%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT268-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 5.63s 1.30s
% Output : CNFRefutation 5.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 19
% Syntax : Number of clauses : 101 ( 101 unt; 0 nHn; 64 RR)
% Number of literals : 101 ( 100 equ; 8 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 17 con; 0-4 aty)
% Number of variables : 98 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t13,axiom,
sF3 = c_Tarski_Odual(v_cl,t_a),
introduced(definition) ).
cnf(t19,plain,
c_Tarski_Odual(v_cl,t_a) = sF3,
inference(orient,[status(thm)],[t13]) ).
cnf(t14,axiom,
sF4 = c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),
introduced(definition) ).
cnf(t77,plain,
sF4 = c_Tarski_Olub(v_S,sF3,t_a),
inference(step,[status(thm)],[t14,t19]) ).
cnf(t34,plain,
c_Tarski_Olub(v_S,sF3,t_a) = sF4,
inference(orient,[status(thm)],[t77]) ).
cnf(t15,axiom,
sF5 = c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),
introduced(definition) ).
cnf(t80,plain,
sF5 = c_Pair(c_Tarski_Olub(v_S,sF3,t_a),v_x,t_a,t_a),
inference(step,[status(thm)],[t15,t19]) ).
cnf(t81,plain,
sF5 = c_Pair(sF4,v_x,t_a,t_a),
inference(step,[status(thm)],[t80,t34]) ).
cnf(t36,plain,
c_Pair(sF4,v_x,t_a,t_a) = sF5,
inference(orient,[status(thm)],[t81]) ).
cnf(t16,axiom,
sF6 = tc_prod(t_a,t_a),
introduced(definition) ).
cnf(t20,plain,
tc_prod(t_a,t_a) = sF6,
inference(orient,[status(thm)],[t16]) ).
cnf(t17,axiom,
sF7 = c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
introduced(definition) ).
cnf(t82,plain,
sF7 = c_in(c_Pair(c_Tarski_Olub(v_S,sF3,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(step,[status(thm)],[t17,t19]) ).
cnf(t83,plain,
sF7 = c_in(c_Pair(sF4,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(step,[status(thm)],[t82,t34]) ).
cnf(t84,plain,
sF7 = c_in(sF5,v_r,tc_prod(t_a,t_a)),
inference(step,[status(thm)],[t83,t36]) ).
cnf(t85,plain,
sF7 = c_in(sF5,v_r,sF6),
inference(step,[status(thm)],[t84,t20]) ).
cnf(t37,plain,
c_in(sF5,v_r,sF6) = sF7,
inference(orient,[status(thm)],[t85]) ).
cnf(t8,axiom,
ifeq(c_in(c_Pair(X1,X2,X3,X3),c_Tarski_Opotype_Oorder(c_Tarski_Odual(X4,X3),X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),true,c_in(c_Pair(X2,X1,X3,X3),c_Tarski_Opotype_Oorder(X4,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t10,axiom,
sF0 = c_in(v_x,v_S,t_a),
introduced(definition) ).
cnf(t2,axiom,
c_in(v_x,v_S,t_a) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t23,plain,
c_in(v_x,v_S,t_a) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t67,plain,
sF0 = true,
inference(step,[status(thm)],[t10,t23]) ).
cnf(t24,plain,
true = sF0,
inference(orient,[status(thm)],[t67]) ).
cnf(t86,plain,
ifeq(c_in(c_Pair(X1,X2,X3,X3),c_Tarski_Opotype_Oorder(c_Tarski_Odual(X4,X3),X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),sF0,c_in(c_Pair(X2,X1,X3,X3),c_Tarski_Opotype_Oorder(X4,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),true) = true,
inference(step,[status(thm)],[t8,t24]) ).
cnf(t87,plain,
ifeq(c_in(c_Pair(X1,X2,X3,X3),c_Tarski_Opotype_Oorder(c_Tarski_Odual(X4,X3),X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),sF0,c_in(c_Pair(X2,X1,X3,X3),c_Tarski_Opotype_Oorder(X4,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),sF0) = true,
inference(step,[status(thm)],[t86,t24]) ).
cnf(t88,plain,
ifeq(c_in(c_Pair(X1,X2,X3,X3),c_Tarski_Opotype_Oorder(c_Tarski_Odual(X4,X3),X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),sF0,c_in(c_Pair(X2,X1,X3,X3),c_Tarski_Opotype_Oorder(X4,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),sF0) = sF0,
inference(step,[status(thm)],[t87,t24]) ).
