%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ALG235-1 : TPTP v9.3.1. Released v4.0.0.
% 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 : n017.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 10:08:35 AM UTC 2026
% Result : Unsatisfiable 0.24s 0.37s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 84 ( 50 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 322 ( 6 ~; 0 |; 0 &; 316 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 66 ( 0 ^; 66 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_d,type,
d: $i ).
thf(tp_mult,type,
mult: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( mult @ ( mult @ A @ ( mult @ B @ ( mult @ C @ B ) ) ) @ D )
= ( mult @ A @ ( mult @ D @ ( mult @ ( mult @ C @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
thf(2,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ C @ D ) ) )
= ( mult @ C @ ( mult @ B @ ( mult @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ A @ B ) ) )
= ( mult @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
thf(4,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(5,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,negated_conjecture,
( ( mult @ a @ ( mult @ b @ ( mult @ a @ ( mult @ c @ ( mult @ d @ c ) ) ) ) )
!= ( mult @ a @ ( mult @ b @ ( mult @ d @ c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(7,plain,
$false = $false,
inference(unfold_def,[status(thm)],[5]) ).
thf(8,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( mult @ ( mult @ A @ ( mult @ B @ ( mult @ C @ B ) ) ) @ D )
= ( mult @ A @ ( mult @ D @ ( mult @ ( mult @ C @ B ) @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ C @ D ) ) )
= ( mult @ C @ ( mult @ B @ ( mult @ A @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(10,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ A @ B ) ) )
= ( mult @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(11,plain,
( ( ( mult @ a @ ( mult @ b @ ( mult @ a @ ( mult @ c @ ( mult @ d @ c ) ) ) ) )
!= ( mult @ a @ ( mult @ b @ ( mult @ d @ c ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(12,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(13,plain,
( ( ( mult @ a @ ( mult @ b @ ( mult @ a @ ( mult @ c @ ( mult @ d @ c ) ) ) ) )
!= ( mult @ a @ ( mult @ b @ ( mult @ d @ c ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(14,plain,
( ( ( mult @ a @ ( mult @ b @ ( mult @ a @ ( mult @ c @ ( mult @ d @ c ) ) ) ) )
!= ( mult @ a @ ( mult @ b @ ( mult @ d @ c ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ A @ B ) ) )
= ( mult @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ C @ D ) ) )
= ( mult @ C @ ( mult @ B @ ( mult @ A @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( mult @ ( mult @ A @ ( mult @ B @ ( mult @ C @ B ) ) ) @ D )
= ( mult @ A @ ( mult @ D @ ( mult @ ( mult @ C @ B ) @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(18,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[12]) ).
thf(19,plain,
( ( ( mult @ a @ ( mult @ b @ ( mult @ a @ ( mult @ c @ ( mult @ d @ c ) ) ) ) )
= ( mult @ a @ ( mult @ b @ ( mult @ d @ c ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(20,plain,
! [SV1: $i] :
( ( ! [SY10: $i] :
( ( mult @ SV1 @ ( mult @ SY10 @ ( mult @ SV1 @ SY10 ) ) )
= ( mult @ SV1 @ SY10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(21,plain,
! [SV2: $i] :
( ( ! [SY11: $i,SY12: $i,SY13: $i] :
( ( mult @ SV2 @ ( mult @ SY11 @ ( mult @ SY12 @ SY13 ) ) )
= ( mult @ SY12 @ ( mult @ SY11 @ ( mult @ SV2 @ SY13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(22,plain,
! [SV3: $i] :
( ( ! [SY14: $i,SY15: $i,SY16: $i] :
( ( mult @ ( mult @ SV3 @ ( mult @ SY14 @ ( mult @ SY15 @ SY14 ) ) ) @ SY16 )
= ( mult @ SV3 @ ( mult @ SY16 @ ( mult @ ( mult @ SY15 @ SY14 ) @ SY16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(23,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(24,plain,
! [SV4: $i,SV1: $i] :
( ( ( mult @ SV1 @ ( mult @ SV4 @ ( mult @ SV1 @ SV4 ) ) )
= ( mult @ SV1 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV5: $i,SV2: $i] :
( ( ! [SY17: $i,SY18: $i] :
( ( mult @ SV2 @ ( mult @ SV5 @ ( mult @ SY17 @ SY18 ) ) )
= ( mult @ SY17 @ ( mult @ SV5 @ ( mult @ SV2 @ SY18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV6: $i,SV3: $i] :
( ( ! [SY19: $i,SY20: $i] :
( ( mult @ ( mult @ SV3 @ ( mult @ SV6 @ ( mult @ SY19 @ SV6 ) ) ) @ SY20 )
= ( mult @ SV3 @ ( mult @ SY20 @ ( mult @ ( mult @ SY19 @ SV6 ) @ SY20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ! [SY21: $i] :
( ( mult @ SV2 @ ( mult @ SV5 @ ( mult @ SV7 @ SY21 ) ) )
= ( mult @ SV7 @ ( mult @ SV5 @ ( mult @ SV2 @ SY21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ! [SY22: $i] :
( ( mult @ ( mult @ SV3 @ ( mult @ SV6 @ ( mult @ SV8 @ SV6 ) ) ) @ SY22 )
= ( mult @ SV3 @ ( mult @ SY22 @ ( mult @ ( mult @ SV8 @ SV6 ) @ SY22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV9: $i,SV7: $i,SV5: $i,SV2: $i] :
( ( ( mult @ SV2 @ ( mult @ SV5 @ ( mult @ SV7 @ SV9 ) ) )
= ( mult @ SV7 @ ( mult @ SV5 @ ( mult @ SV2 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(30,plain,
! [SV10: $i,SV8: $i,SV6: $i,SV3: $i] :
( ( ( mult @ ( mult @ SV3 @ ( mult @ SV6 @ ( mult @ SV8 @ SV6 ) ) ) @ SV10 )
= ( mult @ SV3 @ ( mult @ SV10 @ ( mult @ ( mult @ SV8 @ SV6 ) @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(31,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,30,29,24,23]) ).
thf(32,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG235-1 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.08/0.20 % Computer : n017.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Oct 6 18:04:30 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.24/0.37
% 0.24/0.37 No.of.Axioms: 4
% 0.24/0.37
% 0.24/0.37 Length.of.Defs: 0
% 0.24/0.37
% 0.24/0.37 Contains.Choice.Funs: false
% 0.24/0.37 .
% 0.24/0.37
% 0.24/0.37 ********************************
% 0.24/0.37 * All subproblems solved! *
% 0.24/0.37 ********************************
% 0.24/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:31,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.24/0.37
% 0.24/0.37 %**** Beginning of derivation protocol ****
% 0.24/0.37 % SZS output start CNFRefutation
% See solution above
% 0.24/0.37
% 0.24/0.37 %**** End of derivation protocol ****
% 0.24/0.37 %**** no. of clauses in derivation: 32 ****
% 0.24/0.37 %**** clause counter: 31 ****
% 0.24/0.37
% 0.24/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:31,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------