%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM002-1 : 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 : n004.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 08:51:36 AM UTC 2026
% Result : Unsatisfiable 2.47s 2.75s
% Output : Proof 2.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 21 ( 16 unt; 0 nHn; 18 RR)
% Number of literals : 31 ( 0 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 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 : 15 ( 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(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(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(subtract(a,b),c),add(a,subtract(c,b))),
file('theBenchmark.p',prove_equation) ).
cnf(t1,plain,
~ equalish(add(subtract(a,b),c),add(a,subtract(c,b))),
inference(start,[status(thm),parent(0:0)],[prove_equation]) ).
cnf(t2,plain,
( ~ equalish(subtract(add(c,a),b),add(a,subtract(c,b)))
| ~ equalish(add(subtract(a,b),c),subtract(add(c,a),b))
| equalish(add(subtract(a,b),c),add(a,subtract(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(add(subtract(a,b),c),subtract(add(a,c),b))
| ~ equalish(add(a,c),add(c,a))
| equalish(add(subtract(a,b),c),subtract(add(c,a),b)) ),
inference(extension,[status(thm),parent(t2:2)],[subtract_substitution1]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
equalish(add(a,c),add(c,a)),
inference(extension,[status(thm),parent(t4:2)],[commutativity_of_addition]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
equalish(add(subtract(a,b),c),subtract(add(a,c),b)),
inference(extension,[status(thm),parent(t4:3)],[commutativity1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( ~ equalish(add(subtract(c,b),a),add(a,subtract(c,b)))
| ~ equalish(subtract(add(c,a),b),add(subtract(c,b),a))
| equalish(subtract(add(c,a),b),add(a,subtract(c,b))) ),
inference(extension,[status(thm),parent(t2:3)],[transitivity]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
equalish(subtract(add(c,a),b),add(subtract(c,b),a)),
inference(extension,[status(thm),parent(t10:2)],[commutativity2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
equalish(add(subtract(c,b),a),add(a,subtract(c,b))),
inference(extension,[status(thm),parent(t10:3)],[commutativity_of_addition]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM002-1 : 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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % 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 17:33:49 UTC 2026
% 0.09/0.36 % CPUTime :
% 2.47/2.75 % SZS status Unsatisfiable for theBenchmark
% 2.47/2.75 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------