cnf(t38,plain,
ifeq(c_in(c_Pair(X1,X2,X3,X3),c_Tarski_Opotype_Oorder(c_Tarski_Odual(X4,X3),X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),sF0,c_in(c_Pair(X2,X1,X3,X3),c_Tarski_Opotype_Oorder(X4,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),sF0) = sF0,
inference(orient,[status(thm)],[t88]) ).
cnf(t39,plain,
sF0 = ifeq(c_in(c_Pair(X1,X2,t_a,t_a),c_Tarski_Opotype_Oorder(sF3,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),sF0,c_in(c_Pair(X2,X1,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),sF0),
inference(cp,[status(thm)],[t38,t19]) ).
cnf(t89,plain,
sF0 = ifeq(c_in(c_Pair(X1,X2,t_a,t_a),c_Tarski_Opotype_Oorder(sF3,t_a,tc_Product__Type_Ounit),sF6),sF0,c_in(c_Pair(X2,X1,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),sF0),
inference(step,[status(thm)],[t39,t20]) ).
cnf(t0,axiom,
c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) = v_r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t21,plain,
c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) = v_r,
inference(orient,[status(thm)],[t0]) ).
cnf(t90,plain,
sF0 = ifeq(c_in(c_Pair(X1,X2,t_a,t_a),c_Tarski_Opotype_Oorder(sF3,t_a,tc_Product__Type_Ounit),sF6),sF0,c_in(c_Pair(X2,X1,t_a,t_a),v_r,tc_prod(t_a,t_a)),sF0),
inference(step,[status(thm)],[t89,t21]) ).
cnf(t91,plain,
sF0 = ifeq(c_in(c_Pair(X1,X2,t_a,t_a),c_Tarski_Opotype_Oorder(sF3,t_a,tc_Product__Type_Ounit),sF6),sF0,c_in(c_Pair(X2,X1,t_a,t_a),v_r,sF6),sF0),
inference(step,[status(thm)],[t90,t20]) ).
cnf(t43,plain,
ifeq(c_in(c_Pair(X1,X2,t_a,t_a),c_Tarski_Opotype_Oorder(sF3,t_a,tc_Product__Type_Ounit),sF6),sF0,c_in(c_Pair(X2,X1,t_a,t_a),v_r,sF6),sF0) = sF0,
inference(orient,[status(thm)],[t91]) ).
cnf(t9,axiom,
ifeq(c_lessequals(X1,c_Tarski_Opotype_Opset(X2,X3,tc_Product__Type_Ounit),tc_set(X3)),true,ifeq(c_in(X2,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),true,ifeq(c_in(X2,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),true,ifeq(c_in(X4,X1,X3),true,c_in(c_Pair(X4,c_Tarski_Olub(X1,X2,X3),X3,X3),c_Tarski_Opotype_Oorder(X2,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t93,plain,
ifeq(c_lessequals(X1,c_Tarski_Opotype_Opset(X2,X3,tc_Product__Type_Ounit),tc_set(X3)),sF0,ifeq(c_in(X2,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),true,ifeq(c_in(X2,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),true,ifeq(c_in(X4,X1,X3),true,c_in(c_Pair(X4,c_Tarski_Olub(X1,X2,X3),X3,X3),c_Tarski_Opotype_Oorder(X2,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),true),true),true),true) = true,
inference(step,[status(thm)],[t9,t24]) ).
cnf(t94,plain,
ifeq(c_lessequals(X1,c_Tarski_Opotype_Opset(X2,X3,tc_Product__Type_Ounit),tc_set(X3)),sF0,ifeq(c_in(X2,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X2,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),true,ifeq(c_in(X4,X1,X3),true,c_in(c_Pair(X4,c_Tarski_Olub(X1,X2,X3),X3,X3),c_Tarski_Opotype_Oorder(X2,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),true),true),true),true) = true,
inference(step,[status(thm)],[t93,t24]) ).
cnf(t95,plain,
ifeq(c_lessequals(X1,c_Tarski_Opotype_Opset(X2,X3,tc_Product__Type_Ounit),tc_set(X3)),sF0,ifeq(c_in(X2,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X2,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X4,X1,X3),true,c_in(c_Pair(X4,c_Tarski_Olub(X1,X2,X3),X3,X3),c_Tarski_Opotype_Oorder(X2,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),true),true),true),true) = true,
inference(step,[status(thm)],[t94,t24]) ).
