%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : RNG009-5 : 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 10:37:28 AM UTC 2026
% Result : Unsatisfiable 114.03s 23.06s
% Output : CNFRefutation 114.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 54 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 140 ( 89 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 298 ( 6 ~; 0 |; 0 &; 292 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 94 ( 0 ^; 94 !; 0 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_add,type,
add: $i > $i > $i ).
thf(tp_additive_identity,type,
additive_identity: $i ).
thf(tp_additive_inverse,type,
additive_inverse: $i > $i ).
thf(tp_b,type,
b: $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_multiplication) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( add @ X @ Y )
= ( add @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutative_addition) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( add @ ( add @ X @ Y ) @ Z )
= ( add @ X @ ( add @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_addition) ).
thf(4,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( add @ X @ Y ) @ Z )
= ( add @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute2) ).
thf(5,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( add @ Y @ Z ) )
= ( add @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute1) ).
thf(6,axiom,
! [X: $i] :
( ( add @ X @ ( additive_inverse @ X ) )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_additive_inverse) ).
thf(7,axiom,
! [X: $i] :
( ( add @ X @ additive_identity )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
thf(8,axiom,
! [X: $i] :
( ( multiply @ X @ ( multiply @ X @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_cubed_is_x) ).
thf(9,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(10,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[9]) ).
thf(11,negated_conjecture,
( ( multiply @ a @ b )
!= ( multiply @ b @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).
thf(12,plain,
$false = $false,
inference(unfold_def,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i] :
( ( add @ X @ Y )
= ( add @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(15,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( add @ ( add @ X @ Y ) @ Z )
= ( add @ X @ ( add @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( add @ X @ Y ) @ Z )
= ( add @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( add @ Y @ Z ) )
= ( add @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(18,plain,
( ( ! [X: $i] :
( ( add @ X @ ( additive_inverse @ X ) )
= additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(19,plain,
( ( ! [X: $i] :
( ( add @ X @ additive_identity )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(20,plain,
( ( ! [X: $i] :
( ( multiply @ X @ ( multiply @ X @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(21,plain,
( ( ( multiply @ a @ b )
!= ( multiply @ b @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(22,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(23,plain,
( ( ( multiply @ a @ b )
!= ( multiply @ b @ a ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(24,plain,
( ( ! [X: $i] :
( ( multiply @ X @ ( multiply @ X @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(25,plain,
( ( ! [X: $i] :
( ( add @ X @ additive_identity )
= X ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(26,plain,
( ( ! [X: $i] :
( ( add @ X @ ( additive_inverse @ X ) )
= additive_identity ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( add @ Y @ Z ) )
= ( add @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( add @ X @ Y ) @ Z )
= ( add @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( add @ ( add @ X @ Y ) @ Z )
= ( add @ X @ ( add @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i] :
( ( add @ X @ Y )
= ( add @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(32,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[22]) ).
thf(33,plain,
( ( ( multiply @ a @ b )
!= ( multiply @ b @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(34,plain,
! [SV1: $i] :
( ( ( multiply @ SV1 @ ( multiply @ SV1 @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(35,plain,
! [SV2: $i] :
( ( ( add @ SV2 @ additive_identity )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(36,plain,
! [SV3: $i] :
