%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM651_8 : TPTP v9.3.1. Released v8.0.0.
% 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 : n004.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 : Sun Sep 27 08:09:26 AM UTC 2026
% Result : Theorem 11.87s 14.53s
% Output : Refutation 11.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 68 ( 29 unt; 0 typ; 4 def)
% Number of atoms : 163 ( 135 equ; 0 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 446 ( 111 ~; 61 |; 5 &; 244 @)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 9 con; 0-2 aty)
% Number of variables : 98 ( 0 ^; 88 !; 6 ?; 98 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% 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(sk1_decl,type,
sk1: $o ).
thf(sk2_decl,type,
sk2: nat ).
thf(sk3_decl,type,
sk3: nat ).
thf(sk4_decl,type,
sk4: nat ).
thf(sk5_decl,type,
sk5: nat ).
thf(sk2_def,definition,
( sk2
= ( @+[A: nat] :
( x
= ( A @ ( y @ pl ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: nat] :
( x
= ( A @ ( y @ pl ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: nat] :
( y
= ( A @ ( x @ pl ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: nat] :
( y
= ( A @ ( x @ pl ) ) ) ) ) ).
thf(1,conjecture,
~ ( ( ( x = y )
=> ~ ~ ! [A: nat] :
( x
!= ( A @ ( y @ pl ) ) ) )
=> ~ ~ ( ( ~ ! [A: nat] :
( x
!= ( A @ ( y @ pl ) ) )
=> ~ ~ ! [A: nat] :
( y
!= ( A @ ( x @ pl ) ) ) )
=> ~ ( ~ ! [A: nat] :
( y
!= ( A @ ( x @ pl ) ) )
=> ( x != y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz9b) ).
thf(2,negated_conjecture,
~ ~ ( ( ( x = y )
=> ~ ~ ! [A: nat] :
( x
!= ( A @ ( y @ pl ) ) ) )
=> ~ ~ ( ( ~ ! [A: nat] :
( x
!= ( A @ ( y @ pl ) ) )
=> ~ ~ ! [A: nat] :
( y
!= ( A @ ( x @ pl ) ) ) )
=> ~ ( ~ ! [A: nat] :
( y
!= ( A @ ( x @ pl ) ) )
=> ( x != y ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ~ ( ( ( x = y )
=> ! [A: nat] :
( x
!= ( A @ ( y @ pl ) ) ) )
=> ( ( ~ ! [A: nat] :
( x
!= ( A @ ( y @ pl ) ) )
=> ! [A: nat] :
( y
!= ( A @ ( x @ pl ) ) ) )
=> ~ ( ~ ! [A: nat] :
( y
!= ( A @ ( x @ pl ) ) )
=> ( x != y ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
( ( ( x = y )
=> ! [A: nat] :
( x
!= ( A @ ( y @ pl ) ) ) )
=> ( ( ~ ! [A: nat] :
( x
!= ( A @ ( y @ pl ) ) )
=> ! [A: nat] :
( y
!= ( A @ ( x @ pl ) ) ) )
=> ~ ( ~ ! [A: nat] :
( y
!= ( A @ ( x @ pl ) ) )
=> ( x != y ) ) ) ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ( x = y )
=> ~ ? [A: nat] :
( x
= ( A @ ( y @ pl ) ) ) )
=> ( ( ~ ~ ? [A: nat] :
( x
= ( A @ ( y @ pl ) ) )
=> ~ ? [A: nat] :
( y
= ( A @ ( x @ pl ) ) ) )
=> ~ ( ~ ~ ? [A: nat] :
( y
= ( A @ ( x @ pl ) ) )
=> ( x != y ) ) ) ),
inference(miniscope,[status(thm)],[8]) ).
