%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP163^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:07:01 AM UTC 2026
% Result : Theorem 166.63s 89.65s
% Output : Refutation 166.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 138 ( 39 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 216 ( 16 ~; 4 |; 6 &; 190 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 28 ^; 28 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr384614482nres_a_type,type,
set_Pr384614482nres_a: $tType ).
thf(produc1609974940nres_a_type,type,
produc1609974940nres_a: $tType ).
thf(refine424419629nres_a_type,type,
refine424419629nres_a: $tType ).
thf(set_set_a_type,type,
set_set_a: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(a_type,type,
a: $tType ).
thf(ord_le519537037nres_a_decl,type,
ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
thf(refine2063221604TURN_a_decl,type,
refine2063221604TURN_a: a > refine424419629nres_a ).
thf(refine1001002027nres_a_decl,type,
refine1001002027nres_a: refine424419629nres_a > a > $o ).
thf(refine1312857699nres_a_decl,type,
refine1312857699nres_a: refine424419629nres_a > a > $o ).
thf(refine412683989fail_a_decl,type,
refine412683989fail_a: refine424419629nres_a > $o ).
thf(refine1198353288_RES_a_decl,type,
refine1198353288_RES_a: set_a > refine424419629nres_a ).
thf(collect_a_decl,type,
collect_a: ( a > $o ) > set_a ).
thf(member_a_decl,type,
member_a: a > set_a > $o ).
thf(phi_decl,type,
phi: a > $o ).
thf(x_decl,type,
x: a ).
thf(256,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_Collect__mem__eq) ).
thf(1505,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(1506,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(cnf,[status(esa)],[1505]) ).
thf(1507,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(lifteq,[status(thm)],[1506]) ).
thf(232,axiom,
! [A: set_a] :
( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ A ) )
= ( ^ [B: a] : ( member_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_inres__simps_I2_J) ).
thf(1225,plain,
! [A: set_a] :
( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ A ) )
= ( ^ [B: a] : ( member_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(1226,plain,
! [A: set_a] :
( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ A ) )
= ( ^ [B: a] : ( member_a @ B @ A ) ) ),
inference(cnf,[status(esa)],[1225]) ).
thf(1227,plain,
! [A: set_a] :
( ( ^ [B: a] : ( member_a @ B @ A ) )
= ( refine1001002027nres_a @ ( refine1198353288_RES_a @ A ) ) ),
inference(lifteq,[status(thm)],[1226]) ).
thf(2638,plain,
! [A: set_a] :
( ( collect_a @ ( refine1001002027nres_a @ ( refine1198353288_RES_a @ A ) ) )
= A ),
inference(rewrite,[status(thm)],[1507,1227]) ).
thf(50,axiom,
( refine1001002027nres_a
= ( ^ [A: refine424419629nres_a,B: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_inres__def) ).
thf(437,plain,
( refine1001002027nres_a
= ( ^ [A: refine424419629nres_a,B: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(438,plain,
( refine1001002027nres_a
= ( ^ [A: refine424419629nres_a,B: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ A ) ) ),
inference(lifteq,[status(thm)],[437]) ).
thf(1555,plain,
! [A: refine424419629nres_a] :
( ( refine1001002027nres_a @ A )
= ( ^ [B: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ A ) ) ),
inference(func_ext,[status(esa)],[438]) ).
thf(2708,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ ( refine1198353288_RES_a @ A ) ) )
= A ),
inference(rewrite,[status(thm)],[2638,1555]) ).
thf(229,axiom,
! [A: set_a] : ( refine412683989fail_a @ ( refine1198353288_RES_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_nofail__simps_I2_J) ).
thf(1216,plain,
! [A: set_a] : ( refine412683989fail_a @ ( refine1198353288_RES_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(1217,plain,
! [A: set_a] : ( refine412683989fail_a @ ( refine1198353288_RES_a @ A ) ),
inference(cnf,[status(esa)],[1216]) ).
thf(240,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_mem__Collect__eq) ).
thf(1359,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(1360,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(cnf,[status(esa)],[1359]) ).
thf(1361,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(lifteq,[status(thm)],[1360]) ).
thf(1,conjecture,
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
= ( phi @ x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
!= ( phi @ x ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(267,plain,
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
!= ( phi @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(268,plain,
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
!= ( phi @ x ) ),
inference(lifteq,[status(thm)],[267]) ).
thf(30238,plain,
! [B: a > $o,A: a] :
( ( ( member_a @ A @ ( collect_a @ B ) )
!= ( phi @ x ) )
| ( ( B @ A )
!= ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x ) ) ),
inference(paramod_ordered,[status(thm)],[1361,268]) ).
