%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET724^4 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 Oct 7 10:40:56 AM UTC 2026
% Result : Theorem 0.07s 0.22s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 31 unt; 0 typ; 8 def)
% Number of atoms : 102 ( 67 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 104 ( 2 ~; 0 |; 9 &; 84 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 68 ( 30 ^; 30 !; 8 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_fun_bijective,type,
fun_bijective: ( $i > $i ) > $o ).
thf(tp_fun_composition,type,
fun_composition: ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(tp_fun_decreasing,type,
fun_decreasing: ( $i > $i ) > ( $i > $i > $o ) > $o ).
thf(tp_fun_image,type,
fun_image: ( $i > $i ) > ( $i > $o ) > $i > $o ).
thf(tp_fun_increasing,type,
fun_increasing: ( $i > $i ) > ( $i > $i > $o ) > $o ).
thf(tp_fun_injective,type,
fun_injective: ( $i > $i ) > $o ).
thf(tp_fun_inv_image,type,
fun_inv_image: ( $i > $i ) > ( $i > $o ) > $i > $o ).
thf(tp_fun_surjective,type,
fun_surjective: ( $i > $i ) > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i > $i ).
thf(tp_sK2_SY18,type,
sK2_SY18: $i > $i ).
thf(tp_sK3_SY24,type,
sK3_SY24: $i > $i ).
thf(tp_sK4_SY23,type,
sK4_SY23: $i > $i ).
thf(tp_sK5_SV4,type,
sK5_SV4: $i ).
thf(fun_bijective,definition,
( fun_bijective
= ( ^ [F: $i > $i] :
( ( fun_injective @ F )
& ( fun_surjective @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fun_bijective) ).
thf(fun_composition,definition,
( fun_composition
= ( ^ [F: $i > $i,G: $i > $i,X: $i] : ( G @ ( F @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fun_composition) ).
thf(fun_decreasing,definition,
( fun_decreasing
= ( ^ [F: $i > $i,SMALLER: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( SMALLER @ X @ Y )
=> ( SMALLER @ ( F @ Y ) @ ( F @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fun_decreasing) ).
thf(fun_image,definition,
( fun_image
= ( ^ [F: $i > $i,A: $i > $o,Y: $i] :
? [X: $i] :
( ( A @ X )
& ( Y
= ( F @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fun_image) ).
thf(fun_increasing,definition,
( fun_increasing
= ( ^ [F: $i > $i,SMALLER: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( SMALLER @ X @ Y )
=> ( SMALLER @ ( F @ X ) @ ( F @ Y ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fun_increasing) ).
thf(fun_injective,definition,
( fun_injective
= ( ^ [F: $i > $i] :
! [X: $i,Y: $i] :
( ( ( F @ X )
= ( F @ Y ) )
=> ( X = Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fun_injective) ).
thf(fun_inv_image,definition,
( fun_inv_image
= ( ^ [F: $i > $i,B: $i > $o,X: $i] :
? [Y: $i] :
( ( B @ Y )
& ( Y
= ( F @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fun_inv_image) ).
thf(fun_surjective,definition,
( fun_surjective
= ( ^ [F: $i > $i] :
! [Y: $i] :
? [X: $i] :
( Y
= ( F @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fun_surjective) ).
thf(1,conjecture,
! [F: $i > $i,G: $i > $i,H: $i > $i] :
( ( ( ( fun_composition @ F @ G )
= ( fun_composition @ F @ H ) )
& ( fun_surjective @ F ) )
=> ( G = H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
( ( ! [F: $i > $i,G: $i > $i,H: $i > $i] :
( ( ( ( fun_composition @ F @ G )
= ( fun_composition @ F @ H ) )
& ( fun_surjective @ F ) )
=> ( G = H ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i > $i,SY1: $i > $i,SY2: $i > $i] :
( ( ( ( ^ [SY5: $i] : ( SY1 @ ( SY0 @ SY5 ) ) )
= ( ^ [SY8: $i] : ( SY2 @ ( SY0 @ SY8 ) ) ) )
& ! [SY9: $i] :
? [SY10: $i] :
( SY9
= ( SY0 @ SY10 ) ) )
=> ( SY1 = SY2 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,fun_bijective,fun_composition,fun_decreasing,fun_image,fun_increasing,fun_injective,fun_inv_image,fun_surjective]) ).
