%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN138-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 03:33:54 PM UTC 2026
% Result : Unsatisfiable 3.68s 6.12s
% Output : Proof 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of formulae : 94 ( 62 unt; 0 def)
% Number of atoms : 158 ( 31 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 134 ( 70 ~; 64 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-4 aty)
% Number of variables : 105 ( 21 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f129,axiom,
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_092) ).
fof(f129_nnf,plain,
! [J,A,B,C] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
inference(nnf_transformation,[status(thm)],[f129]) ).
fof(f129_sk,plain,
! [J,A,B,C] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
inference(skolemisation,[status(esa)],[f129_nnf]) ).
cnf(c129,plain,
( ~ p0(X3,X0)
| ~ n0(X2,X1)
| q1(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f129_sk]) ).
cnf(hi127,axiom,
ifeq(n0(X0,X1),true,ifeq(p0(X2,X3),true,q1(X3,X1,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c129]) ).
cnf(f2,axiom,
n0(d,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f2_nnf,plain,
n0(d,e),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
n0(d,e),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(hi2,axiom,
n0(d,e) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f13,axiom,
p0(b,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
fof(f13_nnf,plain,
! [X] : p0(b,X),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X] : p0(b,X),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
p0(b,X0),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
p0(b,X0) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h10,plain,
q1(e,e,e) = true,
inference(hyper_resolution,[status(thm)],[hi127,hi2,hi13]) ).
cnf(f166,axiom,
( ~ q1(A,J,J)
| k2(J,J) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_129) ).
fof(f166_nnf,plain,
! [J,A] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(nnf_transformation,[status(thm)],[f166]) ).
fof(f166_sk,plain,
! [J,A] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(skolemisation,[status(esa)],[f166_nnf]) ).
cnf(c166,plain,
( ~ q1(X1,X0,X0)
| k2(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f166_sk]) ).
cnf(hi164,axiom,
ifeq(q1(X0,X1,X1),true,k2(X1,X1),true) = true,
inference(equality_encoding,[status(esa)],[c166]) ).
cnf(h11,plain,
k2(e,e) = true,
inference(hyper_resolution,[status(thm)],[hi164,h10]) ).
cnf(f38,axiom,
( ~ n0(J,I)
| k1(I) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_001) ).
fof(f38_nnf,plain,
! [I,J] :
( ~ n0(J,I)
| k1(I) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [I,J] :
( ~ n0(J,I)
| k1(I) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c38,plain,
( ~ n0(X1,X0)
| k1(X0) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(hi38,axiom,
ifeq(n0(X0,X1),true,k1(X1),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(h7,plain,
k1(e) = true,
inference(hyper_resolution,[status(thm)],[hi38,hi2]) ).
cnf(f27,axiom,
k0(e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_28) ).
fof(f27_nnf,plain,
k0(e),
inference(nnf_transformation,[status(thm)],[f27]) ).
cnf(c27,plain,
k0(e),
inference(cnf_transformation,[status(esa)],[f27_nnf]) ).
cnf(hi27,axiom,
k0(e) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(h6,plain,
k0(e) = true,
inference(hyper_resolution,[status(thm)],[hi27]) ).
cnf(f23,axiom,
l0(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).
fof(f23_nnf,plain,
l0(c),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c23,plain,
l0(c),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(hi23,axiom,
l0(c) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(h3,plain,
l0(c) = true,
inference(hyper_resolution,[status(thm)],[hi23]) ).
cnf(f58,axiom,
( ~ k0(J)
| ~ l0(I)
| m1(I,J,I) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_021) ).
fof(f58_nnf,plain,
! [I,J] :
( ~ k0(J)
| ~ l0(I)
| m1(I,J,I) ),
inference(nnf_transformation,[status(thm)],[f58]) ).
fof(f58_sk,plain,
! [I,J] :
( ~ k0(J)
| ~ l0(I)
| m1(I,J,I) ),
inference(skolemisation,[status(esa)],[f58_nnf]) ).
cnf(c58,plain,
( ~ k0(X1)
| ~ l0(X0)
| m1(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
cnf(hi58,axiom,
ifeq(l0(X0),true,ifeq(k0(X1),true,m1(X0,X1,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c58]) ).
cnf(h9,plain,
m1(c,e,c) = true,
inference(hyper_resolution,[status(thm)],[hi58,h3,h6]) ).
cnf(f164,axiom,
( ~ k2(F,D)
| ~ k1(F)
| ~ m1(E,D,C)
| k2(C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_127) ).
fof(f164_nnf,plain,
! [C,D,E,F] :
( ~ k2(F,D)
| ~ k1(F)
| ~ m1(E,D,C)
| k2(C,D) ),
inference(nnf_transformation,[status(thm)],[f164]) ).
fof(f164_sk,plain,
! [C,D,E,F] :
( ~ k2(F,D)
| ~ k1(F)
| ~ m1(E,D,C)
| k2(C,D) ),
inference(skolemisation,[status(esa)],[f164_nnf]) ).
cnf(c164,plain,
( ~ k2(X3,X1)
| ~ k1(X3)
| ~ m1(X2,X1,X0)
| k2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f164_sk]) ).
cnf(hi162,axiom,
ifeq(m1(X0,X1,X2),true,ifeq(k1(X3),true,ifeq(k2(X3,X1),true,k2(X2,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c164]) ).
