%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET618+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:26:01 AM UTC 2025
% Result : Theorem 0.18s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET618+3 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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 05:31:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.36 % SZS status Theorem
% 0.18/0.36 % SZS output start Proof
% 0.18/0.36 tff(empty_set_type, type, (
% 0.18/0.36 empty_set: $i)).
% 0.18/0.36 tff(symmetric_difference_type, type, (
% 0.18/0.36 symmetric_difference: ( $i * $i ) > $i)).
% 0.18/0.36 tff(tptp_fun_B_3_type, type, (
% 0.18/0.36 tptp_fun_B_3: $i)).
% 0.18/0.36 tff(difference_type, type, (
% 0.18/0.36 difference: ( $i * $i ) > $i)).
% 0.18/0.36 tff(union_type, type, (
% 0.18/0.36 union: ( $i * $i ) > $i)).
% 0.18/0.36 tff(1,plain,
% 0.18/0.36 (^[B: $i] : refl((difference(B, B) = empty_set) <=> (difference(B, B) = empty_set))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(2,plain,
% 0.18/0.36 (![B: $i] : (difference(B, B) = empty_set) <=> ![B: $i] : (difference(B, B) = empty_set)),
% 0.18/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.36 tff(3,plain,
% 0.18/0.36 (![B: $i] : (difference(B, B) = empty_set) <=> ![B: $i] : (difference(B, B) = empty_set)),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(4,axiom,(![B: $i] : (difference(B, B) = empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','self_difference_is_empty_set')).
% 0.18/0.36 tff(5,plain,
% 0.18/0.36 (![B: $i] : (difference(B, B) = empty_set)),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.36 tff(6,plain,(
% 0.18/0.36 ![B: $i] : (difference(B, B) = empty_set)),
% 0.18/0.36 inference(skolemize,[status(sab)],[5])).
% 0.18/0.36 tff(7,plain,
% 0.18/0.36 (![B: $i] : (difference(B, B) = empty_set)),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.36 tff(8,plain,
% 0.18/0.36 ((~![B: $i] : (difference(B, B) = empty_set)) | (difference(B!3, B!3) = empty_set)),
% 0.18/0.36 inference(quant_inst,[status(thm)],[])).
% 0.18/0.36 tff(9,plain,
% 0.18/0.36 (difference(B!3, B!3) = empty_set),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.18/0.36 tff(10,plain,
% 0.18/0.36 (^[B: $i] : refl((union(B, B) = B) <=> (union(B, B) = B))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(11,plain,
% 0.18/0.36 (![B: $i] : (union(B, B) = B) <=> ![B: $i] : (union(B, B) = B)),
% 0.18/0.36 inference(quant_intro,[status(thm)],[10])).
% 0.18/0.36 tff(12,plain,
% 0.18/0.36 (![B: $i] : (union(B, B) = B) <=> ![B: $i] : (union(B, B) = B)),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(13,axiom,(![B: $i] : (union(B, B) = B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','idempotency_of_union')).
% 0.18/0.36 tff(14,plain,
% 0.18/0.36 (![B: $i] : (union(B, B) = B)),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.18/0.36 tff(15,plain,(
% 0.18/0.36 ![B: $i] : (union(B, B) = B)),
% 0.18/0.36 inference(skolemize,[status(sab)],[14])).
% 0.18/0.36 tff(16,plain,
% 0.18/0.36 (![B: $i] : (union(B, B) = B)),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.18/0.36 tff(17,plain,
% 0.18/0.36 ((~![B: $i] : (union(B, B) = B)) | (union(difference(B!3, B!3), difference(B!3, B!3)) = difference(B!3, B!3))),
% 0.18/0.36 inference(quant_inst,[status(thm)],[])).
% 0.18/0.36 tff(18,plain,
% 0.18/0.36 (union(difference(B!3, B!3), difference(B!3, B!3)) = difference(B!3, B!3)),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.18/0.36 tff(19,plain,
% 0.18/0.36 (^[B: $i, C: $i] : refl((symmetric_difference(B, C) = union(difference(B, C), difference(C, B))) <=> (symmetric_difference(B, C) = union(difference(B, C), difference(C, B))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(20,plain,
% 0.18/0.36 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B))) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[19])).
% 0.18/0.36 tff(21,plain,
% 0.18/0.36 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B))) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(22,axiom,(![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetric_difference_defn')).
% 0.18/0.36 tff(23,plain,
% 0.18/0.36 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.18/0.36 tff(24,plain,(
% 0.18/0.36 ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.18/0.36 inference(skolemize,[status(sab)],[23])).
% 0.18/0.36 tff(25,plain,
% 0.18/0.36 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.18/0.36 tff(26,plain,
% 0.18/0.36 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))) | (symmetric_difference(B!3, B!3) = union(difference(B!3, B!3), difference(B!3, B!3)))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(27,plain,
% 0.18/0.37 (symmetric_difference(B!3, B!3) = union(difference(B!3, B!3), difference(B!3, B!3))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.18/0.37 tff(28,plain,
% 0.18/0.37 (symmetric_difference(B!3, B!3) = empty_set),
% 0.18/0.37 inference(transitivity,[status(thm)],[27, 18, 9])).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 ((~![B: $i] : (symmetric_difference(B, B) = empty_set)) <=> (~![B: $i] : (symmetric_difference(B, B) = empty_set))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(30,axiom,(~![B: $i] : (symmetric_difference(B, B) = empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th93')).
% 0.18/0.37 tff(31,plain,
% 0.18/0.37 (~![B: $i] : (symmetric_difference(B, B) = empty_set)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.18/0.37 tff(32,plain,
% 0.18/0.37 (~![B: $i] : (symmetric_difference(B, B) = empty_set)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[31, 29])).
% 0.18/0.37 tff(33,plain,
% 0.18/0.37 (~![B: $i] : (symmetric_difference(B, B) = empty_set)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[32, 29])).
% 0.18/0.37 tff(34,plain,
% 0.18/0.37 (~![B: $i] : (symmetric_difference(B, B) = empty_set)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.18/0.37 tff(35,plain,(
% 0.18/0.37 ~(symmetric_difference(B!3, B!3) = empty_set)),
% 0.18/0.37 inference(skolemize,[status(sab)],[34])).
% 0.18/0.37 tff(36,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[35, 28])).
% 0.18/0.37 % SZS output end Proof
% 0.18/0.37 % E exiting
%------------------------------------------------------------------------------