%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM696^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n014.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 08:18:00 AM UTC 2026
% Result : Theorem 75.75s 30.02s
% Output : Refutation 75.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 25 unt; 0 typ; 3 def)
% Number of atoms : 80 ( 79 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 369 ( 59 ~; 16 |; 1 &; 283 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 75 ( 4 ^; 63 !; 5 ?; 75 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_decl,type,
x: nat ).
thf(y_decl,type,
y: nat ).
thf(pl_decl,type,
pl: nat > nat > nat ).
thf(n_1_decl,type,
n_1: nat ).
thf(sk1_decl,type,
sk1: nat ).
thf(sk2_decl,type,
sk2: nat > nat ).
thf(sk3_decl,type,
sk3: nat > nat > nat > nat ).
thf(sk1_def,definition,
( sk1
= ( @+[A: nat] :
( y
= ( pl @ x @ A ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: nat] :
@+[B: nat] :
( A
= ( pl @ n_1 @ B ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: nat,B: nat,C: nat] :
@+[D: nat] :
( ( pl @ C @ A )
= ( pl @ ( pl @ B @ A ) @ D ) ) ) ) ).
thf(3,axiom,
~ ! [A: nat] :
( y
!= ( pl @ x @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(15,plain,
~ ! [A: nat] :
( y
!= ( pl @ x @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,plain,
~ ! [A: nat] :
( y
!= ( pl @ x @ A ) ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(17,plain,
~ ~ ? [A: nat] :
( y
= ( pl @ x @ A ) ),
inference(miniscope,[status(thm)],[16]) ).
thf(18,plain,
( y
= ( pl @ x @ sk1 ) ),
inference(cnf,[status(esa)],[17]) ).
thf(19,plain,
( ( pl @ x @ sk1 )
= y ),
inference(lifteq,[status(thm)],[18]) ).
thf(7,axiom,
! [A: nat,B: nat] :
( ( pl @ A @ B )
= ( pl @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz6) ).
thf(30,plain,
! [A: nat,B: nat] :
( ( pl @ A @ B )
= ( pl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(31,plain,
! [B: nat,A: nat] :
( ( pl @ A @ B )
= ( pl @ B @ A ) ),
inference(cnf,[status(esa)],[30]) ).
thf(32,plain,
! [B: nat,A: nat] :
( ( pl @ A @ B )
= ( pl @ B @ A ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(473,plain,
! [B: nat,A: nat] :
( ( ( pl @ B @ A )
= y )
| ( ( pl @ x @ sk1 )
!= ( pl @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19,32]) ).
thf(474,plain,
( ( pl @ sk1 @ x )
= y ),
inference(pattern_uni,[status(thm)],[473:[bind(A,$thf( x )),bind(B,$thf( sk1 ))]]) ).
thf(5,axiom,
! [A: nat] :
( ~ ~ ! [B: nat] :
( A
!= ( pl @ n_1 @ B ) )
=> ( A = n_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz24) ).
thf(21,plain,
! [A: nat] :
( ! [B: nat] :
( A
!= ( pl @ n_1 @ B ) )
=> ( A = n_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(22,plain,
! [A: nat] :
( ~ ? [B: nat] :
( A
= ( pl @ n_1 @ B ) )
=> ( A = n_1 ) ),
inference(miniscope,[status(thm)],[21]) ).
thf(23,plain,
! [A: nat] :
( ( A
= ( pl @ n_1 @ ( sk2 @ A ) ) )
| ( A = n_1 ) ),
inference(cnf,[status(esa)],[22]) ).
thf(24,plain,
! [A: nat] :
( ( ( pl @ n_1 @ ( sk2 @ A ) )
= A )
| ( A = n_1 ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ~ ! [D: nat] :
( A
!= ( pl @ B @ D ) )
=> ~ ! [D: nat] :
( ( pl @ A @ C )
!= ( pl @ ( pl @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19a) ).
thf(25,plain,
! [A: nat,B: nat,C: nat] :
( ~ ! [D: nat] :
( A
!= ( pl @ B @ D ) )
=> ~ ! [D: nat] :
( ( pl @ A @ C )
!= ( pl @ ( pl @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(26,plain,
! [A: nat,B: nat] :
( ~ ~ ? [C: nat] :
( A
= ( pl @ B @ C ) )
=> ~ ~ ! [C: nat] :
? [D: nat] :
( ( pl @ A @ C )
= ( pl @ ( pl @ B @ C ) @ D ) ) ),
inference(miniscope,[status(thm)],[25]) ).
thf(27,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( A
!= ( pl @ B @ C ) )
| ( ( pl @ A @ D )
= ( pl @ ( pl @ B @ D ) @ ( sk3 @ D @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[26]) ).
thf(28,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( A
!= ( pl @ B @ C ) )
| ( ( pl @ A @ D )
= ( pl @ ( pl @ B @ D ) @ ( sk3 @ D @ B @ A ) ) ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(29,plain,
! [C: nat,B: nat,A: nat] :
( ( pl @ ( pl @ A @ B ) @ C )
= ( pl @ ( pl @ A @ C ) @ ( sk3 @ C @ A @ ( pl @ A @ B ) ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(69,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( A = n_1 )
| ( ( pl @ A @ D )
= ( pl @ ( pl @ B @ D ) @ ( sk3 @ D @ B @ ( pl @ B @ C ) ) ) )
| ( ( pl @ n_1 @ ( sk2 @ A ) )
!= ( pl @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[24,29]) ).
thf(70,plain,
! [B: nat,A: nat] :
( ( B = n_1 )
| ( ( pl @ B @ A )
= ( pl @ ( pl @ n_1 @ A ) @ ( sk3 @ A @ n_1 @ ( pl @ n_1 @ ( sk2 @ B ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[69:[bind(A,$thf( E )),bind(B,$thf( n_1 )),bind(C,$thf( sk2 @ E ))]]) ).