thf(10,plain,
( ( ( x = y )
| ( y
= ( sk4 @ ( x @ pl ) ) )
| ~ sk1 )
& ( ( y
= ( sk5 @ ( x @ pl ) ) )
| ( y
= ( sk4 @ ( x @ pl ) ) )
| ~ sk1 )
& ( ( x = y )
| ( x
= ( sk3 @ ( y @ pl ) ) )
| ~ sk1 )
& ( ( y
= ( sk5 @ ( x @ pl ) ) )
| ( x
= ( sk3 @ ( y @ pl ) ) )
| ~ sk1 )
& ( sk1
| ( x
= ( sk2 @ ( y @ pl ) ) ) )
& ( sk1
| ( x = y ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
( ( x = y )
| ( y
= ( sk4 @ ( x @ pl ) ) )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[10]) ).
thf(21,plain,
( ~ sk1
| ( y = x )
| ( ( sk4 @ ( x @ pl ) )
= y ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(14,plain,
( sk1
| ( x = y ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(17,plain,
( sk1
| ( y = x ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(16,plain,
( sk1
| ( x
= ( sk2 @ ( y @ pl ) ) ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(20,plain,
( sk1
| ( ( sk2 @ ( y @ pl ) )
= x ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(4,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ pl ) )
= ( A @ ( B @ pl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz6) ).
thf(27,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ pl ) )
= ( A @ ( B @ pl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,plain,
! [B: nat,A: nat] :
( ( B @ ( A @ pl ) )
= ( A @ ( B @ pl ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(29,plain,
! [B: nat,A: nat] :
( ( B @ ( A @ pl ) )
= ( A @ ( B @ pl ) ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(3,axiom,
! [A: nat,B: nat] :
( B
!= ( B @ ( A @ pl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz7) ).
thf(23,plain,
! [A: nat,B: nat] :
( B
!= ( B @ ( A @ pl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(24,plain,
~ ? [A: nat,B: nat] :
( B
= ( B @ ( A @ pl ) ) ),
inference(miniscope,[status(thm)],[23]) ).
thf(25,plain,
! [B: nat,A: nat] :
( B
!= ( B @ ( A @ pl ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(26,plain,
! [B: nat,A: nat] :
( ( B @ ( A @ pl ) )
!= B ),
inference(lifteq,[status(thm)],[25]) ).
thf(36,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( ( A @ ( B @ pl ) )
!= ( D @ ( C @ pl ) ) )
| ( ( B @ ( A @ pl ) )
!= D ) ),
inference(paramod_ordered,[status(thm)],[29,26]) ).
thf(37,plain,
! [B: nat,A: nat] :
( ( B @ ( A @ pl ) )
!= A ),
inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(50,plain,
! [B: nat,A: nat] :
( ( ( sk2 @ ( y @ pl ) )
!= ( B @ ( A @ pl ) ) )
| ( x != A )
| sk1 ),
inference(paramod_ordered,[status(thm)],[20,37]) ).
thf(51,plain,
( ( y != x )
| sk1 ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( y )),bind(B,$thf( sk2 ))]]) ).
thf(67,plain,
( ( y != y )
| ( x != x )
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[17,51]) ).
thf(68,plain,
( ( y != y )
| sk1 ),
inference(simp,[status(thm)],[67]) ).
thf(69,plain,
sk1,
inference(pattern_uni,[status(thm)],[68:[]]) ).
thf(352,plain,
( ~ $true
| ( y = x )
| ( ( sk4 @ ( x @ pl ) )
= y ) ),
inference(rewrite,[status(thm)],[21,69]) ).
thf(353,plain,
( ( y = x )
| ( ( sk4 @ ( x @ pl ) )
= y ) ),
inference(simp,[status(thm)],[352]) ).
thf(359,plain,
! [B: nat,A: nat] :
( ( ( sk4 @ ( x @ pl ) )
!= ( B @ ( A @ pl ) ) )
| ( ( A @ ( B @ pl ) )
= y )
| ( y = x ) ),
inference(paramod_ordered,[status(thm)],[353,29]) ).
thf(360,plain,
( ( ( x @ ( sk4 @ pl ) )
= y )
| ( y = x ) ),
inference(pattern_uni,[status(thm)],[359:[bind(A,$thf( x )),bind(B,$thf( sk4 ))]]) ).
