%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO146-1 : TPTP v9.0.0. Released v2.4.0.
% 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 05:05:41 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO146-1 : TPTP v9.0.0. Released v2.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 : Thu Jun 19 14:38:03 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(once_type, type, (
% 0.19/0.40 once: $i > $o)).
% 0.19/0.40 tff(at_the_same_time_type, type, (
% 0.19/0.40 at_the_same_time: ( $i * $i ) > $i)).
% 0.19/0.40 tff(at_type, type, (
% 0.19/0.40 at: ( $i * $i ) > $i)).
% 0.19/0.40 tff(sk29_type, type, (
% 0.19/0.40 sk29: $i)).
% 0.19/0.40 tff(sk28_type, type, (
% 0.19/0.40 sk28: $i)).
% 0.19/0.40 tff(sk27_type, type, (
% 0.19/0.40 sk27: $i)).
% 0.19/0.40 tff(connect_type, type, (
% 0.19/0.40 connect: ( $i * $i * $i ) > $o)).
% 0.19/0.40 tff(1,assumption,(~connect(sk28, sk27, sk29)), introduced(assumption)).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 (^[B: $i, A: $i, C: $i] : refl(((~once(at_the_same_time(at(A, B), at(C, B)))) | connect(A, C, B)) <=> ((~once(at_the_same_time(at(A, B), at(C, B)))) | connect(A, C, B)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (![B: $i, A: $i, C: $i] : ((~once(at_the_same_time(at(A, B), at(C, B)))) | connect(A, C, B)) <=> ![B: $i, A: $i, C: $i] : ((~once(at_the_same_time(at(A, B), at(C, B)))) | connect(A, C, B))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (![B: $i, A: $i, C: $i] : ((~once(at_the_same_time(at(A, B), at(C, B)))) | connect(A, C, B)) <=> ![B: $i, A: $i, C: $i] : ((~once(at_the_same_time(at(A, B), at(C, B)))) | connect(A, C, B))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(5,axiom,(![B: $i, A: $i, C: $i] : ((~once(at_the_same_time(at(A, B), at(C, B)))) | connect(A, C, B))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-3.ax','connect_defn_2')).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (![B: $i, A: $i, C: $i] : ((~once(at_the_same_time(at(A, B), at(C, B)))) | connect(A, C, B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.40 tff(7,plain,(
% 0.19/0.40 ![B: $i, A: $i, C: $i] : ((~once(at_the_same_time(at(A, B), at(C, B)))) | connect(A, C, B))),
% 0.19/0.40 inference(skolemize,[status(sab)],[6])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (![B: $i, A: $i, C: $i] : ((~once(at_the_same_time(at(A, B), at(C, B)))) | connect(A, C, B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (((~![B: $i, A: $i, C: $i] : ((~once(at_the_same_time(at(A, B), at(C, B)))) | connect(A, C, B))) | ((~once(at_the_same_time(at(sk28, sk29), at(sk27, sk29)))) | connect(sk28, sk27, sk29))) <=> ((~![B: $i, A: $i, C: $i] : ((~once(at_the_same_time(at(A, B), at(C, B)))) | connect(A, C, B))) | (~once(at_the_same_time(at(sk28, sk29), at(sk27, sk29)))) | connect(sk28, sk27, sk29))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 ((~![B: $i, A: $i, C: $i] : ((~once(at_the_same_time(at(A, B), at(C, B)))) | connect(A, C, B))) | ((~once(at_the_same_time(at(sk28, sk29), at(sk27, sk29)))) | connect(sk28, sk27, sk29))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 ((~![B: $i, A: $i, C: $i] : ((~once(at_the_same_time(at(A, B), at(C, B)))) | connect(A, C, B))) | (~once(at_the_same_time(at(sk28, sk29), at(sk27, sk29)))) | connect(sk28, sk27, sk29)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (~once(at_the_same_time(at(sk28, sk29), at(sk27, sk29)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 ((connect(sk27, sk28, sk29) | connect(sk28, sk27, sk29)) <=> (connect(sk27, sk28, sk29) | connect(sk28, sk27, sk29))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(14,axiom,(connect(sk27, sk28, sk29) | connect(sk28, sk27, sk29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t12_156')).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (connect(sk27, sk28, sk29) | connect(sk28, sk27, sk29)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (connect(sk27, sk28, sk29)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[15, 1])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (^[B: $i, A: $i, C: $i] : refl(((~connect(A, B, C)) | once(at_the_same_time(at(A, C), at(B, C)))) <=> ((~connect(A, B, C)) | once(at_the_same_time(at(A, C), at(B, C)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (![B: $i, A: $i, C: $i] : ((~connect(A, B, C)) | once(at_the_same_time(at(A, C), at(B, C)))) <=> ![B: $i, A: $i, C: $i] : ((~connect(A, B, C)) | once(at_the_same_time(at(A, C), at(B, C))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (![B: $i, A: $i, C: $i] : ((~connect(A, B, C)) | once(at_the_same_time(at(A, C), at(B, C)))) <=> ![B: $i, A: $i, C: $i] : ((~connect(A, B, C)) | once(at_the_same_time(at(A, C), at(B, C))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(20,axiom,(![B: $i, A: $i, C: $i] : ((~connect(A, B, C)) | once(at_the_same_time(at(A, C), at(B, C))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-3.ax','connect_defn_1')).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (![B: $i, A: $i, C: $i] : ((~connect(A, B, C)) | once(at_the_same_time(at(A, C), at(B, C))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.40 tff(22,plain,(
