%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM746^1 : 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 : 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 : Wed Sep 30 08:18:05 AM UTC 2026
% Result : Theorem 18.32s 5.28s
% Output : Refutation 18.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 6
% Syntax : Number of formulae : 60 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 210 ( 18 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 562 ( 90 ~; 80 |; 3 &; 358 @)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 83 ( 0 ^; 83 !; 0 ?; 83 :)
% 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(lessf_decl,type,
lessf: frac > frac > $o ).
thf(eq_decl,type,
eq: frac > frac > $o ).
thf(3,axiom,
( ~ ( lessf @ x @ y )
=> ( eq @ x @ y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(13,plain,
( ~ ( lessf @ x @ y )
=> ( eq @ x @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,plain,
( ( lessf @ x @ y )
| ( eq @ x @ y ) ),
inference(cnf,[status(esa)],[13]) ).
thf(4,axiom,
( ~ ( lessf @ y @ z )
=> ( eq @ y @ z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k) ).
thf(15,plain,
( ~ ( lessf @ y @ z )
=> ( eq @ y @ z ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,plain,
( ( lessf @ y @ z )
| ( eq @ y @ z ) ),
inference(cnf,[status(esa)],[15]) ).
thf(6,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(18,plain,
! [A: frac,B: frac,C: frac] :
( ( eq @ A @ B )
=> ( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,plain,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ! [C: frac] :
( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
inference(miniscope,[status(thm)],[18]) ).
thf(20,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ B @ C )
| ( eq @ A @ C ) ),
inference(cnf,[status(esa)],[19]) ).
thf(1,conjecture,
( ~ ( lessf @ x @ z )
=> ( eq @ x @ z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz52) ).
thf(2,negated_conjecture,
~ ( ~ ( lessf @ x @ z )
=> ( eq @ x @ z ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ( ~ ( lessf @ x @ z )
=> ( eq @ x @ z ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
( ~ ( lessf @ x @ z )
& ~ ( eq @ x @ z ) ),
inference(cnf,[status(esa)],[9]) ).
thf(12,plain,
~ ( eq @ x @ z ),
inference(cnfConj,[status(thm)],[10]) ).
thf(51,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ B @ C )
| ~ $true
| ( ( eq @ A @ C )
!= ( eq @ x @ z ) ) ),
inference(paramod_ordered,[status(thm)],[20,12]) ).
thf(52,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ B @ C )
| ( ( eq @ A @ C )
!= ( eq @ x @ z ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(53,plain,
! [A: frac] :
( ~ ( eq @ x @ A )
| ~ ( eq @ A @ z ) ),
inference(pattern_uni,[status(thm)],[52:[bind(A,$thf( x )),bind(B,$thf( B )),bind(C,$thf( z ))]]) ).
thf(56,plain,
! [A: frac] :
( ~ ( eq @ x @ A )
| ~ ( eq @ A @ z ) ),
inference(simp,[status(thm)],[53]) ).
thf(89,plain,
! [A: frac] :
( ( lessf @ x @ y )
| ~ $true
| ~ ( eq @ A @ z )
| ( ( eq @ x @ y )
!= ( eq @ x @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14,56]) ).
thf(90,plain,
! [A: frac] :
( ( lessf @ x @ y )
| ~ ( eq @ A @ z )
| ( ( eq @ x @ y )
!= ( eq @ x @ A ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(91,plain,
( ( lessf @ x @ y )
| ~ ( eq @ y @ z ) ),
inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( y ))]]) ).
thf(131,plain,
( ( lessf @ y @ z )
| ( lessf @ x @ y )
| ~ $true
| ( ( eq @ y @ z )
!= ( eq @ y @ z ) ) ),
inference(paramod_ordered,[status(thm)],[16,91]) ).
thf(132,plain,
( ( lessf @ y @ z )
| ( lessf @ x @ y )
| ( ( eq @ y @ z )
!= ( eq @ y @ z ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(133,plain,
( ( lessf @ y @ z )
| ( lessf @ x @ y ) ),
inference(pattern_uni,[status(thm)],[132:[]]) ).
thf(8,axiom,
! [A: frac,B: frac,C: frac] :
( ( ~ ( lessf @ A @ B )
=> ( eq @ A @ B ) )
=> ( ( lessf @ B @ C )
=> ( lessf @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz51a) ).
