%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWX105_1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n009.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 : Fri Sep 25 03:32:41 PM UTC 2026
% Result : Theorem 0.42s 11.18s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 27
% Syntax : Number of formulae : 83 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 162 ( 42 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 108 ( 48 ~; 48 |; 4 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 19 ( 19 fml; 0 var)
% Number arithmetic : 205 ( 40 atm; 52 fun; 21 num; 92 var)
% Number of types : 2 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 12 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 141 ( 0 sgn 135 !; 6 ?; 141 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
f__integer__: $int > general ).
tff(pred_def_1,type,
p__is_integer__: general > $o ).
tff(pred_def_2,type,
p__is_symbolic__: general > $o ).
tff(pred_def_3,type,
p__less_equal__: ( general * general ) > $o ).
tff(pred_def_4,type,
p__less__: ( general * general ) > $o ).
tff(pred_def_5,type,
p__greater_equal__: ( general * general ) > $o ).
tff(pred_def_6,type,
p__greater__: ( general * general ) > $o ).
tff(pred_def_8,type,
p: general > $o ).
tff(func_def_11,type,
sK0: general > $int ).
tff(func_def_12,type,
sK1: general > symbol ).
tff(func_def_13,type,
sK2: $int ).
tff(f1,axiom,
! [X0: general] :
( p__is_integer__(X0)
<=> ? [X1: $int] : ( X0 = f__integer__(X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV014_0.ax',p__is_integer__def_ax) ).
tff(f2,axiom,
! [X0: general] :
( p__is_symbolic__(X0)
<=> ? [X1: symbol] : ( X0 = f__symbolic__(X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV014_0.ax',p__is_symbolic__def_ax) ).
tff(f6,axiom,
! [X0: $int,X1: $int] :
( p__less_equal__(f__integer__(X0),f__integer__(X1))
<=> $lesseq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV014_0.ax',numeral_ordering_ax) ).
tff(f9,axiom,
! [X0: general,X1: general] :
( p__less_equal__(X1,X0)
| p__less_equal__(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV014_0.ax',strongly_connected_ordering_ax) ).
tff(f10,axiom,
! [X0: general,X1: general] :
( p__less__(X0,X1)
<=> ( ( X0 != X1 )
& p__less_equal__(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV014_0.ax',p__less__def_ax) ).
tff(f13,axiom,
! [X0: $int] : p__less__(c__infimum__,f__integer__(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV014_0.ax',minimal_element_ax) ).
tff(f14,axiom,
! [X0: $int,X1: symbol] : p__less__(f__integer__(X0),f__symbolic__(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV014_0.ax',numerals_less_than_symbols_ax) ).
tff(f15,axiom,
! [X0: symbol] : p__less__(f__symbolic__(X0),c__supremum__),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV014_0.ax',maximal_element_ax) ).
tff(f19,plain,
! [X0: $int,X1: $int] :
( p__less_equal__(f__integer__(X0),f__integer__(X1))
<=> ~ $less(X1,X0) ),
inference(theory_normalization,[],[f6]) ).
tff(f21,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f22,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(definition,[],[tha_associativity]) ).
tff(f23,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(definition,[],[tha_right_identity]) ).
tff(f24,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(definition,[],[tha_inverse_op_op_inverses]) ).
tff(f25,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(definition,[],[tha_inverse_op_unit]) ).
tff(f26,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
tff(f27,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X2)
| ~ $less(X1,X2)
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_transitivity]) ).
tff(f28,plain,
! [X0: $int,X1: $int] :
( ( X0 = X1 )
| $less(X1,X0)
| $less(X0,X1) ),
introduced(definition,[],[tha_order_totality]) ).
tff(f29,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_order_monotonicity]) ).
tff(f30,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(definition,[],[tha_order_plus_one_dichotomy]) ).
tff(f31,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(definition,[],[tha_minus_minus_x]) ).
tff(f32,plain,
! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f33,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ),
introduced(definition,[],[tha_associativity]) ).
tff(f34,plain,
! [X0: $int] : ( $product(X0,1) = X0 ),
introduced(definition,[],[tha_right_identity]) ).
tff(f35,plain,
! [X0: $int] : ( 0 = $product(X0,0) ),
introduced(definition,[],[tha_times_zero]) ).
tff(f36,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ),
introduced(definition,[],[tha_distributivity]) ).
