%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MSC004-1 : TPTP v9.0.0. Released v1.0.0.
% 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 05:17:30 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MSC004-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Jun 19 23:32:10 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.40 % SZS status Unsatisfiable
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(in_type, type, (
% 0.13/0.40 in: ( $i * $i ) > $o)).
% 0.13/0.40 tff(arm_type, type, (
% 0.13/0.40 arm: $i)).
% 0.13/0.40 tff(object_in_type, type, (
% 0.13/0.40 object_in: ( $i * $i * $i * $i * $i ) > $i)).
% 0.13/0.40 tff(n1_type, type, (
% 0.13/0.40 n1: $i)).
% 0.13/0.40 tff(n2_type, type, (
% 0.13/0.40 n2: $i)).
% 0.13/0.40 tff(hand_type, type, (
% 0.13/0.40 hand: $i)).
% 0.13/0.40 tff(john_type, type, (
% 0.13/0.40 john: $i)).
% 0.13/0.40 tff(has_parts_type, type, (
% 0.13/0.40 has_parts: ( $i * $i * $i ) > $o)).
% 0.13/0.40 tff(times_type, type, (
% 0.13/0.40 times: ( $i * $i ) > $i)).
% 0.13/0.40 tff(fingers_type, type, (
% 0.13/0.40 fingers: $i)).
% 0.13/0.40 tff(n5_type, type, (
% 0.13/0.40 n5: $i)).
% 0.13/0.40 tff(human_type, type, (
% 0.13/0.40 human: $i)).
% 0.13/0.40 tff(boy_type, type, (
% 0.13/0.40 boy: $i)).
% 0.13/0.40 tff(1,assumption,(has_parts(john, times(n2, n1), hand)), introduced(assumption)).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 ((~has_parts(john, times(times(n2, n1), n5), fingers)) <=> (~has_parts(john, times(times(n2, n1), n5), fingers))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(3,axiom,(~has_parts(john, times(times(n2, n1), n5), fingers)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_john_has_10_fingers')).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (~has_parts(john, times(times(n2, n1), n5), fingers)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (^[Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : refl(((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part)) <=> ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 (![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part)) <=> ![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[5])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part)) <=> ![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (^[Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : rewrite(((in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part)) | (~has_parts(Big_part, Number_of_mid_parts, Mid_part))) <=> ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part)) | (~has_parts(Big_part, Number_of_mid_parts, Mid_part))) <=> ![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.13/0.40 tff(10,axiom,(![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part)) | (~has_parts(Big_part, Number_of_mid_parts, Mid_part)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_part_inheritance')).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.13/0.40 tff(13,plain,(
% 0.13/0.40 ![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))),
% 0.13/0.40 inference(skolemize,[status(sab)],[12])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))) | (has_parts(john, times(times(n2, n1), n5), fingers) | in(object_in(john, hand, fingers, times(n2, n1), n5), hand) | (~has_parts(john, times(n2, n1), hand)))) <=> ((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))) | has_parts(john, times(times(n2, n1), n5), fingers) | in(object_in(john, hand, fingers, times(n2, n1), n5), hand) | (~has_parts(john, times(n2, n1), hand)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (((~has_parts(john, times(n2, n1), hand)) | has_parts(john, times(times(n2, n1), n5), fingers) | in(object_in(john, hand, fingers, times(n2, n1), n5), hand)) <=> (has_parts(john, times(times(n2, n1), n5), fingers) | in(object_in(john, hand, fingers, times(n2, n1), n5), hand) | (~has_parts(john, times(n2, n1), hand)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(17,plain,
% 0.21/0.40 (((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))) | ((~has_parts(john, times(n2, n1), hand)) | has_parts(john, times(times(n2, n1), n5), fingers) | in(object_in(john, hand, fingers, times(n2, n1), n5), hand))) <=> ((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))) | (has_parts(john, times(times(n2, n1), n5), fingers) | in(object_in(john, hand, fingers, times(n2, n1), n5), hand) | (~has_parts(john, times(n2, n1), hand))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[16])).
