%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET011-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 : Thu Sep 24 08:55:52 AM UTC 2026
% Result : Unsatisfiable 22.65s 22.94s
% Output : Proof 22.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 11
% Syntax : Number of clauses : 77 ( 55 unt; 13 nHn; 74 RR)
% Number of literals : 129 ( 0 equ; 41 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 27 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(intersection_axiom1,axiom,
( member(h(Set1,Set2,Intersection),Set1)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
file('SET001-2.ax',intersection_axiom1) ).
cnf(intersection_axiom2,axiom,
( member(h(Set1,Set2,Intersection),Set2)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
file('SET001-2.ax',intersection_axiom2) ).
cnf(intersection_axiom3,axiom,
( intersection(Set1,Set2,Intersection)
| ~ member(h(Set1,Set2,Intersection),Set1)
| ~ member(h(Set1,Set2,Intersection),Set2)
| ~ member(h(Set1,Set2,Intersection),Intersection) ),
file('SET001-2.ax',intersection_axiom3) ).
cnf(member_of_difference,axiom,
( member(Element,Set1)
| ~ member(Element,Difference)
| ~ difference(Set1,Set2,Difference) ),
file('SET001-3.ax',member_of_difference) ).
cnf(not_member_of_difference,axiom,
( ~ difference(A_set,Set1,Set2)
| ~ member(Element,Set2)
| ~ member(Element,Set1) ),
file('SET001-3.ax',not_member_of_difference) ).
cnf(member_of_difference_or_set2,axiom,
( member(Element,Set2)
| member(Element,Difference)
| ~ difference(Set1,Set2,Difference)
| ~ member(Element,Set1) ),
file('SET001-3.ax',member_of_difference_or_set2) ).
cnf(difference_axiom2,axiom,
( member(k(Set1,Set2,Difference),Difference)
| member(k(Set1,Set2,Difference),Set1)
| difference(Set1,Set2,Difference) ),
file('SET001-3.ax',difference_axiom2) ).
cnf(difference_axiom3,axiom,
( difference(Set1,Set2,Difference)
| member(k(Set1,Set2,Difference),Set2)
| ~ member(k(Set1,Set2,Difference),Set1)
| ~ member(k(Set1,Set2,Difference),Difference) ),
file('SET001-3.ax',difference_axiom3) ).
cnf(a_minus_b,hypothesis,
difference(a,b,aDb),
file('theBenchmark.p',a_minus_b) ).
cnf(a_minus_aDb,hypothesis,
difference(a,aDb,aD_aDb),
file('theBenchmark.p',a_minus_aDb) ).
cnf(prove_a_intersection_b_is_aD_aDb,negated_conjecture,
~ intersection(a,b,aD_aDb),
file('theBenchmark.p',prove_a_intersection_b_is_aD_aDb) ).
cnf(t1,plain,
( ~ member(h(a,b,aD_aDb),aDb)
| ~ difference(a,b,aDb)
| ~ member(h(a,b,aD_aDb),b) ),
inference(start,[status(thm),parent(0:0)],[not_member_of_difference]) ).
cnf(t2,plain,
( ~ difference(a,b,aDb)
| member(h(a,b,aD_aDb),aDb)
| ~ member(h(a,b,aD_aDb),a)
| member(h(a,b,aD_aDb),b) ),
inference(extension,[status(thm),parent(t1:1)],[member_of_difference_or_set2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ member(h(a,b,aD_aDb),aD_aDb)
| ~ difference(a,aDb,aD_aDb)
| member(h(a,b,aD_aDb),a) ),
inference(extension,[status(thm),parent(t2:2)],[member_of_difference]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
difference(a,aDb,aD_aDb),
inference(extension,[status(thm),parent(t4:2)],[a_minus_aDb]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( intersection(a,b,aD_aDb)
| member(h(a,b,aD_aDb),b)
| member(h(a,b,aD_aDb),aD_aDb) ),
inference(extension,[status(thm),parent(t4:3)],[intersection_axiom2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
$false,
inference(reduction,[status(thm),parent(t8:2)],[t8:2,t1:1]) ).
cnf(t11,plain,
~ intersection(a,b,aD_aDb),
inference(extension,[status(thm),parent(t8:3)],[prove_a_intersection_b_is_aD_aDb]) ).
cnf(t12,plain,
$false,
inference(connection,[status(thm),parent(t11:1)],[t11:1,t8:3]) ).
cnf(t13,plain,
( ~ member(h(a,b,aD_aDb),aD_aDb)
| ~ difference(a,aDb,aD_aDb)
| ~ member(h(a,b,aD_aDb),aDb) ),
inference(extension,[status(thm),parent(t2:3)],[not_member_of_difference]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t2:3]) ).
cnf(t15,plain,
difference(a,aDb,aD_aDb),
inference(extension,[status(thm),parent(t13:2)],[a_minus_aDb]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t13:2]) ).
cnf(t17,plain,
( intersection(a,b,aD_aDb)
| member(h(a,b,aD_aDb),b)
| member(h(a,b,aD_aDb),aD_aDb) ),
inference(extension,[status(thm),parent(t13:3)],[intersection_axiom2]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t13:3]) ).
cnf(t19,plain,
$false,
inference(reduction,[status(thm),parent(t17:2)],[t17:2,t1:1]) ).
cnf(t20,plain,
~ intersection(a,b,aD_aDb),
inference(extension,[status(thm),parent(t17:3)],[prove_a_intersection_b_is_aD_aDb]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t17:3]) ).
cnf(t22,plain,
difference(a,b,aDb),
inference(extension,[status(thm),parent(t2:4)],[a_minus_b]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t2:4]) ).
cnf(l1,lemma,
member(h(a,b,aD_aDb),b),
inference(lemma,[status(cth),parent(t1:1),below(0:0)],[t1:1]) ).
