%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM003-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 08:51:37 AM UTC 2026
% Result : Unsatisfiable 249.26s 249.51s
% Output : Proof 249.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of clauses : 40 ( 30 unt; 0 nHn; 30 RR)
% Number of literals : 60 ( 0 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity,axiom,
( equalish(A,C)
| ~ equalish(B,C)
| ~ equalish(A,B) ),
file('NUM002-0.ax',transitivity) ).
cnf(commutativity_of_addition,axiom,
equalish(add(A,B),add(B,A)),
file('NUM002-0.ax',commutativity_of_addition) ).
cnf(addition_inverts_subtraction1,axiom,
equalish(subtract(add(A,B),B),A),
file('NUM002-0.ax',addition_inverts_subtraction1) ).
cnf(addition_inverts_subtraction2,axiom,
equalish(A,subtract(add(A,B),B)),
file('NUM002-0.ax',addition_inverts_subtraction2) ).
cnf(commutativity1,axiom,
equalish(add(subtract(A,B),C),subtract(add(A,C),B)),
file('NUM002-0.ax',commutativity1) ).
cnf(commutativity2,axiom,
equalish(subtract(add(A,B),C),add(subtract(A,C),B)),
file('NUM002-0.ax',commutativity2) ).
cnf(add_substitution2,axiom,
( equalish(C,add(D,B))
| ~ equalish(C,add(D,A))
| ~ equalish(A,B) ),
file('NUM002-0.ax',add_substitution2) ).
cnf(subtract_substitution1,axiom,
( equalish(C,subtract(B,D))
| ~ equalish(C,subtract(A,D))
| ~ equalish(A,B) ),
file('NUM002-0.ax',subtract_substitution1) ).
cnf(prove_equation,negated_conjecture,
~ equalish(add(a,subtract(b,c)),add(subtract(a,c),b)),
file('theBenchmark.p',prove_equation) ).
cnf(t1,plain,
~ equalish(add(a,subtract(b,c)),add(subtract(a,c),b)),
inference(start,[status(thm),parent(0:0)],[prove_equation]) ).
cnf(t2,plain,
( ~ equalish(add(a,subtract(b,c)),subtract(add(a,subtract(add(b,U_3920),U_3920)),c))
| ~ equalish(subtract(add(a,subtract(add(b,U_3920),U_3920)),c),add(subtract(a,c),b))
| equalish(add(a,subtract(b,c)),add(subtract(a,c),b)) ),
inference(extension,[status(thm),parent(t1:1)],[transitivity]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ equalish(subtract(add(a,subtract(add(b,U_3920),U_3920)),c),subtract(add(a,subtract(add(b,U_3920),U_3920)),c))
| ~ equalish(subtract(add(a,subtract(add(b,U_3920),U_3920)),c),add(subtract(a,c),b))
| equalish(subtract(add(a,subtract(add(b,U_3920),U_3920)),c),add(subtract(a,c),b)) ),
inference(extension,[status(thm),parent(t2:2)],[transitivity]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ equalish(subtract(add(a,subtract(add(b,U_3920),U_3920)),c),add(subtract(a,c),subtract(add(b,U_3920),U_3920)))
| ~ equalish(subtract(add(b,U_3920),U_3920),b)
| equalish(subtract(add(a,subtract(add(b,U_3920),U_3920)),c),add(subtract(a,c),b)) ),
inference(extension,[status(thm),parent(t4:2)],[add_substitution2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
equalish(subtract(add(b,U_3920),U_3920),b),
inference(extension,[status(thm),parent(t6:2)],[addition_inverts_subtraction1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
equalish(subtract(add(a,subtract(add(b,U_3920),U_3920)),c),add(subtract(a,c),subtract(add(b,U_3920),U_3920))),
inference(extension,[status(thm),parent(t6:3)],[commutativity2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
( ~ equalish(subtract(add(a,subtract(add(b,U_3920),U_3920)),c),add(subtract(a,c),subtract(add(b,U_3920),U_3920)))
| ~ equalish(add(subtract(a,c),subtract(add(b,U_3920),U_3920)),subtract(add(a,subtract(add(b,U_3920),U_3920)),c))
| equalish(subtract(add(a,subtract(add(b,U_3920),U_3920)),c),subtract(add(a,subtract(add(b,U_3920),U_3920)),c)) ),
inference(extension,[status(thm),parent(t4:3)],[transitivity]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:3]) ).
cnf(t14,plain,
equalish(add(subtract(a,c),subtract(add(b,U_3920),U_3920)),subtract(add(a,subtract(add(b,U_3920),U_3920)),c)),
inference(extension,[status(thm),parent(t12:2)],[commutativity1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
equalish(subtract(add(a,subtract(add(b,U_3920),U_3920)),c),add(subtract(a,c),subtract(add(b,U_3920),U_3920))),
inference(extension,[status(thm),parent(t12:3)],[commutativity2]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
( ~ equalish(add(a,subtract(b,c)),subtract(add(b,a),c))
| ~ equalish(add(b,a),add(a,subtract(add(b,U_3920),U_3920)))
| equalish(add(a,subtract(b,c)),subtract(add(a,subtract(add(b,U_3920),U_3920)),c)) ),
inference(extension,[status(thm),parent(t2:3)],[subtract_substitution1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t2:3]) ).
cnf(t20,plain,
( ~ equalish(add(b,a),add(a,b))
| ~ equalish(b,subtract(add(b,U_3920),U_3920))
| equalish(add(b,a),add(a,subtract(add(b,U_3920),U_3920))) ),
inference(extension,[status(thm),parent(t18:2)],[add_substitution2]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
equalish(b,subtract(add(b,U_3920),U_3920)),
inference(extension,[status(thm),parent(t20:2)],[addition_inverts_subtraction2]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
equalish(add(b,a),add(a,b)),
inference(extension,[status(thm),parent(t20:3)],[commutativity_of_addition]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
( ~ equalish(add(a,subtract(b,c)),add(subtract(b,c),a))
| ~ equalish(add(subtract(b,c),a),subtract(add(b,a),c))
| equalish(add(a,subtract(b,c)),subtract(add(b,a),c)) ),
inference(extension,[status(thm),parent(t18:3)],[transitivity]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t18:3]) ).
cnf(t28,plain,
equalish(add(subtract(b,c),a),subtract(add(b,a),c)),
inference(extension,[status(thm),parent(t26:2)],[commutativity1]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
equalish(add(a,subtract(b,c)),add(subtract(b,c),a)),
inference(extension,[status(thm),parent(t26:3)],[commutativity_of_addition]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t26:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_HRN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 17:29:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 249.26/249.51 % SZS status Unsatisfiable for theBenchmark
% 249.26/249.51 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------