%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN270-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 03:34:13 PM UTC 2026
% Result : Unsatisfiable 5.44s 1.26s
% Output : Proof 5.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 74 ( 46 unt; 0 def)
% Number of atoms : 122 ( 24 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 102 ( 54 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 110 ( 24 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f8,axiom,
r0(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
fof(f8_nnf,plain,
r0(b),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
r0(b),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(hi8,axiom,
r0(b) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h0,plain,
r0(b) = true,
inference(hyper_resolution,[status(thm)],[hi8]) ).
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(h7,plain,
m1(b,c,b) = true,
inference(hyper_resolution,[status(thm)],[hi44,hi13,h0]) ).
cnf(f213,axiom,
( ~ m1(E,D,E)
| p2(D,E,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_176) ).
fof(f213_nnf,plain,
! [D,E] :
( ~ m1(E,D,E)
| p2(D,E,D) ),
inference(nnf_transformation,[status(thm)],[f213]) ).
fof(f213_sk,plain,
! [D,E] :
( ~ m1(E,D,E)
| p2(D,E,D) ),
inference(skolemisation,[status(esa)],[f213_nnf]) ).
cnf(c213,plain,
( ~ m1(X1,X0,X1)
| p2(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f213_sk]) ).
cnf(hi210,axiom,
ifeq(m1(X0,X1,X0),true,p2(X1,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c213]) ).
cnf(h8,plain,
p2(c,b,c) = true,
inference(hyper_resolution,[status(thm)],[hi210,h7]) ).
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(f25,axiom,
n0(d,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_26) ).
fof(f25_nnf,plain,
n0(d,c),
inference(nnf_transformation,[status(thm)],[f25]) ).
cnf(c25,plain,
n0(d,c),
inference(cnf_transformation,[status(esa)],[f25_nnf]) ).
cnf(hi25,axiom,
n0(d,c) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(h10,plain,
l1(c,c) = true,
inference(hyper_resolution,[status(thm)],[hi39,hi25]) ).
cnf(f23,axiom,
l0(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).
fof(f23_nnf,plain,
l0(c),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c23,plain,
l0(c),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(hi23,axiom,
l0(c) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(h6,plain,
l0(c) = true,
inference(hyper_resolution,[status(thm)],[hi23]) ).
cnf(f101,axiom,
( ~ l0(A)
| ~ m0(B,C,b)
| p1(A,A,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_064) ).
fof(f101_nnf,plain,
! [A,B,C] :
( ~ l0(A)
| ~ m0(B,C,b)
| p1(A,A,A) ),
inference(nnf_transformation,[status(thm)],[f101]) ).
fof(f101_sk,plain,
! [A,B,C] :
( ~ l0(A)
| ~ m0(B,C,b)
| p1(A,A,A) ),
inference(skolemisation,[status(esa)],[f101_nnf]) ).
cnf(c101,plain,
( ~ l0(X0)
| ~ m0(X1,X2,b)
| p1(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f101_sk]) ).
cnf(hi100,axiom,
ifeq(m0(X0,X1,b),true,ifeq(l0(X2),true,p1(X2,X2,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c101]) ).
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(h11,plain,
p1(c,c,c) = true,
inference(hyper_resolution,[status(thm)],[hi100,hi18,h6]) ).
cnf(f183,axiom,
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_146) ).
fof(f183_nnf,plain,
! [C,D,E,F] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ),
inference(nnf_transformation,[status(thm)],[f183]) ).
fof(f183_sk,plain,
! [C,D,E,F] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ),
inference(skolemisation,[status(esa)],[f183_nnf]) ).
cnf(c183,plain,
( ~ p2(X0,X1,X0)
| ~ l1(X2,X3)
| ~ p1(X0,X2,X3)
| p2(X0,X1,X1) ),
inference(cnf_transformation,[status(esa)],[f183_sk]) ).
cnf(hi180,axiom,
ifeq(p1(X0,X1,X2),true,ifeq(l1(X1,X2),true,ifeq(p2(X0,X3,X0),true,p2(X0,X3,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c183]) ).
cnf(h12,plain,
p2(c,b,b) = true,
inference(hyper_resolution,[status(thm)],[hi180,h11,h10,h8]) ).
cnf(f304,axiom,
( ~ p2(B,D,C)
| r3(B,C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_267) ).
fof(f304_nnf,plain,
! [B,C,D] :
( ~ p2(B,D,C)
| r3(B,C,B) ),
inference(nnf_transformation,[status(thm)],[f304]) ).
fof(f304_sk,plain,
! [B,C,D] :
( ~ p2(B,D,C)
| r3(B,C,B) ),
inference(skolemisation,[status(esa)],[f304_nnf]) ).
cnf(c304,plain,
( ~ p2(X0,X2,X1)
| r3(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f304_sk]) ).
cnf(hi299,axiom,
ifeq(p2(X0,X1,X2),true,r3(X0,X2,X0),true) = true,
inference(equality_encoding,[status(esa)],[c304]) ).
cnf(h13,plain,
r3(c,b,c) = true,
inference(hyper_resolution,[status(thm)],[hi299,h12]) ).
cnf(f322,axiom,
( ~ r3(H,G,H)
| ~ r0(G)
| p4(G,G,H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_285) ).
fof(f322_nnf,plain,
! [G,H] :
( ~ r3(H,G,H)
| ~ r0(G)
| p4(G,G,H) ),
inference(nnf_transformation,[status(thm)],[f322]) ).
fof(f322_sk,plain,
! [G,H] :
( ~ r3(H,G,H)
| ~ r0(G)
| p4(G,G,H) ),
inference(skolemisation,[status(esa)],[f322_nnf]) ).
cnf(c322,plain,
( ~ r3(X1,X0,X1)
| ~ r0(X0)
| p4(X0,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f322_sk]) ).
cnf(hi315,axiom,
ifeq(r0(X0),true,ifeq(r3(X1,X0,X1),true,p4(X0,X0,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c322]) ).
cnf(t34,plain,
p4(b,b,c) = true,
inference(hyper_resolution,[status(thm)],[hi315,h0,h13]) ).
cnf(t746,plain,
p4(b,b,c) = true,
inference(orient,[status(thm)],[t34]) ).
cnf(f368,negated_conjecture,
~ p4(b,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
~ p4(b,b,c),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
~ p4(b,b,c),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ p4(b,b,c),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(goal_0,negated_conjecture,
p4(b,b,c) != true,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t746]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN270-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n010.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 00:41:29 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.44/1.26 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.44/1.26 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------