%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL012-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 02:00:40 PM UTC 2026
% Result : Unsatisfiable 206.17s 31.18s
% Output : Proof 206.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 4
% Syntax : Number of formulae : 85 ( 81 unt; 0 def)
% Number of atoms : 93 ( 72 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 241 ( 2 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f0_nnf,plain,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t255,plain,
ifeq(is_a_theorem(equivalent(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t482,plain,
ifeq(is_a_theorem(equivalent(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) = true,
inference(orient,[status(thm)],[t255]) ).
cnf(hi0,axiom,
ifeq(is_a_theorem(equivalent(X0,X1)),true,ifeq(is_a_theorem(X0),true,is_a_theorem(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f1,axiom,
is_a_theorem(equivalent(equivalent(equivalent(X,Y),Z),equivalent(Y,equivalent(Z,X)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',um) ).
fof(f1_nnf,plain,
! [X,Y,Z] : is_a_theorem(equivalent(equivalent(equivalent(X,Y),Z),equivalent(Y,equivalent(Z,X)))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z] : is_a_theorem(equivalent(equivalent(equivalent(X,Y),Z),equivalent(Y,equivalent(Z,X)))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(X1,equivalent(X2,X0)))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(X1,equivalent(X2,X0)))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h0,plain,
is_a_theorem(equivalent(V0,equivalent(equivalent(V1,equivalent(V0,V2)),equivalent(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(h1,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(equivalent(V1,equivalent(equivalent(V2,equivalent(V1,V3)),equivalent(V3,V2))),V4)),equivalent(V4,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h0]) ).
cnf(h6,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,equivalent(equivalent(V1,equivalent(V0,V2)),equivalent(V2,V1))),V3),equivalent(equivalent(V3,V4),V4))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h1]) ).
cnf(h3,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(equivalent(equivalent(equivalent(V1,V2),V3),equivalent(V2,equivalent(V3,V1))),V4)),equivalent(V4,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,hi1]) ).
cnf(h46,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(V1,V2)),equivalent(equivalent(V3,equivalent(equivalent(V4,equivalent(V3,V5)),equivalent(V5,V4))),equivalent(equivalent(V2,V0),V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3,h6]) ).
cnf(h1168,plain,
is_a_theorem(equivalent(equivalent(V0,V1),equivalent(equivalent(equivalent(V2,equivalent(equivalent(V3,equivalent(V2,V4)),equivalent(V4,V3))),equivalent(equivalent(V1,V5),V0)),V5))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h46]) ).
cnf(h20,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,V1),equivalent(equivalent(V1,V2),V0)),V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3,h0]) ).
cnf(h66,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,V1),V1),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h20,h0]) ).
cnf(h110,plain,
is_a_theorem(equivalent(V0,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h66,h66]) ).
cnf(h171,plain,
is_a_theorem(equivalent(V0,equivalent(equivalent(V1,V0),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h110]) ).
cnf(h5,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(equivalent(equivalent(V1,equivalent(equivalent(V2,equivalent(equivalent(V3,equivalent(V2,V4)),equivalent(V4,V3))),V5)),equivalent(V5,V1)),V6)),equivalent(V6,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h1]) ).
cnf(h42,plain,
is_a_theorem(equivalent(equivalent(V0,V1),equivalent(equivalent(V1,equivalent(equivalent(V2,equivalent(equivalent(V3,equivalent(equivalent(V4,equivalent(V3,V5)),equivalent(V5,V4))),V6)),equivalent(V6,V2))),V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h5,hi1]) ).
cnf(h1007,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(V0,V1),V0),equivalent(equivalent(V2,equivalent(equivalent(V3,equivalent(equivalent(V4,equivalent(V3,V5)),equivalent(V5,V4))),V6)),equivalent(V6,V2))),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h42,h171]) ).
cnf(h235140,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,equivalent(V1,V2)),equivalent(V2,V0)),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1007,h1168]) ).
cnf(h236554,plain,
is_a_theorem(equivalent(equivalent(V0,V1),equivalent(V2,equivalent(V1,equivalent(V2,V0))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h235140]) ).
cnf(h119,plain,
is_a_theorem(equivalent(V0,equivalent(V1,equivalent(V1,V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h66]) ).
cnf(h229,plain,
is_a_theorem(equivalent(V0,equivalent(V0,equivalent(equivalent(equivalent(V1,V2),V2),V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h119,h66]) ).
cnf(h1759,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(V1,equivalent(V1,equivalent(equivalent(equivalent(V2,V3),V3),V2)))),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h171,h229]) ).
cnf(h237180,plain,
is_a_theorem(equivalent(V0,equivalent(equivalent(V0,V1),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1759,h236554]) ).
cnf(t143,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(equivalent(X3,X1),X2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3,h237180]) ).
cnf(t364,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(equivalent(X3,X1),X2))) = true,
inference(orient,[status(thm)],[t143]) ).
cnf(t665,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(X1,equivalent(X2,X3))),true,is_a_theorem(equivalent(equivalent(X3,X1),X2)),true),true),
inference(cp,[status(thm)],[t482,t364]) ).
cnf(t1,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(t137342,plain,
true = ifeq(is_a_theorem(equivalent(X1,equivalent(X2,X3))),true,is_a_theorem(equivalent(equivalent(X3,X1),X2)),true),
inference(step,[status(thm)],[t665,t256]) ).
cnf(t98241,plain,
ifeq(is_a_theorem(equivalent(X1,equivalent(X2,X3))),true,is_a_theorem(equivalent(equivalent(X3,X1),X2)),true) = true,
inference(orient,[status(thm)],[t137342]) ).
