%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG030-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 : Thu Sep 24 11:50:28 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.46s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 42 ( 42 unt; 0 nHn; 22 RR)
% Number of literals : 42 ( 41 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 36 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1,negated_conjecture,
ifeq(sorti1(X1),true,sorti2(h(X1)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
cnf(ax3_1,axiom,
sorti1(sK1_ax3_V) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3_1) ).
cnf(ifeq_axiom_001,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(co1_3,negated_conjecture,
ifeq(sorti2(X1),true,sorti1(j(X1)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
cnf(ax3,axiom,
sorti1(sK2_ax3_U) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
cnf(co1_2,negated_conjecture,
ifeq2(sorti1(X1),true,j(h(X1)),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
cnf(ifeq_axiom,axiom,
ifeq2(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
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(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(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(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(co1_4,negated_conjecture,
ifeq2(sorti2(X1),true,ifeq2(sorti2(X2),true,op1(j(X2),j(X1)),j(op2(X2,X1))),j(op2(X2,X1))) = j(op2(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
cnf(c_0_12,negated_conjecture,
ifeq(sorti1(X1),true,sorti2(h(X1)),true) = true,
co1 ).
cnf(c_0_13,axiom,
sorti1(sK1_ax3_V) = true,
ax3_1 ).
cnf(c_0_14,negated_conjecture,
ifeq(true,true,sorti2(h(sK1_ax3_V)),true) = true,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom_001 ).
cnf(c_0_16,negated_conjecture,
ifeq(sorti2(X1),true,sorti1(j(X1)),true) = true,
co1_3 ).
cnf(c_0_17,negated_conjecture,
sorti2(h(sK1_ax3_V)) = true,
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,axiom,
sorti1(sK2_ax3_U) = true,
ax3 ).
cnf(c_0_19,negated_conjecture,
sorti1(j(h(sK1_ax3_V))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_15]) ).
cnf(c_0_20,negated_conjecture,
ifeq2(sorti1(X1),true,j(h(X1)),X1) = X1,
co1_2 ).
cnf(c_0_21,axiom,
ifeq2(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_22,negated_conjecture,
sorti2(h(sK2_ax3_U)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_18]),c_0_15]) ).
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,
sorti2(h(j(h(sK1_ax3_V)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_19]),c_0_15]) ).
cnf(c_0_25,negated_conjecture,
j(h(sK1_ax3_V)) = sK1_ax3_V,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_13]),c_0_21]) ).
cnf(c_0_26,negated_conjecture,
sorti1(j(h(sK2_ax3_U))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_22]),c_0_15]) ).
cnf(c_0_27,axiom,
ifeq(sorti1(X1),true,ifeq(sorti1(X2),true,sorti1(op1(X2,X1)),true),true) = true,
ax1 ).
cnf(c_0_28,negated_conjecture,
ifeq2(sorti2(X1),true,op2(h(sK1_ax3_V),X1),op2(X1,h(sK1_ax3_V))) = op2(X1,h(sK1_ax3_V)),
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_25]),c_0_21]),c_0_25]),c_0_25]) ).
cnf(c_0_29,negated_conjecture,
sorti2(h(j(h(sK2_ax3_U)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_26]),c_0_15]) ).
cnf(c_0_30,negated_conjecture,
j(h(sK2_ax3_U)) = sK2_ax3_U,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_18]),c_0_21]) ).
cnf(c_0_31,plain,
ifeq(sorti1(X1),true,sorti1(op1(sK2_ax3_U,X1)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_18]),c_0_15]) ).
cnf(c_0_32,negated_conjecture,
sorti1(j(h(j(h(sK1_ax3_V))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_24]),c_0_15]) ).
cnf(c_0_33,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_34,negated_conjecture,
op2(h(sK2_ax3_U),h(sK1_ax3_V)) = op2(h(sK1_ax3_V),h(sK2_ax3_U)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_30]),c_0_21]),c_0_30]) ).
cnf(c_0_35,negated_conjecture,
sorti1(op1(sK2_ax3_U,sK1_ax3_V)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_25]),c_0_25]),c_0_15]) ).
cnf(c_0_36,plain,
op1(sK2_ax3_U,sK1_ax3_V) != op1(sK1_ax3_V,sK2_ax3_U),
inference(fof_simplification,[status(thm)],[ax3_2]) ).
cnf(c_0_37,negated_conjecture,
ifeq2(sorti2(X1),true,ifeq2(sorti2(X2),true,op1(j(X2),j(X1)),j(op2(X2,X1))),j(op2(X2,X1))) = j(op2(X2,X1)),
co1_4 ).
cnf(c_0_38,negated_conjecture,
op2(h(sK1_ax3_V),h(sK2_ax3_U)) = h(op1(sK2_ax3_U,sK1_ax3_V)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_13]),c_0_18]),c_0_21]),c_0_21]) ).
cnf(c_0_39,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_20,c_0_35]),c_0_21]) ).
cnf(c_0_40,plain,
op1(sK2_ax3_U,sK1_ax3_V) != op1(sK1_ax3_V,sK2_ax3_U),
c_0_36 ).
