%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP209^1 : TPTP v9.3.1. Released v8.1.0.
% 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 : n026.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 10:24:51 AM UTC 2026
% Result : Theorem 0.11s 0.22s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 45 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 169 ( 2 ~; 0 |; 0 &; 167 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 : 46 ( 0 ^; 46 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_a2,type,
a2: a ).
thf(tp_b,type,
b: a ).
thf(tp_c,type,
c: a ).
thf(tp_f,type,
f: a > a > a ).
thf(tp_syntax_ac_operator_a,type,
syntax_ac_operator_a: ( a > a > a ) > $o ).
thf(7,axiom,
! [A: a,B: a,C: a] :
( ( f @ ( f @ A @ B ) @ C )
= ( f @ A @ ( f @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_right__assoc) ).
thf(8,axiom,
! [A: a,B: a,C: a] :
( ( f @ A @ ( f @ B @ C ) )
= ( f @ B @ ( f @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_left__commute) ).
thf(9,axiom,
! [A: a,B: a] :
( ( f @ A @ B )
= ( f @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_commute) ).
thf(10,axiom,
syntax_ac_operator_a @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_ac__operator__axioms) ).
thf(11,conjecture,
( ( f @ ( f @ a2 @ b ) @ c )
= ( f @ ( f @ a2 @ c ) @ b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(12,negated_conjecture,
( ( ( f @ ( f @ a2 @ b ) @ c )
= ( f @ ( f @ a2 @ c ) @ b ) )
= $false ),
inference(negate_conjecture,[status(cth)],[11]) ).
thf(13,plain,
( ( ( f @ ( f @ a2 @ b ) @ c )
= ( f @ ( f @ a2 @ c ) @ b ) )
= $false ),
inference(unfold_def,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [A: a,B: a,C: a] :
( ( f @ ( f @ A @ B ) @ C )
= ( f @ A @ ( f @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(15,plain,
( ( ! [A: a,B: a,C: a] :
( ( f @ A @ ( f @ B @ C ) )
= ( f @ B @ ( f @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( ! [A: a,B: a] :
( ( f @ A @ B )
= ( f @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(17,plain,
( ( syntax_ac_operator_a @ f )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(18,plain,
( ( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ ( f @ a2 @ c ) @ b ) )
= $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(19,plain,
( ( syntax_ac_operator_a @ f )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(20,plain,
( ( ! [A: a,B: a] :
( ( f @ A @ B )
= ( f @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(21,plain,
( ( ! [A: a,B: a,C: a] :
( ( f @ A @ ( f @ B @ C ) )
= ( f @ B @ ( f @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(22,plain,
( ( ! [A: a,B: a,C: a] :
( ( f @ ( f @ A @ B ) @ C )
= ( f @ A @ ( f @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(23,plain,
( ( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ ( f @ a2 @ c ) @ b ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(24,plain,
! [SV1: a] :
( ( ! [SY8: a] :
( ( f @ SV1 @ SY8 )
= ( f @ SY8 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV2: a] :
( ( ! [SY9: a,SY10: a] :
( ( f @ SV2 @ ( f @ SY9 @ SY10 ) )
= ( f @ SY9 @ ( f @ SV2 @ SY10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV3: a] :
( ( ! [SY11: a,SY12: a] :
( ( f @ ( f @ SV3 @ SY11 ) @ SY12 )
= ( f @ SV3 @ ( f @ SY11 @ SY12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
( ( ( f @ ( f @ a2 @ b ) @ c )
= ( f @ ( f @ a2 @ c ) @ b ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV4: a,SV1: a] :
( ( ( f @ SV1 @ SV4 )
= ( f @ SV4 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV5: a,SV2: a] :
( ( ! [SY13: a] :
( ( f @ SV2 @ ( f @ SV5 @ SY13 ) )
= ( f @ SV5 @ ( f @ SV2 @ SY13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV6: a,SV3: a] :
( ( ! [SY14: a] :
( ( f @ ( f @ SV3 @ SV6 ) @ SY14 )
= ( f @ SV3 @ ( f @ SV6 @ SY14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV7: a,SV5: a,SV2: a] :
( ( ( f @ SV2 @ ( f @ SV5 @ SV7 ) )
= ( f @ SV5 @ ( f @ SV2 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV8: a,SV6: a,SV3: a] :
( ( ( f @ ( f @ SV3 @ SV6 ) @ SV8 )
= ( f @ SV3 @ ( f @ SV6 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(33,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,32,31,28,27]) ).
thf(34,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP209^1 : TPTP v9.3.1. Released v8.1.0.
% 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
% 0.11/0.18 % Computer : n026.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Oct 6 11:23:02 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.22
% 0.11/0.22 No.of.Axioms: 4
% 0.11/0.22
% 0.11/0.22 Length.of.Defs: 0
% 0.11/0.22
% 0.11/0.22 Contains.Choice.Funs: false
% 0.11/0.22
% 0.11/0.22 ********************************
% 0.11/0.22 * All subproblems solved! *
% 0.11/0.22 ********************************
% 0.11/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:4,ps:0,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:33,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.22
% 0.11/0.22 %**** Beginning of derivation protocol ****
% 0.11/0.22 % SZS output start CNFRefutation
% See solution above
% 0.11/0.22
% 0.11/0.22 %**** End of derivation protocol ****
% 0.11/0.22 %**** no. of clauses in derivation: 28 ****
% 0.11/0.22 %**** clause counter: 33 ****
% 0.11/0.22
% 0.11/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:4,ps:0,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:33,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------