cnf(h219,plain,
is_a_theorem(equivalent(V0,equivalent(V0,equivalent(V1,equivalent(V2,equivalent(V2,V1)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h119,h119]) ).
cnf(h1367,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(V1,equivalent(V1,equivalent(V2,equivalent(V3,equivalent(V3,V2)))))),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h171,h219]) ).
cnf(h237186,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(V0,V1)),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1367,h236554]) ).
cnf(t10,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X2,X1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h237186]) ).
cnf(t344,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X2,X1))) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t676,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(X1,X2)),true,is_a_theorem(equivalent(X2,X1)),true),true),
inference(cp,[status(thm)],[t482,t344]) ).
cnf(t136901,plain,
true = ifeq(is_a_theorem(equivalent(X1,X2)),true,is_a_theorem(equivalent(X2,X1)),true),
inference(step,[status(thm)],[t676,t256]) ).
cnf(t3666,plain,
ifeq(is_a_theorem(equivalent(X1,X2)),true,is_a_theorem(equivalent(X2,X1)),true) = true,
inference(orient,[status(thm)],[t136901]) ).
cnf(t197,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(X2,equivalent(X3,X1)))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t413,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(X2,equivalent(X3,X1)))) = true,
inference(orient,[status(thm)],[t197]) ).
cnf(t626,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,X2),X3)),true,is_a_theorem(equivalent(X2,equivalent(X3,X1))),true),true),
inference(cp,[status(thm)],[t482,t413]) ).
cnf(t137068,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,X2),X3)),true,is_a_theorem(equivalent(X2,equivalent(X3,X1))),true),
inference(step,[status(thm)],[t626,t256]) ).
cnf(t41408,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,X2),X3)),true,is_a_theorem(equivalent(X2,equivalent(X3,X1))),true) = true,
inference(orient,[status(thm)],[t137068]) ).
cnf(h58,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(V0,V1),V1),V0),V2),V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h6,h20]) ).
cnf(t35,plain,
is_a_theorem(equivalent(X1,equivalent(X2,equivalent(X1,equivalent(equivalent(X2,X3),X3))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h58,h236554]) ).
cnf(t269,plain,
is_a_theorem(equivalent(X1,equivalent(X2,equivalent(X1,equivalent(equivalent(X2,X3),X3))))) = true,
inference(orient,[status(thm)],[t35]) ).
cnf(t3675,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(X1,X3),X3))),X2)),true),
inference(cp,[status(thm)],[t3666,t269]) ).
cnf(t136912,plain,
true = is_a_theorem(equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(X1,X3),X3))),X2)),
inference(step,[status(thm)],[t3675,t256]) ).
cnf(t3865,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(X1,X3),X3))),X2)) = true,
inference(orient,[status(thm)],[t136912]) ).
cnf(t41413,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X3)),equivalent(X1,X2))),true),
inference(cp,[status(thm)],[t41408,t3865]) ).
cnf(t137074,plain,
true = is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X3)),equivalent(X1,X2))),
inference(step,[status(thm)],[t41413,t256]) ).
cnf(t42451,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X3)),equivalent(X1,X2))) = true,
inference(orient,[status(thm)],[t137074]) ).
cnf(t42454,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),X3))),true,is_a_theorem(equivalent(X1,X2)),true),true),
inference(cp,[status(thm)],[t482,t42451]) ).
cnf(t137391,plain,
true = ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),X3))),true,is_a_theorem(equivalent(X1,X2)),true),
inference(step,[status(thm)],[t42454,t256]) ).
cnf(t122115,plain,
ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),X3))),true,is_a_theorem(equivalent(X1,X2)),true) = true,
inference(orient,[status(thm)],[t137391]) ).
cnf(t41425,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X2,X3),X1),X3))),true),
inference(cp,[status(thm)],[t41408,t364]) ).
cnf(t137086,plain,
true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X2,X3),X1),X3))),
inference(step,[status(thm)],[t41425,t256]) ).
cnf(t44238,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X2,X3),X1),X3))) = true,
inference(orient,[status(thm)],[t137086]) ).
cnf(t44239,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X2),equivalent(X3,X1))),true),
inference(cp,[status(thm)],[t3666,t44238]) ).
cnf(t137128,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X2),equivalent(X3,X1))),
inference(step,[status(thm)],[t44239,t256]) ).
cnf(t51045,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X2),equivalent(X3,X1))) = true,
inference(orient,[status(thm)],[t137128]) ).
cnf(t122147,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X1)),X2),X3)),true),
inference(cp,[status(thm)],[t122115,t51045]) ).
cnf(t137398,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X1)),X2),X3)),
inference(step,[status(thm)],[t122147,t256]) ).
cnf(t124374,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X1)),X2),X3)) = true,
inference(orient,[status(thm)],[t137398]) ).
cnf(t124375,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X1,X2)),X3))),true),
inference(cp,[status(thm)],[t3666,t124374]) ).
cnf(t137416,plain,
true = is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X1,X2)),X3))),
inference(step,[status(thm)],[t124375,t256]) ).
cnf(t128922,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X1,X2)),X3))) = true,
inference(orient,[status(thm)],[t137416]) ).
cnf(t128930,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),equivalent(X2,X3)))),true),
inference(cp,[status(thm)],[t98241,t128922]) ).
cnf(t137445,plain,
true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),equivalent(X2,X3)))),
inference(step,[status(thm)],[t128930,t256]) ).
cnf(t136666,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),equivalent(X2,X3)))) = true,
inference(orient,[status(thm)],[t137445]) ).
cnf(f2,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(b,c)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_yqj) ).
fof(f2_nnf,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(b,c)))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(b,c)))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(b,c)))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(b,c)))) != true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t136666]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL012-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 21:36:20 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 206.17/31.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 206.17/31.18 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------