%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM739^1 : 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 : n013.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 08:18:04 AM UTC 2026
% Result : Theorem 24.05s 6.86s
% Output : Refutation 24.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 153 ( 14 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 394 ( 64 ~; 51 |; 1 &; 256 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 73 ( 0 ^; 73 !; 0 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
thf(frac_type,type,
frac: $tType ).
thf(x_decl,type,
x: frac ).
thf(y_decl,type,
y: frac ).
thf(z_decl,type,
z: frac ).
thf(u_decl,type,
u: frac ).
thf(moref_decl,type,
moref: frac > frac > $o ).
thf(eq_decl,type,
eq: frac > frac > $o ).
thf(4,axiom,
eq @ x @ z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e) ).
thf(16,plain,
eq @ x @ z,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
eq @ y @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f) ).
thf(17,plain,
eq @ y @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( moref @ A @ B )
=> ( ( eq @ A @ C )
=> ( ( eq @ B @ D )
=> ( moref @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz44) ).
thf(24,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( moref @ A @ B )
=> ( ( eq @ A @ C )
=> ( ( eq @ B @ D )
=> ( moref @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(25,plain,
! [A: frac,B: frac] :
( ( moref @ A @ B )
=> ! [C: frac] :
( ( eq @ A @ C )
=> ! [D: frac] :
( ( eq @ B @ D )
=> ( moref @ C @ D ) ) ) ),
inference(miniscope,[status(thm)],[24]) ).
thf(26,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( eq @ A @ C )
| ~ ( eq @ B @ D )
| ( moref @ C @ D ) ),
inference(cnf,[status(esa)],[25]) ).
thf(433,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( eq @ A @ C )
| ~ $true
| ( moref @ C @ D )
| ( ( eq @ y @ u )
!= ( eq @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[17,26]) ).
thf(434,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( eq @ A @ C )
| ( moref @ C @ D )
| ( ( eq @ y @ u )
!= ( eq @ B @ D ) ) ),
inference(simp,[status(thm)],[433]) ).
thf(435,plain,
! [B: frac,A: frac] :
( ~ ( moref @ A @ y )
| ~ ( eq @ A @ B )
| ( moref @ B @ u ) ),
inference(pattern_uni,[status(thm)],[434:[bind(A,$thf( A )),bind(B,$thf( y )),bind(C,$thf( C )),bind(D,$thf( u ))]]) ).
thf(484,plain,
! [B: frac,A: frac] :
( ~ ( moref @ A @ y )
| ~ ( eq @ A @ B )
| ( moref @ B @ u ) ),
inference(simp,[status(thm)],[435]) ).
thf(8432,plain,
! [B: frac,A: frac] :
( ~ ( moref @ A @ y )
| ~ $true
| ( moref @ B @ u )
| ( ( eq @ x @ z )
!= ( eq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16,484]) ).
thf(8433,plain,
! [B: frac,A: frac] :
( ~ ( moref @ A @ y )
| ( moref @ B @ u )
| ( ( eq @ x @ z )
!= ( eq @ A @ B ) ) ),
inference(simp,[status(thm)],[8432]) ).
thf(8434,plain,
( ~ ( moref @ x @ y )
| ( moref @ z @ u ) ),
inference(pattern_uni,[status(thm)],[8433:[bind(A,$thf( x )),bind(B,$thf( z ))]]) ).
thf(3,axiom,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(14,plain,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,plain,
( ( moref @ x @ y )
| ( eq @ x @ y ) ),
inference(cnf,[status(esa)],[14]) ).
thf(7,axiom,
! [A: frac,B: frac,C: frac] :
( ( eq @ A @ B )
=> ( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz39) ).
thf(19,plain,
! [A: frac,B: frac,C: frac] :
( ( eq @ A @ B )
=> ( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(20,plain,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ! [C: frac] :
( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
inference(miniscope,[status(thm)],[19]) ).
thf(21,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ B @ C )
| ( eq @ A @ C ) ),
inference(cnf,[status(esa)],[20]) ).
thf(47,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ $true
| ( eq @ A @ C )
| ( ( eq @ y @ u )
!= ( eq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17,21]) ).
thf(48,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ( eq @ A @ C )
| ( ( eq @ y @ u )
!= ( eq @ B @ C ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(49,plain,
! [A: frac] :
( ~ ( eq @ A @ y )
| ( eq @ A @ u ) ),
inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( A )),bind(B,$thf( y )),bind(C,$thf( u ))]]) ).