thf(30685,plain,
( ( member_a @ x @ ( collect_a @ ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ) )
!= ( phi @ x ) ),
inference(pre_uni,[status(thm)],[30238:[bind(A,$thf( x )),bind(B,$thf( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ))]]) ).
thf(238,axiom,
( refine1312857699nres_a
= ( ^ [A: refine424419629nres_a,B: a] :
( ( refine412683989fail_a @ A )
& ( refine1001002027nres_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_nf__inres__def) ).
thf(1333,plain,
( refine1312857699nres_a
= ( ^ [A: refine424419629nres_a,B: a] :
( ( refine412683989fail_a @ A )
& ( refine1001002027nres_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(1334,plain,
( refine1312857699nres_a
= ( ^ [A: refine424419629nres_a,B: a] :
( ( refine412683989fail_a @ A )
& ( refine1001002027nres_a @ A @ B ) ) ) ),
inference(lifteq,[status(thm)],[1333]) ).
thf(1625,plain,
! [A: refine424419629nres_a] :
( ( refine1312857699nres_a @ A )
= ( ^ [B: a] :
( ( refine412683989fail_a @ A )
& ( refine1001002027nres_a @ A @ B ) ) ) ),
inference(func_ext,[status(esa)],[1334]) ).
thf(31186,plain,
( ( member_a @ x
@ ( collect_a
@ ^ [A: a] :
( ( refine412683989fail_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) )
& ( refine1001002027nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ A ) ) ) )
!= ( phi @ x ) ),
inference(rewrite,[status(thm)],[30685,1625]) ).
thf(31225,plain,
! [A: set_a] :
( ( ( member_a @ x
@ ( collect_a
@ ^ [B: a] :
( $true
& ( refine1001002027nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ B ) ) ) )
!= ( phi @ x ) )
| ( ( refine412683989fail_a @ ( refine1198353288_RES_a @ A ) )
!= ( refine412683989fail_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1217,31186]) ).
thf(31226,plain,
! [A: set_a] :
( ( ( member_a @ x @ ( collect_a @ ( refine1001002027nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ) )
!= ( phi @ x ) )
| ( ( refine412683989fail_a @ ( refine1198353288_RES_a @ A ) )
!= ( refine412683989fail_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ) ),
inference(simp,[status(thm)],[31225]) ).
thf(31227,plain,
( ( member_a @ x @ ( collect_a @ ( refine1001002027nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ) )
!= ( phi @ x ) ),
inference(pattern_uni,[status(thm)],[31226:[bind(A,$thf( collect_a @ phi ))]]) ).
thf(31352,plain,
( ( member_a @ x
@ ( collect_a
@ ^ [A: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ) )
!= ( phi @ x ) ),
inference(rewrite,[status(thm)],[31227,1555]) ).
thf(31368,plain,
! [A: set_a] :
( ( ( member_a @ x @ A )
!= ( phi @ x ) )
| ( ( collect_a
@ ^ [B: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ ( refine1198353288_RES_a @ A ) ) )
!= ( collect_a
@ ^ [B: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2708,31352]) ).
thf(31369,plain,
( ( member_a @ x @ ( collect_a @ phi ) )
!= ( phi @ x ) ),
inference(pattern_uni,[status(thm)],[31368:[bind(A,$thf( collect_a @ phi ))]]) ).
thf(31449,plain,
$false,
inference(simplifyReflect,[status(thm)],[31369,1361]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP163^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.21 % Computer : n001.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 20:10:06 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.92/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.12/1.20 % [INFO] Parsing done (400ms).
% 2.41/1.21 % [INFO] Running in sequential loop mode.
% 3.46/1.59 % [INFO] eprover registered as external prover.
% 3.68/1.60 % [INFO] Scanning for conjecture ...
% 3.88/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 269 axioms. Running axiom selection ...
% 4.08/1.86 % [INFO] Axiom selection finished. Selected 264 axioms (removed 5 axioms).
% 4.72/2.12 % [INFO] Problem is higher-order (TPTP THF).
% 5.06/2.15 % [INFO] Type checking passed.
% 5.06/2.15 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 166.63/89.64 % [INFO] Killing All external provers ...
% 166.63/89.65 % Time passed: 89279ms (effective reasoning time: 88424ms)
% 166.63/89.65 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 166.63/89.65 % Axioms used in derivation (6): fact_5_nofail__simps_I2_J, fact_41_mem__Collect__eq, fact_31_inres__def, fact_4_inres__simps_I2_J, fact_42_Collect__mem__eq, fact_17_nf__inres__def
% 166.63/89.65 % No. of inferences in proof: 39
% 166.63/89.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 89279 ms resp. 88424 ms w/o parsing
% 166.63/89.70 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 166.97/89.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------