%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN121-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 03:33:52 PM UTC 2026
% Result : Unsatisfiable 6.78s 1.39s
% Output : Proof 6.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 62 ( 42 unt; 0 def)
% Number of atoms : 106 ( 20 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 : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-4 aty)
% Number of variables : 70 ( 15 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f30,axiom,
m0(b,b,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_31) ).
fof(f30_nnf,plain,
m0(b,b,e),
inference(nnf_transformation,[status(thm)],[f30]) ).
cnf(c30,plain,
m0(b,b,e),
inference(cnf_transformation,[status(esa)],[f30_nnf]) ).
cnf(hi30,axiom,
m0(b,b,e) = true,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(h5,plain,
m0(b,b,e) = true,
inference(hyper_resolution,[status(thm)],[hi30]) ).
cnf(f52,axiom,
( ~ m0(C,C,B)
| ~ l0(D)
| m1(B,C,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_015) ).
fof(f52_nnf,plain,
! [B,C,D] :
( ~ m0(C,C,B)
| ~ l0(D)
| m1(B,C,C) ),
inference(nnf_transformation,[status(thm)],[f52]) ).
fof(f52_sk,plain,
! [B,C,D] :
( ~ m0(C,C,B)
| ~ l0(D)
| m1(B,C,C) ),
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c52,plain,
( ~ m0(X1,X1,X0)
| ~ l0(X2)
| m1(X0,X1,X1) ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi52,axiom,
ifeq(l0(X0),true,ifeq(m0(X1,X1,X2),true,m1(X2,X1,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c52]) ).
cnf(f19,axiom,
l0(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).
fof(f19_nnf,plain,
l0(a),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
l0(a),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(hi19,axiom,
l0(a) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(h6,plain,
m1(e,b,b) = true,
inference(hyper_resolution,[status(thm)],[hi52,hi19,h5]) ).
cnf(f171,axiom,
( ~ p0(H,G)
| ~ m1(I,H,H)
| ~ m0(H,G,I)
| l2(G,G) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_134) ).
fof(f171_nnf,plain,
! [G,H,I] :
( ~ p0(H,G)
| ~ m1(I,H,H)
| ~ m0(H,G,I)
| l2(G,G) ),
inference(nnf_transformation,[status(thm)],[f171]) ).
fof(f171_sk,plain,
! [G,H,I] :
( ~ p0(H,G)
| ~ m1(I,H,H)
| ~ m0(H,G,I)
| l2(G,G) ),
inference(skolemisation,[status(esa)],[f171_nnf]) ).
cnf(c171,plain,
( ~ p0(X1,X0)
| ~ m1(X2,X1,X1)
| ~ m0(X1,X0,X2)
| l2(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f171_sk]) ).
cnf(hi168,axiom,
ifeq(m0(X0,X1,X2),true,ifeq(m1(X2,X0,X0),true,ifeq(p0(X0,X1),true,l2(X1,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c171]) ).
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(h7,plain,
l2(b,b) = true,
inference(hyper_resolution,[status(thm)],[hi168,hi30,h6,hi13]) ).
cnf(f10,axiom,
n0(e,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
fof(f10_nnf,plain,
n0(e,b),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
n0(e,b),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(hi10,axiom,
n0(e,b) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h2,plain,
n0(e,b) = true,
inference(hyper_resolution,[status(thm)],[hi10]) ).
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(h0,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(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(h1,plain,
s1(a) = true,
inference(hyper_resolution,[status(thm)],[hi161,hi16,h0]) ).
cnf(f168,axiom,
( ~ l2(E,E)
| ~ n0(e,E)
| ~ s1(D)
| l2(D,E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_131) ).
fof(f168_nnf,plain,
! [D,E] :
( ~ l2(E,E)
| ~ n0(e,E)
| ~ s1(D)
| l2(D,E) ),
inference(nnf_transformation,[status(thm)],[f168]) ).
fof(f168_sk,plain,
! [D,E] :
( ~ l2(E,E)
| ~ n0(e,E)
| ~ s1(D)
| l2(D,E) ),
inference(skolemisation,[status(esa)],[f168_nnf]) ).
cnf(c168,plain,
( ~ l2(X1,X1)
| ~ n0(e,X1)
| ~ s1(X0)
| l2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f168_sk]) ).
cnf(hi166,axiom,
ifeq(s1(X0),true,ifeq(n0(e,X1),true,ifeq(l2(X1,X1),true,l2(X0,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c168]) ).
cnf(t8,plain,
l2(a,b) = true,
inference(hyper_resolution,[status(thm)],[hi166,h1,h2,h7]) ).
cnf(t913,plain,
l2(a,b) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(f368,negated_conjecture,
~ l2(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
~ l2(a,b),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
~ l2(a,b),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ l2(a,b),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(goal_0,negated_conjecture,
l2(a,b) != true,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t913]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN121-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 00:14:17 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.78/1.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.78/1.39 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------