%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU150+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:27:02 AM UTC 2025
% Result : Theorem 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU150+1 : TPTP v9.0.0. Released v3.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 : Fri Jun 20 06:07:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(unordered_pair_type, type, (
% 0.18/0.37 unordered_pair: ( $i * $i ) > $i)).
% 0.18/0.37 tff(tptp_fun_B_1_type, type, (
% 0.18/0.37 tptp_fun_B_1: $i)).
% 0.18/0.37 tff(tptp_fun_C_0_type, type, (
% 0.18/0.37 tptp_fun_C_0: $i)).
% 0.18/0.37 tff(singleton_type, type, (
% 0.18/0.37 singleton: $i > $i)).
% 0.18/0.37 tff(tptp_fun_A_2_type, type, (
% 0.18/0.37 tptp_fun_A_2: $i)).
% 0.18/0.37 tff(1,plain,
% 0.18/0.37 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(4,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.37 tff(6,plain,(
% 0.18/0.37 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.18/0.37 inference(skolemize,[status(sab)],[5])).
% 0.18/0.37 tff(7,plain,
% 0.18/0.37 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(B!1, C!0) = unordered_pair(C!0, B!1))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 (unordered_pair(B!1, C!0) = unordered_pair(C!0, B!1)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))) <=> (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(11,plain,
% 0.18/0.37 ((~![A: $i, B: $i, C: $i] : ((singleton(A) = unordered_pair(B, C)) => (B = C))) <=> (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(12,axiom,(~![A: $i, B: $i, C: $i] : ((singleton(A) = unordered_pair(B, C)) => (B = C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t9_zfmisc_1')).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.18/0.37 tff(14,plain,
% 0.18/0.37 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.18/0.37 tff(15,plain,
% 0.18/0.37 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.18/0.37 tff(16,plain,
% 0.18/0.37 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.18/0.37 tff(17,plain,(
% 0.18/0.37 ~((~(singleton(A!2) = unordered_pair(B!1, C!0))) | (B!1 = C!0))),
% 0.18/0.37 inference(skolemize,[status(sab)],[16])).
% 0.18/0.37 tff(18,plain,
% 0.18/0.37 (singleton(A!2) = unordered_pair(B!1, C!0)),
% 0.18/0.37 inference(or_elim,[status(thm)],[17])).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 (^[A: $i, B: $i, C: $i] : refl(((~(singleton(A) = unordered_pair(B, C))) | (A = B)) <=> ((~(singleton(A) = unordered_pair(B, C))) | (A = B)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(20,plain,
% 0.18/0.37 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B)) <=> ![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[19])).
% 0.18/0.37 tff(21,plain,
% 0.18/0.37 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B)) <=> ![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(22,plain,
% 0.18/0.37 (^[A: $i, B: $i, C: $i] : rewrite(((singleton(A) = unordered_pair(B, C)) => (A = B)) <=> ((~(singleton(A) = unordered_pair(B, C))) | (A = B)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(23,plain,
% 0.18/0.37 (![A: $i, B: $i, C: $i] : ((singleton(A) = unordered_pair(B, C)) => (A = B)) <=> ![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[22])).
% 0.18/0.37 tff(24,axiom,(![A: $i, B: $i, C: $i] : ((singleton(A) = unordered_pair(B, C)) => (A = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_zfmisc_1')).
% 0.18/0.37 tff(25,plain,
% 0.18/0.37 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.18/0.37 tff(26,plain,
% 0.18/0.37 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.18/0.37 tff(27,plain,(
% 0.18/0.37 ![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.18/0.37 inference(skolemize,[status(sab)],[26])).
% 0.18/0.37 tff(28,plain,
% 0.18/0.37 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 (((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | ((~(singleton(A!2) = unordered_pair(B!1, C!0))) | (A!2 = B!1))) <=> ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | (~(singleton(A!2) = unordered_pair(B!1, C!0))) | (A!2 = B!1))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(30,plain,
% 0.18/0.37 ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | ((~(singleton(A!2) = unordered_pair(B!1, C!0))) | (A!2 = B!1))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(31,plain,
% 0.18/0.37 ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | (~(singleton(A!2) = unordered_pair(B!1, C!0))) | (A!2 = B!1)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.18/0.37 tff(32,plain,
% 0.18/0.37 (A!2 = B!1),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[31, 28, 18])).
% 0.18/0.37 tff(33,plain,
% 0.18/0.37 (B!1 = A!2),
% 0.18/0.37 inference(symmetry,[status(thm)],[32])).
% 0.18/0.37 tff(34,plain,
% 0.18/0.37 (singleton(B!1) = singleton(A!2)),
% 0.18/0.37 inference(monotonicity,[status(thm)],[33])).
% 0.18/0.37 tff(35,plain,
% 0.18/0.37 (singleton(B!1) = unordered_pair(C!0, B!1)),
% 0.18/0.37 inference(transitivity,[status(thm)],[34, 18, 9])).
% 0.18/0.37 tff(36,plain,
% 0.18/0.37 (~(B!1 = C!0)),
% 0.18/0.37 inference(or_elim,[status(thm)],[17])).
% 0.18/0.37 tff(37,plain,
% 0.18/0.37 (((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | ((~(singleton(B!1) = unordered_pair(C!0, B!1))) | (B!1 = C!0))) <=> ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | (~(singleton(B!1) = unordered_pair(C!0, B!1))) | (B!1 = C!0))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(38,plain,
% 0.18/0.37 ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | ((~(singleton(B!1) = unordered_pair(C!0, B!1))) | (B!1 = C!0))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(39,plain,
% 0.18/0.37 ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | (~(singleton(B!1) = unordered_pair(C!0, B!1))) | (B!1 = C!0)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.18/0.37 tff(40,plain,
% 0.18/0.37 (~(singleton(B!1) = unordered_pair(C!0, B!1))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[39, 28, 36])).
% 0.18/0.37 tff(41,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[40, 35])).
% 0.18/0.37 % SZS output end Proof
% 0.18/0.37 % E exiting
%------------------------------------------------------------------------------