tff(f37,plain,
! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ( X2 = X3 )
| ( $product(X0,X3) != X1 )
| ( $product(X0,X2) != X1 )
| ( 0 = X0 ) ),
introduced(definition,[],[tha_divisibility]) ).
tff(f38,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_extra_integer_ordering]) ).
tff(f40,plain,
! [X0: general,X1: general] :
( p__less__(X0,X1)
=> ( ( X0 != X1 )
& p__less_equal__(X0,X1) ) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
tff(f41,plain,
! [X0: general] :
( p__is_symbolic__(X0)
=> ? [X1: symbol] : ( X0 = f__symbolic__(X1) ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
tff(f42,plain,
! [X0: general] :
( p__is_integer__(X0)
=> ? [X1: $int] : ( X0 = f__integer__(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
tff(f43,plain,
! [X0: general] :
( ~ p__is_integer__(X0)
| ? [X1: $int] : ( X0 = f__integer__(X1) ) ),
inference(ennf_transformation,[],[f42]) ).
tff(f44,plain,
! [X0: general] :
( ~ p__is_symbolic__(X0)
| ? [X1: symbol] : ( X0 = f__symbolic__(X1) ) ),
inference(ennf_transformation,[],[f41]) ).
tff(f49,plain,
! [X0: general,X1: general] :
( ~ p__less__(X0,X1)
| ( ( X0 != X1 )
& p__less_equal__(X0,X1) ) ),
inference(ennf_transformation,[],[f40]) ).
tff(f51,plain,
! [X0: general] :
( ~ p__is_integer__(X0)
| ( f__integer__(sK0(X0)) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f43]) ).
tff(f52,plain,
! [X0: general] :
( ~ p__is_symbolic__(X0)
| ( f__symbolic__(sK1(X0)) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f44]) ).
tff(f55,plain,
! [X0: $int,X1: $int] :
( ( ~ p__less_equal__(f__integer__(X0),f__integer__(X1))
| ~ $less(X1,X0) )
& ( $less(X1,X0)
| p__less_equal__(f__integer__(X0),f__integer__(X1)) ) ),
inference(nnf_transformation,[],[f19]) ).
tff(f57,plain,
! [X0: general] :
( ~ p__is_integer__(X0)
| ( f__integer__(sK0(X0)) = X0 ) ),
inference(cnf_transformation,[],[f51]) ).
tff(f58,plain,
! [X0: general] :
( ~ p__is_symbolic__(X0)
| ( f__symbolic__(sK1(X0)) = X0 ) ),
inference(cnf_transformation,[],[f52]) ).
tff(f64,plain,
! [X0: $int,X1: $int] :
( ~ p__less_equal__(f__integer__(X0),f__integer__(X1))
| ~ $less(X1,X0) ),
inference(cnf_transformation,[],[f55]) ).
tff(f65,plain,
! [X0: $int,X1: $int] :
( $less(X1,X0)
| p__less_equal__(f__integer__(X0),f__integer__(X1)) ),
inference(cnf_transformation,[],[f55]) ).
tff(f68,plain,
! [X0: general,X1: general] :
( p__less_equal__(X1,X0)
| p__less_equal__(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
tff(f69,plain,
! [X0: general,X1: general] :
( ~ p__less__(X0,X1)
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f49]) ).
tff(f70,plain,
! [X0: general,X1: general] :
( ~ p__less__(X0,X1)
| p__less_equal__(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
tff(f71,plain,
! [X0: $int] : p__less__(c__infimum__,f__integer__(X0)),
inference(cnf_transformation,[],[f13]) ).
tff(f72,plain,
! [X0: $int,X1: symbol] : p__less__(f__integer__(X0),f__symbolic__(X1)),
inference(cnf_transformation,[],[f14]) ).
tff(f73,plain,
! [X0: symbol] : p__less__(f__symbolic__(X0),c__supremum__),
inference(cnf_transformation,[],[f15]) ).
tff(f78,plain,
! [X1: general] : ~ p__less__(X1,X1),
inference(equality_resolution,[],[f69]) ).
tcf(c_49,negated_conjecture,
! [X0_int: $int,X1_int: $int] :
( ~ $less(X1_int,X0_int)
| ~ $less(X0_int,$sum(X1_int,1)) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_52,negated_conjecture,
! [X0_int: $int] : $product(X0_int,0) = 0,
inference(cnf_transformation,[],[f35]) ).
tcf(c_53,negated_conjecture,
! [X0_int: $int] : $product(X0_int,1) = X0_int,
inference(cnf_transformation,[],[f34]) ).
