%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ133+2 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 : Sat Jun 21 05:23:28 AM UTC 2025
% Result : Theorem 1.47s 1.65s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : PUZ133+2 : TPTP v9.0.0. Released v4.1.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n001.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 : 300
% 0.12/0.34 % DateTime : Fri Jun 20 02:51:34 EDT 2025
% 0.19/0.34 % CPUTime :
% 1.47/1.65 % SZS status Theorem
% 1.47/1.65 % SZS output start Proof
% 1.47/1.65 tff(plus_type, type, (
% 1.47/1.65 plus: ( $i * $i ) > $i)).
% 1.47/1.65 tff(tptp_fun_I_1_type, type, (
% 1.47/1.65 tptp_fun_I_1: $i)).
% 1.47/1.65 tff(p_type, type, (
% 1.47/1.65 p: $i > $i)).
% 1.47/1.65 tff(perm_type, type, (
% 1.47/1.65 perm: $i > $i)).
% 1.47/1.65 tff(tptp_fun_J_0_type, type, (
% 1.47/1.65 tptp_fun_J_0: $i)).
% 1.47/1.65 tff(q_type, type, (
% 1.47/1.65 q: $i > $i)).
% 1.47/1.65 tff(queens_p_type, type, (
% 1.47/1.65 queens_p: $o)).
% 1.47/1.65 tff(queens_q_type, type, (
% 1.47/1.65 queens_q: $o)).
% 1.47/1.65 tff(minus_type, type, (
% 1.47/1.65 minus: ( $i * $i ) > $i)).
% 1.47/1.65 tff(le_type, type, (
% 1.47/1.65 le: ( $i * $i ) > $o)).
% 1.47/1.65 tff(s_type, type, (
% 1.47/1.65 s: $i > $i)).
% 1.47/1.65 tff(n_type, type, (
% 1.47/1.65 n: $i)).
% 1.47/1.65 tff(n0_type, type, (
% 1.47/1.65 n0: $i)).
% 1.47/1.65 tff(1,plain,
% 1.47/1.65 (^[I: $i] : refl((q(I) = p(perm(I))) <=> (q(I) = p(perm(I))))),
% 1.47/1.65 inference(bind,[status(th)],[])).
% 1.47/1.65 tff(2,plain,
% 1.47/1.65 (![I: $i] : (q(I) = p(perm(I))) <=> ![I: $i] : (q(I) = p(perm(I)))),
% 1.47/1.65 inference(quant_intro,[status(thm)],[1])).
% 1.47/1.65 tff(3,plain,
% 1.47/1.65 (![I: $i] : (q(I) = p(perm(I))) <=> ![I: $i] : (q(I) = p(perm(I)))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(4,plain,
% 1.47/1.65 ((~((queens_p & ![I: $i] : (q(I) = p(perm(I)))) => queens_q)) <=> (~(queens_q | (~(queens_p & ![I: $i] : (q(I) = p(perm(I)))))))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(5,axiom,(~((queens_p & ![I: $i] : (q(I) = p(perm(I)))) => queens_q)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','queens_sym')).
% 1.47/1.65 tff(6,plain,
% 1.47/1.65 (~(queens_q | (~(queens_p & ![I: $i] : (q(I) = p(perm(I))))))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[5, 4])).
% 1.47/1.65 tff(7,plain,
% 1.47/1.65 (queens_p & ![I: $i] : (q(I) = p(perm(I)))),
% 1.47/1.65 inference(or_elim,[status(thm)],[6])).
% 1.47/1.65 tff(8,plain,
% 1.47/1.65 (![I: $i] : (q(I) = p(perm(I)))),
% 1.47/1.65 inference(and_elim,[status(thm)],[7])).
% 1.47/1.65 tff(9,plain,
% 1.47/1.65 (![I: $i] : (q(I) = p(perm(I)))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[8, 3])).
% 1.47/1.65 tff(10,plain,(
% 1.47/1.65 ![I: $i] : (q(I) = p(perm(I)))),
% 1.47/1.65 inference(skolemize,[status(sab)],[9])).
% 1.47/1.65 tff(11,plain,
% 1.47/1.65 (![I: $i] : (q(I) = p(perm(I)))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[10, 2])).
% 1.47/1.65 tff(12,plain,
% 1.47/1.65 ((~![I: $i] : (q(I) = p(perm(I)))) | (q(I!1) = p(perm(I!1)))),
% 1.47/1.65 inference(quant_inst,[status(thm)],[])).
% 1.47/1.65 tff(13,plain,
% 1.47/1.65 (q(I!1) = p(perm(I!1))),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[12, 11])).
% 1.47/1.65 tff(14,plain,
% 1.47/1.65 (p(perm(I!1)) = q(I!1)),
% 1.47/1.65 inference(symmetry,[status(thm)],[13])).
% 1.47/1.65 tff(15,plain,
% 1.47/1.65 (plus(p(perm(I!1)), I!1) = plus(q(I!1), I!1)),
% 1.47/1.65 inference(monotonicity,[status(thm)],[14])).
