%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT270-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 01:56:32 PM UTC 2026
% Result : Unsatisfiable 5.93s 1.22s
% Output : Proof 5.93s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t5,axiom,
sFlat0 = tc_set(t_a),
introduced(definition) ).
cnf(t17,plain,
tc_set(t_a) = sFlat0,
inference(orient,[status(thm)],[t5]) ).
cnf(t6,axiom,
sFlat1 = c_lessequals(v_S,v_A,tc_set(t_a)),
introduced(definition) ).
cnf(t40,plain,
sFlat1 = c_lessequals(v_S,v_A,sFlat0),
inference(step,[status(thm)],[t6,t17]) ).
cnf(t20,plain,
c_lessequals(v_S,v_A,sFlat0) = sFlat1,
inference(orient,[status(thm)],[t40]) ).
cnf(f4,axiom,
( c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_h8733540e4778f7e8) ).
fof(f4_nnf,plain,
! [V_b,V_a,V_S] :
( c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [V_b,V_a,V_S] :
( c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( c_lessequals(X2,v_A,tc_set(t_a))
| ~ c_lessequals(X2,c_Tarski_Ointerval(v_r,X1,X0,t_a),tc_set(t_a))
| ~ c_in(X1,v_A,t_a)
| ~ c_in(X0,v_A,t_a) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t4,plain,
ifeq(c_in(X1,v_A,t_a),true,ifeq(c_in(X2,v_A,t_a),true,ifeq(c_lessequals(X3,c_Tarski_Ointerval(v_r,X2,X1,t_a),tc_set(t_a)),true,c_lessequals(X3,v_A,tc_set(t_a)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t11,plain,
ifeq(c_in(X1,v_A,t_a),true,ifeq(c_in(X2,v_A,t_a),true,ifeq(c_lessequals(X3,c_Tarski_Ointerval(v_r,X2,X1,t_a),tc_set(t_a)),true,c_lessequals(X3,v_A,tc_set(t_a)),true),true),true) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t38,plain,
ifeq(c_in(X1,v_A,t_a),true,ifeq(c_in(X2,v_A,t_a),true,ifeq(c_lessequals(X3,c_Tarski_Ointerval(v_r,X2,X1,t_a),sFlat0),true,c_lessequals(X3,v_A,tc_set(t_a)),true),true),true) = true,
inference(step,[status(thm)],[t11,t17]) ).
cnf(t39,plain,
ifeq(c_in(X1,v_A,t_a),true,ifeq(c_in(X2,v_A,t_a),true,ifeq(c_lessequals(X3,c_Tarski_Ointerval(v_r,X2,X1,t_a),sFlat0),true,c_lessequals(X3,v_A,sFlat0),true),true),true) = true,
inference(step,[status(thm)],[t38,t17]) ).
cnf(t19,plain,
ifeq(c_in(X1,v_A,t_a),true,ifeq(c_in(X2,v_A,t_a),true,ifeq(c_lessequals(X3,c_Tarski_Ointerval(v_r,X2,X1,t_a),sFlat0),true,c_lessequals(X3,v_A,sFlat0),true),true),true) = true,
inference(rw,[status(thm)],[t39]) ).
cnf(t22,plain,
ifeq(c_in(X1,v_A,t_a),true,ifeq(c_in(X2,v_A,t_a),true,ifeq(c_lessequals(X3,c_Tarski_Ointerval(v_r,X2,X1,t_a),sFlat0),true,c_lessequals(X3,v_A,sFlat0),true),true),true) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(f2,negated_conjecture,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f2_nnf,plain,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(t3,plain,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t10,plain,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t37,plain,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),sFlat0) = true,
inference(step,[status(thm)],[t10,t17]) ).
cnf(t18,plain,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),sFlat0) = true,
inference(rw,[status(thm)],[t37]) ).
cnf(t21,plain,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),sFlat0) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(t27,plain,
true = ifeq(c_in(v_b,v_A,t_a),true,ifeq(c_in(v_a,v_A,t_a),true,ifeq(true,true,c_lessequals(v_S,v_A,sFlat0),true),true),true),
inference(cp,[status(thm)],[t22,t21]) ).
cnf(f1,negated_conjecture,
c_in(v_b,v_A,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1_nnf,plain,
c_in(v_b,v_A,t_a),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
c_in(v_b,v_A,t_a),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(t1,plain,
c_in(v_b,v_A,t_a) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t9,plain,
c_in(v_b,v_A,t_a) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t41,plain,
true = ifeq(true,true,ifeq(c_in(v_a,v_A,t_a),true,ifeq(true,true,c_lessequals(v_S,v_A,sFlat0),true),true),true),
inference(step,[status(thm)],[t27,t9]) ).
cnf(t2,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t7,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(t42,plain,
true = ifeq(c_in(v_a,v_A,t_a),true,ifeq(true,true,c_lessequals(v_S,v_A,sFlat0),true),true),
inference(step,[status(thm)],[t41,t7]) ).
cnf(f0,negated_conjecture,
c_in(v_a,v_A,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
c_in(v_a,v_A,t_a),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
c_in(v_a,v_A,t_a),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(t0,plain,
c_in(v_a,v_A,t_a) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t8,plain,
c_in(v_a,v_A,t_a) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t43,plain,
true = ifeq(true,true,ifeq(true,true,c_lessequals(v_S,v_A,sFlat0),true),true),
inference(step,[status(thm)],[t42,t8]) ).
cnf(t44,plain,
true = ifeq(true,true,c_lessequals(v_S,v_A,sFlat0),true),
inference(step,[status(thm)],[t43,t7]) ).
cnf(t45,plain,
true = c_lessequals(v_S,v_A,sFlat0),
inference(step,[status(thm)],[t44,t7]) ).
cnf(t46,plain,
true = sFlat1,
inference(step,[status(thm)],[t45,t20]) ).
cnf(t29,plain,
true = sFlat1,
inference(orient,[status(thm)],[t46]) ).
cnf(f3,negated_conjecture,
~ c_lessequals(v_S,v_A,tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f3_nnf,plain,
~ c_lessequals(v_S,v_A,tc_set(t_a)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
~ c_lessequals(v_S,v_A,tc_set(t_a)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
~ c_lessequals(v_S,v_A,tc_set(t_a)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(goal_0,negated_conjecture,
c_lessequals(v_S,v_A,tc_set(t_a)) != true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(g0_0,plain,
c_lessequals(v_S,v_A,sFlat0) != true,
inference(rw,[status(thm)],[goal_0,t17]) ).
cnf(g0_1,plain,
sFlat1 != true,
inference(rw,[status(thm)],[g0_0,t20]) ).
cnf(g0_2,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_1,t29]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT270-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n011.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 20:45:42 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.93/1.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.93/1.22 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------