%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM019-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 : Fri Sep 25 02:18:32 PM UTC 2026
% Result : Unsatisfiable 6.25s 1.70s
% Output : Proof 6.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 43 unt; 0 def)
% Number of atoms : 63 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 25 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 49 ( 4 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,axiom,
( equalish(successor(A),successor(B))
| ~ equalish(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_substitution) ).
fof(f5_nnf,plain,
! [A,B] :
( equalish(successor(A),successor(B))
| ~ equalish(A,B) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B] :
( equalish(successor(A),successor(B))
| ~ equalish(A,B) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( equalish(successor(X0),successor(X1))
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t9,plain,
ifeq(equalish(X1,X2),true,equalish(successor(X1),successor(X2)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t19,plain,
ifeq(equalish(X1,X2),true,equalish(successor(X1),successor(X2)),true) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(f9,hypothesis,
equalish(a,aa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_aa) ).
fof(f9_nnf,plain,
equalish(a,aa),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
equalish(a,aa),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(t1,plain,
equalish(a,aa) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t18,plain,
equalish(a,aa) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t20,plain,
true = ifeq(true,true,equalish(successor(a),successor(aa)),true),
inference(cp,[status(thm)],[t19,t18]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t86,plain,
true = equalish(successor(a),successor(aa)),
inference(step,[status(thm)],[t20,t12]) ).
cnf(t52,plain,
equalish(successor(a),successor(aa)) = true,
inference(orient,[status(thm)],[t86]) ).
cnf(t57,plain,
true = ifeq(true,true,equalish(successor(successor(a)),successor(successor(aa))),true),
inference(cp,[status(thm)],[t19,t52]) ).
cnf(t89,plain,
true = equalish(successor(successor(a)),successor(successor(aa))),
inference(step,[status(thm)],[t57,t12]) ).
cnf(t70,plain,
equalish(successor(successor(a)),successor(successor(aa))) = true,
inference(orient,[status(thm)],[t89]) ).
cnf(f7,hypothesis,
( equalish(Y,Z)
| ~ equalish(X,Z)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
fof(f7_nnf,plain,
! [X,Y,Z] :
( equalish(Y,Z)
| ~ equalish(X,Z)
| ~ equalish(X,Y) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y,Z] :
( equalish(Y,Z)
| ~ equalish(X,Z)
| ~ equalish(X,Y) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( equalish(X1,X2)
| ~ equalish(X0,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t11,plain,
ifeq(equalish(X1,X2),true,ifeq(equalish(X1,X3),true,equalish(X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t25,plain,
ifeq(equalish(X1,X2),true,ifeq(equalish(X1,X3),true,equalish(X2,X3),true),true) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t27,plain,
true = ifeq(true,true,ifeq(equalish(a,X1),true,equalish(aa,X1),true),true),
inference(cp,[status(thm)],[t25,t18]) ).
cnf(t91,plain,
true = ifeq(equalish(a,X1),true,equalish(aa,X1),true),
inference(step,[status(thm)],[t27,t12]) ).
cnf(t77,plain,
ifeq(equalish(a,X1),true,equalish(aa,X1),true) = true,
inference(orient,[status(thm)],[t91]) ).
cnf(f6,hypothesis,
equalish(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
fof(f6_nnf,plain,
! [X] : equalish(X,X),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X] : equalish(X,X),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
equalish(X0,X0),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t0,plain,
equalish(X1,X1) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t13,plain,
equalish(X1,X1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t78,plain,
true = ifeq(true,true,equalish(aa,a),true),
inference(cp,[status(thm)],[t77,t13]) ).
cnf(t92,plain,
true = equalish(aa,a),
inference(step,[status(thm)],[t78,t12]) ).
cnf(t79,plain,
equalish(aa,a) = true,
inference(orient,[status(thm)],[t92]) ).
cnf(f8,hypothesis,
~ equalish(successor(A),n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_the_first_number) ).
fof(f8_nnf,plain,
! [A] : ~ equalish(successor(A),n0),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A] : ~ equalish(successor(A),n0),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ equalish(successor(X0),n0),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(f10,negated_conjecture,
~ equalish(aa,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_equals_a) ).
fof(f10_nnf,plain,
~ equalish(aa,a),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
~ equalish(aa,a),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
~ equalish(aa,a),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c8,c10]) ).
cnf(g0_0,plain,
true != ifeq(equalish(aa,a),true,false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(equalish(aa,a),true,false,equalish(successor(successor(a)),successor(successor(aa)))),
inference(rw,[status(thm)],[g0_0,t70]) ).
cnf(g0_2,plain,
true != ifeq(equalish(aa,a),equalish(aa,a),false,equalish(successor(successor(a)),successor(successor(aa)))),
inference(rw,[status(thm)],[g0_1,t79]) ).
cnf(g0_3,plain,
true != false,
inference(rw,[status(thm)],[g0_2,t12]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM019-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.43 % Computer : n015.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Thu Sep 24 02:43:41 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.25/1.70 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.25/1.70 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------