%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN223-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 03:34:07 PM UTC 2026
% Result : Unsatisfiable 5.59s 1.50s
% Output : Proof 5.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 78 ( 50 unt; 0 def)
% Number of atoms : 130 ( 29 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 110 ( 58 ~; 52 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 64 ( 20 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f368,negated_conjecture,
~ l3(X,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
! [X] : ~ l3(X,e),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
! [X] : ~ l3(X,e),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ l3(X0,e),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(t161,plain,
eq(l3(X1,e),true) = efalse,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(t510,plain,
eq(l3(X1,e),true) = efalse,
inference(orient,[status(thm)],[t161]) ).
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(f6,axiom,
n0(d,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
fof(f6_nnf,plain,
n0(d,b),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
n0(d,b),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(hi6,axiom,
n0(d,b) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h30,plain,
k1(b) = true,
inference(hyper_resolution,[status(thm)],[hi38,hi6]) ).
cnf(f173,axiom,
( ~ k1(b)
| m2(b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_136) ).
fof(f173_nnf,plain,
( ~ k1(b)
| m2(b) ),
inference(nnf_transformation,[status(thm)],[f173]) ).
fof(f173_sk,plain,
( ~ k1(b)
| m2(b) ),
inference(skolemisation,[status(esa)],[f173_nnf]) ).
cnf(c173,plain,
( ~ k1(b)
| m2(b) ),
inference(cnf_transformation,[status(esa)],[f173_sk]) ).
cnf(hi170,axiom,
ifeq(k1(b),true,m2(b),true) = true,
inference(equality_encoding,[status(esa)],[c173]) ).
cnf(h32,plain,
m2(b) = true,
inference(hyper_resolution,[status(thm)],[hi170,h30]) ).
cnf(f109,axiom,
( ~ s0(F)
| ~ s0(G)
| p1(F,F,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_072) ).
fof(f109_nnf,plain,
! [F,G] :
( ~ s0(F)
| ~ s0(G)
| p1(F,F,F) ),
inference(nnf_transformation,[status(thm)],[f109]) ).
fof(f109_sk,plain,
! [F,G] :
( ~ s0(F)
| ~ s0(G)
| p1(F,F,F) ),
inference(skolemisation,[status(esa)],[f109_nnf]) ).
cnf(c109,plain,
( ~ s0(X0)
| ~ s0(X1)
| p1(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f109_sk]) ).
cnf(hi108,axiom,
ifeq(s0(X0),true,ifeq(s0(X1),true,p1(X1,X1,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c109]) ).
cnf(f4,axiom,
s0(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
fof(f4_nnf,plain,
s0(b),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
s0(b),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(hi4,axiom,
s0(b) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h5,plain,
p1(b,b,b) = true,
inference(hyper_resolution,[status(thm)],[hi108,hi4,hi4]) ).
cnf(f143,axiom,
( ~ s0(B)
| q1(B,B,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_106) ).
fof(f143_nnf,plain,
! [B] :
( ~ s0(B)
| q1(B,B,B) ),
inference(nnf_transformation,[status(thm)],[f143]) ).
fof(f143_sk,plain,
! [B] :
( ~ s0(B)
| q1(B,B,B) ),
inference(skolemisation,[status(esa)],[f143_nnf]) ).
cnf(c143,plain,
( ~ s0(X0)
| q1(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f143_sk]) ).
cnf(hi141,axiom,
ifeq(s0(X0),true,q1(X0,X0,X0),true) = true,
inference(equality_encoding,[status(esa)],[c143]) ).
cnf(f0,axiom,
s0(d),
file('/export/starexec/sandbox2/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,
q1(d,d,d) = true,
inference(hyper_resolution,[status(thm)],[hi141,hi0]) ).
cnf(f161,axiom,
( ~ q1(d,E,d)
| ~ s0(d)
| ~ q0(D,E)
| r1(D) ),
file('/export/starexec/sandbox2/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/sandbox2/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(h187,plain,
r1(V0) = true,
inference(hyper_resolution,[status(thm)],[hi159,hi16,hi0,h0]) ).
cnf(f177,axiom,
( ~ p1(b,I,J)
| ~ r0(e)
| ~ r1(b)
| n2(e) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_140) ).
fof(f177_nnf,plain,
! [I,J] :
( ~ p1(b,I,J)
| ~ r0(e)
| ~ r1(b)
| n2(e) ),
inference(nnf_transformation,[status(thm)],[f177]) ).
fof(f177_sk,plain,
! [I,J] :
( ~ p1(b,I,J)
| ~ r0(e)
| ~ r1(b)
| n2(e) ),
inference(skolemisation,[status(esa)],[f177_nnf]) ).
cnf(c177,plain,
( ~ p1(b,X0,X1)
| ~ r0(e)
| ~ r1(b)
| n2(e) ),
inference(cnf_transformation,[status(esa)],[f177_sk]) ).
cnf(hi174,axiom,
ifeq(r1(b),true,ifeq(r0(e),true,ifeq(p1(b,X0,X1),true,n2(e),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c177]) ).
cnf(f12,axiom,
r0(e),
file('/export/starexec/sandbox2/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(h201,plain,
n2(e) = true,
inference(hyper_resolution,[status(thm)],[hi174,h187,hi12,h5]) ).
cnf(f254,axiom,
( ~ m2(b)
| ~ n2(C)
| l3(C,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_217) ).
fof(f254_nnf,plain,
! [C] :
( ~ m2(b)
| ~ n2(C)
| l3(C,C) ),
inference(nnf_transformation,[status(thm)],[f254]) ).
fof(f254_sk,plain,
! [C] :
( ~ m2(b)
| ~ n2(C)
| l3(C,C) ),
inference(skolemisation,[status(esa)],[f254_nnf]) ).
cnf(c254,plain,
( ~ m2(b)
| ~ n2(X0)
| l3(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f254_sk]) ).
cnf(hi249,axiom,
ifeq(n2(X0),true,ifeq(m2(b),true,l3(X0,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c254]) ).
cnf(t41,plain,
l3(e,e) = true,
inference(hyper_resolution,[status(thm)],[hi249,h201,h32]) ).
cnf(t419,plain,
l3(e,e) = true,
inference(orient,[status(thm)],[t41]) ).
cnf(t511,plain,
efalse = eq(true,true),
inference(cp,[status(thm)],[t510,t419]) ).
cnf(t16,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t509,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t16]) ).
cnf(t549,plain,
efalse = etrue,
inference(step,[status(thm)],[t511,t509]) ).
cnf(t512,plain,
efalse = etrue,
inference(orient,[status(thm)],[t549]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t512]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN223-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n019.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 00:33:07 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.59/1.50 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.59/1.50 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------