thf(12,plain,
( ( y
= ( sk5 @ ( x @ pl ) ) )
| ( y
= ( sk4 @ ( x @ pl ) ) )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[10]) ).
thf(19,plain,
( ~ sk1
| ( ( sk5 @ ( x @ pl ) )
= y )
| ( ( sk4 @ ( x @ pl ) )
= y ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(190,plain,
( ~ $true
| ( ( sk5 @ ( x @ pl ) )
= y )
| ( ( sk4 @ ( x @ pl ) )
= y ) ),
inference(rewrite,[status(thm)],[19,69]) ).
thf(191,plain,
( ( ( sk5 @ ( x @ pl ) )
= y )
| ( ( sk4 @ ( x @ pl ) )
= y ) ),
inference(simp,[status(thm)],[190]) ).
thf(192,plain,
! [B: nat,A: nat] :
( ( ( sk5 @ ( x @ pl ) )
!= ( B @ ( A @ pl ) ) )
| ( y != A )
| ( ( sk4 @ ( x @ pl ) )
= y ) ),
inference(paramod_ordered,[status(thm)],[191,37]) ).
thf(193,plain,
( ( y != x )
| ( ( sk4 @ ( x @ pl ) )
= y ) ),
inference(pattern_uni,[status(thm)],[192:[bind(A,$thf( x )),bind(B,$thf( sk5 ))]]) ).
thf(836,plain,
! [B: nat,A: nat] :
( ( ( sk4 @ ( x @ pl ) )
!= ( B @ ( A @ pl ) ) )
| ( y != A )
| ( y != x ) ),
inference(paramod_ordered,[status(thm)],[193,37]) ).
thf(837,plain,
( ( y != x )
| ( y != x ) ),
inference(pattern_uni,[status(thm)],[836:[bind(A,$thf( x )),bind(B,$thf( sk4 ))]]) ).
thf(922,plain,
y != x,
inference(simp,[status(thm)],[837]) ).
thf(1074,plain,
( ( x @ ( sk4 @ pl ) )
= y ),
inference(simplifyReflect,[status(thm)],[360,922]) ).
thf(13,plain,
( ( x = y )
| ( x
= ( sk3 @ ( y @ pl ) ) )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[10]) ).
thf(18,plain,
( ~ sk1
| ( y = x )
| ( ( sk3 @ ( y @ pl ) )
= x ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(90,plain,
! [B: nat,A: nat] :
( ( ( sk3 @ ( y @ pl ) )
!= ( B @ ( A @ pl ) ) )
| ( ( A @ ( B @ pl ) )
= x )
| ~ sk1
| ( y = x ) ),
inference(paramod_ordered,[status(thm)],[18,29]) ).
thf(91,plain,
( ( ( y @ ( sk3 @ pl ) )
= x )
| ~ sk1
| ( y = x ) ),
inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( y )),bind(B,$thf( sk3 ))]]) ).
thf(947,plain,
( ( ( y @ ( sk3 @ pl ) )
= x )
| ~ $true
| ( y = x ) ),
inference(rewrite,[status(thm)],[91,69]) ).
thf(948,plain,
( ( ( y @ ( sk3 @ pl ) )
= x )
| ( y = x ) ),
inference(simp,[status(thm)],[947]) ).
thf(1071,plain,
( ( y @ ( sk3 @ pl ) )
= x ),
inference(simplifyReflect,[status(thm)],[948,922]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ pl ) @ pl ) )
= ( C @ ( B @ pl ) @ ( A @ pl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz5) ).
thf(31,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ pl ) @ pl ) )
= ( C @ ( B @ pl ) @ ( A @ pl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(32,plain,
! [C: nat,B: nat,A: nat] :
( ( C @ ( B @ ( A @ pl ) @ pl ) )
= ( C @ ( B @ pl ) @ ( A @ pl ) ) ),
inference(cnf,[status(esa)],[31]) ).
