%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET038-3 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n006.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 : 300s
% DateTime : Tue May 5 05:06:59 PM UTC 2026
% Result : Unsatisfiable 4.44s 3.61s
% Output : CNFRefutation 4.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 21
% Syntax : Number of clauses : 67 ( 23 unt; 0 nHn; 62 RR)
% Number of literals : 139 ( 31 equ; 74 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-2 aty)
% Number of variables : 91 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(maps2,axiom,
( domain_of(X1) = X2
| ~ maps(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',maps2) ).
cnf(a_mapping,hypothesis,
maps(a_function,a_domain,a_range),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_mapping) ).
cnf(domain2,axiom,
( member(f8(X1,X2),X2)
| ~ member(X1,domain_of(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',domain2) ).
cnf(member_of_domain,hypothesis,
member(a,a_domain),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_domain) ).
cnf(relation1,axiom,
( ordered_pair_predicate(X2)
| ~ relation(X1)
| ~ member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',relation1) ).
cnf(maps1,axiom,
( function(X1)
| ~ maps(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',maps1) ).
cnf(range_of4,axiom,
( member(X1,range_of(X2))
| ~ little_set(X1)
| ~ ordered_pair_predicate(X3)
| ~ member(X3,X2)
| X1 != second(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',range_of4) ).
cnf(second_component_is_small,axiom,
( little_set(second(X1))
| ~ ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',second_component_is_small) ).
cnf(function1,axiom,
( relation(X1)
| ~ function(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',function1) ).
cnf(ordered_pair,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',singleton_set) ).
cnf(domain3,axiom,
( X1 = first(f8(X1,X2))
| ~ member(X1,domain_of(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',domain3) ).
cnf(property_of_first,axiom,
( first(ordered_pair(X1,X2)) = X1
| ~ little_set(X1)
| ~ little_set(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_first) ).
cnf(ordered_pair_predicate3,axiom,
( X1 = ordered_pair(f2(X1),f3(X1))
| ~ ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate3) ).
cnf(subset1,axiom,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',subset1) ).
cnf(maps3,axiom,
( subset(range_of(X1),X3)
| ~ maps(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',maps3) ).
cnf(property_of_second,axiom,
( second(ordered_pair(X1,X2)) = X2
| ~ little_set(X1)
| ~ little_set(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_second) ).
cnf(apply_for_functions1,axiom,
( apply(X3,X1) = X2
| ~ little_set(X1)
| ~ little_set(X2)
| ~ function(X3)
| ~ member(ordered_pair(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_for_functions1) ).
cnf(ordered_pair_predicate1,axiom,
( little_set(f2(X1))
| ~ ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate1) ).
cnf(ordered_pair_predicate2,axiom,
( little_set(f3(X1))
| ~ ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate2) ).
cnf(prove_mapping_in_range,negated_conjecture,
~ member(apply(a_function,a),a_range),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_mapping_in_range) ).
cnf(c_0_21,axiom,
( domain_of(X1) = X2
| ~ maps(X1,X2,X3) ),
maps2 ).
cnf(c_0_22,hypothesis,
maps(a_function,a_domain,a_range),
a_mapping ).
cnf(c_0_23,axiom,
( member(f8(X1,X2),X2)
| ~ member(X1,domain_of(X2)) ),
domain2 ).
cnf(c_0_24,hypothesis,
domain_of(a_function) = a_domain,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,hypothesis,
( member(f8(X1,a_function),a_function)
| ~ member(X1,a_domain) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,hypothesis,
member(a,a_domain),
member_of_domain ).
cnf(c_0_27,axiom,
( ordered_pair_predicate(X2)
| ~ relation(X1)
| ~ member(X2,X1) ),
relation1 ).
cnf(c_0_28,hypothesis,
member(f8(a,a_function),a_function),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,axiom,
( function(X1)
| ~ maps(X1,X2,X3) ),
maps1 ).
cnf(c_0_30,axiom,
( member(X1,range_of(X2))
| ~ little_set(X1)
| ~ ordered_pair_predicate(X3)
| ~ member(X3,X2)
| X1 != second(X3) ),
range_of4 ).
cnf(c_0_31,axiom,
( little_set(second(X1))
| ~ ordered_pair_predicate(X1) ),
second_component_is_small ).
cnf(c_0_32,hypothesis,
( ordered_pair_predicate(f8(a,a_function))
| ~ relation(a_function) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,axiom,
( relation(X1)
| ~ function(X1) ),
function1 ).
cnf(c_0_34,hypothesis,
function(a_function),
inference(spm,[status(thm)],[c_0_29,c_0_22]) ).
cnf(c_0_35,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
ordered_pair ).
cnf(c_0_36,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
singleton_set ).
cnf(c_0_37,plain,
( member(second(X1),range_of(X2))
| ~ ordered_pair_predicate(X1)
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_30]),c_0_31]) ).
