%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : CAT019-2 : TPTP v9.3.1. Released v1.0.0.
% 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 : n018.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 10:10:46 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.22s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 70 ( 52 unt; 0 typ; 0 def)
% Number of atoms : 268 ( 187 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 377 ( 49 ~; 52 |; 0 &; 276 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 95 ( 0 ^; 95 !; 0 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c1,type,
c1: $i ).
thf(tp_c2,type,
c2: $i ).
thf(tp_codomain,type,
codomain: $i > $i ).
thf(tp_compose,type,
compose: $i > $i > $i ).
thf(tp_domain,type,
domain: $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( codomain @ Y )
!= ( domain @ Z ) )
| ( ( compose @ X @ ( compose @ Y @ Z ) )
= ( compose @ ( compose @ X @ Y ) @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_property) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( codomain @ ( compose @ X @ Y ) )
= ( codomain @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_domain2) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( domain @ ( compose @ X @ Y ) )
= ( domain @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_domain1) ).
thf(4,axiom,
! [X: $i] :
( ( compose @ X @ ( codomain @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_composition) ).
thf(5,axiom,
! [X: $i] :
( ( compose @ ( domain @ X ) @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_composition) ).
thf(6,axiom,
! [X: $i] :
( ( domain @ ( codomain @ X ) )
= ( codomain @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of_codomain_is_codomain) ).
thf(7,axiom,
! [X: $i] :
( ( codomain @ ( domain @ X ) )
= ( domain @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_domain_is_domain) ).
thf(8,axiom,
! [Z: $i] :
( ( c2 = Z )
| ( c1 != Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality_to_c1_and_c2_2) ).
thf(9,axiom,
! [Z: $i] :
( ( c2 != Z )
| ( c1 = Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality_to_c1_and_c2_1) ).
thf(10,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(11,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[10]) ).
thf(12,negated_conjecture,
c2 != c1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c1_equals_c2) ).
thf(13,plain,
$false = $false,
inference(unfold_def,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( codomain @ Y )
!= ( domain @ Z ) )
| ( ( compose @ X @ ( compose @ Y @ Z ) )
= ( compose @ ( compose @ X @ Y ) @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(15,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( codomain @ ( compose @ X @ Y ) )
= ( codomain @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( domain @ ( compose @ X @ Y ) )
= ( domain @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [X: $i] :
( ( compose @ X @ ( codomain @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(18,plain,
( ( ! [X: $i] :
( ( compose @ ( domain @ X ) @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(19,plain,
( ( ! [X: $i] :
( ( domain @ ( codomain @ X ) )
= ( codomain @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(20,plain,
( ( ! [X: $i] :
( ( codomain @ ( domain @ X ) )
= ( domain @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(21,plain,
( ( ! [Z: $i] :
( ( c2 = Z )
| ( c1 != Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(22,plain,
( ( ! [Z: $i] :
( ( c2 != Z )
| ( c1 = Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(23,plain,
( ( c2 != c1 )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(24,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(25,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ! [Z: $i] :
( ( ( codomain @ Y )
!= ( domain @ Z ) )
| ( ( compose @ X @ ( compose @ Y @ Z ) )
= ( compose @ ( compose @ X @ Y ) @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(26,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( codomain @ ( compose @ X @ Y ) )
= ( codomain @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( domain @ ( compose @ X @ Y ) )
= ( domain @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(28,plain,
( ( ! [Z: $i] :
( ( c1 != Z )
| ( c2 = Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(29,plain,
( ( ! [Z: $i] :
( ( c2 != Z )
| ( c1 = Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(30,plain,
( ( c2 != c1 )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(31,plain,
( ( c2 != c1 )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(32,plain,
( ( ! [Z: $i] :
( ( c2 != Z )
| ( c1 = Z ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(33,plain,
( ( ! [Z: $i] :
( ( c1 != Z )
| ( c2 = Z ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(34,plain,
( ( ! [X: $i] :
( ( codomain @ ( domain @ X ) )
= ( domain @ X ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(35,plain,
( ( ! [X: $i] :
( ( domain @ ( codomain @ X ) )
= ( codomain @ X ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(36,plain,
( ( ! [X: $i] :
( ( compose @ ( domain @ X ) @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(37,plain,
( ( ! [X: $i] :
( ( compose @ X @ ( codomain @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( domain @ ( compose @ X @ Y ) )
= ( domain @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( codomain @ ( compose @ X @ Y ) )
= ( codomain @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ! [Z: $i] :
( ( ( codomain @ Y )
!= ( domain @ Z ) )
| ( ( compose @ X @ ( compose @ Y @ Z ) )
= ( compose @ ( compose @ X @ Y ) @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(41,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[24]) ).