% 0.21/0.40 tff(18,plain,
% 0.21/0.40 (((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))) | ((~has_parts(john, times(n2, n1), hand)) | has_parts(john, times(times(n2, n1), n5), fingers) | in(object_in(john, hand, fingers, times(n2, n1), n5), hand))) <=> ((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))) | has_parts(john, times(times(n2, n1), n5), fingers) | in(object_in(john, hand, fingers, times(n2, n1), n5), hand) | (~has_parts(john, times(n2, n1), hand)))),
% 0.21/0.40 inference(transitivity,[status(thm)],[17, 15])).
% 0.21/0.40 tff(19,plain,
% 0.21/0.40 ((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))) | ((~has_parts(john, times(n2, n1), hand)) | has_parts(john, times(times(n2, n1), n5), fingers) | in(object_in(john, hand, fingers, times(n2, n1), n5), hand))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(20,plain,
% 0.21/0.40 ((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))) | has_parts(john, times(times(n2, n1), n5), fingers) | in(object_in(john, hand, fingers, times(n2, n1), n5), hand) | (~has_parts(john, times(n2, n1), hand))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.21/0.40 tff(21,plain,
% 0.21/0.40 (in(object_in(john, hand, fingers, times(n2, n1), n5), hand) | (~has_parts(john, times(n2, n1), hand))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[20, 14, 4])).
% 0.21/0.40 tff(22,plain,
% 0.21/0.40 (in(object_in(john, hand, fingers, times(n2, n1), n5), hand)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[21, 1])).
% 0.21/0.40 tff(23,plain,
% 0.21/0.40 (^[X: $i] : refl(((~in(X, hand)) | has_parts(X, n5, fingers)) <=> ((~in(X, hand)) | has_parts(X, n5, fingers)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(24,plain,
% 0.21/0.40 (![X: $i] : ((~in(X, hand)) | has_parts(X, n5, fingers)) <=> ![X: $i] : ((~in(X, hand)) | has_parts(X, n5, fingers))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (![X: $i] : ((~in(X, hand)) | has_parts(X, n5, fingers)) <=> ![X: $i] : ((~in(X, hand)) | has_parts(X, n5, fingers))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (^[X: $i] : rewrite((has_parts(X, n5, fingers) | (~in(X, hand))) <=> ((~in(X, hand)) | has_parts(X, n5, fingers)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 (![X: $i] : (has_parts(X, n5, fingers) | (~in(X, hand))) <=> ![X: $i] : ((~in(X, hand)) | has_parts(X, n5, fingers))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.41 tff(28,axiom,(![X: $i] : (has_parts(X, n5, fingers) | (~in(X, hand)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','hands_have_5_fingers')).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (![X: $i] : ((~in(X, hand)) | has_parts(X, n5, fingers))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (![X: $i] : ((~in(X, hand)) | has_parts(X, n5, fingers))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.21/0.41 tff(31,plain,(
% 0.21/0.41 ![X: $i] : ((~in(X, hand)) | has_parts(X, n5, fingers))),
% 0.21/0.41 inference(skolemize,[status(sab)],[30])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (![X: $i] : ((~in(X, hand)) | has_parts(X, n5, fingers))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 (((~![X: $i] : ((~in(X, hand)) | has_parts(X, n5, fingers))) | ((~in(object_in(john, hand, fingers, times(n2, n1), n5), hand)) | has_parts(object_in(john, hand, fingers, times(n2, n1), n5), n5, fingers))) <=> ((~![X: $i] : ((~in(X, hand)) | has_parts(X, n5, fingers))) | (~in(object_in(john, hand, fingers, times(n2, n1), n5), hand)) | has_parts(object_in(john, hand, fingers, times(n2, n1), n5), n5, fingers))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 ((~![X: $i] : ((~in(X, hand)) | has_parts(X, n5, fingers))) | ((~in(object_in(john, hand, fingers, times(n2, n1), n5), hand)) | has_parts(object_in(john, hand, fingers, times(n2, n1), n5), n5, fingers))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 ((~![X: $i] : ((~in(X, hand)) | has_parts(X, n5, fingers))) | (~in(object_in(john, hand, fingers, times(n2, n1), n5), hand)) | has_parts(object_in(john, hand, fingers, times(n2, n1), n5), n5, fingers)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (has_parts(object_in(john, hand, fingers, times(n2, n1), n5), n5, fingers)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[35, 32, 22])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (^[Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : