%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL121-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 01:02:08 PM UTC 2026
% Result : Unsatisfiable 6.49s 1.46s
% Output : Proof 6.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 30 unt; 0 def)
% Number of atoms : 106 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 102 ( 54 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-4 aty)
% Number of variables : 105 ( 0 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f7,negated_conjecture,
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f7_nnf,plain,
! [V_U] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [V_U] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ c_in(c_Pair(v_y,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(X0),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,negated_conjecture,
ifeq(c_in(c_Pair(v_y,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),true,c_in(c_Pair(v_ya,v_x(X0),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(f6,negated_conjecture,
c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f6_nnf,plain,
c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(hi6,negated_conjecture,
c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h2,plain,
c_in(c_Pair(v_ya,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi6]) ).
cnf(f0,axiom,
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Odiamond__strip__lemmaE_0) ).
fof(f0_nnf,plain,
! [V_r,T_a,V_x,V_y_H,V_y] :
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [V_r,T_a,V_x,V_y_H,V_y] :
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( c_in(c_Pair(X3,c_Comb_Odiamond__strip__lemmaE__1(X0,X4,X3,X1),X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X3,X1,X1),X0,tc_prod(X1,X1))
| ~ c_Comb_Odiamond(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(c_Comb_Odiamond(X0,X1),true,ifeq(c_in(c_Pair(X2,X3,X1,X1),X0,tc_prod(X1,X1)),true,ifeq(c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1)),true,c_in(c_Pair(X3,c_Comb_Odiamond__strip__lemmaE__1(X0,X4,X3,X1),X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f4,negated_conjecture,
c_Comb_Odiamond(v_r,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f4_nnf,plain,
c_Comb_Odiamond(v_r,t_a),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
c_Comb_Odiamond(v_r,t_a),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(hi4,negated_conjecture,
c_Comb_Odiamond(v_r,t_a) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(f5,negated_conjecture,
c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f5_nnf,plain,
c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(hi5,negated_conjecture,
c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h12,plain,
c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi4,hi5,h2]) ).
cnf(f8,negated_conjecture,
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f8_nnf,plain,
! [V_U] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [V_U] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( ~ c_in(c_Pair(v_y,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X0,v_x(X0),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,negated_conjecture,
ifeq(c_in(c_Pair(v_y,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),true,c_in(c_Pair(X0,v_x(X0),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h1,plain,
c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi6]) ).
cnf(f1,axiom,
( c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Odiamond__strip__lemmaE_1) ).
fof(f1_nnf,plain,
! [V_r,T_a,V_x,V_y_H,V_y] :
( c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [V_r,T_a,V_x,V_y_H,V_y] :
( c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( c_in(c_Pair(X4,c_Comb_Odiamond__strip__lemmaE__1(X0,X4,X3,X1),X1,X1),X0,tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X3,X1,X1),X0,tc_prod(X1,X1))
| ~ c_Comb_Odiamond(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(c_Comb_Odiamond(X0,X1),true,ifeq(c_in(c_Pair(X2,X3,X1,X1),X0,tc_prod(X1,X1)),true,ifeq(c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1)),true,c_in(c_Pair(X4,c_Comb_Odiamond__strip__lemmaE__1(X0,X4,X3,X1),X1,X1),X0,tc_prod(X1,X1)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h11,plain,
c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi4,hi5,h2]) ).
cnf(f2,axiom,
( c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(V_p,V_r,tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
fof(f2_nnf,plain,
! [V_p,V_r,T_a] :
( c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(V_p,V_r,tc_prod(T_a,T_a)) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_p,V_r,T_a] :
( c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(V_p,V_r,tc_prod(T_a,T_a)) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( c_in(X0,c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_in(X0,X1,tc_prod(X2,X2)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(c_in(X0,X1,tc_prod(X2,X2)),true,c_in(X0,c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h33,plain,
c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) = true,
inference(hyper_resolution,[status(thm)],[hi2,h11]) ).
cnf(f3,axiom,
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__trans_0) ).
fof(f3_nnf,plain,
! [V_b,V_c,T_a,V_r,V_a] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [V_b,V_c,T_a,V_r,V_a] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)),true,ifeq(c_in(c_Pair(X4,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)),true,c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h51,plain,
c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h33,h1]) ).
cnf(f9,negated_conjecture,
( ~ c_in(c_Pair(v_z,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f9_nnf,plain,
! [V_U] :
( ~ c_in(c_Pair(v_z,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [V_U] :
( ~ c_in(c_Pair(v_z,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( ~ c_in(c_Pair(v_z,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,negated_conjecture,
ifeq(c_in(c_Pair(v_xaa,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),true,ifeq(c_in(c_Pair(v_z,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi9,h51,h12]) ).
cnf(t560,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t560]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL121-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n003.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 07:43:07 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.49/1.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.49/1.46 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------