%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET621+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SET621+3 : TPTP v9.0.0. Released v2.2.0.
% 0.09/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 05:30:55 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.39 % SZS status Theorem
% 0.14/0.39 % SZS output start Proof
% 0.14/0.39 tff(union_type, type, (
% 0.14/0.39 union: ( $i * $i ) > $i)).
% 0.14/0.39 tff(difference_type, type, (
% 0.14/0.39 difference: ( $i * $i ) > $i)).
% 0.14/0.39 tff(tptp_fun_D_2_type, type, (
% 0.14/0.39 tptp_fun_D_2: $i)).
% 0.14/0.39 tff(tptp_fun_B_4_type, type, (
% 0.14/0.39 tptp_fun_B_4: $i)).
% 0.14/0.39 tff(tptp_fun_C_3_type, type, (
% 0.14/0.39 tptp_fun_C_3: $i)).
% 0.14/0.39 tff(symmetric_difference_type, type, (
% 0.14/0.39 symmetric_difference: ( $i * $i ) > $i)).
% 0.14/0.39 tff(1,plain,
% 0.14/0.39 (^[B: $i, C: $i, D: $i] : refl((difference(difference(B, C), D) = difference(B, union(C, D))) <=> (difference(difference(B, C), D) = difference(B, union(C, D))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(2,plain,
% 0.14/0.39 (![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D))) <=> ![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.39 tff(3,plain,
% 0.14/0.39 (![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D))) <=> ![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(4,axiom,(![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_difference_union')).
% 0.14/0.39 tff(5,plain,
% 0.14/0.39 (![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.14/0.39 tff(6,plain,(
% 0.14/0.39 ![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))),
% 0.14/0.39 inference(skolemize,[status(sab)],[5])).
% 0.14/0.39 tff(7,plain,
% 0.14/0.39 (![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.14/0.39 tff(8,plain,
% 0.14/0.39 ((~![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))) | (difference(difference(C!3, B!4), D!2) = difference(C!3, union(B!4, D!2)))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(9,plain,
% 0.14/0.39 (difference(difference(C!3, B!4), D!2) = difference(C!3, union(B!4, D!2))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.14/0.39 tff(10,plain,
% 0.14/0.39 (difference(C!3, union(B!4, D!2)) = difference(difference(C!3, B!4), D!2)),
% 0.14/0.39 inference(symmetry,[status(thm)],[9])).
% 0.14/0.39 tff(11,plain,
% 0.14/0.39 ((~![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))) | (difference(difference(B!4, C!3), D!2) = difference(B!4, union(C!3, D!2)))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(12,plain,
% 0.14/0.39 (difference(difference(B!4, C!3), D!2) = difference(B!4, union(C!3, D!2))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[11, 7])).
% 0.14/0.39 tff(13,plain,
% 0.14/0.39 (difference(B!4, union(C!3, D!2)) = difference(difference(B!4, C!3), D!2)),
% 0.14/0.39 inference(symmetry,[status(thm)],[12])).
% 0.14/0.39 tff(14,plain,
% 0.14/0.39 (union(difference(B!4, union(C!3, D!2)), difference(C!3, union(B!4, D!2))) = union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2))),
% 0.14/0.39 inference(monotonicity,[status(thm)],[13, 10])).
% 0.14/0.39 tff(15,plain,
% 0.14/0.39 (union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)) = union(difference(B!4, union(C!3, D!2)), difference(C!3, union(B!4, D!2)))),
% 0.14/0.39 inference(symmetry,[status(thm)],[14])).
% 0.14/0.39 tff(16,plain,
% 0.14/0.39 (^[B: $i, C: $i, D: $i] : refl((difference(union(B, C), D) = union(difference(B, D), difference(C, D))) <=> (difference(union(B, C), D) = union(difference(B, D), difference(C, D))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(17,plain,
% 0.14/0.39 (![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D))) <=> ![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[16])).
% 0.14/0.39 tff(18,plain,
% 0.14/0.39 (![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D))) <=> ![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(19,axiom,(![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_distributes_over_union')).