refl(((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part))) <=> ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part))) <=> ![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[37])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part))) <=> ![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (^[Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : trans(monotonicity(rewrite((has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(Big_part, Number_of_mid_parts, Mid_part))) <=> ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part))), (((has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(Big_part, Number_of_mid_parts, Mid_part))) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part))) <=> (((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part)) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part))))), rewrite((((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part)) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part))) <=> ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))), (((has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(Big_part, Number_of_mid_parts, Mid_part))) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part))) <=> ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(Big_part, Number_of_mid_parts, Mid_part))) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part))) <=> ![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[40])).
% 0.21/0.41 tff(42,axiom,(![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(Big_part, Number_of_mid_parts, Mid_part))) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','part_inheritance')).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.21/0.41 tff(45,plain,(
% 0.21/0.41 ![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[44])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))) | (has_parts(john, times(times(n2, n1), n5), fingers) | (~has_parts(john, times(n2, n1), hand)) | (~has_parts(object_in(john, hand, fingers, times(n2, n1), n5), n5, fingers)))) <=> ((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))) | has_parts(john, times(times(n2, n1), n5), fingers) | (~has_parts(john, times(n2, n1), hand)) | (~has_parts(object_in(john, hand, fingers, times(n2, n1), n5), n5, fingers)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (((~has_parts(john, times(n2, n1), hand)) | has_parts(john, times(times(n2, n1), n5), fingers) | (~has_parts(object_in(john, hand, fingers, times(n2, n1), n5), n5, fingers))) <=> (has_parts(john, times(times(n2, n1), n5), fingers) | (~has_parts(john, times(n2, n1), hand)) | (~has_parts(object_in(john, hand, fingers, times(n2, n1), n5), n5, fingers)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))) | ((~has_parts(john, times(n2, n1), hand)) | has_parts(john, times(times(n2, n1), n5), fingers) | (~has_parts(object_in(john, hand, fingers, times(n2, n1), n5), n5, fingers)))) <=> ((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))) | (has_parts(john, times(times(n2, n1), n5), fingers) | (~has_parts(john, times(n2, n1), hand)) | (~has_parts(object_in(john, hand, fingers, times(n2, n1), n5), n5, fingers))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[48])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))) | ((~has_parts(john, times(n2, n1), hand)) | has_parts(john, times(times(n2, n1), n5), fingers) | (~has_parts(object_in(john, hand, fingers, times(n2, n1), n5), n5, fingers)))) <=> ((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))) | has_parts(john, times(times(n2, n1), n5), fingers) | (~has_parts(john, times(n2, n1), hand)) | (~has_parts(object_in(john, hand, fingers, times(n2, n1), n5), n5, fingers)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[49, 47])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 ((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))) | ((~has_parts(john, times(n2, n1), hand)) | has_parts(john, times(times(n2, n1), n5), fingers) | (~has_parts(object_in(john, hand, fingers, times(n2, n1), n5), n5, fingers)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 ((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))) | has_parts(john, times(times(n2, n1), n5), fingers) | (~has_parts(john, times(n2, n1), hand)) | (~has_parts(object_in(john, hand, fingers, times(n2, n1), n5), n5, fingers))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[52, 46, 4, 1, 36])).