thf(42,plain,
( ( c2 = c1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(43,plain,
! [SV1: $i] :
( ( ( c2 != SV1 )
| ( c1 = SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(44,plain,
! [SV2: $i] :
( ( ( c1 != SV2 )
| ( c2 = SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(45,plain,
! [SV3: $i] :
( ( ( codomain @ ( domain @ SV3 ) )
= ( domain @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(46,plain,
! [SV4: $i] :
( ( ( domain @ ( codomain @ SV4 ) )
= ( codomain @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(47,plain,
! [SV5: $i] :
( ( ( compose @ ( domain @ SV5 ) @ SV5 )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(48,plain,
! [SV6: $i] :
( ( ( compose @ SV6 @ ( codomain @ SV6 ) )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(49,plain,
! [SV7: $i] :
( ( ! [SY13: $i] :
( ( ( codomain @ SV7 )
!= ( domain @ SY13 ) )
| ( ( domain @ ( compose @ SV7 @ SY13 ) )
= ( domain @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(50,plain,
! [SV8: $i] :
( ( ! [SY14: $i] :
( ( ( codomain @ SV8 )
!= ( domain @ SY14 ) )
| ( ( codomain @ ( compose @ SV8 @ SY14 ) )
= ( codomain @ SY14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(51,plain,
! [SV9: $i] :
( ( ! [SY15: $i] :
( ( ( codomain @ SV9 )
!= ( domain @ SY15 ) )
| ! [SY16: $i] :
( ( ( codomain @ SY15 )
!= ( domain @ SY16 ) )
| ( ( compose @ SV9 @ ( compose @ SY15 @ SY16 ) )
= ( compose @ ( compose @ SV9 @ SY15 ) @ SY16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(52,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(53,plain,
! [SV1: $i] :
( ( ( c2 != SV1 )
= $true )
| ( ( c1 = SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(54,plain,
! [SV2: $i] :
( ( ( c1 != SV2 )
= $true )
| ( ( c2 = SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(55,plain,
! [SV10: $i,SV7: $i] :
( ( ( ( codomain @ SV7 )
!= ( domain @ SV10 ) )
| ( ( domain @ ( compose @ SV7 @ SV10 ) )
= ( domain @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV11: $i,SV8: $i] :
( ( ( ( codomain @ SV8 )
!= ( domain @ SV11 ) )
| ( ( codomain @ ( compose @ SV8 @ SV11 ) )
= ( codomain @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(57,plain,
! [SV12: $i,SV9: $i] :
( ( ( ( codomain @ SV9 )
!= ( domain @ SV12 ) )
| ! [SY17: $i] :
( ( ( codomain @ SV12 )
!= ( domain @ SY17 ) )
| ( ( compose @ SV9 @ ( compose @ SV12 @ SY17 ) )
= ( compose @ ( compose @ SV9 @ SV12 ) @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(58,plain,
! [SV1: $i] :
( ( ( c2 = SV1 )
= $false )
| ( ( c1 = SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV2: $i] :
( ( ( c1 = SV2 )
= $false )
| ( ( c2 = SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV10: $i,SV7: $i] :
( ( ( ( codomain @ SV7 )
!= ( domain @ SV10 ) )
= $true )
| ( ( ( domain @ ( compose @ SV7 @ SV10 ) )
= ( domain @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV11: $i,SV8: $i] :
( ( ( ( codomain @ SV8 )
!= ( domain @ SV11 ) )
= $true )
| ( ( ( codomain @ ( compose @ SV8 @ SV11 ) )
= ( codomain @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(62,plain,
! [SV12: $i,SV9: $i] :
