%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG030-10 : TPTP v9.2.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:04:14 PM UTC 2026
% Result : Unsatisfiable 1.33s 1.74s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of clauses : 34 ( 34 unt; 0 nHn; 16 RR)
% Number of literals : 34 ( 33 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-4 aty)
% Number of variables : 32 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ax1,axiom,
ifeq(sorti1(X1),true,ifeq(sorti1(X2),true,sorti1(op1(X2,X1)),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
cnf(ax3,axiom,
sorti1(sK2_ax3_U) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
cnf(ifeq_axiom_001,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(co1_1,negated_conjecture,
ifeq2(sorti1(X1),true,ifeq2(sorti1(X2),true,op2(h(X2),h(X1)),h(op1(X2,X1))),h(op1(X2,X1))) = h(op1(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
cnf(ifeq_axiom,axiom,
ifeq2(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(ax3_1,axiom,
sorti1(sK1_ax3_V) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3_1) ).
cnf(co1,negated_conjecture,
ifeq(sorti1(X1),true,sorti2(h(X1)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
cnf(co1_2,negated_conjecture,
ifeq2(sorti1(X1),true,j(h(X1)),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
cnf(ax4,axiom,
ifeq2(sorti2(X1),true,ifeq2(sorti2(X2),true,op2(X2,X1),op2(X1,X2)),op2(X1,X2)) = op2(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
cnf(ax3_2,axiom,
op1(sK2_ax3_U,sK1_ax3_V) != op1(sK1_ax3_V,sK2_ax3_U),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3_2) ).
cnf(c_0_10,axiom,
ifeq(sorti1(X1),true,ifeq(sorti1(X2),true,sorti1(op1(X2,X1)),true),true) = true,
ax1 ).
cnf(c_0_11,axiom,
sorti1(sK2_ax3_U) = true,
ax3 ).
cnf(c_0_12,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom_001 ).
cnf(c_0_13,negated_conjecture,
ifeq2(sorti1(X1),true,ifeq2(sorti1(X2),true,op2(h(X2),h(X1)),h(op1(X2,X1))),h(op1(X2,X1))) = h(op1(X2,X1)),
co1_1 ).
cnf(c_0_14,axiom,
ifeq2(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_15,axiom,
sorti1(sK1_ax3_V) = true,
ax3_1 ).
cnf(c_0_16,plain,
ifeq(sorti1(X1),true,sorti1(op1(sK2_ax3_U,X1)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_17,negated_conjecture,
ifeq2(sorti1(X1),true,op2(h(sK2_ax3_U),h(X1)),h(op1(sK2_ax3_U,X1))) = h(op1(sK2_ax3_U,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_11]),c_0_14]) ).
cnf(c_0_18,negated_conjecture,
ifeq(sorti1(X1),true,sorti2(h(X1)),true) = true,
co1 ).
cnf(c_0_19,negated_conjecture,
ifeq2(sorti1(X1),true,op2(h(sK1_ax3_V),h(X1)),h(op1(sK1_ax3_V,X1))) = h(op1(sK1_ax3_V,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_15]),c_0_14]) ).
cnf(c_0_20,plain,
ifeq(sorti1(X1),true,sorti1(op1(sK1_ax3_V,X1)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_15]),c_0_12]) ).
cnf(c_0_21,negated_conjecture,
ifeq2(sorti1(X1),true,j(h(X1)),X1) = X1,
co1_2 ).
cnf(c_0_22,plain,
sorti1(op1(sK2_ax3_U,sK1_ax3_V)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_15]),c_0_12]) ).
cnf(c_0_23,axiom,
ifeq2(sorti2(X1),true,ifeq2(sorti2(X2),true,op2(X2,X1),op2(X1,X2)),op2(X1,X2)) = op2(X1,X2),
ax4 ).
cnf(c_0_24,negated_conjecture,
op2(h(sK2_ax3_U),h(sK1_ax3_V)) = h(op1(sK2_ax3_U,sK1_ax3_V)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_15]),c_0_14]) ).
cnf(c_0_25,negated_conjecture,
sorti2(h(sK1_ax3_V)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_15]),c_0_12]) ).
cnf(c_0_26,negated_conjecture,
sorti2(h(sK2_ax3_U)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_11]),c_0_12]) ).
cnf(c_0_27,negated_conjecture,
op2(h(sK1_ax3_V),h(sK2_ax3_U)) = h(op1(sK1_ax3_V,sK2_ax3_U)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_11]),c_0_14]) ).
cnf(c_0_28,plain,
sorti1(op1(sK1_ax3_V,sK2_ax3_U)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_11]),c_0_12]) ).
cnf(c_0_29,negated_conjecture,
j(h(op1(sK2_ax3_U,sK1_ax3_V))) = op1(sK2_ax3_U,sK1_ax3_V),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_14]) ).
cnf(c_0_30,negated_conjecture,
h(op1(sK2_ax3_U,sK1_ax3_V)) = h(op1(sK1_ax3_V,sK2_ax3_U)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_14]),c_0_27]),c_0_14]),c_0_27]) ).
cnf(c_0_31,negated_conjecture,
j(h(op1(sK1_ax3_V,sK2_ax3_U))) = op1(sK1_ax3_V,sK2_ax3_U),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_28]),c_0_14]) ).
cnf(c_0_32,axiom,
op1(sK2_ax3_U,sK1_ax3_V) != op1(sK1_ax3_V,sK2_ax3_U),
ax3_2 ).
cnf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG030-10 : TPTP v9.2.1. Released v7.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n009.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 10:16:26 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.33/1.74 % Version : CSE_E---1.7
% 1.33/1.74 % Problem : theBenchmark.p
% 1.33/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 1.33/1.74 % SZS output start CNFRefutation
% See solution above
% 1.33/1.74 % Total time : 1.368s
%------------------------------------------------------------------------------