thf(26,plain,
! [A: frac,B: frac,C: frac] :
( ( ~ ( lessf @ A @ B )
=> ( eq @ A @ B ) )
=> ( ( lessf @ B @ C )
=> ( lessf @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,plain,
! [A: frac,B: frac] :
( ( ~ ( lessf @ A @ B )
=> ( eq @ A @ B ) )
=> ! [C: frac] :
( ( lessf @ B @ C )
=> ( lessf @ A @ C ) ) ),
inference(miniscope,[status(thm)],[26]) ).
thf(28,plain,
! [C: frac,B: frac,A: frac] :
( ( ~ ( lessf @ A @ B )
| ~ ( lessf @ B @ C )
| ( lessf @ A @ C ) )
& ( ~ ( eq @ A @ B )
| ~ ( lessf @ B @ C )
| ( lessf @ A @ C ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(30,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( lessf @ B @ C )
| ( lessf @ A @ C ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(443,plain,
! [C: frac,B: frac,A: frac] :
( ( lessf @ x @ y )
| ~ ( eq @ A @ B )
| ~ $true
| ( lessf @ A @ C )
| ( ( lessf @ y @ z )
!= ( lessf @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[133,30]) ).
thf(444,plain,
! [C: frac,B: frac,A: frac] :
( ( lessf @ x @ y )
| ~ ( eq @ A @ B )
| ( lessf @ A @ C )
| ( ( lessf @ y @ z )
!= ( lessf @ B @ C ) ) ),
inference(simp,[status(thm)],[443]) ).
thf(445,plain,
! [A: frac] :
( ( lessf @ x @ y )
| ~ ( eq @ A @ y )
| ( lessf @ A @ z ) ),
inference(pattern_uni,[status(thm)],[444:[bind(A,$thf( A )),bind(B,$thf( y )),bind(C,$thf( z ))]]) ).
thf(9057,plain,
! [A: frac] :
( ( lessf @ x @ y )
| ( lessf @ x @ y )
| ~ $true
| ( lessf @ A @ z )
| ( ( eq @ x @ y )
!= ( eq @ A @ y ) ) ),
inference(paramod_ordered,[status(thm)],[14,445]) ).
thf(9058,plain,
! [A: frac] :
( ( lessf @ x @ y )
| ( lessf @ A @ z )
| ( ( eq @ x @ y )
!= ( eq @ A @ y ) ) ),
inference(simp,[status(thm)],[9057]) ).
thf(9059,plain,
( ( lessf @ x @ y )
| ( lessf @ x @ z ) ),
inference(pattern_uni,[status(thm)],[9058:[bind(A,$thf( x ))]]) ).
thf(11,plain,
~ ( lessf @ x @ z ),
inference(cnfConj,[status(thm)],[10]) ).
thf(9079,plain,
( ( lessf @ x @ y )
| $false ),
inference(rewrite,[status(thm)],[9059,11]) ).
thf(9080,plain,
lessf @ x @ y,
inference(simp,[status(thm)],[9079]) ).
thf(7,axiom,
! [A: frac,B: frac,C: frac] :
( ( lessf @ A @ B )
=> ( ( ~ ( lessf @ B @ C )
=> ( eq @ B @ C ) )
=> ( lessf @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz51b) ).
thf(21,plain,
! [A: frac,B: frac,C: frac] :
( ( lessf @ A @ B )
=> ( ( ~ ( lessf @ B @ C )
=> ( eq @ B @ C ) )
=> ( lessf @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(22,plain,
! [A: frac,B: frac] :
( ( lessf @ A @ B )
=> ! [C: frac] :
( ( ~ ( lessf @ B @ C )
=> ( eq @ B @ C ) )
=> ( lessf @ A @ C ) ) ),
inference(miniscope,[status(thm)],[21]) ).
thf(23,plain,
! [C: frac,B: frac,A: frac] :
( ( ~ ( lessf @ A @ B )
| ~ ( lessf @ B @ C )
| ( lessf @ A @ C ) )
& ( ~ ( lessf @ A @ B )
| ~ ( eq @ B @ C )
| ( lessf @ A @ C ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(25,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ A @ B )
| ~ ( eq @ B @ C )
| ( lessf @ A @ C ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(194,plain,
! [C: frac,B: frac,A: frac] :
( ( lessf @ y @ z )
| ~ ( lessf @ A @ B )
| ~ $true
| ( lessf @ A @ C )
| ( ( eq @ y @ z )
!= ( eq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[16,25]) ).
