%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM001-1 : 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 : n016.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 24.55s 24.82s
% Output : Proof 24.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 5
% Syntax : Number of clauses : 24 ( 18 unt; 0 nHn; 22 RR)
% Number of literals : 36 ( 0 equ; 14 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 12 ( 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(associativity_of_addition,axiom,
equalish(add(A,add(B,C)),add(add(A,B),C)),
file('NUM002-0.ax',associativity_of_addition) ).
cnf(add_substitution2,axiom,
( equalish(C,add(D,B))
| ~ equalish(C,add(D,A))
| ~ equalish(A,B) ),
file('NUM002-0.ax',add_substitution2) ).
cnf(prove_equation,negated_conjecture,
~ equalish(add(add(a,b),c),add(a,add(b,c))),
file('theBenchmark.p',prove_equation) ).
cnf(t1,plain,
~ equalish(add(add(a,b),c),add(a,add(b,c))),
inference(start,[status(thm),parent(0:0)],[prove_equation]) ).
cnf(t2,plain,
( ~ equalish(add(add(a,b),c),add(a,add(c,b)))
| ~ equalish(add(c,b),add(b,c))
| equalish(add(add(a,b),c),add(a,add(b,c))) ),
inference(extension,[status(thm),parent(t1:1)],[add_substitution2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
equalish(add(c,b),add(b,c)),
inference(extension,[status(thm),parent(t2:2)],[commutativity_of_addition]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ equalish(add(c,add(b,a)),add(a,add(c,b)))
| ~ equalish(add(add(a,b),c),add(c,add(b,a)))
| equalish(add(add(a,b),c),add(a,add(c,b))) ),
inference(extension,[status(thm),parent(t2:3)],[transitivity]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( ~ equalish(add(add(a,b),c),add(c,add(a,b)))
| ~ equalish(add(a,b),add(b,a))
| equalish(add(add(a,b),c),add(c,add(b,a))) ),
inference(extension,[status(thm),parent(t6:2)],[add_substitution2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
equalish(add(a,b),add(b,a)),
inference(extension,[status(thm),parent(t8:2)],[commutativity_of_addition]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
equalish(add(add(a,b),c),add(c,add(a,b))),
inference(extension,[status(thm),parent(t8:3)],[commutativity_of_addition]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
( ~ equalish(add(add(c,b),a),add(a,add(c,b)))
| ~ equalish(add(c,add(b,a)),add(add(c,b),a))
| equalish(add(c,add(b,a)),add(a,add(c,b))) ),
inference(extension,[status(thm),parent(t6:3)],[transitivity]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t6:3]) ).
cnf(t16,plain,
equalish(add(c,add(b,a)),add(add(c,b),a)),
inference(extension,[status(thm),parent(t14:2)],[associativity_of_addition]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
equalish(add(add(c,b),a),add(a,add(c,b))),
inference(extension,[status(thm),parent(t14:3)],[commutativity_of_addition]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM001-1 : 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 : n016.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
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 17:38:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 24.55/24.82 % SZS status Unsatisfiable for theBenchmark
% 24.55/24.82 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------