%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN250-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 03:34:10 PM UTC 2026
% Result : Unsatisfiable 5.27s 1.10s
% Output : Proof 5.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 64 ( 44 unt; 0 def)
% Number of atoms : 108 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 94 ( 50 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 86 ( 22 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f36,axiom,
n0(b,a),
file('/export/starexec/sandbox/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(f71,axiom,
( ~ q0(A,A)
| ~ k1(B)
| ~ k1(a)
| m1(A,B,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_034) ).
fof(f71_nnf,plain,
! [A,B] :
( ~ q0(A,A)
| ~ k1(B)
| ~ k1(a)
| m1(A,B,B) ),
inference(nnf_transformation,[status(thm)],[f71]) ).
fof(f71_sk,plain,
! [A,B] :
( ~ q0(A,A)
| ~ k1(B)
| ~ k1(a)
| m1(A,B,B) ),
inference(skolemisation,[status(esa)],[f71_nnf]) ).
cnf(c71,plain,
( ~ q0(X0,X0)
| ~ k1(X1)
| ~ k1(a)
| m1(X0,X1,X1) ),
inference(cnf_transformation,[status(esa)],[f71_sk]) ).
cnf(hi71,axiom,
ifeq(k1(a),true,ifeq(k1(X0),true,ifeq(q0(X1,X1),true,m1(X1,X0,X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c71]) ).
cnf(f5,axiom,
q0(b,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(f5_nnf,plain,
q0(b,b),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
q0(b,b),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(hi5,axiom,
q0(b,b) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h153,plain,
m1(b,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi71,h110,h110,hi5]) ).
cnf(f44,axiom,
( ~ r0(G)
| ~ p0(I,H)
| m1(G,H,G) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_007) ).
fof(f44_nnf,plain,
! [G,H,I] :
( ~ r0(G)
| ~ p0(I,H)
| m1(G,H,G) ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [G,H,I] :
( ~ r0(G)
| ~ p0(I,H)
| m1(G,H,G) ),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c44,plain,
( ~ r0(X0)
| ~ p0(X2,X1)
| m1(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(hi44,axiom,
ifeq(p0(X0,X1),true,ifeq(r0(X2),true,m1(X2,X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
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(f12,axiom,
r0(e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
fof(f12_nnf,plain,
r0(e),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
r0(e),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(hi12,axiom,
r0(e) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h35,plain,
m1(e,V0,e) = true,
inference(hyper_resolution,[status(thm)],[hi44,hi13,hi12]) ).
cnf(f61,axiom,
( ~ m1(G,c,G)
| ~ q0(F,G)
| ~ m0(a,H,a)
| m1(F,a,G) ),
file('/export/starexec/sandbox/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(f18,axiom,
m0(X,d,Y),
file('/export/starexec/sandbox/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(f20,axiom,
q0(b,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_21) ).
fof(f20_nnf,plain,
q0(b,e),
inference(nnf_transformation,[status(thm)],[f20]) ).
cnf(c20,plain,
q0(b,e),
inference(cnf_transformation,[status(esa)],[f20_nnf]) ).
cnf(hi20,axiom,
q0(b,e) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(h188,plain,
m1(b,a,e) = true,
inference(hyper_resolution,[status(thm)],[hi61,hi18,hi20,h35]) ).
cnf(f53,axiom,
( ~ m1(J,A,I)
| ~ m1(J,I,H)
| m1(H,I,I) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_016) ).
fof(f53_nnf,plain,
! [H,I,J,A] :
( ~ m1(J,A,I)
| ~ m1(J,I,H)
| m1(H,I,I) ),
inference(nnf_transformation,[status(thm)],[f53]) ).
fof(f53_sk,plain,
! [H,I,J,A] :
( ~ m1(J,A,I)
| ~ m1(J,I,H)
| m1(H,I,I) ),
inference(skolemisation,[status(esa)],[f53_nnf]) ).
cnf(c53,plain,
( ~ m1(X2,X3,X1)
| ~ m1(X2,X1,X0)
| m1(X0,X1,X1) ),
inference(cnf_transformation,[status(esa)],[f53_sk]) ).
cnf(hi53,axiom,
ifeq(m1(X0,X1,X2),true,ifeq(m1(X0,X3,X1),true,m1(X2,X1,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c53]) ).
cnf(t13,plain,
m1(e,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi53,h188,h153]) ).
cnf(t134,plain,
m1(e,a,a) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(f368,negated_conjecture,
~ m1(e,a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
~ m1(e,a,a),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
~ m1(e,a,a),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ m1(e,a,a),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(goal_0,negated_conjecture,
m1(e,a,a) != true,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t134]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN250-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 00:37:17 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.27/1.10 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.27/1.10 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------