%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN157-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 03:33:57 PM UTC 2026
% Result : Unsatisfiable 6.35s 6.56s
% Output : Proof 6.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 22
% Syntax : Number of formulae : 119 ( 75 unt; 0 def)
% Number of atoms : 203 ( 43 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 174 ( 90 ~; 84 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-4 aty)
% Number of variables : 166 ( 42 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f368,negated_conjecture,
~ n5(X,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
! [X] : ~ n5(X,d),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
! [X] : ~ n5(X,d),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ n5(X0,d),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(t10,plain,
eq(n5(X1,d),true) = efalse,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(t27,plain,
eq(n5(X1,d),true) = efalse,
inference(orient,[status(thm)],[t10]) ).
cnf(f162,axiom,
( ~ p0(I,I)
| s1(I) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/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(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/sandbox2/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/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(h63,plain,
s2(d) = true,
inference(hyper_resolution,[status(thm)],[hi224,h59,hi0]) ).
cnf(f24,axiom,
q0(d,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_25) ).
fof(f24_nnf,plain,
q0(d,d),
inference(nnf_transformation,[status(thm)],[f24]) ).
cnf(c24,plain,
q0(d,d),
inference(cnf_transformation,[status(esa)],[f24_nnf]) ).
cnf(hi24,axiom,
q0(d,d) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(h75,plain,
s1(d) = true,
inference(hyper_resolution,[status(thm)],[hi161,hi24,h59]) ).
cnf(f170,axiom,
( ~ m0(C,B,J)
| ~ s1(B)
| ~ p0(A,A)
| l2(J,J) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_133) ).
fof(f170_nnf,plain,
! [J,A,B,C] :
( ~ m0(C,B,J)
| ~ s1(B)
| ~ p0(A,A)
| l2(J,J) ),
inference(nnf_transformation,[status(thm)],[f170]) ).
fof(f170_sk,plain,
! [J,A,B,C] :
( ~ m0(C,B,J)
| ~ s1(B)
| ~ p0(A,A)
| l2(J,J) ),
inference(skolemisation,[status(esa)],[f170_nnf]) ).
cnf(c170,plain,
( ~ m0(X3,X2,X0)
| ~ s1(X2)
| ~ p0(X1,X1)
| l2(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f170_sk]) ).
cnf(hi167,axiom,
ifeq(p0(X0,X0),true,ifeq(s1(X1),true,ifeq(m0(X2,X1,X3),true,l2(X3,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c170]) ).
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(h135,plain,
l2(V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi167,hi13,h75,hi18]) ).
cnf(f262,axiom,
( ~ s2(B)
| ~ m0(J,C,C)
| ~ l2(C,J)
| ~ m0(B,B,A)
| m3(J,A,J) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_225) ).
fof(f262_nnf,plain,
! [J,A,B,C] :
( ~ s2(B)
| ~ m0(J,C,C)
| ~ l2(C,J)
| ~ m0(B,B,A)
| m3(J,A,J) ),
inference(nnf_transformation,[status(thm)],[f262]) ).
fof(f262_sk,plain,
! [J,A,B,C] :
( ~ s2(B)
| ~ m0(J,C,C)
| ~ l2(C,J)
| ~ m0(B,B,A)
| m3(J,A,J) ),
inference(skolemisation,[status(esa)],[f262_nnf]) ).
cnf(c262,plain,
( ~ s2(X2)
| ~ m0(X0,X3,X3)
| ~ l2(X3,X0)
| ~ m0(X2,X2,X1)
| m3(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f262_sk]) ).
cnf(hi257,axiom,
ifeq(m0(X0,X0,X1),true,ifeq(l2(X2,X3),true,ifeq(m0(X3,X2,X2),true,ifeq(s2(X0),true,m3(X3,X1,X3),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c262]) ).
cnf(h154,plain,
m3(d,V0,d) = true,
inference(hyper_resolution,[status(thm)],[hi257,hi18,h135,hi18,h63]) ).
cnf(f39,axiom,
( ~ n0(H,G)
| l1(G,G) ),
file('/export/starexec/sandbox2/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/sandbox2/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(h88,plain,
l1(d,d) = true,
inference(hyper_resolution,[status(thm)],[hi39,hi33]) ).
cnf(f223,axiom,
( ~ l1(H,G)
| q2(G,G,H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_186) ).
fof(f223_nnf,plain,
! [G,H] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(nnf_transformation,[status(thm)],[f223]) ).
fof(f223_sk,plain,
! [G,H] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(skolemisation,[status(esa)],[f223_nnf]) ).
cnf(c223,plain,
( ~ l1(X1,X0)
| q2(X0,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f223_sk]) ).
cnf(hi220,axiom,
ifeq(l1(X0,X1),true,q2(X1,X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c223]) ).