cnf(c_0_41,negated_conjecture,
$false,
inference(sr,[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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_22]),c_0_17]),c_0_25]),c_0_30]),c_0_39]),c_0_21]),c_0_39]),c_0_21]),c_0_39]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG030-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n016.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 12:58:25 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46 % Version: 3.5.1
% 0.18/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.18/0.46 % Starting sh5l with 300s (1) cores
% 0.18/0.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2459615 completed with status 0
% 0.18/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.18/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.46 % No SInE strategy applied
% 0.18/0.46 % Search class: FUUPM-FFSF32-MFFFFFNN
% 0.18/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.18/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.18/0.46 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 0.18/0.46 % Starting G-E--_208_B02_F1_AE_CS_SP_PS_S0Y with 136s (1) cores
% 0.18/0.46 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 0.18/0.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2459622 completed with status 0
% 0.18/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.18/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.46 % No SInE strategy applied
% 0.18/0.46 % Search class: FUUPM-FFSF32-MFFFFFNN
% 0.18/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.18/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.18/0.46 % Preprocessing time : 0.001 s
% 0.18/0.46 % Presaturation interreduction done
% 0.18/0.46
% 0.18/0.46 % Proof found!
% 0.18/0.46 % SZS status Unsatisfiable
% 0.18/0.46 % SZS output start CNFRefutation
% See solution above
% 0.18/0.46 % Parsed axioms : 14
% 0.18/0.46 % Removed by relevancy pruning/SinE : 0
% 0.18/0.46 % Initial clauses : 14
% 0.18/0.46 % Removed in clause preprocessing : 0
% 0.18/0.46 % Initial clauses in saturation : 14
% 0.18/0.46 % Processed clauses : 152
% 0.18/0.46 % ...of these trivial : 26
% 0.18/0.46 % ...subsumed : 0
% 0.18/0.46 % ...remaining for further processing : 126
% 0.18/0.46 % Other redundant clauses eliminated : 0
% 0.18/0.46 % Clauses deleted for lack of memory : 0
% 0.18/0.46 % Backward-subsumed : 0
% 0.18/0.46 % Backward-rewritten : 10
% 0.18/0.46 % Generated clauses : 1050
% 0.18/0.46 % ...of the previous two non-redundant : 869
% 0.18/0.46 % ...aggressively subsumed : 0
% 0.18/0.46 % Contextual simplify-reflections : 0
% 0.18/0.46 % Paramodulations : 1050
% 0.18/0.46 % Factorizations : 0
% 0.18/0.46 % NegExts : 0
% 0.18/0.46 % Equation resolutions : 0
% 0.18/0.46 % Disequality decompositions : 0
% 0.18/0.46 % Total rewrite steps : 1460
% 0.18/0.46 % ...of those cached : 541
% 0.18/0.46 % Propositional unsat checks : 0
% 0.18/0.46 % Propositional check models : 0
% 0.18/0.46 % Propositional check unsatisfiable : 0
% 0.18/0.46 % Propositional clauses : 0
% 0.18/0.46 % Propositional clauses after purity: 0
% 0.18/0.46 % Propositional unsat core size : 0
% 0.18/0.46 % Propositional preprocessing time : 0.000
% 0.18/0.46 % Propositional encoding time : 0.000
% 0.18/0.46 % Propositional solver time : 0.000
% 0.18/0.46 % Success case prop preproc time : 0.000
% 0.18/0.46 % Success case prop encoding time : 0.000
% 0.18/0.46 % Success case prop solver time : 0.000
% 0.18/0.46 % Current number of processed clauses : 102
% 0.18/0.46 % Positive orientable unit clauses : 101
% 0.18/0.46 % Positive unorientable unit clauses: 0
% 0.18/0.46 % Negative unit clauses : 1
% 0.18/0.46 % Non-unit-clauses : 0
% 0.18/0.46 % Current number of unprocessed clauses: 730
% 0.18/0.46 % ...number of literals in the above : 730
% 0.18/0.46 % Current number of archived formulas : 0
% 0.18/0.46 % Current number of archived clauses : 24
% 0.18/0.46 % Clause-clause subsumption calls (NU) : 0
% 0.18/0.46 % Rec. Clause-clause subsumption calls : 0
% 0.18/0.46 % Non-unit clause-clause subsumptions : 0
% 0.18/0.46 % Unit Clause-clause subsumption calls : 0
% 0.18/0.46 % Rewrite failures with RHS unbound : 0
% 0.18/0.46 % BW rewrite match attempts : 487
% 0.18/0.46 % BW rewrite match successes : 9
% 0.18/0.46 % Condensation attempts : 0
% 0.18/0.46 % Condensation successes : 0
% 0.18/0.46 % Termbank termtop insertions : 23461
% 0.18/0.46 % Search garbage collected termcells : 2
% 0.18/0.46
% 0.18/0.46 % -------------------------------------------------
% 0.18/0.46 % User time : 0.017 s
% 0.18/0.46 % System time : 0.003 s
% 0.18/0.46 % Total time : 0.020 s
% 0.18/0.46 % Maximum resident set size: 3640 pages
% 0.18/0.46
% 0.18/0.46 % -------------------------------------------------
% 0.18/0.46 % User time : 0.068 s
% 0.18/0.46 % System time : 0.021 s
% 0.18/0.46 % Total time : 0.089 s
% 0.18/0.46 % Maximum resident set size: 4608 pages
% 0.18/0.46 % E exiting
%------------------------------------------------------------------------------