( ( ( ( codomain @ SV9 )
!= ( domain @ SV12 ) )
= $true )
| ( ( ! [SY17: $i] :
( ( ( codomain @ SV12 )
!= ( domain @ SY17 ) )
| ( ( compose @ SV9 @ ( compose @ SV12 @ SY17 ) )
= ( compose @ ( compose @ SV9 @ SV12 ) @ SY17 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(63,plain,
! [SV10: $i,SV7: $i] :
( ( ( ( codomain @ SV7 )
= ( domain @ SV10 ) )
= $false )
| ( ( ( domain @ ( compose @ SV7 @ SV10 ) )
= ( domain @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(64,plain,
! [SV11: $i,SV8: $i] :
( ( ( ( codomain @ SV8 )
= ( domain @ SV11 ) )
= $false )
| ( ( ( codomain @ ( compose @ SV8 @ SV11 ) )
= ( codomain @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(65,plain,
! [SV12: $i,SV9: $i] :
( ( ( ( codomain @ SV9 )
= ( domain @ SV12 ) )
= $false )
| ( ( ! [SY17: $i] :
( ( ( codomain @ SV12 )
!= ( domain @ SY17 ) )
| ( ( compose @ SV9 @ ( compose @ SV12 @ SY17 ) )
= ( compose @ ( compose @ SV9 @ SV12 ) @ SY17 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(66,plain,
! [SV9: $i,SV13: $i,SV12: $i] :
( ( ( ( ( codomain @ SV12 )
!= ( domain @ SV13 ) )
| ( ( compose @ SV9 @ ( compose @ SV12 @ SV13 ) )
= ( compose @ ( compose @ SV9 @ SV12 ) @ SV13 ) ) )
= $true )
| ( ( ( codomain @ SV9 )
= ( domain @ SV12 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(67,plain,
! [SV9: $i,SV13: $i,SV12: $i] :
( ( ( ( codomain @ SV12 )
!= ( domain @ SV13 ) )
= $true )
| ( ( ( compose @ SV9 @ ( compose @ SV12 @ SV13 ) )
= ( compose @ ( compose @ SV9 @ SV12 ) @ SV13 ) )
= $true )
| ( ( ( codomain @ SV9 )
= ( domain @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(68,plain,
! [SV9: $i,SV13: $i,SV12: $i] :
( ( ( ( codomain @ SV12 )
= ( domain @ SV13 ) )
= $false )
| ( ( ( compose @ SV9 @ ( compose @ SV12 @ SV13 ) )
= ( compose @ ( compose @ SV9 @ SV12 ) @ SV13 ) )
= $true )
| ( ( ( codomain @ SV9 )
= ( domain @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(69,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[42,68,64,63,59,58,52,48,47,46,45]) ).
thf(70,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT019-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n018.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 18:31:37 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.22
% 0.08/0.22 No.of.Axioms: 10
% 0.08/0.22
% 0.08/0.22 Length.of.Defs: 0
% 0.08/0.22
% 0.08/0.22 Contains.Choice.Funs: false
% 0.08/0.22 .
% 0.08/0.22
% 0.08/0.22 ********************************
% 0.08/0.22 * All subproblems solved! *
% 0.08/0.22 ********************************
% 0.08/0.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:69,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.22
% 0.08/0.22 %**** Beginning of derivation protocol ****
% 0.08/0.22 % SZS output start CNFRefutation
% See solution above
% 0.08/0.22
% 0.08/0.22 %**** End of derivation protocol ****
% 0.08/0.22 %**** no. of clauses in derivation: 70 ****
% 0.08/0.22 %**** clause counter: 69 ****
% 0.08/0.22
% 0.08/0.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:69,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------