% 0.14/0.39 tff(20,plain,
% 0.14/0.39 (![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.14/0.39 tff(21,plain,(
% 0.14/0.39 ![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.14/0.39 inference(skolemize,[status(sab)],[20])).
% 0.14/0.39 tff(22,plain,
% 0.14/0.39 (![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.14/0.39 tff(23,plain,
% 0.14/0.39 ((~![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))) | (difference(union(difference(B!4, C!3), difference(C!3, B!4)), D!2) = union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(24,plain,
% 0.14/0.39 (difference(union(difference(B!4, C!3), difference(C!3, B!4)), D!2) = union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.14/0.39 tff(25,plain,
% 0.14/0.39 (^[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))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(26,plain,
% 0.14/0.39 (![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)))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.14/0.39 tff(27,plain,
% 0.14/0.39 (![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)))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(28,axiom,(![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','symmetric_difference_defn')).
% 0.14/0.39 tff(29,plain,
% 0.14/0.39 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.14/0.39 tff(30,plain,(
% 0.14/0.39 ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.14/0.39 inference(skolemize,[status(sab)],[29])).
% 0.14/0.39 tff(31,plain,
% 0.14/0.39 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.14/0.39 tff(32,plain,
% 0.14/0.39 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))) | (symmetric_difference(B!4, C!3) = union(difference(B!4, C!3), difference(C!3, B!4)))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(33,plain,
% 0.14/0.39 (symmetric_difference(B!4, C!3) = union(difference(B!4, C!3), difference(C!3, B!4))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.14/0.39 tff(34,plain,
% 0.14/0.39 (difference(symmetric_difference(B!4, C!3), D!2) = difference(union(difference(B!4, C!3), difference(C!3, B!4)), D!2)),
% 0.14/0.39 inference(monotonicity,[status(thm)],[33])).
% 0.14/0.39 tff(35,plain,
% 0.14/0.39 (difference(symmetric_difference(B!4, C!3), D!2) = union(difference(B!4, union(C!3, D!2)), difference(C!3, union(B!4, D!2)))),
% 0.14/0.39 inference(transitivity,[status(thm)],[34, 24, 15])).
% 0.14/0.39 tff(36,plain,
% 0.14/0.39 ((~![B: $i, C: $i, D: $i] : (difference(symmetric_difference(B, C), D) = union(difference(B, union(C, D)), difference(C, union(B, D))))) <=> (~![B: $i, C: $i, D: $i] : (difference(symmetric_difference(B, C), D) = union(difference(B, union(C, D)), difference(C, union(B, D)))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(37,axiom,(~![B: $i, C: $i, D: $i] : (difference(symmetric_difference(B, C), D) = union(difference(B, union(C, D)), difference(C, union(B, D))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th97')).
% 0.14/0.39 tff(38,plain,
% 0.14/0.39 (~![B: $i, C: $i, D: $i] : (difference(symmetric_difference(B, C), D) = union(difference(B, union(C, D)), difference(C, union(B, D))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.14/0.39 tff(39,plain,
% 0.14/0.39 (~![B: $i, C: $i, D: $i] : (difference(symmetric_difference(B, C), D) = union(difference(B, union(C, D)), difference(C, union(B, D))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[38, 36])).
% 0.14/0.39 tff(40,plain,
% 0.14/0.39 (~![B: $i, C: $i, D: $i] : (difference(symmetric_difference(B, C), D) = union(difference(B, union(C, D)), difference(C, union(B, D))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[39, 36])).
% 0.14/0.39 tff(41,plain,
% 0.14/0.39 (~![B: $i, C: $i, D: $i] : (difference(symmetric_difference(B, C), D) = union(difference(B, union(C, D)), difference(C, union(B, D))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.14/0.39 tff(42,plain,(
% 0.14/0.39 ~(difference(symmetric_difference(B!4, C!3), D!2) = union(difference(B!4, union(C!3, D!2)), difference(C!3, union(B!4, D!2))))),
% 0.14/0.39 inference(skolemize,[status(sab)],[41])).
% 0.14/0.39 tff(43,plain,
% 0.14/0.39 ($false),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[42, 35])).
% 0.14/0.39 % SZS output end Proof
% 0.14/0.39 % E exiting
%------------------------------------------------------------------------------