cnf(t96,plain,
ifeq(c_lessequals(X1,c_Tarski_Opotype_Opset(X2,X3,tc_Product__Type_Ounit),tc_set(X3)),sF0,ifeq(c_in(X2,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X2,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X4,X1,X3),sF0,c_in(c_Pair(X4,c_Tarski_Olub(X1,X2,X3),X3,X3),c_Tarski_Opotype_Oorder(X2,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),true),true),true),true) = true,
inference(step,[status(thm)],[t95,t24]) ).
cnf(t97,plain,
ifeq(c_lessequals(X1,c_Tarski_Opotype_Opset(X2,X3,tc_Product__Type_Ounit),tc_set(X3)),sF0,ifeq(c_in(X2,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X2,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X4,X1,X3),sF0,c_in(c_Pair(X4,c_Tarski_Olub(X1,X2,X3),X3,X3),c_Tarski_Opotype_Oorder(X2,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),sF0),true),true),true) = true,
inference(step,[status(thm)],[t96,t24]) ).
cnf(t98,plain,
ifeq(c_lessequals(X1,c_Tarski_Opotype_Opset(X2,X3,tc_Product__Type_Ounit),tc_set(X3)),sF0,ifeq(c_in(X2,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X2,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X4,X1,X3),sF0,c_in(c_Pair(X4,c_Tarski_Olub(X1,X2,X3),X3,X3),c_Tarski_Opotype_Oorder(X2,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),sF0),sF0),true),true) = true,
inference(step,[status(thm)],[t97,t24]) ).
cnf(t99,plain,
ifeq(c_lessequals(X1,c_Tarski_Opotype_Opset(X2,X3,tc_Product__Type_Ounit),tc_set(X3)),sF0,ifeq(c_in(X2,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X2,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X4,X1,X3),sF0,c_in(c_Pair(X4,c_Tarski_Olub(X1,X2,X3),X3,X3),c_Tarski_Opotype_Oorder(X2,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),sF0),sF0),sF0),true) = true,
inference(step,[status(thm)],[t98,t24]) ).
cnf(t100,plain,
ifeq(c_lessequals(X1,c_Tarski_Opotype_Opset(X2,X3,tc_Product__Type_Ounit),tc_set(X3)),sF0,ifeq(c_in(X2,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X2,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X4,X1,X3),sF0,c_in(c_Pair(X4,c_Tarski_Olub(X1,X2,X3),X3,X3),c_Tarski_Opotype_Oorder(X2,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),sF0),sF0),sF0),sF0) = true,
inference(step,[status(thm)],[t99,t24]) ).
cnf(t101,plain,
ifeq(c_lessequals(X1,c_Tarski_Opotype_Opset(X2,X3,tc_Product__Type_Ounit),tc_set(X3)),sF0,ifeq(c_in(X2,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X2,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X4,X1,X3),sF0,c_in(c_Pair(X4,c_Tarski_Olub(X1,X2,X3),X3,X3),c_Tarski_Opotype_Oorder(X2,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),sF0),sF0),sF0),sF0) = sF0,
inference(step,[status(thm)],[t100,t24]) ).
cnf(t48,plain,
ifeq(c_lessequals(X1,c_Tarski_Opotype_Opset(X2,X3,tc_Product__Type_Ounit),tc_set(X3)),sF0,ifeq(c_in(X2,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X2,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X4,X1,X3),sF0,c_in(c_Pair(X4,c_Tarski_Olub(X1,X2,X3),X3,X3),c_Tarski_Opotype_Oorder(X2,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),sF0),sF0),sF0),sF0) = sF0,
inference(orient,[status(thm)],[t101]) ).
cnf(t55,plain,
sF0 = ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(sF3,t_a,tc_Product__Type_Ounit),tc_set(t_a)),sF0,ifeq(c_in(sF3,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),sF0,ifeq(c_in(sF3,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X1,v_S,t_a),sF0,c_in(c_Pair(X1,sF4,t_a,t_a),c_Tarski_Opotype_Oorder(sF3,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),sF0),sF0),sF0),sF0),
inference(cp,[status(thm)],[t48,t34]) ).
cnf(t7,axiom,
c_Tarski_Opotype_Opset(c_Tarski_Odual(X1,X2),X2,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(X1,X2,tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t31,plain,
c_Tarski_Opotype_Opset(c_Tarski_Odual(X1,X2),X2,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(X1,X2,tc_Product__Type_Ounit),
inference(orient,[status(thm)],[t7]) ).
cnf(t32,plain,
c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(sF3,t_a,tc_Product__Type_Ounit),
inference(cp,[status(thm)],[t31,t19]) ).
