%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : QUA002^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/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 10:37:03 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 17 ( 17 unt; 0 typ; 7 def)
% Number of atoms : 70 ( 50 equ; 0 cnn)
% Maximal formula atoms : 1 ( 4 avg)
% Number of connectives : 54 ( 2 ~; 13 |; 4 &; 35 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 38 ( 27 ^; 7 !; 4 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_addition,type,
addition: $i > $i > $i ).
thf(tp_crossmult,type,
crossmult: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_emptyset,type,
emptyset: $i > $o ).
thf(tp_leq,type,
leq: $i > $i > $o ).
thf(tp_multiplication,type,
multiplication: $i > $i > $i ).
thf(tp_one,type,
one: $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY32,type,
sK2_SY32: $i ).
thf(tp_sK3_E,type,
sK3_E: $i ).
thf(tp_singleton,type,
singleton: $i > $i > $o ).
thf(tp_sup,type,
sup: ( $i > $o ) > $i ).
thf(tp_supset,type,
supset: ( ( $i > $o ) > $o ) > $i > $o ).
thf(tp_union,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_unionset,type,
unionset: ( ( $i > $o ) > $o ) > $i > $o ).
thf(tp_zero,type,
zero: $i ).
thf(addition,definition,
( addition
= ( ^ [X: $i,Y: $i] : ( sup @ ( union @ ( singleton @ X ) @ ( singleton @ Y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_def) ).
thf(crossmult,definition,
( crossmult
= ( ^ [X: $i > $o,Y: $i > $o,A: $i] :
? [X1: $i,Y1: $i] :
( ( X @ X1 )
& ( Y @ Y1 )
& ( A
= ( multiplication @ X1 @ Y1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',crossmult_def) ).
thf(emptyset,definition,
( emptyset
= ( ^ [X: $i] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset_def) ).
thf(singleton,definition,
( singleton
= ( ^ [X: $i,U: $i] : ( U = X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_def) ).
thf(supset,definition,
( supset
= ( ^ [F: ( $i > $o ) > $o,X: $i] :
? [Y: $i > $o] :
( ( F @ Y )
& ( ( sup @ Y )
= X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',supset) ).
thf(union,definition,
( union
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_def) ).
thf(unionset,definition,
( unionset
= ( ^ [F: ( $i > $o ) > $o,X: $i] :
? [Y: $i > $o] :
( ( F @ Y )
& ( Y @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unionset) ).
thf(8,conjecture,
! [X1: $i,X2: $i] :
( ( addition @ X1 @ X2 )
= ( addition @ X2 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_comm) ).
thf(9,negated_conjecture,
( ( ! [X1: $i,X2: $i] :
( ( addition @ X1 @ X2 )
= ( addition @ X2 @ X1 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,plain,
( ( ! [SY0: $i,SY1: $i] :
( ( sup
@ ^ [SY8: $i] :
( ( SY8 = SY0 )
| ( SY8 = SY1 ) ) )
= ( sup
@ ^ [SY15: $i] :
( ( SY15 = SY1 )
| ( SY15 = SY0 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[9,addition,crossmult,emptyset,singleton,supset,union,unionset]) ).
thf(12,plain,
( ( ! [SY32: $i] :
( ( sup
@ ^ [SY33: $i] :
( ( SY33 = sK1_SY0 )
| ( SY33 = SY32 ) ) )
= ( sup
@ ^ [SY34: $i] :
( ( SY34 = SY32 )
| ( SY34 = sK1_SY0 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(13,plain,
( ( ( sup
@ ^ [SY35: $i] :
( ( SY35 = sK1_SY0 )
| ( SY35 = sK2_SY32 ) ) )
= ( sup
@ ^ [SY36: $i] :
( ( SY36 = sK2_SY32 )
| ( SY36 = sK1_SY0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(14,plain,
( ( ( sup
@ ^ [SY35: $i] :
( ( SY35 = sK1_SY0 )
| ( SY35 = sK2_SY32 ) ) )
!= ( sup
@ ^ [SY36: $i] :
( ( SY36 = sK2_SY32 )
| ( SY36 = sK1_SY0 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(16,plain,
( ( ( sup
@ ^ [SY35: $i] :
( ( SY35 = sK1_SY0 )
| ( SY35 = sK2_SY32 ) ) )
!= ( sup
@ ^ [SY36: $i] :
( ( SY36 = sK2_SY32 )
| ( SY36 = sK1_SY0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(18,plain,
( ( ( sup
@ ^ [SY35: $i] :
( ( SY35 = sK1_SY0 )
| ( SY35 = sK2_SY32 ) ) )
= ( sup
@ ^ [SY36: $i] :
( ( SY36 = sK2_SY32 )
| ( SY36 = sK1_SY0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(30,plain,
$false = $true,
inference(extuni,[status(esa)],[18]) ).
thf(31,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : QUA002^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n014.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 14:00:56 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.25
% 0.07/0.25 No.of.Axioms: 1
% 0.07/0.25
% 0.07/0.25 Length.of.Defs: 1142
% 0.07/0.25
% 0.07/0.25 Contains.Choice.Funs: true
% 0.07/0.25 .
% 0.07/0.25
% 0.07/0.25 ********************************
% 0.07/0.25 * All subproblems solved! *
% 0.07/0.25 ********************************
% 0.07/0.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,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:30,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.25
% 0.07/0.25 %**** Beginning of derivation protocol ****
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25
% 0.07/0.25 %**** End of derivation protocol ****
% 0.07/0.25 %**** no. of clauses in derivation: 10 ****
% 0.07/0.25 %**** clause counter: 30 ****
% 0.07/0.25
% 0.07/0.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,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:30,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------