%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN231-1 : 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 03:34:08 PM UTC 2026
% Result : Unsatisfiable 5.05s 1.18s
% Output : Proof 5.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 68 ( 48 unt; 0 def)
% Number of atoms : 100 ( 26 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 70 ( 38 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-4 aty)
% Number of variables : 59 ( 23 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f368,negated_conjecture,
~ l3(d,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
! [X] : ~ l3(d,X),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
! [X] : ~ l3(d,X),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ l3(d,X0),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(t110,plain,
eq(l3(d,X1),true) = efalse,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(t1176,plain,
eq(l3(d,X1),true) = efalse,
inference(orient,[status(thm)],[t110]) ).
cnf(f39,axiom,
( ~ n0(H,G)
| l1(G,G) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_002) ).
fof(f39_nnf,plain,
! [G,H] :
( ~ n0(H,G)
| l1(G,G) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [G,H] :
( ~ n0(H,G)
| l1(G,G) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
( ~ n0(X1,X0)
| l1(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(hi39,axiom,
ifeq(n0(X0,X1),true,l1(X1,X1),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
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(h89,plain,
l1(d,d) = true,
inference(hyper_resolution,[status(thm)],[hi39,hi33]) ).
cnf(f162,axiom,
( ~ p0(I,I)
| s1(I) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_125) ).
fof(f162_nnf,plain,
! [I] :
( ~ p0(I,I)
| s1(I) ),
inference(nnf_transformation,[status(thm)],[f162]) ).
fof(f162_sk,plain,
! [I] :
( ~ p0(I,I)
| s1(I) ),
inference(skolemisation,[status(esa)],[f162_nnf]) ).
cnf(c162,plain,
( ~ p0(X0,X0)
| s1(X0) ),
inference(cnf_transformation,[status(esa)],[f162_sk]) ).
cnf(hi160,axiom,
ifeq(p0(X0,X0),true,s1(X0),true) = true,
inference(equality_encoding,[status(esa)],[c162]) ).
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(h42,plain,
s1(b) = true,
inference(hyper_resolution,[status(thm)],[hi160,hi13]) ).
cnf(f163,axiom,
( ~ s1(H)
| ~ q0(F,G)
| s1(F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_126) ).
fof(f163_nnf,plain,
! [F,G,H] :
( ~ s1(H)
| ~ q0(F,G)
| s1(F) ),
inference(nnf_transformation,[status(thm)],[f163]) ).
fof(f163_sk,plain,
! [F,G,H] :
( ~ s1(H)
| ~ q0(F,G)
| s1(F) ),
inference(skolemisation,[status(esa)],[f163_nnf]) ).
cnf(c163,plain,
( ~ s1(X2)
| ~ q0(X0,X1)
| s1(X0) ),
inference(cnf_transformation,[status(esa)],[f163_sk]) ).
cnf(hi161,axiom,
ifeq(q0(X0,X1),true,ifeq(s1(X2),true,s1(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c163]) ).
cnf(f1,axiom,
q0(e,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f1_nnf,plain,
q0(e,d),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
q0(e,d),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(hi1,axiom,
q0(e,d) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h58,plain,
s1(e) = true,
inference(hyper_resolution,[status(thm)],[hi161,hi1,h42]) ).
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(h59,plain,
s1(V0) = true,
inference(hyper_resolution,[status(thm)],[hi161,hi16,h58]) ).
cnf(f227,axiom,
( ~ s0(d)
| ~ s1(a)
| s2(d) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_190) ).
fof(f227_nnf,plain,
( ~ s0(d)
| ~ s1(a)
| s2(d) ),
inference(nnf_transformation,[status(thm)],[f227]) ).
fof(f227_sk,plain,
( ~ s0(d)
| ~ s1(a)
| s2(d) ),
inference(skolemisation,[status(esa)],[f227_nnf]) ).
cnf(c227,plain,
( ~ s0(d)
| ~ s1(a)
| s2(d) ),
inference(cnf_transformation,[status(esa)],[f227_sk]) ).
cnf(hi224,axiom,
ifeq(s1(a),true,ifeq(s0(d),true,s2(d),true),true) = true,
inference(equality_encoding,[status(esa)],[c227]) ).
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(h63,plain,
s2(d) = true,
inference(hyper_resolution,[status(thm)],[hi224,h59,hi0]) ).
cnf(f257,axiom,
( ~ l1(G,G)
| ~ s2(H)
| l3(G,G) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_220) ).
fof(f257_nnf,plain,
! [G,H] :
( ~ l1(G,G)
| ~ s2(H)
| l3(G,G) ),
inference(nnf_transformation,[status(thm)],[f257]) ).
fof(f257_sk,plain,
! [G,H] :
( ~ l1(G,G)
| ~ s2(H)
| l3(G,G) ),
inference(skolemisation,[status(esa)],[f257_nnf]) ).
cnf(c257,plain,
( ~ l1(X0,X0)
| ~ s2(X1)
| l3(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f257_sk]) ).
cnf(hi252,axiom,
ifeq(s2(X0),true,ifeq(l1(X1,X1),true,l3(X1,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c257]) ).
cnf(t15,plain,
l3(d,d) = true,
inference(hyper_resolution,[status(thm)],[hi252,h63,h89]) ).
cnf(t1167,plain,
l3(d,d) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(t1177,plain,
efalse = eq(true,true),
inference(cp,[status(thm)],[t1176,t1167]) ).
cnf(t7,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t1175,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t7]) ).
cnf(t1220,plain,
efalse = etrue,
inference(step,[status(thm)],[t1177,t1175]) ).
cnf(t1178,plain,
efalse = etrue,
inference(orient,[status(thm)],[t1220]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t1178]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN231-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 00:34:28 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.05/1.18 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.05/1.18 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------