cnf(t1,axiom,
c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = v_A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t22,plain,
c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = v_A,
inference(orient,[status(thm)],[t1]) ).
cnf(t76,plain,
v_A = c_Tarski_Opotype_Opset(sF3,t_a,tc_Product__Type_Ounit),
inference(step,[status(thm)],[t32,t22]) ).
cnf(t33,plain,
c_Tarski_Opotype_Opset(sF3,t_a,tc_Product__Type_Ounit) = v_A,
inference(orient,[status(thm)],[t76]) ).
cnf(t102,plain,
sF0 = ifeq(c_lessequals(v_S,v_A,tc_set(t_a)),sF0,ifeq(c_in(sF3,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),sF0,ifeq(c_in(sF3,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X1,v_S,t_a),sF0,c_in(c_Pair(X1,sF4,t_a,t_a),c_Tarski_Opotype_Oorder(sF3,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),sF0),sF0),sF0),sF0),
inference(step,[status(thm)],[t55,t33]) ).
cnf(t11,axiom,
sF1 = tc_set(t_a),
introduced(definition) ).
cnf(t18,plain,
tc_set(t_a) = sF1,
inference(orient,[status(thm)],[t11]) ).
cnf(t103,plain,
sF0 = ifeq(c_lessequals(v_S,v_A,sF1),sF0,ifeq(c_in(sF3,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),sF0,ifeq(c_in(sF3,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X1,v_S,t_a),sF0,c_in(c_Pair(X1,sF4,t_a,t_a),c_Tarski_Opotype_Oorder(sF3,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),sF0),sF0),sF0),sF0),
inference(step,[status(thm)],[t102,t18]) ).
cnf(t3,axiom,
c_lessequals(v_S,v_A,tc_set(t_a)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t70,plain,
c_lessequals(v_S,v_A,sF1) = true,
inference(step,[status(thm)],[t3,t18]) ).
cnf(t71,plain,
c_lessequals(v_S,v_A,sF1) = sF0,
inference(step,[status(thm)],[t70,t24]) ).
cnf(t27,plain,
c_lessequals(v_S,v_A,sF1) = sF0,
inference(orient,[status(thm)],[t71]) ).
cnf(t104,plain,
sF0 = ifeq(sF0,sF0,ifeq(c_in(sF3,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),sF0,ifeq(c_in(sF3,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X1,v_S,t_a),sF0,c_in(c_Pair(X1,sF4,t_a,t_a),c_Tarski_Opotype_Oorder(sF3,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),sF0),sF0),sF0),sF0),
inference(step,[status(thm)],[t103,t27]) ).
cnf(t4,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t28,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t105,plain,
sF0 = ifeq(c_in(sF3,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),sF0,ifeq(c_in(sF3,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X1,v_S,t_a),sF0,c_in(c_Pair(X1,sF4,t_a,t_a),c_Tarski_Opotype_Oorder(sF3,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),sF0),sF0),sF0),
inference(step,[status(thm)],[t104,t28]) ).
cnf(t5,axiom,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t74,plain,
c_in(sF3,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = true,
inference(step,[status(thm)],[t5,t19]) ).
cnf(t75,plain,
c_in(sF3,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = sF0,
inference(step,[status(thm)],[t74,t24]) ).
cnf(t30,plain,
c_in(sF3,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = sF0,
inference(orient,[status(thm)],[t75]) ).
cnf(t106,plain,
sF0 = ifeq(sF0,sF0,ifeq(c_in(sF3,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X1,v_S,t_a),sF0,c_in(c_Pair(X1,sF4,t_a,t_a),c_Tarski_Opotype_Oorder(sF3,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),sF0),sF0),sF0),
inference(step,[status(thm)],[t105,t30]) ).
cnf(t107,plain,
sF0 = ifeq(c_in(sF3,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),sF0,ifeq(c_in(X1,v_S,t_a),sF0,c_in(c_Pair(X1,sF4,t_a,t_a),c_Tarski_Opotype_Oorder(sF3,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),sF0),sF0),
inference(step,[status(thm)],[t106,t28]) ).
cnf(t6,axiom,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t78,plain,
c_in(sF3,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = true,
inference(step,[status(thm)],[t6,t19]) ).
cnf(t79,plain,
c_in(sF3,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = sF0,
inference(step,[status(thm)],[t78,t24]) ).
cnf(t35,plain,
c_in(sF3,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = sF0,
inference(orient,[status(thm)],[t79]) ).