% 0.21/0.41 tff(54,plain,(~has_parts(john, times(n2, n1), hand)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 (^[X: $i] : refl((in(X, human) | (~in(X, boy))) <=> (in(X, human) | (~in(X, boy))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (![X: $i] : (in(X, human) | (~in(X, boy))) <=> ![X: $i] : (in(X, human) | (~in(X, boy)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[55])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 (![X: $i] : (in(X, human) | (~in(X, boy))) <=> ![X: $i] : (in(X, human) | (~in(X, boy)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(58,axiom,(![X: $i] : (in(X, human) | (~in(X, boy)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','in_boy_in_human')).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (![X: $i] : (in(X, human) | (~in(X, boy)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.21/0.41 tff(60,plain,(
% 0.21/0.41 ![X: $i] : (in(X, human) | (~in(X, boy)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[59])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 (![X: $i] : (in(X, human) | (~in(X, boy)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.21/0.42 tff(62,plain,
% 0.21/0.42 (in(john, boy) <=> in(john, boy)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(63,axiom,(in(john, boy)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','john_is_a_boy')).
% 0.21/0.42 tff(64,plain,
% 0.21/0.42 (in(john, boy)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.42 tff(65,plain,
% 0.21/0.42 (((~![X: $i] : (in(X, human) | (~in(X, boy)))) | (in(john, human) | (~in(john, boy)))) <=> ((~![X: $i] : (in(X, human) | (~in(X, boy)))) | in(john, human) | (~in(john, boy)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(66,plain,
% 0.21/0.42 ((~![X: $i] : (in(X, human) | (~in(X, boy)))) | (in(john, human) | (~in(john, boy)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(67,plain,
% 0.21/0.42 ((~![X: $i] : (in(X, human) | (~in(X, boy)))) | in(john, human) | (~in(john, boy))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.21/0.42 tff(68,plain,
% 0.21/0.42 (in(john, human)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[67, 64, 61])).
% 0.21/0.42 tff(69,plain,
% 0.21/0.42 (^[X: $i] : refl(((~in(X, human)) | has_parts(X, n2, arm)) <=> ((~in(X, human)) | has_parts(X, n2, arm)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(70,plain,
% 0.21/0.42 (![X: $i] : ((~in(X, human)) | has_parts(X, n2, arm)) <=> ![X: $i] : ((~in(X, human)) | has_parts(X, n2, arm))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[69])).
% 0.21/0.42 tff(71,plain,
% 0.21/0.42 (![X: $i] : ((~in(X, human)) | has_parts(X, n2, arm)) <=> ![X: $i] : ((~in(X, human)) | has_parts(X, n2, arm))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(72,plain,
% 0.21/0.42 (^[X: $i] : rewrite((has_parts(X, n2, arm) | (~in(X, human))) <=> ((~in(X, human)) | has_parts(X, n2, arm)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 (![X: $i] : (has_parts(X, n2, arm) | (~in(X, human))) <=> ![X: $i] : ((~in(X, human)) | has_parts(X, n2, arm))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.42 tff(74,axiom,(![X: $i] : (has_parts(X, n2, arm) | (~in(X, human)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','humans_have_two_arms')).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 (![X: $i] : ((~in(X, human)) | has_parts(X, n2, arm))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 (![X: $i] : ((~in(X, human)) | has_parts(X, n2, arm))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.21/0.42 tff(77,plain,(
% 0.21/0.42 ![X: $i] : ((~in(X, human)) | has_parts(X, n2, arm))),
% 0.21/0.42 inference(skolemize,[status(sab)],[76])).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 (![X: $i] : ((~in(X, human)) | has_parts(X, n2, arm))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.21/0.42 tff(79,plain,
% 0.21/0.42 (((~![X: $i] : ((~in(X, human)) | has_parts(X, n2, arm))) | ((~in(john, human)) | has_parts(john, n2, arm))) <=> ((~![X: $i] : ((~in(X, human)) | has_parts(X, n2, arm))) | (~in(john, human)) | has_parts(john, n2, arm))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 ((~![X: $i] : ((~in(X, human)) | has_parts(X, n2, arm))) | ((~in(john, human)) | has_parts(john, n2, arm))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(81,plain,