tcf(c_55,negated_conjecture,
! [X0_int: $int,X1_int: $int] : $product(X0_int,X1_int) = $product(X1_int,X0_int),
inference(cnf_transformation,[],[f32]) ).
tcf(c_56,negated_conjecture,
! [X0_int: $int] : $uminus($uminus(X0_int)) = X0_int,
inference(cnf_transformation,[],[f31]) ).
tcf(c_57,negated_conjecture,
! [X0_int: $int,X1_int: $int] :
( $less(X1_int,X0_int)
| $less(X0_int,$sum(X1_int,1)) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_59,negated_conjecture,
! [X0_int: $int,X1_int: $int] :
( $less(X1_int,X0_int)
| $less(X0_int,X1_int)
| ( X0_int = X1_int ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_61,negated_conjecture,
! [X0_int: $int] : ~ $less(X0_int,X0_int),
inference(cnf_transformation,[],[f26]) ).
tcf(c_62,negated_conjecture,
! [X0_int: $int] : $sum(X0_int,$uminus(X0_int)) = 0,
inference(cnf_transformation,[],[f25]) ).
tcf(c_64,negated_conjecture,
! [X0_int: $int] : $sum(X0_int,0) = X0_int,
inference(cnf_transformation,[],[f23]) ).
tcf(c_66,negated_conjecture,
! [X0_int: $int,X1_int: $int] : $sum(X0_int,X1_int) = $sum(X1_int,X0_int),
inference(cnf_transformation,[],[f21]) ).
tcf(c_67,plain,
! [X0_general: general] :
( ( f__integer__(sK0(X0_general)) = X0_general )
| ~ p__is_integer__(X0_general) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_68,plain,
! [X0_general: general] :
( ( f__symbolic__(sK1(X0_general)) = X0_general )
| ~ p__is_symbolic__(X0_general) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_72,negated_conjecture,
! [X0_int: $int,X1_int: $int] :
( $less(X1_int,X0_int)
| p__less_equal__(f__integer__(X0_int),f__integer__(X1_int)) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_73,negated_conjecture,
! [X0_int: $int,X1_int: $int] :
( ~ $less(X1_int,X0_int)
| ~ p__less_equal__(f__integer__(X0_int),f__integer__(X1_int)) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_76,negated_conjecture,
! [X0_general: general,X1_general: general] :
( p__less_equal__(X1_general,X0_general)
| p__less_equal__(X0_general,X1_general) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_77,plain,
! [X0_general: general,X1_general: general] :
( p__less_equal__(X0_general,X1_general)
| ~ p__less__(X0_general,X1_general) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_78,negated_conjecture,
! [X0_general: general] : ~ p__less__(X0_general,X0_general),
inference(cnf_transformation,[],[f78]) ).
tcf(c_79,negated_conjecture,
! [X0_int: $int] : p__less__(c__infimum__,f__integer__(X0_int)),
inference(cnf_transformation,[],[f71]) ).
tcf(c_80,negated_conjecture,
! [X0_int: $int,X0_symbol: symbol] : p__less__(f__integer__(X0_int),f__symbolic__(X0_symbol)),
inference(cnf_transformation,[],[f72]) ).
tcf(c_81,negated_conjecture,
! [X0_symbol: symbol] : p__less__(f__symbolic__(X0_symbol),c__supremum__),
inference(cnf_transformation,[],[f73]) ).
tcf(c_83,plain,
$less(0,1),
theory(arith) ).
tcf(c_111,plain,
! [X0_int: $int,X1_int: $int] :
( ~ $less(X0_int,$sum(X1_int,1))
| ~ $less(X1_int,X0_int) ),
inference(prop_impl_just,[status(thm)],[c_49]) ).
tcf(c_112,plain,
! [X0_int: $int,X1_int: $int] :
( ~ $less(X1_int,X0_int)
| ~ $less(X0_int,$sum(X1_int,1)) ),
inference(renaming,[status(thm)],[c_111]) ).
tcf(c_113,plain,
! [X0_int: $int,X1_int: $int] :
( $less(X0_int,$sum(X1_int,1))
| $less(X1_int,X0_int) ),
inference(prop_impl_just,[status(thm)],[c_57]) ).
tcf(c_114,plain,
! [X0_int: $int,X1_int: $int] :
( $less(X1_int,X0_int)
| $less(X0_int,$sum(X1_int,1)) ),
inference(renaming,[status(thm)],[c_113]) ).