cnf(h12,plain,
k2(c,e) = true,
inference(hyper_resolution,[status(thm)],[hi162,h9,h7,h11]) ).
cnf(f33,axiom,
n0(c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_34) ).
fof(f33_nnf,plain,
n0(c,d),
inference(nnf_transformation,[status(thm)],[f33]) ).
cnf(c33,plain,
n0(c,d),
inference(cnf_transformation,[status(esa)],[f33_nnf]) ).
cnf(hi33,axiom,
n0(c,d) = true,
inference(equality_encoding,[status(esa)],[c33]) ).
cnf(f9,axiom,
p0(b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
fof(f9_nnf,plain,
p0(b,d),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
p0(b,d),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(hi9,axiom,
p0(b,d) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h1,plain,
q1(d,d,d) = true,
inference(hyper_resolution,[status(thm)],[hi127,hi33,hi9]) ).
cnf(f0,axiom,
s0(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f0_nnf,plain,
s0(d),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
s0(d),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(hi0,axiom,
s0(d) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h0,plain,
s0(d) = true,
inference(hyper_resolution,[status(thm)],[hi0]) ).
cnf(f161,axiom,
( ~ q1(d,E,d)
| ~ s0(d)
| ~ q0(D,E)
| r1(D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_124) ).
fof(f161_nnf,plain,
! [D,E] :
( ~ q1(d,E,d)
| ~ s0(d)
| ~ q0(D,E)
| r1(D) ),
inference(nnf_transformation,[status(thm)],[f161]) ).
fof(f161_sk,plain,
! [D,E] :
( ~ q1(d,E,d)
| ~ s0(d)
| ~ q0(D,E)
| r1(D) ),
inference(skolemisation,[status(esa)],[f161_nnf]) ).
cnf(c161,plain,
( ~ q1(d,X1,d)
| ~ s0(d)
| ~ q0(X0,X1)
| r1(X0) ),
inference(cnf_transformation,[status(esa)],[f161_sk]) ).
cnf(hi159,axiom,
ifeq(q0(X0,X1),true,ifeq(s0(d),true,ifeq(q1(d,X1,d),true,r1(X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c161]) ).
cnf(f16,axiom,
q0(X,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
fof(f16_nnf,plain,
! [X] : q0(X,d),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X] : q0(X,d),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
q0(X0,d),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,axiom,
q0(X0,d) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h2,plain,
r1(c) = true,
inference(hyper_resolution,[status(thm)],[hi159,hi16,h0,h1]) ).
cnf(f225,axiom,
( ~ l0(G)
| ~ r1(G)
| r2(G) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_188) ).
fof(f225_nnf,plain,
! [G] :
( ~ l0(G)
| ~ r1(G)
| r2(G) ),
inference(nnf_transformation,[status(thm)],[f225]) ).
fof(f225_sk,plain,
! [G] :
( ~ l0(G)
| ~ r1(G)
| r2(G) ),
inference(skolemisation,[status(esa)],[f225_nnf]) ).
cnf(c225,plain,
( ~ l0(X0)
| ~ r1(X0)
| r2(X0) ),
inference(cnf_transformation,[status(esa)],[f225_sk]) ).
cnf(hi222,axiom,
ifeq(r1(X0),true,ifeq(l0(X0),true,r2(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c225]) ).
cnf(h4,plain,
r2(c) = true,
inference(hyper_resolution,[status(thm)],[hi222,h2,h3]) ).
cnf(f268,axiom,
( ~ k2(c,I)
| ~ r2(H)
| m3(H,I,H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_231) ).
fof(f268_nnf,plain,
! [H,I] :
( ~ k2(c,I)
| ~ r2(H)
| m3(H,I,H) ),
inference(nnf_transformation,[status(thm)],[f268]) ).
fof(f268_sk,plain,
! [H,I] :
( ~ k2(c,I)
| ~ r2(H)
| m3(H,I,H) ),
inference(skolemisation,[status(esa)],[f268_nnf]) ).
cnf(c268,plain,
( ~ k2(c,X1)
| ~ r2(X0)
| m3(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f268_sk]) ).
cnf(hi263,axiom,
ifeq(r2(X0),true,ifeq(k2(c,X1),true,m3(X0,X1,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c268]) ).
cnf(t0,plain,
m3(c,e,c) = true,
inference(hyper_resolution,[status(thm)],[hi263,h4,h12]) ).
cnf(t13,plain,
m3(c,e,c) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(f368,negated_conjecture,
~ m3(c,e,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
~ m3(c,e,c),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
~ m3(c,e,c),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ m3(c,e,c),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(goal_0,negated_conjecture,
m3(c,e,c) != true,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t13]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN138-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.58 % Computer : n009.cluster.edu
% 0.10/5.58 % Model : x86_64 x86_64
% 0.10/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.58 % Memory : 8046.5625MB
% 0.10/5.58 % OS : Linux 6.8.0-71-generic
% 0.10/5.58 % CPULimit : 300
% 0.10/5.58 % WCLimit : 300
% 0.10/5.58 % DateTime : Fri Sep 25 00:16:35 UTC 2026
% 0.10/5.59 % CPUTime :
% 0.10/5.59 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.68/6.12 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.68/6.12 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------