cnf(c_0_38,hypothesis,
ordered_pair_predicate(f8(a,a_function)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_39,axiom,
( X1 = first(f8(X1,X2))
| ~ member(X1,domain_of(X2)) ),
domain3 ).
cnf(c_0_40,axiom,
( first(ordered_pair(X1,X2)) = X1
| ~ little_set(X1)
| ~ little_set(X2) ),
property_of_first ).
cnf(c_0_41,plain,
ordered_pair(X1,X2) = non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,axiom,
( X1 = ordered_pair(f2(X1),f3(X1))
| ~ ordered_pair_predicate(X1) ),
ordered_pair_predicate3 ).
cnf(c_0_43,axiom,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
subset1 ).
cnf(c_0_44,hypothesis,
member(second(f8(a,a_function)),range_of(a_function)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_28]),c_0_38])]) ).
cnf(c_0_45,axiom,
( subset(range_of(X1),X3)
| ~ maps(X1,X2,X3) ),
maps3 ).
cnf(c_0_46,axiom,
( second(ordered_pair(X1,X2)) = X2
| ~ little_set(X1)
| ~ little_set(X2) ),
property_of_second ).
cnf(c_0_47,axiom,
( apply(X3,X1) = X2
| ~ little_set(X1)
| ~ little_set(X2)
| ~ function(X3)
| ~ member(ordered_pair(X1,X2),X3) ),
apply_for_functions1 ).
cnf(c_0_48,hypothesis,
( first(f8(X1,a_function)) = X1
| ~ member(X1,a_domain) ),
inference(spm,[status(thm)],[c_0_39,c_0_24]) ).
cnf(c_0_49,plain,
( first(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))) = X1
| ~ little_set(X2)
| ~ little_set(X1) ),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_50,plain,
( X1 = non_ordered_pair(non_ordered_pair(f2(X1),f2(X1)),non_ordered_pair(f2(X1),f3(X1)))
| ~ ordered_pair_predicate(X1) ),
inference(rw,[status(thm)],[c_0_42,c_0_41]) ).
cnf(c_0_51,axiom,
( little_set(f2(X1))
| ~ ordered_pair_predicate(X1) ),
ordered_pair_predicate1 ).
cnf(c_0_52,axiom,
( little_set(f3(X1))
| ~ ordered_pair_predicate(X1) ),
ordered_pair_predicate2 ).
cnf(c_0_53,hypothesis,
( member(second(f8(a,a_function)),X1)
| ~ subset(range_of(a_function),X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_54,hypothesis,
subset(range_of(a_function),a_range),
inference(spm,[status(thm)],[c_0_45,c_0_22]) ).
cnf(c_0_55,plain,
( second(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))) = X2
| ~ little_set(X2)
| ~ little_set(X1) ),
inference(rw,[status(thm)],[c_0_46,c_0_41]) ).
cnf(c_0_56,plain,
( apply(X3,X1) = X2
| ~ little_set(X2)
| ~ little_set(X1)
| ~ function(X3)
| ~ member(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),X3) ),
inference(rw,[status(thm)],[c_0_47,c_0_41]) ).
cnf(c_0_57,hypothesis,
first(f8(a,a_function)) = a,
inference(spm,[status(thm)],[c_0_48,c_0_26]) ).
cnf(c_0_58,plain,
( first(X1) = f2(X1)
| ~ ordered_pair_predicate(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_52]) ).
cnf(c_0_59,hypothesis,
member(second(f8(a,a_function)),a_range),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,plain,
( second(X1) = f3(X1)
| ~ ordered_pair_predicate(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_50]),c_0_51]),c_0_52]) ).
cnf(c_0_61,plain,
( apply(X1,f2(X2)) = f3(X2)
| ~ function(X1)
| ~ ordered_pair_predicate(X2)
| ~ member(X2,X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_50]),c_0_51]),c_0_52]) ).
cnf(c_0_62,hypothesis,
f2(f8(a,a_function)) = a,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_38])]) ).
cnf(c_0_63,hypothesis,
member(f3(f8(a,a_function)),a_range),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_38])]) ).
cnf(c_0_64,hypothesis,
f3(f8(a,a_function)) = apply(a_function,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_28]),c_0_62]),c_0_34]),c_0_38])]) ).
cnf(c_0_65,negated_conjecture,
~ member(apply(a_function,a),a_range),
prove_mapping_in_range ).
cnf(c_0_66,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64]),c_0_65]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET038-3 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n006.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:06:31 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 4.44/3.61 % Version : CSE_E---1.7
% 4.44/3.61 % Problem : theBenchmark.p
% 4.44/3.61 % SZS status Unsatisfiable for theBenchmark.p
% 4.44/3.61 % SZS output start CNFRefutation
% See solution above
% 4.44/3.63 % Total time : 2.373s
%------------------------------------------------------------------------------