TSTP Solution File: QUA002^1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : QUA002^1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 18:38:14 EDT 2022
% Result : Theorem 25.25s 25.44s
% Output : CNFRefutation 25.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 23
% Syntax : Number of formulae : 32 ( 17 unt; 15 typ; 7 def)
% Number of atoms : 54 ( 34 equ; 0 cnn)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 55 ( 3 ~; 5 |; 4 &; 43 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 39 ( 39 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 28 ( 19 ^ 5 !; 4 ?; 28 :)
% 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_X1,type,
sK1_X1: $i ).
thf(tp_sK2_SY0,type,
sK2_SY0: $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/sandbox/benchmark/theBenchmark.p',addition) ).
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/sandbox/benchmark/theBenchmark.p',crossmult) ).
thf(emptyset,definition,
( emptyset
= ( ^ [X: $i] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset) ).
thf(singleton,definition,
( singleton
= ( ^ [X: $i,U: $i] : ( U = X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(supset,definition,
( supset
= ( ^ [F: ( $i > $o ) > $o,X: $i] :
? [Y: $i > $o] :
( ( F @ Y )
& ( ( sup @ Y )
= X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',supset) ).
thf(union,definition,
( union
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
thf(unionset,definition,
( unionset
= ( ^ [F: ( $i > $o ) > $o,X: $i] :
? [Y: $i > $o] :
( ( F @ Y )
& ( Y @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unionset) ).
thf(8,conjecture,
! [X1: $i,X2: $i] :
( ( addition @ X1 @ X2 )
= ( addition @ X2 @ X1 ) ),
file('/export/starexec/sandbox/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] :
( ( addition @ sK1_X1 @ SY0 )
= ( addition @ SY0 @ sK1_X1 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(11,plain,
( ( ( addition @ sK1_X1 @ sK2_SY0 )
= ( addition @ sK2_SY0 @ sK1_X1 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(12,plain,
( ( ( ( addition @ sK1_X1 @ sK2_SY0 )
!= ( addition @ sK2_SY0 @ sK1_X1 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(21,plain,
( ( ( ( addition @ sK1_X1 @ sK2_SY0 )
!= ( addition @ sK2_SY0 @ sK1_X1 ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(24,plain,
( ( ( ( sup
@ ^ [SX0: $i] :
( ( SX0 = sK1_X1 )
| ( SX0 = sK2_SY0 ) ) )
!= ( sup
@ ^ [SX0: $i] :
( ( SX0 = sK2_SY0 )
| ( SX0 = sK1_X1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21,addition,crossmult,emptyset,singleton,supset,union,unionset]) ).
thf(31,plain,
( ( ( sup
@ ^ [SX0: $i] :
( ( SX0 = sK1_X1 )
| ( SX0 = sK2_SY0 ) ) )
= ( sup
@ ^ [SX0: $i] :
( ( SX0 = sK2_SY0 )
| ( SX0 = sK1_X1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(48,plain,
$false = $true,
inference(extuni,[status(esa)],[31]) ).
thf(49,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : QUA002^1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 11:02:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 7
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 1115
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: true
% 0.12/0.35 (rf:0,axioms:7,ps:3,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:9,loop_count:0,foatp_calls:0,translation:fof_full)....eprover: CPU time limit exceeded, terminating
% 25.25/25.44 .
% 25.25/25.44
% 25.25/25.44 ********************************
% 25.25/25.44 * All subproblems solved! *
% 25.25/25.44 ********************************
% 25.25/25.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,ps:3,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:48,loop_count:0,foatp_calls:1,translation:fof_full)
% 25.25/25.44
% 25.25/25.44 %**** Beginning of derivation protocol ****
% 25.25/25.44 % SZS output start CNFRefutation
% See solution above
% 25.25/25.44
% 25.25/25.44 %**** End of derivation protocol ****
% 25.25/25.44 %**** no. of clauses in derivation: 10 ****
% 25.25/25.44 %**** clause counter: 48 ****
% 25.25/25.44
% 25.25/25.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,ps:3,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:48,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------