thf(4,plain,
( ( ! [SY18: $i > $i,SY19: $i > $i] :
( ( ( ( ^ [SY20: $i] : ( SY18 @ ( sK1_SY0 @ SY20 ) ) )
= ( ^ [SY21: $i] : ( SY19 @ ( sK1_SY0 @ SY21 ) ) ) )
& ! [SY22: $i] :
? [SY23: $i] :
( SY22
= ( sK1_SY0 @ SY23 ) ) )
=> ( SY18 = SY19 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY24: $i > $i] :
( ( ( ( ^ [SY25: $i] : ( sK2_SY18 @ ( sK1_SY0 @ SY25 ) ) )
= ( ^ [SY21: $i] : ( SY24 @ ( sK1_SY0 @ SY21 ) ) ) )
& ! [SY22: $i] :
? [SY23: $i] :
( SY22
= ( sK1_SY0 @ SY23 ) ) )
=> ( sK2_SY18 = SY24 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ( ( ( ^ [SY25: $i] : ( sK2_SY18 @ ( sK1_SY0 @ SY25 ) ) )
= ( ^ [SY30: $i] : ( sK3_SY24 @ ( sK1_SY0 @ SY30 ) ) ) )
& ! [SY22: $i] :
? [SY23: $i] :
( SY22
= ( sK1_SY0 @ SY23 ) ) )
=> ( sK2_SY18 = sK3_SY24 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ( ^ [SY25: $i] : ( sK2_SY18 @ ( sK1_SY0 @ SY25 ) ) )
= ( ^ [SY30: $i] : ( sK3_SY24 @ ( sK1_SY0 @ SY30 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SY22: $i] :
? [SY23: $i] :
( SY22
= ( sK1_SY0 @ SY23 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(9,plain,
( ( sK2_SY18 = sK3_SY24 )
= $false ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(10,plain,
( ( sK2_SY18 != sK3_SY24 )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [SY22: $i] :
( SY22
= ( sK1_SY0 @ ( sK4_SY23 @ SY22 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(12,plain,
( ( ! [SY22: $i] :
( SY22
= ( sK1_SY0 @ ( sK4_SY23 @ SY22 ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(13,plain,
( ( ( ^ [SY25: $i] : ( sK2_SY18 @ ( sK1_SY0 @ SY25 ) ) )
= ( ^ [SY30: $i] : ( sK3_SY24 @ ( sK1_SY0 @ SY30 ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(14,plain,
( ( sK2_SY18 != sK3_SY24 )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
! [SV1: $i] :
( ( SV1
= ( sK1_SY0 @ ( sK4_SY23 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
( ( ! [SV2: $i] :
( ( sK2_SY18 @ ( sK1_SY0 @ SV2 ) )
= ( sK3_SY24 @ ( sK1_SY0 @ SV2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[13]) ).
thf(17,plain,
( ( ( ^ [SY25: $i] : ( sK2_SY18 @ ( sK1_SY0 @ SY25 ) ) )
= ( ^ [SY30: $i] : ( sK3_SY24 @ ( sK1_SY0 @ SY30 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[13]) ).
thf(18,plain,
( ( sK2_SY18 = sK3_SY24 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(19,plain,
! [SV3: $i] :
( ( ( sK2_SY18 @ ( sK1_SY0 @ SV3 ) )
= ( sK3_SY24 @ ( sK1_SY0 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ! [SV4: $i] :
( ( sK2_SY18 @ SV4 )
= ( sK3_SY24 @ SV4 ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[18]) ).
thf(21,plain,
( ( sK2_SY18 = sK3_SY24 )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[18]) ).
thf(22,plain,
( ( ( sK2_SY18 @ sK5_SV4 )
= ( sK3_SY24 @ sK5_SV4 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(23,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[15,22,21,19,17]) ).
thf(24,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET724^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n014.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 14:50:11 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.22
% 0.07/0.22 No.of.Axioms: 0
% 0.07/0.22
% 0.07/0.22 Length.of.Defs: 1512
% 0.07/0.22
% 0.07/0.22 Contains.Choice.Funs: false
% 0.07/0.22
% 0.07/0.22 ********************************
% 0.07/0.22 * All subproblems solved! *
% 0.07/0.22 ********************************
% 0.07/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:2,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:23,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.22
% 0.07/0.22 %**** Beginning of derivation protocol ****
% 0.07/0.22 % SZS output start CNFRefutation
% See solution above
% 0.07/0.22
% 0.07/0.22 %**** End of derivation protocol ****
% 0.07/0.22 %**** no. of clauses in derivation: 24 ****
% 0.07/0.22 %**** clause counter: 23 ****
% 0.07/0.22
% 0.07/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:2,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:23,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------