fcartprod @ X1178 @ X1179)|~p2)&((fin @ (esk588_3 @ X1178 @ X1179 @ X1180) @ X1179|~fin @ X1180 @ (fcartprod @ X1178 @ X1179)|~p2)&((X1180)=(fkpair @ (esk587_3 @ X1178 @ X1179 @ X1180) @ (esk588_3 @ X1178 @ X1179 @ X1180))|~fin @ X1180 @ (fcartprod @ X1178 @ X1179)|~p2))), 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)],[pax2])])])])])])).
% 1.47/1.65 thf(c_0_7, plain, (p1|p2), inference(split_conjunct,[status(thm)],[ax1127])).
% 1.47/1.65 thf(c_0_8, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_4])).
% 1.47/1.65 thf(c_0_9, plain, ![X1:$i, X2:$i]:((fksnd @ (fkpair @ X1 @ X2))=(X2)|p1), inference(split_conjunct,[status(thm)],[c_0_5])).
% 1.47/1.65 thf(c_0_10, plain, ![X1:$i, X2:$i, X3:$i]:((X1)=(fkpair @ (esk587_3 @ X2 @ X3 @ X1) @ (esk588_3 @ X2 @ X3 @ X1))|~fin @ X1 @ (fcartprod @ X2 @ X3)|~p2), inference(split_conjunct,[status(thm)],[c_0_6])).
% 1.47/1.65 thf(c_0_11, plain, p2, inference(sr,[status(thm)],[c_0_7, c_0_8])).
% 1.47/1.65 thf(c_0_12, plain, ![X1:$i, X3:$i, X2:$i]:(fin @ (esk588_3 @ X1 @ X2 @ X3) @ X2|~fin @ X3 @ (fcartprod @ X1 @ X2)|~p2), inference(split_conjunct,[status(thm)],[c_0_6])).
% 1.47/1.65 thf(c_0_13, plain, ![X1:$i, X2:$i]:(fksnd @ (fkpair @ X1 @ X2))=(X2), inference(sr,[status(thm)],[c_0_9, c_0_8])).
% 1.47/1.65 thf(c_0_14, plain, ![X1:$i, X3:$i, X2:$i]:((fkpair @ (esk587_3 @ X1 @ X2 @ X3) @ (esk588_3 @ X1 @ X2 @ X3))=(X3)|~fin @ X3 @ (fcartprod @ X1 @ X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10, c_0_11])])).
% 1.47/1.65 thf(c_0_15, plain, ![X1:$i, X3:$i, X2:$i]:(fin @ (esk588_3 @ X1 @ X2 @ X3) @ X2|~fin @ X3 @ (fcartprod @ X1 @ X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_11])])).
% 1.47/1.65 thf(c_0_16, plain, ![X1:$i, X3:$i, X2:$i]:((esk588_3 @ X1 @ X2 @ X3)=(fksnd @ X3)|~fin @ X3 @ (fcartprod @ X1 @ X2)), inference(spm,[status(thm)],[c_0_13, c_0_14])).
% 1.47/1.65 thf(c_0_17, plain, (fin @ esk601_0 @ (fcartprod @ esk599_0 @ esk600_0)|p1), inference(split_conjunct,[status(thm)],[c_0_5])).
% 1.47/1.65 thf(c_0_18, plain, (p1|~fin @ (fksnd @ esk601_0) @ esk600_0), inference(split_conjunct,[status(thm)],[c_0_5])).
% 1.47/1.65 thf(c_0_19, plain, ![X1:$i, X3:$i, X2:$i]:(fin @ (fksnd @ X1) @ X2|~fin @ X1 @ (fcartprod @ X3 @ X2)), inference(spm,[status(thm)],[c_0_15, c_0_16])).
% 1.47/1.65 thf(c_0_20, plain, fin @ esk601_0 @ (fcartprod @ esk599_0 @ esk600_0), inference(sr,[status(thm)],[c_0_17, c_0_8])).
% 1.47/1.65 thf(c_0_21, plain, ~fin @ (fksnd @ esk601_0) @ esk600_0, inference(sr,[status(thm)],[c_0_18, c_0_8])).
% 1.47/1.65 thf(c_0_22, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19, c_0_20]), c_0_21]), ['proof']).
% 1.47/1.65 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 1.47/1.65 thf(0,theorem,((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 1.47/1.65 % SZS output end Proof
%------------------------------------------------------------------------------