% 0.21/0.42 ((~![X: $i] : ((~in(X, human)) | has_parts(X, n2, arm))) | (~in(john, human)) | has_parts(john, n2, arm)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 (has_parts(john, n2, arm)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[81, 78, 68])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 (((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))) | (has_parts(john, times(n2, n1), hand) | (~has_parts(john, n2, arm)) | (~has_parts(object_in(john, arm, hand, n2, n1), n1, hand)))) <=> ((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))) | has_parts(john, times(n2, n1), hand) | (~has_parts(john, n2, arm)) | (~has_parts(object_in(john, arm, hand, n2, n1), n1, hand)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 (((~has_parts(john, n2, arm)) | has_parts(john, times(n2, n1), hand) | (~has_parts(object_in(john, arm, hand, n2, n1), n1, hand))) <=> (has_parts(john, times(n2, n1), hand) | (~has_parts(john, n2, arm)) | (~has_parts(object_in(john, arm, hand, n2, n1), n1, hand)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 (((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))) | ((~has_parts(john, n2, arm)) | has_parts(john, times(n2, n1), hand) | (~has_parts(object_in(john, arm, hand, n2, n1), n1, hand)))) <=> ((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))) | (has_parts(john, times(n2, n1), hand) | (~has_parts(john, n2, arm)) | (~has_parts(object_in(john, arm, hand, n2, n1), n1, hand))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[84])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 (((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))) | ((~has_parts(john, n2, arm)) | has_parts(john, times(n2, n1), hand) | (~has_parts(object_in(john, arm, hand, n2, n1), n1, hand)))) <=> ((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))) | has_parts(john, times(n2, n1), hand) | (~has_parts(john, n2, arm)) | (~has_parts(object_in(john, arm, hand, n2, n1), n1, hand)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[85, 83])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 ((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))) | ((~has_parts(john, n2, arm)) | has_parts(john, times(n2, n1), hand) | (~has_parts(object_in(john, arm, hand, n2, n1), n1, hand)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 ((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | (~has_parts(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Number_of_small_parts, Small_part)))) | has_parts(john, times(n2, n1), hand) | (~has_parts(john, n2, arm)) | (~has_parts(object_in(john, arm, hand, n2, n1), n1, hand))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 (has_parts(john, times(n2, n1), hand) | (~has_parts(object_in(john, arm, hand, n2, n1), n1, hand))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[88, 46, 82])).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 (~has_parts(object_in(john, arm, hand, n2, n1), n1, hand)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[89, 54])).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 (^[X: $i] : refl(((~in(X, arm)) | has_parts(X, n1, hand)) <=> ((~in(X, arm)) | has_parts(X, n1, hand)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 (![X: $i] : ((~in(X, arm)) | has_parts(X, n1, hand)) <=> ![X: $i] : ((~in(X, arm)) | has_parts(X, n1, hand))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[91])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 (![X: $i] : ((~in(X, arm)) | has_parts(X, n1, hand)) <=> ![X: $i] : ((~in(X, arm)) | has_parts(X, n1, hand))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 (^[X: $i] : rewrite((has_parts(X, n1, hand) | (~in(X, arm))) <=> ((~in(X, arm)) | has_parts(X, n1, hand)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 (![X: $i] : (has_parts(X, n1, hand) | (~in(X, arm))) <=> ![X: $i] : ((~in(X, arm)) | has_parts(X, n1, hand))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[94])).