cnf(h121,plain,
q2(d,d,d) = true,
inference(hyper_resolution,[status(thm)],[hi220,h88]) ).
cnf(f2,axiom,
n0(d,e),
file('/export/starexec/sandbox2/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(h25,plain,
l1(e,e) = true,
inference(hyper_resolution,[status(thm)],[hi39,hi2]) ).
cnf(f172,axiom,
( ~ l1(G,H)
| ~ s0(F)
| m2(F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_135) ).
fof(f172_nnf,plain,
! [F,G,H] :
( ~ l1(G,H)
| ~ s0(F)
| m2(F) ),
inference(nnf_transformation,[status(thm)],[f172]) ).
fof(f172_sk,plain,
! [F,G,H] :
( ~ l1(G,H)
| ~ s0(F)
| m2(F) ),
inference(skolemisation,[status(esa)],[f172_nnf]) ).
cnf(c172,plain,
( ~ l1(X1,X2)
| ~ s0(X0)
| m2(X0) ),
inference(cnf_transformation,[status(esa)],[f172_sk]) ).
cnf(hi169,axiom,
ifeq(s0(X0),true,ifeq(l1(X1,X2),true,m2(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c172]) ).
cnf(h113,plain,
m2(d) = true,
inference(hyper_resolution,[status(thm)],[hi169,hi0,h25]) ).
cnf(f249,axiom,
( ~ m2(B)
| k3(B,B,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_212) ).
fof(f249_nnf,plain,
! [B] :
( ~ m2(B)
| k3(B,B,B) ),
inference(nnf_transformation,[status(thm)],[f249]) ).
fof(f249_sk,plain,
! [B] :
( ~ m2(B)
| k3(B,B,B) ),
inference(skolemisation,[status(esa)],[f249_nnf]) ).
cnf(c249,plain,
( ~ m2(X0)
| k3(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f249_sk]) ).
cnf(hi244,axiom,
ifeq(m2(X0),true,k3(X0,X0,X0),true) = true,
inference(equality_encoding,[status(esa)],[c249]) ).
cnf(h115,plain,
k3(d,d,d) = true,
inference(hyper_resolution,[status(thm)],[hi244,h113]) ).
cnf(f332,axiom,
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_295) ).
fof(f332_nnf,plain,
! [B,C,D,E,F] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ),
inference(nnf_transformation,[status(thm)],[f332]) ).
fof(f332_sk,plain,
! [B,C,D,E,F] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ),
inference(skolemisation,[status(esa)],[f332_nnf]) ).
cnf(c332,plain,
( ~ m3(X3,X4,X3)
| ~ q2(X3,X1,X0)
| ~ k3(X2,X2,X0)
| q4(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f332_sk]) ).
cnf(hi325,axiom,
ifeq(k3(X0,X0,X1),true,ifeq(q2(X2,X3,X1),true,ifeq(m3(X2,X4,X2),true,q4(X1,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c332]) ).
cnf(h388,plain,
q4(d,d) = true,
inference(hyper_resolution,[status(thm)],[hi325,h115,h121,h154]) ).
cnf(f350,axiom,
( ~ q4(D,C)
| n5(C,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_313) ).
fof(f350_nnf,plain,
! [C,D] :
( ~ q4(D,C)
| n5(C,C) ),
inference(nnf_transformation,[status(thm)],[f350]) ).
fof(f350_sk,plain,
! [C,D] :
( ~ q4(D,C)
| n5(C,C) ),
inference(skolemisation,[status(esa)],[f350_nnf]) ).
cnf(c350,plain,
( ~ q4(X1,X0)
| n5(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f350_sk]) ).
cnf(hi343,axiom,
ifeq(q4(X0,X1),true,n5(X1,X1),true) = true,
inference(equality_encoding,[status(esa)],[c350]) ).
cnf(t6,plain,
n5(d,d) = true,
inference(hyper_resolution,[status(thm)],[hi343,h388]) ).
cnf(t21,plain,
n5(d,d) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t28,plain,
efalse = eq(true,true),
inference(cp,[status(thm)],[t27,t21]) ).
cnf(t5,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t26,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t5]) ).
cnf(t35,plain,
efalse = etrue,
inference(step,[status(thm)],[t28,t26]) ).
cnf(t29,plain,
efalse = etrue,
inference(orient,[status(thm)],[t35]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t29]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN157-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/5.56 % Computer : n017.cluster.edu
% 0.12/5.56 % Model : x86_64 x86_64
% 0.12/5.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.56 % Memory : 8046.5625MB
% 0.12/5.56 % OS : Linux 6.8.0-71-generic
% 0.12/5.56 % CPULimit : 300
% 0.12/5.56 % WCLimit : 300
% 0.12/5.56 % DateTime : Fri Sep 25 00:16:22 UTC 2026
% 0.12/5.56 % CPUTime :
% 0.12/5.56 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.35/6.56 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.35/6.56 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------