%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN101-1.002.002 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 03:33:49 PM UTC 2026
% Result : Unsatisfiable 3.63s 1.03s
% Output : Proof 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 24 unt; 0 def)
% Number of atoms : 60 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 30 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-4 aty)
% Number of variables : 30 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f15,axiom,
nq_2(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_3) ).
fof(f15_nnf,plain,
nq_2(a),
inference(nnf_transformation,[status(thm)],[f15]) ).
cnf(c15,plain,
nq_2(a),
inference(cnf_transformation,[status(esa)],[f15_nnf]) ).
cnf(hi14,axiom,
nq_2(a) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(h1,plain,
nq_2(a) = true,
inference(hyper_resolution,[status(thm)],[hi14]) ).
cnf(f13,axiom,
nq_1(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_1) ).
fof(f13_nnf,plain,
nq_1(a),
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c13,plain,
nq_1(a),
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(hi12,axiom,
nq_1(a) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h0,plain,
nq_1(a) = true,
inference(hyper_resolution,[status(thm)],[hi12]) ).
cnf(f9,axiom,
( ~ nq_2(X_2)
| ~ nq_1(X_1)
| p_1_1(X_1,X_2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_t2_1) ).
fof(f9_nnf,plain,
! [X_1,X_2] :
( ~ nq_2(X_2)
| ~ nq_1(X_1)
| p_1_1(X_1,X_2) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X_1,X_2] :
( ~ nq_2(X_2)
| ~ nq_1(X_1)
| p_1_1(X_1,X_2) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( ~ nq_2(X1)
| ~ nq_1(X0)
| p_1_1(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi8,axiom,
ifeq(nq_1(X0),true,ifeq(nq_2(X1),true,p_1_1(X0,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h3,plain,
p_1_1(a,a) = true,
inference(hyper_resolution,[status(thm)],[hi8,h0,h1]) ).
cnf(f11,axiom,
( ~ nq_2(X_2)
| ~ nq_1(X_1)
| p_2_2(X_1,X_2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_t2_3) ).
fof(f11_nnf,plain,
! [X_1,X_2] :
( ~ nq_2(X_2)
| ~ nq_1(X_1)
| p_2_2(X_1,X_2) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X_1,X_2] :
( ~ nq_2(X_2)
| ~ nq_1(X_1)
| p_2_2(X_1,X_2) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( ~ nq_2(X1)
| ~ nq_1(X0)
| p_2_2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi10,axiom,
ifeq(nq_1(X0),true,ifeq(nq_2(X1),true,p_2_2(X0,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h2,plain,
p_2_2(a,a) = true,
inference(hyper_resolution,[status(thm)],[hi10,h0,h1]) ).
cnf(f1,axiom,
( ~ p_1_1(X_1,X_2)
| ~ p_2_2(X_1,X_2)
| p_1_2(X_1,X_2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s2_type11_1) ).
fof(f1_nnf,plain,
! [X_1,X_2] :
( ~ p_1_1(X_1,X_2)
| ~ p_2_2(X_1,X_2)
| p_1_2(X_1,X_2) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X_1,X_2] :
( ~ p_1_1(X_1,X_2)
| ~ p_2_2(X_1,X_2)
| p_1_2(X_1,X_2) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ p_1_1(X0,X1)
| ~ p_2_2(X0,X1)
| p_1_2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi0,axiom,
ifeq(p_2_2(X0,X1),true,ifeq(p_1_1(X0,X1),true,p_1_2(X0,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t4,plain,
p_1_2(a,a) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2,h3]) ).
cnf(t51,plain,
p_1_2(a,a) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(f0,negated_conjecture,
~ p_1_2(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s2_goal_1) ).
fof(f0_nnf,plain,
~ p_1_2(a,a),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
~ p_1_2(a,a),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ p_1_2(a,a),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(goal_0,negated_conjecture,
p_1_2(a,a) != true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t51]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN101-1.002.002 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 00:11:12 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.63/1.03 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.63/1.03 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------