thf(83,plain,
! [A: frac] :
( ( moref @ x @ y )
| ~ $true
| ( eq @ A @ u )
| ( ( eq @ x @ y )
!= ( eq @ A @ y ) ) ),
inference(paramod_ordered,[status(thm)],[15,49]) ).
thf(84,plain,
! [A: frac] :
( ( moref @ x @ y )
| ( eq @ A @ u )
| ( ( eq @ x @ y )
!= ( eq @ A @ y ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(85,plain,
( ( moref @ x @ y )
| ( eq @ x @ u ) ),
inference(pattern_uni,[status(thm)],[84:[bind(A,$thf( x ))]]) ).
thf(8,axiom,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ( eq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz38) ).
thf(22,plain,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ( eq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(23,plain,
! [B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ( eq @ B @ A ) ),
inference(cnf,[status(esa)],[22]) ).
thf(206,plain,
! [B: frac,A: frac] :
( ~ $true
| ( eq @ B @ A )
| ( ( eq @ x @ z )
!= ( eq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16,23]) ).
thf(207,plain,
! [B: frac,A: frac] :
( ( eq @ B @ A )
| ( ( eq @ x @ z )
!= ( eq @ A @ B ) ) ),
inference(simp,[status(thm)],[206]) ).
thf(208,plain,
eq @ z @ x,
inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( x )),bind(B,$thf( z ))]]) ).
thf(1,conjecture,
( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz46) ).
thf(2,negated_conjecture,
~ ( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,plain,
( ~ ( moref @ z @ u )
& ~ ( eq @ z @ u ) ),
inference(cnf,[status(esa)],[10]) ).
thf(13,plain,
~ ( eq @ z @ u ),
inference(cnfConj,[status(thm)],[11]) ).
thf(41,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ B @ C )
| ~ $true
| ( ( eq @ A @ C )
!= ( eq @ z @ u ) ) ),
inference(paramod_ordered,[status(thm)],[21,13]) ).
thf(42,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ B @ C )
| ( ( eq @ A @ C )
!= ( eq @ z @ u ) ) ),
inference(simp,[status(thm)],[41]) ).
thf(43,plain,
! [A: frac] :
( ~ ( eq @ z @ A )
| ~ ( eq @ A @ u ) ),
inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( z )),bind(B,$thf( B )),bind(C,$thf( u ))]]) ).
thf(74,plain,
! [A: frac] :
( ~ ( eq @ z @ A )
| ~ ( eq @ A @ u ) ),
inference(simp,[status(thm)],[43]) ).
thf(266,plain,
! [A: frac] :
( ~ $true
| ~ ( eq @ A @ u )
| ( ( eq @ z @ x )
!= ( eq @ z @ A ) ) ),
inference(paramod_ordered,[status(thm)],[208,74]) ).
thf(267,plain,
! [A: frac] :
( ~ ( eq @ A @ u )
| ( ( eq @ z @ x )
!= ( eq @ z @ A ) ) ),
inference(simp,[status(thm)],[266]) ).
thf(268,plain,
~ ( eq @ x @ u ),
inference(pattern_uni,[status(thm)],[267:[bind(A,$thf( x ))]]) ).
thf(353,plain,
( ( moref @ x @ y )
| $false ),
inference(rewrite,[status(thm)],[85,268]) ).
thf(354,plain,
moref @ x @ y,
inference(simp,[status(thm)],[353]) ).
thf(12,plain,
~ ( moref @ z @ u ),
inference(cnfConj,[status(thm)],[11]) ).
thf(14677,plain,
( ~ $true
| $false ),
inference(rewrite,[status(thm)],[8434,354,12]) ).
thf(14678,plain,
$false,
inference(simp,[status(thm)],[14677]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM739^1 : 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
% 0.11/0.21 % Computer : n013.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 12:46:21 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.87/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/0.99 % [INFO] Parsing done (191ms).
% 1.21/1.00 % [INFO] Running in sequential loop mode.
% 2.00/1.40 % [INFO] eprover registered as external prover.
% 2.00/1.41 % [INFO] Scanning for conjecture ...
% 2.00/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.18/1.53 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.18/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.18/1.56 % [INFO] Type checking passed.
% 2.18/1.56 % [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 ...
% 24.05/6.85 % [INFO] Killing All external provers ...
% 24.05/6.86 % Time passed: 6502ms (effective reasoning time: 5845ms)
% 24.05/6.86 % 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)>
% 24.05/6.86 % Axioms used in derivation (6): e, f, satz39, m, satz44, satz38
% 24.05/6.86 % No. of inferences in proof: 51
% 24.05/6.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6502 ms resp. 5845 ms w/o parsing
% 24.57/6.90 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.57/6.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------