% 0.21/0.42 tff(96,axiom,(![X: $i] : (has_parts(X, n1, hand) | (~in(X, arm)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','arms_have_one_hand')).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 (![X: $i] : ((~in(X, arm)) | has_parts(X, n1, hand))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 (![X: $i] : ((~in(X, arm)) | has_parts(X, n1, hand))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.21/0.42 tff(99,plain,(
% 0.21/0.42 ![X: $i] : ((~in(X, arm)) | has_parts(X, n1, hand))),
% 0.21/0.42 inference(skolemize,[status(sab)],[98])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 (![X: $i] : ((~in(X, arm)) | has_parts(X, n1, hand))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 (((~![X: $i] : ((~in(X, arm)) | has_parts(X, n1, hand))) | ((~in(object_in(john, arm, hand, n2, n1), arm)) | has_parts(object_in(john, arm, hand, n2, n1), n1, hand))) <=> ((~![X: $i] : ((~in(X, arm)) | has_parts(X, n1, hand))) | (~in(object_in(john, arm, hand, n2, n1), arm)) | has_parts(object_in(john, arm, hand, n2, n1), n1, hand))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 ((~![X: $i] : ((~in(X, arm)) | has_parts(X, n1, hand))) | ((~in(object_in(john, arm, hand, n2, n1), arm)) | has_parts(object_in(john, arm, hand, n2, n1), n1, hand))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 ((~![X: $i] : ((~in(X, arm)) | has_parts(X, n1, hand))) | (~in(object_in(john, arm, hand, n2, n1), arm)) | has_parts(object_in(john, arm, hand, n2, n1), n1, hand)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 (~in(object_in(john, arm, hand, n2, n1), arm)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[103, 100, 90])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 (((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))) | (in(object_in(john, arm, hand, n2, n1), arm) | has_parts(john, times(n2, n1), hand) | (~has_parts(john, n2, arm)))) <=> ((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))) | in(object_in(john, arm, hand, n2, n1), arm) | has_parts(john, times(n2, n1), hand) | (~has_parts(john, n2, arm)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (((~has_parts(john, n2, arm)) | has_parts(john, times(n2, n1), hand) | in(object_in(john, arm, hand, n2, n1), arm)) <=> (in(object_in(john, arm, hand, n2, n1), arm) | has_parts(john, times(n2, n1), hand) | (~has_parts(john, n2, arm)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 (((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))) | ((~has_parts(john, n2, arm)) | has_parts(john, times(n2, n1), hand) | in(object_in(john, arm, hand, n2, n1), arm))) <=> ((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))) | (in(object_in(john, arm, hand, n2, n1), arm) | has_parts(john, times(n2, n1), hand) | (~has_parts(john, n2, arm))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[106])).
% 0.21/0.43 tff(108,plain,
% 0.21/0.43 (((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))) | ((~has_parts(john, n2, arm)) | has_parts(john, times(n2, n1), hand) | in(object_in(john, arm, hand, n2, n1), arm))) <=> ((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))) | in(object_in(john, arm, hand, n2, n1), arm) | has_parts(john, times(n2, n1), hand) | (~has_parts(john, n2, arm)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[107, 105])).
% 0.21/0.43 tff(109,plain,
% 0.21/0.43 ((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))) | ((~has_parts(john, n2, arm)) | has_parts(john, times(n2, n1), hand) | in(object_in(john, arm, hand, n2, n1), arm))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(110,plain,
% 0.21/0.43 ((~![Number_of_mid_parts: $i, Mid_part: $i, Big_part: $i, Number_of_small_parts: $i, Small_part: $i] : ((~has_parts(Big_part, Number_of_mid_parts, Mid_part)) | has_parts(Big_part, times(Number_of_mid_parts, Number_of_small_parts), Small_part) | in(object_in(Big_part, Mid_part, Small_part, Number_of_mid_parts, Number_of_small_parts), Mid_part))) | in(object_in(john, arm, hand, n2, n1), arm) | has_parts(john, times(n2, n1), hand) | (~has_parts(john, n2, arm))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.21/0.43 tff(111,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[110, 14, 82, 54, 104])).
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------