% 0.19/0.40 ![B: $i, A: $i, C: $i] : ((~connect(A, B, C)) | once(at_the_same_time(at(A, C), at(B, C))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[21])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (![B: $i, A: $i, C: $i] : ((~connect(A, B, C)) | once(at_the_same_time(at(A, C), at(B, C))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (((~![B: $i, A: $i, C: $i] : ((~connect(A, B, C)) | once(at_the_same_time(at(A, C), at(B, C))))) | ((~connect(sk27, sk28, sk29)) | once(at_the_same_time(at(sk27, sk29), at(sk28, sk29))))) <=> ((~![B: $i, A: $i, C: $i] : ((~connect(A, B, C)) | once(at_the_same_time(at(A, C), at(B, C))))) | (~connect(sk27, sk28, sk29)) | once(at_the_same_time(at(sk27, sk29), at(sk28, sk29))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 ((~![B: $i, A: $i, C: $i] : ((~connect(A, B, C)) | once(at_the_same_time(at(A, C), at(B, C))))) | ((~connect(sk27, sk28, sk29)) | once(at_the_same_time(at(sk27, sk29), at(sk28, sk29))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 ((~![B: $i, A: $i, C: $i] : ((~connect(A, B, C)) | once(at_the_same_time(at(A, C), at(B, C))))) | (~connect(sk27, sk28, sk29)) | once(at_the_same_time(at(sk27, sk29), at(sk28, sk29)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (once(at_the_same_time(at(sk27, sk29), at(sk28, sk29)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[26, 23, 16])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (^[B: $i, A: $i] : refl((once(at_the_same_time(B, A)) | (~once(at_the_same_time(A, B)))) <=> (once(at_the_same_time(B, A)) | (~once(at_the_same_time(A, B)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (![B: $i, A: $i] : (once(at_the_same_time(B, A)) | (~once(at_the_same_time(A, B)))) <=> ![B: $i, A: $i] : (once(at_the_same_time(B, A)) | (~once(at_the_same_time(A, B))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (![B: $i, A: $i] : (once(at_the_same_time(B, A)) | (~once(at_the_same_time(A, B)))) <=> ![B: $i, A: $i] : (once(at_the_same_time(B, A)) | (~once(at_the_same_time(A, B))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (^[B: $i, A: $i] : rewrite(((~once(at_the_same_time(A, B))) | once(at_the_same_time(B, A))) <=> (once(at_the_same_time(B, A)) | (~once(at_the_same_time(A, B)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~once(at_the_same_time(A, B))) | once(at_the_same_time(B, A))) <=> ![B: $i, A: $i] : (once(at_the_same_time(B, A)) | (~once(at_the_same_time(A, B))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.41 tff(33,axiom,(![B: $i, A: $i] : ((~once(at_the_same_time(A, B))) | once(at_the_same_time(B, A)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-3.ax','symmetry_of_at_the_same_time_3')).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (![B: $i, A: $i] : (once(at_the_same_time(B, A)) | (~once(at_the_same_time(A, B))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (![B: $i, A: $i] : (once(at_the_same_time(B, A)) | (~once(at_the_same_time(A, B))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.19/0.41 tff(36,plain,(
% 0.19/0.41 ![B: $i, A: $i] : (once(at_the_same_time(B, A)) | (~once(at_the_same_time(A, B))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[35])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (![B: $i, A: $i] : (once(at_the_same_time(B, A)) | (~once(at_the_same_time(A, B))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (((~![B: $i, A: $i] : (once(at_the_same_time(B, A)) | (~once(at_the_same_time(A, B))))) | (once(at_the_same_time(at(sk28, sk29), at(sk27, sk29))) | (~once(at_the_same_time(at(sk27, sk29), at(sk28, sk29)))))) <=> ((~![B: $i, A: $i] : (once(at_the_same_time(B, A)) | (~once(at_the_same_time(A, B))))) | once(at_the_same_time(at(sk28, sk29), at(sk27, sk29))) | (~once(at_the_same_time(at(sk27, sk29), at(sk28, sk29)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : (once(at_the_same_time(B, A)) | (~once(at_the_same_time(A, B))))) | (once(at_the_same_time(at(sk28, sk29), at(sk27, sk29))) | (~once(at_the_same_time(at(sk27, sk29), at(sk28, sk29)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : (once(at_the_same_time(B, A)) | (~once(at_the_same_time(A, B))))) | once(at_the_same_time(at(sk28, sk29), at(sk27, sk29))) | (~once(at_the_same_time(at(sk27, sk29), at(sk28, sk29))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[40, 37, 27, 12])).