% 1.47/1.65 tff(16,plain,
% 1.47/1.65 (plus(q(I!1), I!1) = plus(p(perm(I!1)), I!1)),
% 1.47/1.65 inference(symmetry,[status(thm)],[15])).
% 1.47/1.65 tff(17,plain,
% 1.47/1.65 ((~queens_q) <=> (~queens_q)),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(18,plain,
% 1.47/1.65 (~queens_q),
% 1.47/1.65 inference(or_elim,[status(thm)],[6])).
% 1.47/1.65 tff(19,plain,
% 1.47/1.65 (~queens_q),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[18, 17])).
% 1.47/1.65 tff(20,plain,
% 1.47/1.65 ((queens_q | (~((~(le(s(n0), I!1) & le(I!1, n) & le(s(I!1), J!0) & le(J!0, n) & (le(s(I!1), J!0) <=> le(s(perm(J!0)), perm(I!1))))) | ((~(q(I!1) = q(J!0))) & (~(plus(q(I!1), I!1) = plus(q(J!0), J!0))) & (~(minus(q(I!1), I!1) = minus(q(J!0), J!0))))))) <=> (queens_q | (~((~le(s(n0), I!1)) | (~le(I!1, n)) | (~le(s(I!1), J!0)) | (~le(J!0, n)) | (~(le(s(I!1), J!0) <=> le(s(perm(J!0)), perm(I!1)))) | (~((q(I!1) = q(J!0)) | (plus(q(I!1), I!1) = plus(q(J!0), J!0)) | (minus(q(I!1), I!1) = minus(q(J!0), J!0)))))))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(21,plain,
% 1.47/1.65 ((~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))) <=> (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(22,plain,
% 1.47/1.65 ((queens_q | (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))))) <=> (queens_q | (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))))),
% 1.47/1.65 inference(monotonicity,[status(thm)],[21])).
% 1.47/1.65 tff(23,plain,
% 1.47/1.65 ((queens_q | (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))))) <=> (queens_q | (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(24,plain,
% 1.47/1.65 ((![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))) => queens_q) <=> (queens_q | (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(25,plain,
% 1.47/1.65 (^[I: $i, J: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((le(s(n0), I) & le(I, n)) & le(s(I), J)) <=> (le(s(n0), I) & le(I, n) & le(s(I), J))), ((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) <=> ((le(s(n0), I) & le(I, n) & le(s(I), J)) & le(J, n)))), rewrite(((le(s(n0), I) & le(I, n) & le(s(I), J)) & le(J, n)) <=> (le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))), ((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) <=> (le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n)))), (((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) <=> ((le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n)) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))))), rewrite(((le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n)) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) <=> (le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))), (((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) <=> (le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))))), rewrite((((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J)))) & (~(minus(q(I), I) = minus(q(J), J)))) <=> ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))), ((((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) => (((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J)))) & (~(minus(q(I), I) = minus(q(J), J))))) <=> ((le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) => ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))))), rewrite(((le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) => ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))) <=> ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))), ((((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) => (((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J)))) & (~(minus(q(I), I) = minus(q(J), J))))) <=> ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))))),
% 1.47/1.65 inference(bind,[status(th)],[])).
% 1.47/1.65 tff(26,plain,
% 1.47/1.65 (![I: $i, J: $i] : (((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) => (((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J)))) & (~(minus(q(I), I) = minus(q(J), J))))) <=> ![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))),
% 1.47/1.65 inference(quant_intro,[status(thm)],[25])).
% 1.47/1.65 tff(27,plain,
% 1.47/1.65 ((![I: $i, J: $i] : (((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) => (((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J)))) & (~(minus(q(I), I) = minus(q(J), J))))) => queens_q) <=> (![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))) => queens_q)),
% 1.47/1.65 inference(monotonicity,[status(thm)],[26])).
% 1.47/1.65 tff(28,plain,
% 1.47/1.65 ((![I: $i, J: $i] : (((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) => (((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J)))) & (~(minus(q(I), I) = minus(q(J), J))))) => queens_q) <=> (queens_q | (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))))),
% 1.47/1.65 inference(transitivity,[status(thm)],[27, 24])).
% 1.47/1.65 tff(29,axiom,(![I: $i, J: $i] : (((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) => (((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J)))) & (~(minus(q(I), I) = minus(q(J), J))))) => queens_q), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','queens_q')).
% 1.47/1.65 tff(30,plain,
% 1.47/1.65 (queens_q | (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[29, 28])).
% 1.47/1.65 tff(31,plain,
% 1.47/1.65 (queens_q | (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[30, 22])).
% 1.47/1.65 tff(32,plain,
% 1.47/1.65 (queens_q | (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[31, 23])).
% 1.47/1.65 tff(33,plain,
% 1.47/1.65 (queens_q | (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[32, 22])).
% 1.47/1.65 Proof display could not be completed: monotonicity rule is not handled
% 1.47/1.66 % E exiting
%------------------------------------------------------------------------------