cnf(t108,plain,
sF0 = ifeq(sF0,sF0,ifeq(c_in(X1,v_S,t_a),sF0,c_in(c_Pair(X1,sF4,t_a,t_a),c_Tarski_Opotype_Oorder(sF3,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),sF0),sF0),
inference(step,[status(thm)],[t107,t35]) ).
cnf(t109,plain,
sF0 = ifeq(c_in(X1,v_S,t_a),sF0,c_in(c_Pair(X1,sF4,t_a,t_a),c_Tarski_Opotype_Oorder(sF3,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),sF0),
inference(step,[status(thm)],[t108,t28]) ).
cnf(t110,plain,
sF0 = ifeq(c_in(X1,v_S,t_a),sF0,c_in(c_Pair(X1,sF4,t_a,t_a),c_Tarski_Opotype_Oorder(sF3,t_a,tc_Product__Type_Ounit),sF6),sF0),
inference(step,[status(thm)],[t109,t20]) ).
cnf(t58,plain,
ifeq(c_in(X1,v_S,t_a),sF0,c_in(c_Pair(X1,sF4,t_a,t_a),c_Tarski_Opotype_Oorder(sF3,t_a,tc_Product__Type_Ounit),sF6),sF0) = sF0,
inference(orient,[status(thm)],[t110]) ).
cnf(t68,plain,
c_in(v_x,v_S,t_a) = sF0,
inference(step,[status(thm)],[t23,t24]) ).
cnf(t25,plain,
c_in(v_x,v_S,t_a) = sF0,
inference(orient,[status(thm)],[t68]) ).
cnf(t59,plain,
sF0 = ifeq(sF0,sF0,c_in(c_Pair(v_x,sF4,t_a,t_a),c_Tarski_Opotype_Oorder(sF3,t_a,tc_Product__Type_Ounit),sF6),sF0),
inference(cp,[status(thm)],[t58,t25]) ).
cnf(t111,plain,
sF0 = c_in(c_Pair(v_x,sF4,t_a,t_a),c_Tarski_Opotype_Oorder(sF3,t_a,tc_Product__Type_Ounit),sF6),
inference(step,[status(thm)],[t59,t28]) ).
cnf(t60,plain,
c_in(c_Pair(v_x,sF4,t_a,t_a),c_Tarski_Opotype_Oorder(sF3,t_a,tc_Product__Type_Ounit),sF6) = sF0,
inference(orient,[status(thm)],[t111]) ).
cnf(t62,plain,
sF0 = ifeq(sF0,sF0,c_in(c_Pair(sF4,v_x,t_a,t_a),v_r,sF6),sF0),
inference(cp,[status(thm)],[t43,t60]) ).
cnf(t112,plain,
sF0 = c_in(c_Pair(sF4,v_x,t_a,t_a),v_r,sF6),
inference(step,[status(thm)],[t62,t28]) ).
cnf(t113,plain,
sF0 = c_in(sF5,v_r,sF6),
inference(step,[status(thm)],[t112,t36]) ).
cnf(t114,plain,
sF0 = sF7,
inference(step,[status(thm)],[t113,t37]) ).
cnf(t64,plain,
sF7 = sF0,
inference(orient,[status(thm)],[t114]) ).
cnf(t115,plain,
c_in(sF5,v_r,sF6) = sF0,
inference(step,[status(thm)],[t37,t64]) ).
cnf(t65,plain,
c_in(sF5,v_r,sF6) = sF0,
inference(orient,[status(thm)],[t115]) ).
cnf(u0,negated_conjecture,
c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(d0,axiom,
c_Tarski_Oglb(V_S,V_cl,T_a) = c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(goal_0,negated_conjecture,
c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) != true,
inference(definition_unfolding,[status(thm)],[u0,d0]) ).
cnf(g0_0,plain,
c_in(c_Pair(c_Tarski_Olub(v_S,sF3,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) != true,
inference(rw,[status(thm)],[goal_0,t19]) ).
cnf(g0_1,plain,
c_in(c_Pair(sF4,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) != true,
inference(rw,[status(thm)],[g0_0,t34]) ).
cnf(g0_2,plain,
c_in(sF5,v_r,tc_prod(t_a,t_a)) != true,
inference(rw,[status(thm)],[g0_1,t36]) ).
cnf(g0_3,plain,
c_in(sF5,v_r,sF6) != true,
inference(rw,[status(thm)],[g0_2,t20]) ).
cnf(g0_4,plain,
sF0 != true,
inference(rw,[status(thm)],[g0_3,t65]) ).
cnf(g0_5,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_4,t24]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT268-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n009.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 20:44:58 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.63/1.30 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.63/1.30 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------