tcf(c_115,plain,
! [X0_int: $int,X1_int: $int] :
( ~ p__less_equal__(f__integer__(X0_int),f__integer__(X1_int))
| ~ $less(X1_int,X0_int) ),
inference(prop_impl_just,[status(thm)],[c_73]) ).
tcf(c_116,plain,
! [X0_int: $int,X1_int: $int] :
( ~ $less(X1_int,X0_int)
| ~ p__less_equal__(f__integer__(X0_int),f__integer__(X1_int)) ),
inference(renaming,[status(thm)],[c_115]) ).
tcf(c_117,plain,
! [X0_int: $int,X1_int: $int] :
( p__less_equal__(f__integer__(X0_int),f__integer__(X1_int))
| $less(X1_int,X0_int) ),
inference(prop_impl_just,[status(thm)],[c_72]) ).
tcf(c_118,plain,
! [X0_int: $int,X1_int: $int] :
( $less(X1_int,X0_int)
| p__less_equal__(f__integer__(X0_int),f__integer__(X1_int)) ),
inference(renaming,[status(thm)],[c_117]) ).
tcf(c_121,plain,
! [X0_general: general] :
( ( f__integer__(sK0(X0_general)) = X0_general )
| ~ p__is_integer__(X0_general) ),
inference(prop_impl_just,[status(thm)],[c_67]) ).
tcf(c_123,plain,
! [X0_general: general] :
( ( f__symbolic__(sK1(X0_general)) = X0_general )
| ~ p__is_symbolic__(X0_general) ),
inference(prop_impl_just,[status(thm)],[c_68]) ).
tcf(c_129,plain,
! [X0_general: general,X1_general: general] :
( p__less_equal__(X1_general,X0_general)
| p__less_equal__(X0_general,X1_general) ),
inference(prop_impl_just,[status(thm)],[c_76]) ).
tcf(c_131,plain,
! [X0_general: general,X1_general: general] :
( ~ p__less__(X0_general,X1_general)
| p__less_equal__(X0_general,X1_general) ),
inference(prop_impl_just,[status(thm)],[c_77]) ).
tcf(c_132,plain,
! [X0_general: general,X1_general: general] :
( p__less_equal__(X0_general,X1_general)
| ~ p__less__(X0_general,X1_general) ),
inference(renaming,[status(thm)],[c_131]) ).
tcf(c_338,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_83,c_81,c_80,c_79,c_78,c_132,c_129,c_116,c_118,c_123,c_121,c_66,c_64,c_62,c_61,c_59,c_114,c_56,c_55,c_53,c_52,c_112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX105_1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/10.38 % Computer : n009.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Thu Sep 24 23:25:55 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/10.42 Running TFA theorem proving
% 0.16/10.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s tfa_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/10.43
% 0.16/10.43 % ======== iProver multi-core TPTP/SMT =========
% 0.16/10.43
% 0.16/10.43 % Detected problem language: tptp
% 0.16/10.44 % Proving...
% 0.42/11.18 % SZS status Started for theBenchmark.p
% 0.42/11.18 ERROR - "ProverProcess:heur/schedule_none:304.9999794960022" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 0.42/11.18 Fatal error: exception Failure("undefined enum value")
% 0.42/11.18 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --schedule none --sub_typing false --suppress_sat_res true --tptp_safe_out true --stats_out none --out_options none --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode tclausify -t 101.67 --show_fool true" --time_out_real 305.00 /export/starexec/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_gc5hccn6/tu_zvlu0 2>> /export/starexec/sandbox2/tmp/iprover_out_gc5hccn6/tu_zvlu0_error
% 0.42/11.18 % SZS status Theorem for theBenchmark.p
% 0.42/11.18
% 0.42/11.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.42/11.18
% 0.42/11.18 % ------ iProver source info
% 0.42/11.18
% 0.42/11.18 % git: date: 2026-07-19 20:42:38 +0200
% 0.42/11.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.42/11.18 % git: non_committed_changes: false
% 0.42/11.18
% 0.42/11.18 % ------ Parsing...
% 0.42/11.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.42/11.18
% 0.42/11.18 % ------ Preprocessing...%
% 0.42/11.18
% 0.42/11.18 % SZS status Theorem for theBenchmark.p
% 0.42/11.18
% 0.42/11.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.42/11.19
% 0.42/11.19
%------------------------------------------------------------------------------