thf(33,plain,
! [C: nat,B: nat,A: nat] :
( ( C @ ( B @ ( A @ pl ) @ pl ) )
= ( C @ ( B @ pl ) @ ( A @ pl ) ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(34,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( ( B @ ( A @ pl ) )
!= ( D @ ( C @ pl ) ) )
| ( ( A @ ( B @ pl ) )
!= D ) ),
inference(paramod_ordered,[status(thm)],[29,26]) ).
thf(35,plain,
! [B: nat,A: nat] :
( ( A @ ( B @ pl ) )
!= B ),
inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(38,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( ( B @ ( A @ pl ) )
!= ( C @ ( D @ pl ) ) )
| ( ( A @ ( B @ pl ) )
!= D ) ),
inference(paramod_ordered,[status(thm)],[29,35]) ).
thf(39,plain,
! [B: nat,A: nat] :
( ( A @ ( B @ pl ) )
!= A ),
inference(pattern_uni,[status(thm)],[38:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(114,plain,
! [E: nat,D: nat,C: nat,B: nat,A: nat] :
( ( ( C @ ( B @ ( A @ pl ) @ pl ) )
!= ( D @ ( E @ pl ) ) )
| ( ( C @ ( B @ pl ) @ ( A @ pl ) )
!= D ) ),
inference(paramod_ordered,[status(thm)],[33,39]) ).
thf(115,plain,
! [C: nat,B: nat,A: nat] :
( ( A @ ( C @ pl ) @ ( B @ pl ) )
!= A ),
inference(pattern_uni,[status(thm)],[114:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( G @ ( F @ pl ) ))]]) ).
thf(122,plain,
! [C: nat,B: nat,A: nat] :
( ( A @ ( C @ pl ) @ ( B @ pl ) )
!= A ),
inference(simp,[status(thm)],[115]) ).
thf(1105,plain,
! [C: nat,B: nat,A: nat] :
( ( ( y @ ( sk3 @ pl ) )
!= ( A @ ( C @ pl ) ) )
| ( ( x @ ( B @ pl ) )
!= A ) ),
inference(paramod_ordered,[status(thm)],[1071,122]) ).
thf(1106,plain,
! [A: nat] :
( ( x @ ( A @ pl ) )
!= y ),
inference(pattern_uni,[status(thm)],[1105:[bind(A,$thf( y )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).
thf(1155,plain,
! [A: nat] :
( ( x @ ( A @ pl ) )
!= y ),
inference(simp,[status(thm)],[1106]) ).
thf(1677,plain,
$false,
inference(simplifyReflect,[status(thm)],[1074,1155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM651_8 : TPTP v9.3.1. Released v8.0.0.
% 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
% 0.13/10.58 % Computer : n004.cluster.edu
% 0.13/10.58 % Model : x86_64 x86_64
% 0.13/10.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.58 % Memory : 8046.5625MB
% 0.13/10.58 % OS : Linux 6.8.0-71-generic
% 0.13/10.58 % CPULimit : 300
% 0.13/10.58 % WCLimit : 300
% 0.13/10.58 % DateTime : Sat Sep 26 03:36:18 UTC 2026
% 0.13/10.59 % CPUTime :
% 0.13/10.59 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
% 0.83/11.11 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.31/11.30 % [INFO] Parsing done (187ms).
% 1.31/11.31 % [INFO] Running in sequential loop mode.
% 1.90/11.72 % [INFO] eprover registered as external prover.
% 1.90/11.73 % [INFO] Scanning for conjecture ...
% 2.09/11.84 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.09/11.88 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.09/11.89 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.27/11.90 % [INFO] Type checking passed.
% 2.27/11.91 % [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 ...
% 11.87/14.53 % [INFO] Killing All external provers ...
% 11.87/14.53 % Time passed: 3843ms (effective reasoning time: 3206ms)
% 11.87/14.53 % 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)>
% 11.87/14.53 % Axioms used in derivation (3): satz6, satz7, satz5
% 11.87/14.53 % No. of inferences in proof: 64
% 11.87/14.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3843 ms resp. 3206 ms w/o parsing
% 11.87/14.59 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.87/14.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------