% 0.19/0.41 tff(42,plain,(connect(sk28, sk27, sk29)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (((~connect(sk27, sk28, sk29)) | (~connect(sk28, sk27, sk29))) <=> ((~connect(sk27, sk28, sk29)) | (~connect(sk28, sk27, sk29)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (((~connect(sk28, sk27, sk29)) | (~connect(sk27, sk28, sk29))) <=> ((~connect(sk27, sk28, sk29)) | (~connect(sk28, sk27, sk29)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(45,axiom,((~connect(sk28, sk27, sk29)) | (~connect(sk27, sk28, sk29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t12_159')).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 ((~connect(sk27, sk28, sk29)) | (~connect(sk28, sk27, sk29))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 ((~connect(sk27, sk28, sk29)) | (~connect(sk28, sk27, sk29))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[46, 43])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (~connect(sk27, sk28, sk29)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[47, 42])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (((~![B: $i, A: $i, C: $i] : ((~once(at_the_same_time(at(A, B), at(C, B)))) | connect(A, C, B))) | ((~once(at_the_same_time(at(sk27, sk29), at(sk28, sk29)))) | connect(sk27, sk28, sk29))) <=> ((~![B: $i, A: $i, C: $i] : ((~once(at_the_same_time(at(A, B), at(C, B)))) | connect(A, C, B))) | (~once(at_the_same_time(at(sk27, sk29), at(sk28, sk29)))) | connect(sk27, sk28, sk29))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 ((~![B: $i, A: $i, C: $i] : ((~once(at_the_same_time(at(A, B), at(C, B)))) | connect(A, C, B))) | ((~once(at_the_same_time(at(sk27, sk29), at(sk28, sk29)))) | connect(sk27, sk28, sk29))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 ((~![B: $i, A: $i, C: $i] : ((~once(at_the_same_time(at(A, B), at(C, B)))) | connect(A, C, B))) | (~once(at_the_same_time(at(sk27, sk29), at(sk28, sk29)))) | connect(sk27, sk28, sk29)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (~once(at_the_same_time(at(sk27, sk29), at(sk28, sk29)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[51, 8, 48])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (((~![B: $i, A: $i, C: $i] : ((~connect(A, B, C)) | once(at_the_same_time(at(A, C), at(B, C))))) | ((~connect(sk28, sk27, sk29)) | once(at_the_same_time(at(sk28, sk29), at(sk27, sk29))))) <=> ((~![B: $i, A: $i, C: $i] : ((~connect(A, B, C)) | once(at_the_same_time(at(A, C), at(B, C))))) | (~connect(sk28, sk27, sk29)) | once(at_the_same_time(at(sk28, sk29), at(sk27, sk29))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 ((~![B: $i, A: $i, C: $i] : ((~connect(A, B, C)) | once(at_the_same_time(at(A, C), at(B, C))))) | ((~connect(sk28, sk27, sk29)) | once(at_the_same_time(at(sk28, sk29), at(sk27, sk29))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 ((~![B: $i, A: $i, C: $i] : ((~connect(A, B, C)) | once(at_the_same_time(at(A, C), at(B, C))))) | (~connect(sk28, sk27, sk29)) | once(at_the_same_time(at(sk28, sk29), at(sk27, sk29)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (once(at_the_same_time(at(sk28, sk29), at(sk27, sk29)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[55, 23, 42])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (((~![B: $i, A: $i] : (once(at_the_same_time(B, A)) | (~once(at_the_same_time(A, B))))) | (once(at_the_same_time(at(sk27, sk29), at(sk28, sk29))) | (~once(at_the_same_time(at(sk28, sk29), at(sk27, sk29)))))) <=> ((~![B: $i, A: $i] : (once(at_the_same_time(B, A)) | (~once(at_the_same_time(A, B))))) | once(at_the_same_time(at(sk27, sk29), at(sk28, sk29))) | (~once(at_the_same_time(at(sk28, sk29), at(sk27, sk29)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 ((~![B: $i, A: $i] : (once(at_the_same_time(B, A)) | (~once(at_the_same_time(A, B))))) | (once(at_the_same_time(at(sk27, sk29), at(sk28, sk29))) | (~once(at_the_same_time(at(sk28, sk29), at(sk27, sk29)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 ((~![B: $i, A: $i] : (once(at_the_same_time(B, A)) | (~once(at_the_same_time(A, B))))) | once(at_the_same_time(at(sk27, sk29), at(sk28, sk29))) | (~once(at_the_same_time(at(sk28, sk29), at(sk27, sk29))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[59, 37, 56, 52])).
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------