%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN110-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 03:33:50 PM UTC 2026
% Result : Unsatisfiable 10.21s 1.94s
% Output : Proof 10.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 57 ( 33 unt; 0 def)
% Number of atoms : 97 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 86 ( 46 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-4 aty)
% Number of variables : 93 ( 27 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f159,axiom,
( ~ m0(G,H,G)
| q1(G,G,G) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_122) ).
fof(f159_nnf,plain,
! [G,H] :
( ~ m0(G,H,G)
| q1(G,G,G) ),
inference(nnf_transformation,[status(thm)],[f159]) ).
fof(f159_sk,plain,
! [G,H] :
( ~ m0(G,H,G)
| q1(G,G,G) ),
inference(skolemisation,[status(esa)],[f159_nnf]) ).
cnf(c159,plain,
( ~ m0(X0,X1,X0)
| q1(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f159_sk]) ).
cnf(hi157,axiom,
ifeq(m0(X0,X1,X0),true,q1(X0,X0,X0),true) = true,
inference(equality_encoding,[status(esa)],[c159]) ).
cnf(f18,axiom,
m0(X,d,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_19) ).
fof(f18_nnf,plain,
! [X,Y] : m0(X,d,Y),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,Y] : m0(X,d,Y),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
m0(X0,d,X1),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi18,axiom,
m0(X0,d,X1) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h50,plain,
q1(V0,V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi157,hi18]) ).
cnf(f166,axiom,
( ~ q1(A,J,J)
| k2(J,J) ),
file('/export/starexec/sandbox2/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(h210,plain,
k2(V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi164,h50]) ).
cnf(f38,axiom,
( ~ n0(J,I)
| k1(I) ),
file('/export/starexec/sandbox2/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(f36,axiom,
n0(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_37) ).
fof(f36_nnf,plain,
n0(b,a),
inference(nnf_transformation,[status(thm)],[f36]) ).
cnf(c36,plain,
n0(b,a),
inference(cnf_transformation,[status(esa)],[f36_nnf]) ).
cnf(hi36,axiom,
n0(b,a) = true,
inference(equality_encoding,[status(esa)],[c36]) ).
cnf(h110,plain,
k1(a) = true,
inference(hyper_resolution,[status(thm)],[hi38,hi36]) ).
cnf(f62,axiom,
( ~ m0(D,E,C)
| m1(C,C,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_025) ).
fof(f62_nnf,plain,
! [C,D,E] :
( ~ m0(D,E,C)
| m1(C,C,C) ),
inference(nnf_transformation,[status(thm)],[f62]) ).
fof(f62_sk,plain,
! [C,D,E] :
( ~ m0(D,E,C)
| m1(C,C,C) ),
inference(skolemisation,[status(esa)],[f62_nnf]) ).
cnf(c62,plain,
( ~ m0(X1,X2,X0)
| m1(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f62_sk]) ).
cnf(hi62,axiom,
ifeq(m0(X0,X1,X2),true,m1(X2,X2,X2),true) = true,
inference(equality_encoding,[status(esa)],[c62]) ).
cnf(h57,plain,
m1(V0,V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi62,hi18]) ).
cnf(f61,axiom,
( ~ m1(G,c,G)
| ~ q0(F,G)
| ~ m0(a,H,a)
| m1(F,a,G) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_024) ).
fof(f61_nnf,plain,
! [F,G,H] :
( ~ m1(G,c,G)
| ~ q0(F,G)
| ~ m0(a,H,a)
| m1(F,a,G) ),
inference(nnf_transformation,[status(thm)],[f61]) ).
fof(f61_sk,plain,
! [F,G,H] :
( ~ m1(G,c,G)
| ~ q0(F,G)
| ~ m0(a,H,a)
| m1(F,a,G) ),
inference(skolemisation,[status(esa)],[f61_nnf]) ).
cnf(c61,plain,
( ~ m1(X1,c,X1)
| ~ q0(X0,X1)
| ~ m0(a,X2,a)
| m1(X0,a,X1) ),
inference(cnf_transformation,[status(esa)],[f61_sk]) ).
cnf(hi61,axiom,
ifeq(m0(a,X0,a),true,ifeq(q0(X1,X2),true,ifeq(m1(X2,c,X2),true,m1(X1,a,X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c61]) ).
cnf(f32,axiom,
q0(d,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_33) ).
fof(f32_nnf,plain,
q0(d,c),
inference(nnf_transformation,[status(thm)],[f32]) ).
cnf(c32,plain,
q0(d,c),
inference(cnf_transformation,[status(esa)],[f32_nnf]) ).
cnf(hi32,axiom,
q0(d,c) = true,
inference(equality_encoding,[status(esa)],[c32]) ).
cnf(h212,plain,
m1(d,a,c) = true,
inference(hyper_resolution,[status(thm)],[hi61,hi18,hi32,h57]) ).
cnf(f164,axiom,
( ~ k2(F,D)
| ~ k1(F)
| ~ m1(E,D,C)
| k2(C,D) ),
file('/export/starexec/sandbox2/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(t31,plain,
k2(c,a) = true,
inference(hyper_resolution,[status(thm)],[hi162,h212,h110,h210]) ).
cnf(t750,plain,
k2(c,a) = true,
inference(orient,[status(thm)],[t31]) ).
cnf(f368,negated_conjecture,
~ k2(c,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
~ k2(c,a),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
~ k2(c,a),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ k2(c,a),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(goal_0,negated_conjecture,
k2(c,a) != true,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t750]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN110-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n013.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 00:11:27 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.21/1.94 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.21/1.94 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------