cnf(t24,plain,
difference(a,b,aDb),
inference(extension,[status(thm),parent(t1:2)],[a_minus_b]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t1:2]) ).
cnf(t26,plain,
( ~ difference(aD_aDb,aDb,aD_aDb)
| member(h(a,b,aD_aDb),aD_aDb)
| ~ member(h(a,b,aD_aDb),aD_aDb)
| member(h(a,b,aD_aDb),aDb) ),
inference(extension,[status(thm),parent(t1:3)],[member_of_difference_or_set2]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t1:3]) ).
cnf(t28,plain,
( ~ difference(a,aDb,aD_aDb)
| member(h(a,b,aD_aDb),aDb)
| ~ member(h(a,b,aD_aDb),a)
| member(h(a,b,aD_aDb),aD_aDb) ),
inference(extension,[status(thm),parent(t26:2)],[member_of_difference_or_set2]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
( intersection(a,b,aD_aDb)
| member(h(a,b,aD_aDb),aD_aDb)
| member(h(a,b,aD_aDb),a) ),
inference(extension,[status(thm),parent(t28:2)],[intersection_axiom1]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
$false,
inference(reduction,[status(thm),parent(t30:2)],[t30:2,t26:2]) ).
cnf(t33,plain,
~ intersection(a,b,aD_aDb),
inference(extension,[status(thm),parent(t30:3)],[prove_a_intersection_b_is_aD_aDb]) ).
cnf(t34,plain,
$false,
inference(connection,[status(thm),parent(t33:1)],[t33:1,t30:3]) ).
cnf(t35,plain,
$false,
inference(reduction,[status(thm),parent(t28:3)],[t28:3,t1:3]) ).
cnf(t36,plain,
difference(a,aDb,aD_aDb),
inference(extension,[status(thm),parent(t28:4)],[a_minus_aDb]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t28:4]) ).
cnf(l15,lemma,
member(h(a,b,aD_aDb),aD_aDb),
inference(lemma,[status(cth),parent(t26:2),below(t1:3)],[t26:2]) ).
cnf(t38,plain,
( member(h(a,b,aD_aDb),a)
| ~ difference(a,aDb,aD_aDb)
| ~ member(h(a,b,aD_aDb),aD_aDb) ),
inference(extension,[status(thm),parent(t26:3)],[member_of_difference]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t26:3]) ).
cnf(t40,plain,
difference(a,aDb,aD_aDb),
inference(extension,[status(thm),parent(t38:2)],[a_minus_aDb]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
( ~ member(h(a,b,aD_aDb),b)
| intersection(a,b,aD_aDb)
| ~ member(h(a,b,aD_aDb),aD_aDb)
| ~ member(h(a,b,aD_aDb),a) ),
inference(extension,[status(thm),parent(t38:3)],[intersection_axiom3]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t38:3]) ).
cnf(t44,plain,
member(h(a,b,aD_aDb),aD_aDb),
inference(lemma_extension,[status(thm),parent(t42:2)],[l15:1]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
~ intersection(a,b,aD_aDb),
inference(extension,[status(thm),parent(t42:3)],[prove_a_intersection_b_is_aD_aDb]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t42:3]) ).
cnf(t48,plain,
member(h(a,b,aD_aDb),b),
inference(lemma_extension,[status(thm),parent(t42:4)],[l1:1]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t42:4]) ).
cnf(t50,plain,
( ~ member(k(aD_aDb,aDb,aD_aDb),aD_aDb)
| member(k(aD_aDb,aDb,aD_aDb),aDb)
| ~ member(k(aD_aDb,aDb,aD_aDb),aD_aDb)
| difference(aD_aDb,aDb,aD_aDb) ),
inference(extension,[status(thm),parent(t26:4)],[difference_axiom3]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t26:4]) ).
cnf(t52,plain,
( member(k(aD_aDb,aDb,aD_aDb),aD_aDb)
| difference(aD_aDb,aDb,aD_aDb)
| member(k(aD_aDb,aDb,aD_aDb),aD_aDb) ),
inference(extension,[status(thm),parent(t50:2)],[difference_axiom2]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(t54,plain,
$false,
inference(reduction,[status(thm),parent(t52:2)],[t52:2,t26:4]) ).
cnf(t55,plain,
$false,
inference(reduction,[status(thm),parent(t52:3)],[t52:3,t50:2]) ).
cnf(l26,lemma,
member(k(aD_aDb,aDb,aD_aDb),aD_aDb),
inference(lemma,[status(cth),parent(t50:2),below(t26:4)],[t50:2]) ).
cnf(t56,plain,
( ~ member(k(aD_aDb,aDb,aD_aDb),aD_aDb)
| ~ difference(a,aDb,aD_aDb)
| ~ member(k(aD_aDb,aDb,aD_aDb),aDb) ),
inference(extension,[status(thm),parent(t50:3)],[not_member_of_difference]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t50:3]) ).
cnf(t58,plain,
difference(a,aDb,aD_aDb),
inference(extension,[status(thm),parent(t56:2)],[a_minus_aDb]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t56:2]) ).
cnf(t60,plain,
member(k(aD_aDb,aDb,aD_aDb),aD_aDb),
inference(lemma_extension,[status(thm),parent(t56:3)],[l26:1]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t56:3]) ).
cnf(t62,plain,
member(k(aD_aDb,aDb,aD_aDb),aD_aDb),
inference(lemma_extension,[status(thm),parent(t50:4)],[l26:1]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t50:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET011-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 21:31:40 UTC 2026
% 0.09/0.37 % CPUTime :
% 22.65/22.94 % SZS status Unsatisfiable for theBenchmark
% 22.65/22.94 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------