%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM020-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 9.94s 6.98s
% Output : Proof 9.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 32 unt; 0 def)
% Number of atoms : 52 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 22 ~; 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; 4 con; 0-4 aty)
% Number of variables : 53 ( 4 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f10,negated_conjecture,
~ equalish(add(a,successor(n0)),successor(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',deny_addition_lemma) ).
fof(f10_nnf,plain,
~ equalish(add(a,successor(n0)),successor(a)),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
~ equalish(add(a,successor(n0)),successor(a)),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
~ equalish(add(a,successor(n0)),successor(a)),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t197,plain,
ifeq(equalish(add(a,successor(n0)),successor(a)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(f5,axiom,
( equalish(successor(A),successor(B))
| ~ equalish(A,B) ),
file('/export/starexec/sandbox2/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(hi5,axiom,
ifeq(equalish(X0,X1),true,equalish(successor(X0),successor(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f0,axiom,
equalish(add(A,n0),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',adding_zero) ).
fof(f0_nnf,plain,
! [A] : equalish(add(A,n0),A),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A] : equalish(add(A,n0),A),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
equalish(add(X0,n0),X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
equalish(add(X0,n0),X0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h3,plain,
equalish(successor(add(V0,n0)),successor(V0)) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi0]) ).
cnf(f8,axiom,
( equalish(X,Z)
| ~ equalish(Y,Z)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
fof(f8_nnf,plain,
! [X,Y,Z] :
( equalish(X,Z)
| ~ equalish(Y,Z)
| ~ equalish(X,Y) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y,Z] :
( equalish(X,Z)
| ~ equalish(Y,Z)
| ~ equalish(X,Y) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,axiom,
ifeq(equalish(X0,X1),true,ifeq(equalish(X1,X2),true,equalish(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(f1,axiom,
equalish(add(A,successor(B)),successor(add(A,B))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition) ).
fof(f1_nnf,plain,
! [A,B] : equalish(add(A,successor(B)),successor(add(A,B))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : equalish(add(A,successor(B)),successor(add(A,B))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
equalish(add(X0,successor(X1)),successor(add(X0,X1))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
equalish(add(X0,successor(X1)),successor(add(X0,X1))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t30,plain,
equalish(add(X1,successor(n0)),successor(X1)) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi1,h3]) ).
cnf(t268,plain,
equalish(add(X1,successor(n0)),successor(X1)) = true,
inference(orient,[status(thm)],[t30]) ).
cnf(t1080,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t197,t268]) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t16]) ).
cnf(t1081,plain,
false = true,
inference(step,[status(thm)],[t1080,t256]) ).
cnf(t1079,plain,
false = true,
inference(orient,[status(thm)],[t1081]) ).
cnf(f11,negated_conjecture,
~ equalish(successor(A),n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_contradiction) ).
fof(f11_nnf,plain,
! [A] : ~ equalish(successor(A),n0),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A] : ~ equalish(successor(A),n0),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
~ equalish(successor(X0),n0),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c10,c11]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1079]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM020-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/5.39 % Computer : n018.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Thu Sep 24 02:42:40 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.94/6.98 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.94/6.98 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------