thf(127,plain,
! [B: nat,A: nat] :
( ( B = n_1 )
| ( ( pl @ B @ A )
= ( pl @ ( pl @ n_1 @ A ) @ ( sk3 @ A @ n_1 @ ( pl @ n_1 @ ( sk2 @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[70]) ).
thf(8170,plain,
! [B: nat,A: nat] :
( ( B = n_1 )
| ( ( pl @ ( pl @ n_1 @ A ) @ ( sk3 @ A @ n_1 @ ( pl @ n_1 @ ( sk2 @ B ) ) ) )
= y )
| ( ( pl @ sk1 @ x )
!= ( pl @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[474,127]) ).
thf(8171,plain,
( ( sk1 = n_1 )
| ( ( pl @ ( pl @ n_1 @ x ) @ ( sk3 @ x @ n_1 @ ( pl @ n_1 @ ( sk2 @ sk1 ) ) ) )
= y ) ),
inference(pattern_uni,[status(thm)],[8170:[bind(A,$thf( x )),bind(B,$thf( sk1 ))]]) ).
thf(1,conjecture,
( ~ ~ ! [A: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ A ) )
=> ( y
= ( pl @ x @ n_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz25) ).
thf(2,negated_conjecture,
~ ( ~ ~ ! [A: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ A ) )
=> ( y
= ( pl @ x @ n_1 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ( ! [A: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ A ) )
=> ( y
= ( pl @ x @ n_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
~ ( ~ ? [A: nat] :
( y
= ( pl @ ( pl @ x @ n_1 ) @ A ) )
=> ( y
= ( pl @ x @ n_1 ) ) ),
inference(miniscope,[status(thm)],[8]) ).
thf(10,plain,
! [A: nat] :
( ( y
!= ( pl @ ( pl @ x @ n_1 ) @ A ) )
& ( y
!= ( pl @ x @ n_1 ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(12,plain,
( y
!= ( pl @ x @ n_1 ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(14,plain,
( ( pl @ x @ n_1 )
!= y ),
inference(lifteq,[status(thm)],[12]) ).
thf(33,plain,
( ( y != y )
| ( ( pl @ x @ sk1 )
!= ( pl @ x @ n_1 ) ) ),
inference(paramod_ordered,[status(thm)],[19,14]) ).
thf(34,plain,
( ( pl @ x @ sk1 )
!= ( pl @ x @ n_1 ) ),
inference(simp,[status(thm)],[33]) ).
thf(35,plain,
( ( x != x )
| ( sk1 != n_1 ) ),
inference(simp,[status(thm)],[34]) ).
thf(36,plain,
sk1 != n_1,
inference(simp,[status(thm)],[35]) ).
thf(55974,plain,
( ( pl @ ( pl @ n_1 @ x ) @ ( sk3 @ x @ n_1 @ ( pl @ n_1 @ ( sk2 @ sk1 ) ) ) )
= y ),
inference(simplifyReflect,[status(thm)],[8171,36]) ).
thf(11,plain,
! [A: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ A ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(13,plain,
! [A: nat] :
( ( pl @ ( pl @ x @ n_1 ) @ A )
!= y ),
inference(lifteq,[status(thm)],[11]) ).
thf(56213,plain,
! [A: nat] :
( ( y != y )
| ( ( pl @ ( pl @ n_1 @ x ) @ ( sk3 @ x @ n_1 @ ( pl @ n_1 @ ( sk2 @ sk1 ) ) ) )
!= ( pl @ ( pl @ x @ n_1 ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[55974,13]) ).
thf(56214,plain,
! [A: nat] :
( ( pl @ ( pl @ n_1 @ x ) @ ( sk3 @ x @ n_1 @ ( pl @ n_1 @ ( sk2 @ sk1 ) ) ) )
!= ( pl @ ( pl @ x @ n_1 ) @ A ) ),
inference(simp,[status(thm)],[56213]) ).
thf(56826,plain,
! [A: nat] :
( ( ( pl @ n_1 @ x )
!= ( pl @ x @ n_1 ) )
| ( ( sk3 @ x @ n_1 @ ( pl @ n_1 @ ( sk2 @ sk1 ) ) )
!= A ) ),
inference(simp,[status(thm)],[56214]) ).
thf(57036,plain,
( ( pl @ n_1 @ x )
!= ( pl @ x @ n_1 ) ),
inference(simp,[status(thm)],[56826]) ).
thf(57916,plain,
$false,
inference(simplifyReflect,[status(thm)],[57036,32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM696^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % 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
% 0.11/0.22 % Computer : n014.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 12:40:45 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 0.85/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.15/0.98 % [INFO] Parsing done (183ms).
% 1.15/0.99 % [INFO] Running in sequential loop mode.
% 1.76/1.39 % [INFO] eprover registered as external prover.
% 1.95/1.40 % [INFO] Scanning for conjecture ...
% 1.95/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.13/1.53 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.13/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.13/1.56 % [INFO] Type checking passed.
% 2.13/1.56 % [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 ...
% 75.75/30.01 % [INFO] Killing All external provers ...
% 75.75/30.02 % Time passed: 29648ms (effective reasoning time: 29017ms)
% 75.75/30.02 % 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)>
% 75.75/30.02 % Axioms used in derivation (4): m, satz6, satz24, satz19a
% 75.75/30.02 % No. of inferences in proof: 47
% 75.75/30.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 29648 ms resp. 29017 ms w/o parsing
% 75.92/30.07 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 75.92/30.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------