%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET622+3 : TPTP v9.0.0. Released v2.2.0.
% 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 05:26:02 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET622+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n001.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 05:35:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(union_type, type, (
% 0.11/0.37 union: ( $i * $i ) > $i)).
% 0.11/0.37 tff(intersection_type, type, (
% 0.11/0.37 intersection: ( $i * $i ) > $i)).
% 0.11/0.37 tff(tptp_fun_D_2_type, type, (
% 0.11/0.37 tptp_fun_D_2: $i)).
% 0.11/0.37 tff(tptp_fun_C_3_type, type, (
% 0.11/0.37 tptp_fun_C_3: $i)).
% 0.11/0.37 tff(tptp_fun_B_4_type, type, (
% 0.11/0.37 tptp_fun_B_4: $i)).
% 0.11/0.37 tff(difference_type, type, (
% 0.11/0.37 difference: ( $i * $i ) > $i)).
% 0.11/0.37 tff(symmetric_difference_type, type, (
% 0.11/0.37 symmetric_difference: ( $i * $i ) > $i)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 (^[B: $i, C: $i, D: $i] : refl((intersection(intersection(B, C), D) = intersection(B, intersection(C, D))) <=> (intersection(intersection(B, C), D) = intersection(B, intersection(C, D))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D))) <=> ![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D))) <=> ![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(4,axiom,(![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','associativity_of_intersection')).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.37 tff(6,plain,(
% 0.11/0.37 ![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[5])).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 ((~![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))) | (intersection(intersection(B!4, C!3), D!2) = intersection(B!4, intersection(C!3, D!2)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (intersection(intersection(B!4, C!3), D!2) = intersection(B!4, intersection(C!3, D!2))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (union(difference(B!4, union(C!3, D!2)), intersection(intersection(B!4, C!3), D!2)) = union(difference(B!4, union(C!3, D!2)), intersection(B!4, intersection(C!3, D!2)))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[9])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 (union(difference(B!4, union(C!3, D!2)), intersection(B!4, intersection(C!3, D!2))) = union(difference(B!4, union(C!3, D!2)), intersection(intersection(B!4, C!3), D!2))),
% 0.11/0.37 inference(symmetry,[status(thm)],[10])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (^[B: $i, C: $i, D: $i] : refl((difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D))) <=> (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D))) <=> ![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D))) <=> ![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(15,axiom,(![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','difference_difference_union2')).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.11/0.37 tff(17,plain,(
% 0.11/0.37 ![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[16])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 ((~![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D)))) | (difference(B!4, difference(union(C!3, D!2), intersection(C!3, D!2))) = union(difference(B!4, union(C!3, D!2)), intersection(B!4, intersection(C!3, D!2))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (difference(B!4, difference(union(C!3, D!2), intersection(C!3, D!2))) = union(difference(B!4, union(C!3, D!2)), intersection(B!4, intersection(C!3, D!2)))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (^[B: $i, C: $i] : refl((symmetric_difference(B, C) = difference(union(B, C), intersection(B, C))) <=> (symmetric_difference(B, C) = difference(union(B, C), intersection(B, C))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = difference(union(B, C), intersection(B, C))) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = difference(union(B, C), intersection(B, C)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[21])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = difference(union(B, C), intersection(B, C))) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = difference(union(B, C), intersection(B, C)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(24,axiom,(![B: $i, C: $i] : (symmetric_difference(B, C) = difference(union(B, C), intersection(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetric_difference_and_difference')).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = difference(union(B, C), intersection(B, C)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.11/0.37 tff(26,plain,(
% 0.11/0.37 ![B: $i, C: $i] : (symmetric_difference(B, C) = difference(union(B, C), intersection(B, C)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[25])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = difference(union(B, C), intersection(B, C)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = difference(union(B, C), intersection(B, C)))) | (symmetric_difference(C!3, D!2) = difference(union(C!3, D!2), intersection(C!3, D!2)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (symmetric_difference(C!3, D!2) = difference(union(C!3, D!2), intersection(C!3, D!2))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (difference(B!4, symmetric_difference(C!3, D!2)) = difference(B!4, difference(union(C!3, D!2), intersection(C!3, D!2)))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[29])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (difference(B!4, symmetric_difference(C!3, D!2)) = union(difference(B!4, union(C!3, D!2)), intersection(intersection(B!4, C!3), D!2))),
% 0.11/0.37 inference(transitivity,[status(thm)],[30, 20, 11])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 ((~![B: $i, C: $i, D: $i] : (difference(B, symmetric_difference(C, D)) = union(difference(B, union(C, D)), intersection(intersection(B, C), D)))) <=> (~![B: $i, C: $i, D: $i] : (difference(B, symmetric_difference(C, D)) = union(difference(B, union(C, D)), intersection(intersection(B, C), D))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(33,axiom,(~![B: $i, C: $i, D: $i] : (difference(B, symmetric_difference(C, D)) = union(difference(B, union(C, D)), intersection(intersection(B, C), D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th98')).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (~![B: $i, C: $i, D: $i] : (difference(B, symmetric_difference(C, D)) = union(difference(B, union(C, D)), intersection(intersection(B, C), D)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 (~![B: $i, C: $i, D: $i] : (difference(B, symmetric_difference(C, D)) = union(difference(B, union(C, D)), intersection(intersection(B, C), D)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[34, 32])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 (~![B: $i, C: $i, D: $i] : (difference(B, symmetric_difference(C, D)) = union(difference(B, union(C, D)), intersection(intersection(B, C), D)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[35, 32])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 (~![B: $i, C: $i, D: $i] : (difference(B, symmetric_difference(C, D)) = union(difference(B, union(C, D)), intersection(intersection(B, C), D)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.11/0.37 tff(38,plain,(
% 0.11/0.37 ~(difference(B!4, symmetric_difference(C!3, D!2)) = union(difference(B!4, union(C!3, D!2)), intersection(intersection(B!4, C!3), D!2)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[37])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[38, 31])).
% 0.11/0.37 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------