( ( ( add @ SV3 @ ( additive_inverse @ SV3 ) )
= additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(37,plain,
! [SV4: $i] :
( ( ! [SY17: $i,SY18: $i] :
( ( multiply @ SV4 @ ( add @ SY17 @ SY18 ) )
= ( add @ ( multiply @ SV4 @ SY17 ) @ ( multiply @ SV4 @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(38,plain,
! [SV5: $i] :
( ( ! [SY19: $i,SY20: $i] :
( ( multiply @ ( add @ SV5 @ SY19 ) @ SY20 )
= ( add @ ( multiply @ SV5 @ SY20 ) @ ( multiply @ SY19 @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(39,plain,
! [SV6: $i] :
( ( ! [SY21: $i,SY22: $i] :
( ( add @ ( add @ SV6 @ SY21 ) @ SY22 )
= ( add @ SV6 @ ( add @ SY21 @ SY22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(40,plain,
! [SV7: $i] :
( ( ! [SY23: $i] :
( ( add @ SV7 @ SY23 )
= ( add @ SY23 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(41,plain,
! [SV8: $i] :
( ( ! [SY24: $i,SY25: $i] :
( ( multiply @ ( multiply @ SV8 @ SY24 ) @ SY25 )
= ( multiply @ SV8 @ ( multiply @ SY24 @ SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(42,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(43,plain,
( ( ( multiply @ a @ b )
= ( multiply @ b @ a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(44,plain,
! [SV9: $i,SV4: $i] :
( ( ! [SY26: $i] :
( ( multiply @ SV4 @ ( add @ SV9 @ SY26 ) )
= ( add @ ( multiply @ SV4 @ SV9 ) @ ( multiply @ SV4 @ SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV10: $i,SV5: $i] :
( ( ! [SY27: $i] :
( ( multiply @ ( add @ SV5 @ SV10 ) @ SY27 )
= ( add @ ( multiply @ SV5 @ SY27 ) @ ( multiply @ SV10 @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(46,plain,
! [SV11: $i,SV6: $i] :
( ( ! [SY28: $i] :
( ( add @ ( add @ SV6 @ SV11 ) @ SY28 )
= ( add @ SV6 @ ( add @ SV11 @ SY28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(47,plain,
! [SV12: $i,SV7: $i] :
( ( ( add @ SV7 @ SV12 )
= ( add @ SV12 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(48,plain,
! [SV13: $i,SV8: $i] :
( ( ! [SY29: $i] :
( ( multiply @ ( multiply @ SV8 @ SV13 ) @ SY29 )
= ( multiply @ SV8 @ ( multiply @ SV13 @ SY29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(49,plain,
! [SV14: $i,SV9: $i,SV4: $i] :
( ( ( multiply @ SV4 @ ( add @ SV9 @ SV14 ) )
= ( add @ ( multiply @ SV4 @ SV9 ) @ ( multiply @ SV4 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(50,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( multiply @ ( add @ SV5 @ SV10 ) @ SV15 )
= ( add @ ( multiply @ SV5 @ SV15 ) @ ( multiply @ SV10 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV16: $i,SV11: $i,SV6: $i] :
( ( ( add @ ( add @ SV6 @ SV11 ) @ SV16 )
= ( add @ SV6 @ ( add @ SV11 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV17: $i,SV13: $i,SV8: $i] :
( ( ( multiply @ ( multiply @ SV8 @ SV13 ) @ SV17 )
= ( multiply @ SV8 @ ( multiply @ SV13 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(53,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[34,52,51,50,49,47,43,42,36,35]) ).
thf(54,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG009-5 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.05/0.17 % Computer : n018.cluster.edu
% 0.05/0.17 % Model : x86_64 x86_64
% 0.05/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.17 % Memory : 8046.5625MB
% 0.05/0.17 % OS : Linux 6.8.0-71-generic
% 0.05/0.18 % CPULimit : 300
% 0.05/0.18 % WCLimit : 300
% 0.05/0.18 % DateTime : Tue Oct 6 14:12:07 UTC 2026
% 0.05/0.18 % CPUTime :
% 0.05/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 114.03/23.06
% 114.03/23.06 No.of.Axioms: 9
% 114.03/23.06
% 114.03/23.06 Length.of.Defs: 0
% 114.03/23.06
% 114.03/23.06 Contains.Choice.Funs: false
% 114.03/23.06 .
% 114.03/23.06
% 114.03/23.06 ********************************
% 114.03/23.06 * All subproblems solved! *
% 114.03/23.06 ********************************
% 114.03/23.06 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:53,loop_count:0,foatp_calls:1,translation:fof_full)
% 114.03/23.06
% 114.03/23.06 %**** Beginning of derivation protocol ****
% 114.03/23.06 % SZS output start CNFRefutation
% See solution above
% 114.03/23.06
% 114.03/23.06 %**** End of derivation protocol ****
% 114.03/23.06 %**** no. of clauses in derivation: 54 ****
% 114.03/23.06 %**** clause counter: 53 ****
% 114.03/23.06
% 114.03/23.06 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:53,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------