thf(195,plain,
! [C: frac,B: frac,A: frac] :
( ( lessf @ y @ z )
| ~ ( lessf @ A @ B )
| ( lessf @ A @ C )
| ( ( eq @ y @ z )
!= ( eq @ B @ C ) ) ),
inference(simp,[status(thm)],[194]) ).
thf(196,plain,
! [A: frac] :
( ( lessf @ y @ z )
| ~ ( lessf @ A @ y )
| ( lessf @ A @ z ) ),
inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( A )),bind(B,$thf( y )),bind(C,$thf( z ))]]) ).
thf(9085,plain,
! [A: frac] :
( ( lessf @ y @ z )
| ~ $true
| ( lessf @ A @ z )
| ( ( lessf @ x @ y )
!= ( lessf @ A @ y ) ) ),
inference(paramod_ordered,[status(thm)],[9080,196]) ).
thf(9086,plain,
! [A: frac] :
( ( lessf @ y @ z )
| ( lessf @ A @ z )
| ( ( lessf @ x @ y )
!= ( lessf @ A @ y ) ) ),
inference(simp,[status(thm)],[9085]) ).
thf(9087,plain,
( ( lessf @ y @ z )
| ( lessf @ x @ z ) ),
inference(pattern_uni,[status(thm)],[9086:[bind(A,$thf( x ))]]) ).
thf(24,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ A @ B )
| ~ ( lessf @ B @ C )
| ( lessf @ A @ C ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(81,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ A @ B )
| ~ ( lessf @ B @ C )
| ~ $true
| ( ( lessf @ A @ C )
!= ( lessf @ x @ z ) ) ),
inference(paramod_ordered,[status(thm)],[24,11]) ).
thf(82,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ A @ B )
| ~ ( lessf @ B @ C )
| ( ( lessf @ A @ C )
!= ( lessf @ x @ z ) ) ),
inference(simp,[status(thm)],[81]) ).
thf(83,plain,
! [A: frac] :
( ~ ( lessf @ x @ A )
| ~ ( lessf @ A @ z ) ),
inference(pattern_uni,[status(thm)],[82:[bind(A,$thf( x )),bind(B,$thf( B )),bind(C,$thf( z ))]]) ).
thf(86,plain,
! [A: frac] :
( ~ ( lessf @ x @ A )
| ~ ( lessf @ A @ z ) ),
inference(simp,[status(thm)],[83]) ).
thf(9177,plain,
! [A: frac] :
( ~ $true
| ~ ( lessf @ A @ z )
| ( ( lessf @ x @ y )
!= ( lessf @ x @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9080,86]) ).
thf(9178,plain,
! [A: frac] :
( ~ ( lessf @ A @ z )
| ( ( lessf @ x @ y )
!= ( lessf @ x @ A ) ) ),
inference(simp,[status(thm)],[9177]) ).
thf(9179,plain,
~ ( lessf @ y @ z ),
inference(pattern_uni,[status(thm)],[9178:[bind(A,$thf( y ))]]) ).
thf(9877,plain,
( $false
| $false ),
inference(rewrite,[status(thm)],[9087,11,9179]) ).
thf(9878,plain,
$false,
inference(simp,[status(thm)],[9877]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM746^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n004.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 12:47:51 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 0.80/0.58 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.06/0.77 % [INFO] Parsing done (187ms).
% 1.06/0.78 % [INFO] Running in sequential loop mode.
% 1.76/1.17 % [INFO] eprover registered as external prover.
% 1.76/1.18 % [INFO] Scanning for conjecture ...
% 1.90/1.26 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 1.90/1.30 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.08/1.33 % [INFO] Problem is higher-order (TPTP THF).
% 2.08/1.33 % [INFO] Type checking passed.
% 2.08/1.34 % [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 ...
% 18.32/5.27 % [INFO] Killing All external provers ...
% 18.32/5.27 % Time passed: 4945ms (effective reasoning time: 4484ms)
% 18.32/5.27 % 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)>
% 18.32/5.28 % Axioms used in derivation (5): satz51b, satz39, satz51a, l, k
% 18.32/5.28 % No. of inferences in proof: 60
% 18.32/5.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4945 ms resp. 4484 ms w/o parsing
% 18.84/5.30 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.84/5.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------