%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SYN075-1 : 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 09:09:25 AM UTC 2026
% Result : Unsatisfiable 0.24s 0.55s
% Output : Proof 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 11
% Syntax : Number of clauses : 61 ( 38 unt; 7 nHn; 58 RR)
% Number of literals : 104 ( 55 equ; 36 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 23 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_1,axiom,
( X = a
| ~ big_f(X,Y) ),
file('theBenchmark.p',clause_1) ).
cnf(clause_2,axiom,
( Y = b
| ~ big_f(X,Y) ),
file('theBenchmark.p',clause_2) ).
cnf(clause_3,axiom,
( big_f(X,Y)
| Y != b
| X != a ),
file('theBenchmark.p',clause_3) ).
cnf(clause_4,negated_conjecture,
( f(X) = X
| Y != g(X)
| ~ big_f(Y,f(X)) ),
file('theBenchmark.p',clause_4) ).
cnf(clause_6,negated_conjecture,
( f(X) = X
| big_f(Y,f(X))
| Y != g(X) ),
file('theBenchmark.p',clause_6) ).
cnf(clause_7,negated_conjecture,
( h(X,Z) = Z
| big_f(h(X,Z),f(X))
| big_f(Y,f(X))
| Y != g(X) ),
file('theBenchmark.p',clause_7) ).
cnf(clause_8,negated_conjecture,
( ~ big_f(h(X,Z),f(X))
| h(X,Z) != Z
| big_f(Y,f(X))
| Y != g(X) ),
file('theBenchmark.p',clause_8) ).
cnf(clause_9,negated_conjecture,
( h(X,Z) = Z
| big_f(h(X,Z),f(X))
| f(X) != X ),
file('theBenchmark.p',clause_9) ).
cnf(clause_10,negated_conjecture,
( ~ big_f(h(X,Z),f(X))
| h(X,Z) != Z
| f(X) != X ),
file('theBenchmark.p',clause_10) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_5,axiom,
( g(Eq_x_0) = g(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
( h(b,a) != a
| ~ big_f(h(b,a),f(b))
| f(b) != b ),
inference(start,[status(thm),parent(0:0)],[clause_10]) ).
cnf(t2,plain,
( big_f(h(b,g(b)),f(b))
| h(b,g(b)) != g(b)
| f(b) = b ),
inference(extension,[status(thm),parent(t1:1)],[clause_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( big_f(g(b),f(b))
| big_f(h(b,g(b)),f(b))
| g(b) != g(b)
| h(b,g(b)) = g(b) ),
inference(extension,[status(thm),parent(t2:2)],[clause_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( b != b
| g(b) = g(b) ),
inference(extension,[status(thm),parent(t4:2)],[equality_5]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
b = b,
inference(extension,[status(thm),parent(t6:2)],[equality_1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(l3,lemma,
g(b) = g(b),
inference(lemma,[status(cth),parent(t4:2),below(t2:2)],[t4:2]) ).
cnf(t10,plain,
( f(b) = b
| ~ big_f(h(b,g(b)),f(b)) ),
inference(extension,[status(thm),parent(t4:3)],[clause_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:3]) ).
cnf(t12,plain,
$false,
inference(reduction,[status(thm),parent(t10:2)],[t10:2,t1:1]) ).
cnf(t13,plain,
( g(b) != g(b)
| f(b) = b
| ~ big_f(g(b),f(b)) ),
inference(extension,[status(thm),parent(t4:4)],[clause_4]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t4:4]) ).
cnf(t15,plain,
$false,
inference(reduction,[status(thm),parent(t13:2)],[t13:2,t1:1]) ).
cnf(t16,plain,
g(b) = g(b),
inference(lemma_extension,[status(thm),parent(t13:3)],[l3:1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t13:3]) ).
cnf(l2,lemma,
h(b,g(b)) = g(b),
inference(lemma,[status(cth),parent(t2:2),below(t1:1)],[t2:2]) ).
cnf(t18,plain,
( big_f(g(b),f(b))
| h(b,g(b)) != g(b)
| g(b) != g(b)
| ~ big_f(h(b,g(b)),f(b)) ),
inference(extension,[status(thm),parent(t2:3)],[clause_8]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t2:3]) ).
cnf(t20,plain,
( b != b
| g(b) = g(b) ),
inference(extension,[status(thm),parent(t18:2)],[equality_5]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
b = b,
inference(extension,[status(thm),parent(t20:2)],[equality_1]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(l10,lemma,
g(b) = g(b),
inference(lemma,[status(cth),parent(t18:2),below(t2:3)],[t18:2]) ).
cnf(t24,plain,
h(b,g(b)) = g(b),
inference(lemma_extension,[status(thm),parent(t18:3)],[l2:1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t18:3]) ).
cnf(t26,plain,
( g(b) != g(b)
| f(b) = b
| ~ big_f(g(b),f(b)) ),
inference(extension,[status(thm),parent(t18:4)],[clause_4]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t18:4]) ).
cnf(t28,plain,
$false,
inference(reduction,[status(thm),parent(t26:2)],[t26:2,t1:1]) ).
cnf(t29,plain,
g(b) = g(b),
inference(lemma_extension,[status(thm),parent(t26:3)],[l10:1]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t26:3]) ).
cnf(l1,lemma,
f(b) = b,
inference(lemma,[status(cth),parent(t1:1),below(0:0)],[t1:1]) ).
cnf(t31,plain,
( h(b,a) = a
| f(b) != b
| big_f(h(b,a),f(b)) ),
inference(extension,[status(thm),parent(t1:2)],[clause_9]) ).
cnf(t32,plain,
$false,
inference(connection,[status(thm),parent(t31:1)],[t31:1,t1:2]) ).
cnf(t33,plain,
f(b) = b,
inference(lemma_extension,[status(thm),parent(t31:2)],[l1:1]) ).
cnf(t34,plain,
$false,
inference(connection,[status(thm),parent(t33:1)],[t33:1,t31:2]) ).
cnf(t35,plain,
( f(b) != b
| big_f(h(b,a),f(b))
| h(b,a) != a ),
inference(extension,[status(thm),parent(t31:3)],[clause_3]) ).
cnf(t36,plain,
$false,
inference(connection,[status(thm),parent(t35:1)],[t35:1,t31:3]) ).
cnf(t37,plain,
$false,
inference(reduction,[status(thm),parent(t35:2)],[t35:2,t1:2]) ).
cnf(t38,plain,
f(b) = b,
inference(lemma_extension,[status(thm),parent(t35:3)],[l1:1]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t35:3]) ).
cnf(t40,plain,
( big_f(h(b,a),f(b))
| f(b) != b
| h(b,a) = a ),
inference(extension,[status(thm),parent(t1:3)],[clause_9]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t1:3]) ).
cnf(t42,plain,
f(b) = b,
inference(lemma_extension,[status(thm),parent(t40:2)],[l1:1]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
( h(b,a) = a
| ~ big_f(h(b,a),f(b)) ),
inference(extension,[status(thm),parent(t40:3)],[clause_1]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t40:3]) ).
cnf(t46,plain,
$false,
inference(reduction,[status(thm),parent(t44:2)],[t44:2,t1:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN075-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.33 % Computer : n004.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Sun Sep 20 06:24:19 UTC 2026
% 0.06/0.33 % CPUTime :
% 0.24/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.24/0.55 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------